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Contract No. 881803
H2020-S2RJU-2019 /
S2R-OC-IP1-02-2019
23/03/2021 Page 1
NEXT GENERATION METHODS, CONCEPTS AND SOLUTIONS FOR THE DESIGN OF ROBUST AND
SUSTAINABLE RUNNING GEAR
D3.2 – Feasibility study for a hybrid wheelset for a tram of
light rail vehicle and/or feasibility study for a hybrid wheelset
with composite axle
Due date of deliverable: 30/11/2020
Actual submission date: 22/03/2020
Leader/Responsible of this Deliverable: Andrea Bernasconi, POLIMI
Reviewed: Y
Document status
Revision Date Description
1 10/02/21 Draft/Internal
2 23/02/21 First issue for approval by TMT
3 22/03/21 Final/Public
Project funded from the European Union’s Horizon 2020 research and
innovation programme
Dissemination Level
PU Public X
CO Confidential, restricted under conditions set out in Model Grant
Agreement
CI Classified, information as referred to in Commission Decision
2001/844/EC
Start date of project: 01/12/2019 Duration: 24 months
Ref. Ares(2021)2045506 - 23/03/2021
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REPORT CONTRIBUTORS
Name(s) Institution Details of contribution
Michael Johnson
Richard Evans
Preetum Mistry
UNOTT Chapters 1-7
Chapters 5-7
Chapters 1-7, Editing and reviewing
Andrea Bernasconi
Stefano Bruni
Michele Carboni
Rosemere Lima
Luca Michele Martulli
POLIMI Section 9.2, 9.3, 10.3
Editing and reviewing
Reviewing
Section 10, 10.1, 10.2
Section 9.1
Chapter 9: reviewing
Irene Marazzi/
Steven Cervello
LRS Data provisioning, reviewing.
Reviewing
Davide Formaggioni BERCELLA Chapter 8
Sergio Macchiavello
Edoardo Ferrante
RINA-C Chapter 11
Jordi Viñolas
Ingo Kaiser
UNNE Chapter 12, reviewing
Chapter 12
Jose A. Chover MdM Chapter 12, data provisioning, reviewing
Jose Bertolin UNIFE Reviewing
Sebastian Stichel KTH Reviewing
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EXECUTIVE SUMMARY
The objective of Task 3.2 of the NEXTGEAR project was to assess the feasibility of a hybrid metal-
composite (HMC) wheelset, considering one of the following scenarios:
• a complete metal-composite wheelset for light vehicles, like trams or metros;
• a composite axle of a trailer bogie, with integrated connections with wheel rims, brake discs and
bearings.
In Task 3.1 the second scenario was identified as the best candidate for reaching the desired TRL
level of 2. This deliverable presents a detailed analysis of the feasibility of this hybrid metal-
composite axle, characterized by a metallic collar designed to be connected to metal bearings,
wheels and brake discs.
Concept design of the HMC axle developed in T3.2
The feasibility study started from the optimization of the composite layup presented in D3.1 and a
more detailed geometry was defined. Its structural behaviour was analysed by the finite element
method to ensure that the proposed solution minimizes the mass while preserving its strength and
satisfying all the requirements set by the design standards relevant to solid steel axles.
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Finite element analysis of the HMC axle
The feasibility of the manufacturing process was assessed and, among the manufacturing
processes identified in T3.1, roll wrapping and filament were chosen, assessed and compared. The
analysis combined finite element simulations with process simulations, and it was concluded that
both processes are feasible, allowing similar mechanical performance to be achieved, although
filament winding offers the potential for an automated process, characterized by a high level of
repeatability of the results. To reach higher TRL levels, the need of a comprehensive experimental
characterization of the materials used in the different processes was pointed out.
Numerical simulation of the filament winding process
One of the most critical aspects of a hybrid metal-composite structure is the connection between
metallic and composite parts. The proposed axle presents a metallic collar that needs to be
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connected to an inner and an outer composite tube. Both connections were designed to be
adhesively bonded. This joint was optimized to reduce the stresses in the adhesive and increase
the fatigue life of the joint. An optimized adhesive joint geometry was proposed.
The improved design for the adhesive joint between the steel collar and the composite tube
Reaching a higher TRL would require a comprehensive characterization of the chosen adhesives,
particularly under fatigue loading and in different environmental conditions. Mechanical joining is
not an option that has been considered in this project because of the mass increment involved, but
it could be a valid alternative to adhesive bonding, should future tests demonstrate the unfeasibility
of an adhesively bonded joint.
The proposed design was checked against requirements for inspection during maintenance service
interruption. The feasibility of NDT was assessed, focussing particularly on the use of ultrasonic
testing (UT). By simulation, the feasibility of UT was assessed and some limitations of UT were
identified with respect to the possibility of detecting cracks in the adhesive layer, whereas UT would
allow cracks to be detected in the composite tubes and in the metallic collar. Simulations assumed
ideal conditions, therefore, to switch to higher TRL, experimental verification would be needed to
optimize the setup. To overcome the limitations of inspection of the bond line by UT, a possible
structural health monitoring approach was proposed, based on strain profile monitoring, using fibre
optic strain sensors allowing for distributed sensing.
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Numerical simulation of the response of a UT system in the composite and in the steel parts
Dynamic analyses focused on the simulation of the effect of impact loading and on the effects of
the mass reduction on the train-track interaction. Impact loading typical to railway axles is
represented by ballast impact. An impact by a foreign object was simulated and potential damage
was assessed, consisting mainly in damage of the matrix of the external surface of outer tube due
to high compressive stresses. Although this would not impair the overall structural integrity of the
axle, solutions like a protective coating and the installation of sensors capable to detect severe
impacts should be identified.
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Finite element simulation of the impact of a foreign object and damage in the composite tube
Finally, the effect of the reduction of the un-sprung masses achieved with the hybrid metal-
composite design, onto the wheel-rail interaction forces, and consequently onto the wear of both
wheels and rails was assessed numerically. Dynamic simulations were conducted, comparing the
dynamic behaviour of a standard steel wheelset and a wheelset modified with the substitution of a
steel axle with the proposed HMC axle, when mounted on the same reference bogie. Simulations
considered the dynamic effects of the track irregularities and revealed that the reduction of the un-
sprung mass obtained by the substitution on an all steel axle by the proposed HMC one can have
beneficial effects on the wheel-rail contact forces, particularly at higher speeds (greater than 90
km/h).
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The dynamic model and the comparison between vertical forced of the steel (blue lines) and the composite (orange line) axle
At the end of task T3.2, it can be concluded that the mass reduction of a railway axle has been
achieved by replacement of a hollow steel trailer axle with a HMC equivalent axle. The mass of the
HMC axle is 74 kg, a reduction of 63% compared to the steel axle at 198 kg. The HMC railway axle
permits the existing wheels and bearings to be used.
The stresses in the HMC axle are below the design limits and a safety factor of 2 ensures that
strength requirements can be met by the metallic collars and the composite tube. Maximum
deflection in the HMC axle is larger than in the steel axle, but it could be reduced by increasing the
thickness of the secondary composite tube with a relatively low mass increase (on the order of 5
kg).
The high contact stress between the collar and the primary composite tube has been reduced by
proposing a modified, improved geometry of the collar. A margin of improvement still exists, and
future work should focus on the optimization of this joint. Although more experimental validation is
needed to support simulations, in principle, the proposed HMC axle can be inspected by UT, except
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in the bond line. To overcome this limitation, SHM solutions should be implemented, like for
example the distributed strain profile monitoring studied in this project.
The dynamic behaviour of composite tube in the case of impact by a foreign object like ballast
evidenced the need of identify and implement a protection layer or shield, to avoid any possible
damage in the composite. Future work, aiming at reaching higher TRL should consider this point
in detail.
Finally, the analysis of the dynamical forces at the interaction between rail and wheels showed that
the proposed HMC axle can modify the dynamic forces that are responsible of wear mechanisms
of the wheels and the rails. The reduction of the un-sprung mass offered by the HMC axle provides
benefits in terms of reduced dynamic vertical wheel-rail forces, track shift forces and wear number.
Consequently, a reduction of impact forces, wear and rolling contact fatigue damage can be
expected for both the rails and the rolling surfaces of the wheels. These benefits are particularly
significant when the speed is high (90 km/h on a metro line). A reduction of track damage related
to metal fatigue of rails and to permanent settlement in the ballast + embankment can also be
expected. Results confirm the potential positive impact on maintenance costs offered by a lighter
wheelset.
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ABBREVIATIONS AND ACRONYMS
Word/Acronym Description
NEXTGEAR NEXT generation methods, concepts and solutions for the design of
robust and sustainable running GEAR
TRL Technical readiness level
FRP Fibre reinforced polymer (in reference to a type of composite material)
CFRP Carbon fibre reinforced polymer (in reference to a composite material)
HMC Hybrid metallic/composite (in reference to a rail wheelset)
WP Work package (relating to the NEXTGEAR project)
FEA/FEM Finite element analysis/method
NDT Non-destructive testing
VT Visual testing
UT Ultrasonic testing
MT Magnetic particle testing
PT Liquid penetrant testing
ET Eddy current testing
RT Radiographic testing
CT Computed tomography
SHM Structural health monitoring
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TABLE OF CONTENTS
Report Contributors ................................................................................................................. 2
Executive Summary ................................................................................................................. 3
Abbreviations and Acronyms ................................................................................................. 10
Table of Contents................................................................................................................... 11
List of Figures ......................................................................................................................... 14
List of Tables .......................................................................................................................... 19
1. Introduction ................................................................................................................... 20
2. Benchmark hollow steel axle .......................................................................................... 22
2.1 Definition of critical sections along the railway axle ................................................... 23
3. LOAD CASES .................................................................................................................... 25
3.1 Load case 1 ............................................................................................................... 25
3.2 Load case 2 ............................................................................................................... 26
3.3 final load case ........................................................................................................... 27
4. Loading conditions and structural performance parameters of the wheelset ................... 28
4.1 Position of maximum bending stress ......................................................................... 30
4.2 Position of maximum deflection ................................................................................ 30
4.3 Angular misalignment at the journals ........................................................................ 30
4.4 Back-to-back distance between wheel flanges ........................................................... 31
4.5 First critical speed ..................................................................................................... 32
4.6 Position of maximum transverse stress ..................................................................... 32
4.7 Position of maximum torsional stress ........................................................................ 33
4.8 Maximum angular twist ............................................................................................ 33
5. Finite element analysis (FEA) of the wheelset model ....................................................... 34
5.1 Modelled axle systems .............................................................................................. 34
5.2 Loading conditions .................................................................................................... 36
5.3 Boundary conditions ................................................................................................. 36
5.4 Model verification ..................................................................................................... 37
5.5 Assumptions for the FEA wheelset modelling ............................................................ 38
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6. Structural characterisation of the benchmark, hollow steel axle ...................................... 38
7. HMC railway axle design ................................................................................................. 40
7.1 Design of the metallic collars and primary composite tube due to external pressure loading at the interference fit, Position 𝑨 ........................................................................ 42
7.2 Design of the metallic collar and primary composite tube due to static loading, 𝑴𝒙, at Position 𝑪 ....................................................................................................................... 43
7.3 Design of the primary composite tube due to the resultant moment, MR, at Position 𝑬 ....................................................................................................................................... 44
7.4 Design of the primary composite axle due to torsion, 𝑴𝒚′, at Position 𝑪 ................... 46
7.5 Deflection characteristics of the HMC composite axle due to the bending moment, 𝑴𝑹 ....................................................................................................................................... 47
7.6 Structural performance parameters .......................................................................... 48
7.7 Discussion - structural performance the of HMC railway axle ..................................... 50
8. Assessment of the manufacturability and comparison between various manufacturing methods ................................................................................................................................ 52
8.1 Roll wrapping ............................................................................................................ 52
8.2 Filament winding ...................................................................................................... 54
8.3 Comparison among roll wrapping and filament winding process ................................ 63
9. Analysis of the bonded joints .......................................................................................... 64
9.1 Selection of the adhesive and mechanical characterization ........................................ 64
9.2 FEA of the adhesive joint ........................................................................................... 70
9.3 Discussion ................................................................................................................. 81
10. Assessement of the feasibility of NDT AND SHM ...................................................... 85
10.1 Feasibility of NDT methods ...................................................................................... 85
10.2 Feasibility of UT: results of the simulations using CIVAnde software .......................... 87
10.3 Possible solutions for SHM .................................................................................... 105
11. Analysis of the impact response ............................................................................. 110
11.1 Objective of the impact analyses ........................................................................... 110
11.1.1 EN 13261:2009+A1 - Paragraph 3.2.2 Impact Test Characteristics ................. 110
11.1.2 EN 13261:2009+A1 – Annex C .......................................................................... 111
11.2 Software tool ........................................................................................................ 112
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11.3 Geometrical model ................................................................................................ 112
11.4 Materials............................................................................................................... 113
11.5 Numerical model ................................................................................................... 114
11.6 Loading Conditions ................................................................................................ 117
11.7 Results .................................................................................................................. 117
11.7.1 Impact direction: normal to axle surface ......................................................... 118
11.7.2 Impact direction 45° to axle surface ................................................................ 119
11.8 Mitigation measures / Further Developments........................................................ 121
12. Analysis of the dynamic behaviour ......................................................................... 124
12.1 Vehicle model ....................................................................................................... 124
12.2 Wheelset inertia .................................................................................................... 126
12.3 Scenario “Running on a curved measured track” .................................................... 128
12.4 Scenario “Running on a straight track with measured irregularities” ...................... 139
12.5 Conclusions ........................................................................................................... 146
13. Conclusions ........................................................................................................... 147
References ........................................................................................................................... 149
Appendix A. Material propereties used as input to the fEA ................................................... 152
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LIST OF FIGURES
Figure 1 Concept design of a HMC axle having a primary CFRP tube along the length of the axle, a secondary composite tube in the central section and metallic collars bonded to the ends of the axle. (a) External view (b) Cross section through axle. ............................................................... 21
Figure 2. A typical inboard bearing, trailer wheelset with general dimensions including wheels and a hollow axle (Source: Lucchini RS). .......................................................................................... 22
Figure 3. The benchmark, hollow steel (EA1N), inboard bearing trailer axle showing general dimensions (Source: Lucchini RS). ............................................................................................. 23
Figure 4. Critical section diameters a distance 𝑦 along the axle and defined as positions for evaluation. .................................................................................................................................. 23
Figure 5. A typical railway wheelset with the resultant moment, 𝑀𝑅, applied at the loading planes, 𝐷 and 𝐷’, causing the greatest bending about the x-axis. The static load, 𝑃, is used for calculation
of transverse shear, is applied separately at the same position. The torsional moment, 𝑀𝑦′, is applied uniformly about the y-axis. ............................................................................................. 28
Figure 6. Axle loaded with the resultant moment, 𝑀𝑅. The static load, 𝑃, is superimposed for calculation of transverse shear. The torsional moment, 𝑀𝑦′, is constant across the axle. (a) Shear diagram (b) Moment diagram. .................................................................................................... 29
Figure 7. Diagram showing the amount of angular misalignment, 𝜃, at the journal for the axle undergoing bending. ................................................................................................................... 31
Figure 8. Back-to-back distance, 𝐿𝐵𝑡𝐵, as measured between flanges at rail level. As the axle deflects downwards, the overall back-to-back distance increases by ∆𝐿𝐵𝑡𝐵............................... 31
Figure 9. Calculation of the first moment area of inertia, 𝑄, for a hollow tube at the neutral axis of the axle. ..................................................................................................................................... 33
Figure 10. HMC axle model element mesh. (a) Model 1-3D solid model, showing element mesh for the composite axle with the RHS collar attached. The LHS collar is removed to show cohesive elements beneath representing adhesive. (b) Model 2-Axisymmetric model, with element mesh for the primary composite tube, collar and interfacing wheel. ........................................................... 35
Figure 11. Boundary conditions for the wheelset model applied to the running surfaces where the rail and wheel contact. At Position 𝐴, u3=u2=ur2=0 and Position 𝐴’, u3=ur2=0. ......................... 37
Figure 12. HMC railway axle comprising a full length, primary composite tube, a secondary composite tube and metallic collars as introduced in Figure 1. Abaqus 2018 has been used to size the primary and secondary composite tubes as well as the metallic collars. ............................... 41
Figure 13. Cross section through the HMC axle at the running surface (Position 𝐴) showing the diameters of the metallic collar and the primary composite tube. ................................................ 42
Figure 14. von Mises stress at the wheelseat from external pressure loading due to the interference fit between the wheel hub and steel collar. The resultant stresses within the primary composite tube are minimal. Note that the adhesive is not included as a worst case. ........................................ 43
Figure 15. A cross section through the HMC railway axle at Position C showing the absolute maximum value of transverse the shear stress in the primary composite tube. .......................... 44
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Figure 16. (a) Maximum von Mises stress (170.00 MPa) in the composite axle at Position 𝐸, ply 4, bottom of primary composite tube, due to the moment, 𝑀𝑅. (b) Damage field for Hashin failure
criterion highlighting fibre compression in the primary composite tube at Position 𝐸. The secondary composite tube is included in the analysis, but not shown here for clarity. ................................. 45
Figure 17. (a) von Mises stress at Position 𝐸, ply 27, top of primary tube, due to the moment, 𝑀𝑅, showing the peak stress of 528.10 MPa due to penetration of the collar on the top surface of the primary composite tube. (b) Damage field for Hashin failure criterion highlighting fibre compression in the primary composite tube at Position 𝐸. The secondary composite tube is included in the analysis, but not shown here for clarity. ...................................................................................... 45
Figure 18. von Mises stress, Position 𝐸 , at each ply of the primary composite tube (a) and secondary composite tube (b), due to the moment, MR. The high peak stress in the primary composite tube is due to penetration by the collar. ..................................................................... 46
Figure 19. (a) Torsional stress at the outer diameter, ply 2, of the primary composite at Positions 𝐶, due to the torsional moment, 𝑀𝑦′. (b) Damage field for the Hashin failure criterion highlighting matrix compression in the primary composite tube at Positions 𝐶. The secondary composite tube is included in the analysis, but not shown here for clarity. ........................................................... 47
Figure 20. HMC axle under the bending moment, 𝑀𝑅. (a) Vertical displacement field plot compared against the undeformed state, with a scale factor of 20 applied showing maximum deflection, 𝛿𝑚𝑎𝑥,
at Position 𝐹. (b) Angular misalignment angle 𝜃 at Position 𝐷 caused by the axle deflection at the journal seat, with a scale factor 10 applied. ................................................................................ 48
Figure 21 - Section of a tube end. .............................................................................................. 53
Figure 22 - butt joint generation during the mandrel wrapping. ................................................... 53
Figure 23 Filament winding layup optimization routine ............................................................... 56
Figure 24 Simulation of 45° helical winding ................................................................................ 58
Figure 25 Overconservative initial guess for the FW layup ......................................................... 59
Figure 26 Maximum vertical displacement of the roll-wrapped solution [mm] .............................. 61
Figure 27 Maximum rotation about the axis of the roll-wrapped solution [rad] ............................. 61
Figure 28 Maximum vertical displacement of the filament-wound solution [mm] ......................... 62
Figure 29 Maximum rotation about the axis of the filament-wound solution [rad] ........................ 62
Figure 30. Fatigue S-N diagram of the 3M 9323 B/A adhesive [19] ............................................ 68
Figure 31. The tensile stress-strain curve of the bulk adhesive 9323 B/A ................................... 69
Figure 32. results of mode I fracture test, with FE analysis results superimposed, showing the accuracy of cohesive modelling. ................................................................................................. 70
Figure 33. the portion of the composite wheelset used for modelling of the adhesive joint ......... 71
Figure 34. kinematic couplings, reference points and boundary conditions................................. 71
Figure 35. kinematic couplings, reference points and boundary conditions................................. 72
Figure 36. contour plot of the values of the MAXSCRT variable in the adhesive layers .............. 74
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Figure 37. contour plot of the values of the von Mises stress in the adhesive layer .................... 75
Figure 38. contour plot of the out of plane shear stresses in the adhesive layer ......................... 75
Figure 39. contour plot of the out of plane shear stresses in the adhesive layer ......................... 76
Figure 40. the improved joint between the stub axle and the composite tubes ........................... 76
Figure 41. shape and dimensions of the modified stub axle ....................................................... 77
Figure 42. Detail of the adhesive layer of the improved joint between the stub axle and the composite tubes ......................................................................................................................... 78
Figure 43. contour plot of the values of the out of plane shear stress in the adhesive layers of the improved joint ............................................................................................................................. 78
Figure 44. contour plot of the values of the von Mises stress in the adhesive layers of the improved joint ............................................................................................................................................ 79
Figure 45. contour plot of the values of the shear stress amplitude in the adhesive layers between the inner composite tube and the steel axle ................................................................................ 79
Figure 46. contour plot of the values of the shear stress amplitude in the adhesive layers between the inner composite tube and the steel axle, for the 3M AF-163-2 adhesive ............................... 80
Figure 47. contour plot of the values of the von Mises stress in the stub axle ............................. 81
Figure 48. Four different types of mechanical joints between composite and metal parts in wind turbine blades, from [21] ............................................................................................................. 82
Figure 49. Simplified model of the flanged joint .......................................................................... 83
Figure 50. Cross sectional view of the flanged joint .................................................................... 83
Figure 51. Detail of the “tie” constraint between the flanges ....................................................... 84
Figure 52. contour plot of the von Mises stress distribution in the adhesive layers ..................... 84
Figure 53. Geometry of the central region of the composite axles considered for UT numerical simulations. ................................................................................................................................ 88
Figure 54. Stiffness matrices of the inner and outer composite tubes. ........................................ 89
Figure 55. Slowness curves for the inner and outer composite tubes. ........................................ 90
Figure 56.Model of the adopted UT probe for perpendicular incidence of longitudinal waves in the central region of the composite axle. .......................................................................................... 91
Figure 57.Simulation of the physical sound beam for perpendicular incidence of longitudinal sound waves in the central region of the composite axle. ...................................................................... 92
Figure 58. Circular defect representing a delamination in the composite material....................... 92
Figure 59. Ultrasonic responses of the central region of the composite axle inspected by normal incidence of longitudinal waves. ................................................................................................. 93
Figure 60. Model of the adopted UT probe for angled incidence of shear waves in the central region of the composite axle; the inset image shows the probe from a different angle of view. ............. 94
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Figure 61. Refraction angles of the shear waves used in the central region of the composite axle. ................................................................................................................................................... 95
Figure 62. Simulation of the physical sound beam for angled incidence of shear waves in the central region in the central region of the composite axle. ...................................................................... 96
Figure 63. Concave defect representing a transverse crack in the composite material. .............. 96
Figure 64. Ultrasonic responses of the central region of the composite axle inspected by angled incidence of shear waves. .......................................................................................................... 97
Figure 65. Geometry of the lateral region of the composite axles considered for UT numerical simulations. ................................................................................................................................ 98
Figure 66. Simulation of the physical sound beam for perpendicular incidence of longitudinal sound waves in the lateral region of the composite axle. ....................................................................... 99
Figure 67. Simulation of the physical sound beam for angled incidence of shear waves in the lateral region in the central region of the composite axle. .................................................................... 100
Figure 68. Ultrasonic responses of the lateral region of the composite axle inspected by normal incidence of longitudinal waves. ............................................................................................... 101
Figure 69. Ultrasonic responses of the lateral region of the composite axle inspected by angled incidence of shear waves. ........................................................................................................ 103
Figure 70. Ultrasonic responses of the external surface of the metallic collar inspected by angled incidence of shear waves. ........................................................................................................ 104
Figure 71. Schematic view of the installation of a strain sensing fiber optic .............................. 106
Figure 72. Size and position of the simulated crack (10 mm crack length shown in this picture) 107
Figure 73. The node path used for the extraction of the strain values ....................................... 108
Figure 74. The different strain patterns (longitudinal, with reference to the 1 axis of the local coordinate system shown in yellow) for increasing simulated crack length. .............................. 108
Figure 75. Strain values along the longitudinal path, for different simulated crack lengths ........ 109
Figure 76. Location of test pieces for hollow axles according to EN 13261 2009 +A 1 2010 [29] ................................................................................................................................................. 111
Figure 77. Analysis workflow in Ansys© Workbench 2020 R2 suite. ......................................... 112
Figure 78. Simplified geometrical model considered for impact analyses. ................................ 112
Figure 79. Composite material properties table in Ansys© Workbench 2020 R2 suite. ............. 113
Figure 80. Composite layers stacking sequences considered in the analyses. ......................... 114
Figure 81. Composite tubes mesh in radial and tangential direction ......................................... 115
Figure 82. Discretized model of all components ....................................................................... 116
Figure 83. Discretized model of all components (section view) ................................................. 116
Figure 84. Damage plot in the nearby of the impact region - impact angle 90° ......................... 118
Figure 85. Damage plot in the nearby of the impact region (section view) - impact angle 90° ... 119
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Figure 86. Damage plot in the nearby of the impact region - impact angle 45° ......................... 120
Figure 87. Damage plot in the nearby of the impact region (section view) - impact angle 45° ... 120
Figure 88. Bogie of the ML95 vehicle (source [34]) ................................................................... 124
Figure 89. Substitution track model by Chaar and Berg [35] ..................................................... 125
Figure 90. SIMPACK model of the investigated vehicle ............................................................ 126
Figure 91: Parameters of the used metro line: Curvature 1/𝑅𝐶 (upper diagram), superelevation ℎ (middle diagram), cant deficiency Δℎ for 𝑣0 = 54 km/h and 𝐸 = 1.5 m (lower diagram). ........... 129
Figure 92. Comparison of the dynamic vertical wheel-rail forces Δ𝑄 at the leading bogie; 𝑣0 =54 km/h.; blue: steel wheelset; orange: HMC wheelset. ........................................................... 131
Figure 93. Comparison of the dynamic vertical wheel-rail forces Δ𝑄 at the trailing bogie; 𝑣0 =54 km/h; blue: steel wheelset; orange: HMC wheelset. ............................................................ 132
Figure 94. Comparison of the sliding mean values Σ𝑌2m at the four wheelsets; 𝑣0 = 54 km/h; blue: steel wheelset; orange: HMC wheelset. .................................................................................... 134
Figure 95. Comparison of 𝑇𝛾 values (wear numbers) at the leading bogie; 𝑣0 = 54 km/h; blue: steel wheelset; orange: HMC wheelset; magenta: track curvature. ........................................... 136
Figure 96. Comparison of 𝑇𝛾 values (wear numbers) at the trailing bogie; 𝑣0 = 54 km/h; blue: steel wheelset; orange: HMC wheelset; magenta: track curvature. ................................................... 138
Figure 97. Comparison of the dynamic vertical wheel-rail forces Δ𝑄 at the leading bogie; 𝑣0 =90 km/h; blue: steel wheelset; orange: HMC wheelset. ............................................................ 140
Figure 98. Comparison of the sliding mean values Σ𝑌2m at the leading bogie; 𝑣0 = 90 km/h blue: steel wheelset; orange: HMC wheelset. .................................................................................... 141
Figure 99. Comparison of 𝑇𝛾 values (wear numbers) at the leading bogie; 𝑣0 = 90 km/h.; blue: steel wheelset; orange: HMC wheelset. .................................................................................... 142
Figure 100. Comparison of the dynamic vertical wheel-rail forces Δ𝑄 at the leading bogie; 𝑣0 =90 km/h; mainline irregularity profile; blue: steel wheelset; orange: HMC wheelset. ................. 143
Figure 101. Comparison of the sliding mean values Σ𝑌2m at the leading bogie; 𝑣0 = 90 km/h; 𝑣0 =90 km/h; mainline irregularity profile. ; blue: steel wheelset; orange: HMC wheelset. ............... 144
Figure 102. Comparison of 𝑇𝛾 values (wear numbers) at the leading bogie; 𝑣0 = 90 km/h ; mainline irregularity profile; blue: steel wheelset; orange: HMC wheelset. ................................ 145
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LIST OF TABLES
Table 1. Description of the critical section positions along the axle with distance, 𝒚, from the left-hand side (LHS) and a corresponding outer diameter, 𝑫𝒐. ......................................................... 24
Table 2. Moment values at the critical sections along the axle for load case 1. .......................... 26
Table 3.2. Moment values at the critical sections along the axle for load case 2......................... 27
Table 4. Structural performance of the benchmark hollow steel axle. ......................................... 39
Table 5 Summary of Rw and FW comparison. ........................................................................... 62
Table 6. Adhesives’ mechanical properties. ................................................................................ 65
Table 7:The mechanical properties of the studied adhesive joints. ............................................. 66
Table 8. Coefficients of the proposed traction separation law for the 3M 9323 B/A adhesive ..... 69
Table 9. Elastic properties of the materials ................................................................................. 73
Table 10. Pros and Cons of the impact mitigation solutions ...................................................... 122
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1. INTRODUCTION
This deliverable reports on activities performed in Task 3.2 of the NEXTGEAR project and
describes a feasibility study and preliminary design of a wheelset incorporating hybrid metallic-
composite (HMC) railway axle. The work presented here progresses from the three design concept
solutions investigated in Task 3.1. One of these concepts (concept 3, see below) was selected as
the most promising and is further developed in this report with the aim of defining a feasible
configuration for a lightweight wheelset axle made of composite materials. The analyses performed
in Task 3.2 focus on:
• dimensioning and structural optimisation of the axle, including the detailed definition of the composite layup;
• analysis of the manufacturing process and of its feasibility;
• assessment of the manufacturability and comparison between various manufacturing methods;
• feasibility analysis of non-destructive inspection and structural health monitoring of the composite axle;
• effect of the wheelset with composite axle on railway vehicle dynamics;
• analysis of resistance of the axle to impacts (e.g. from flying ballast).
The three HMC railway axle concepts were based upon a replacement for the benchmark, hollow
steel trailer axle with inboard bearings as supplied by Lucchini RS for WP3. The mass of this axle
is 198 kg. The aim of the HMC railway axle is to demonstrate a significant reduction in the mass
of the benchmark steel axle.
The architecture of the initial, two HMC railway axle concept designs are as follows:
• Concept 1. A wound HMC railway axle solution whereby towpreg is wrapped around radial
pins affixed to the stub axles at each end. Complex fibre geometries were possible for
optimised structural performance. However, the overall mass was 190 kg representing a
minimal mass reduction of 4%.
• Concept 2. A carbon fibre reinforced polymer (CFRP) tube of plain diameter with metallic
stub axles adhesively bonded into either end of the tube. This solution provided
manufacturing simplicity, but the joint was complex. The mass of this HMC concept railway
axle was 152 kg, a mass savings of 23%.
Figure 1 illustrates the third HMC railway axle concept which offered a high structural capability
afforded by semi-tailored fibre placement and the manufacturing robustness achieved through roll
wrapping of CFRP prepreg. Importantly, this concept showed the prospect of mass savings of at
least 60%. This concept is distinguished by a primary composite (CFRP) tube running the length
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of the axle. The thickness of the composite tube is increased between the journals using a
secondary composite (CFRP) tube. Metallic collars are bonded onto the ends of the primary tube
and include surface geometry matched to the existing wheel hub and rolling element bearing inner
diameters.
Figure 1 Concept design of a HMC axle having a primary CFRP tube along the length of the axle, a secondary composite tube in the central section and metallic collars bonded to the ends of the axle. (a) External view (b) Cross section through axle.
The axle is designed such that the majority of bending, shear, torque and higher order loads are
taken up by the primary composite tube. The secondary tube provides additional stiffness so that
deflections are minimised. The collars are sufficient to mitigate the radial and circumferential loads
developed by the interference fits onto the journal and wheel seat without transmission to the
primary composite tube.
A parametric approach was taken to size this concept. While successful in specifying an overall
CFRP layup, this approach was considered overly simplistic as bulk strength properties were used
for the laminate. Furthermore, geometric features were not taken into account. To elevate the
fidelity of this concept, it is necessary to treat the composite as a laminate which is analysed using
classical laminate theory (CLT).
This deliverable report for NEXTGEAR WP3.2 first presents a finite element analysis (FEA) of the
benchmark hollow steel axle. The concept HMC railway axle shown in Figure 1 is subjected to the
same FEA analysis, incorporating CLT. Structural conformance of the HMC railway axle is
assessed against the benchmark steel axle. Then, the feasibility of the axle from the perspective
of manufacturing is assessed and different manufacturing routes are proposed. The bonded joint
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between the metallic collars and the primary composite tube is studied in detail and a solution is
proposed to minimize stresses in the adhesive and ensure the desired fatigue life.
This deliverable report covers also other aspect related to service and inspections. Non Destructive
Testing (NDT) and Structural Health Monitoring (SHM) solutions are presented and discussed.
Finally, the behaviour of the composite axle under dynamic loading is studied. Two dynamic
conditions are considered: impact loading due to impact with a foreign object and dynamic loading
under the action forces resulting from wheel rail interaction.
2. BENCHMARK HOLLOW STEEL AXLE
The inboard bearing, trailer wheelset configuration provided by Lucchini RS is shown in Figure 2.
This wheelset, and in particular the axle, serves as a benchmark against which the HMC railway
axle is designed.
Figure 2. A typical inboard bearing, trailer wheelset with general dimensions including wheels and a hollow axle (Source: Lucchini RS).
The axle, item 1, is made from EA1N grade steel and has a mass of 198 kg. Each wheel, item 2,
is made from ER7 Grade steel and has a mass of 331 kg. Two brake discs (not shown) are attached
to the wheel web with fasteners and have an approximate mass of 100 kg each. Therefore, the
estimated mass of the wheelset, excluding bearings, is approximately 1060 kg. While the majority
of mass is associated with the wheels (62%), the axle mass is significant at 16% of the wheelset
mass.
1500 mm
1360 mm
1 2
ɸ1
50
0 m
m
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Figure 3 shows the trailer axle with overall dimensions. The axle is manufactured by a process of
hot forging with interfacing surfaces being post machined. Lightweighting of the steel axle is
accomplished by boring a through hole of 90 mm diameter, 𝐷𝑖.
Figure 3. The benchmark, hollow steel (EA1N), inboard bearing trailer axle showing general dimensions (Source: Lucchini RS).
2.1 DEFINITION OF CRITICAL SECTIONS ALONG THE RAILWAY AXLE
Figure 4. Critical section diameters a distance 𝑦 along the axle and defined as positions
for evaluation.
The axle includes a number of critical sections along the length as set out in Figure 4 and Table 1.
These represent positions where the shaft diameter requires evaluation in terms of stress or is a
where a deflection is measured. A global, right hand coordinate system is established whereby the
1500 mm
1156 mm
1672 mm
ɸ155 mm OD ɸ177 mmID ɸ90 mm
Plane A: running surface
Plane D: loading plane
A B C D E F A’D’
RHSLHS
Plane A’: running surface
Plane D’: loading plane
y
E’
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axis of the axle is along the y-direction with the x-axis pointing in the direction of wheelset travel
(the xy-plane is parallel to the ground) and the z-axis points vertically upward. The Position 𝑦 of
each section is measured from the left-hand side (LHS) in the direction of the right-hand side (RHS).
The outer diameter, 𝐷𝑜, of the axle is specific to the section at Position 𝑦. The running surfaces
(Positions 𝐴 and 𝐴’) are the locations where the reaction forces from the rails are applied to the
wheels. The loading planes (Positions 𝐷 and 𝐷’) are the locations where the bearing loads are
applied to the axle (at the centre of the journal).
Table 1. Description of the critical section positions along the axle with distance, 𝒚, from the left-
hand side (LHS) and a corresponding outer diameter, 𝑫𝒐.
Position Description 𝒚 (mm) 𝑫𝒐 (mm)
A Theoretical wheel centre defining the running
surface on the LHS
0.0 177.0
B Inner edge of the wheel seat 70.0 177.0
C Bottom of the transition between the wheel seat
and bearing journal
90.0 161.5
D Bearings system centre defining the loading plane
on the LHS
172.0 178.5
E Bottom of the transition between the shoulder and
the axle body on the LHS. For the HMC, the
position where the collar ends and the secondary
composite tube begins on the LHS
326.0 155.0
F Middle section of the axle 750.0 155.0
E’ Bottom of the transition between the shoulder and
the axle body on the RHS. For the HMC, the
position where the collar ends and the secondary
composite tube begins on the RHS
1174.0 155.0
D’ Bearings system centre defining the loading plane
on the RHS
1328.0 178.5
A’ Theoretical wheel centre defining the running
surface on the RHS
1500.0 177.0
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3. LOAD CASES
Axle verification is carried out according to the method described in Standard BS 8535 [1]. The
Standard specifies two load cases for consideration when investigating the structural behaviour of
an axle:
Load case 1 – Straight track and mechanical braking.
Load case 2 – Low speed curving and mechanical braking.
For both cases, the axle undergoes four point bending predominantly about the x-axis due to the
static weight of the train. The Standard refers to this as the “masses in motion,” and the associated
bending moment is designated as 𝑀𝑥. Braking introduces additional bending around the x-axis (𝑀𝑥′ )
with a component of bending around the z-axis (𝑀𝑧′) as the braking force is applied. Additionally,
forces develop at the wheel due to conicity and braking so that a moment about the y-axis, 𝑀𝑦′ , is
produced. The Standard specifies this moment, 𝑀𝑦′ , to be constant along the axle, and
representative of the all bending around the y-axis. Intuitively, this manifests itself as torque, or
torsion so these terms are applied to 𝑀𝑦′ within this document.
Importantly, the bending moments applied to the axle causes fully reversed fatigue loading.
Historically, this is the primary cause of failure of a railway axle [2]. For an axle having a service
life of 30 years, the number of fully reversed bending cycles in fatigue is taken as 109 cycles.
Simple and transverse shear stresses occur under static loading with torsion introduced under
braking creating torsional shear. For powered axles, the torsional shear can be significant. For
example, a pinion gear on the axle in mesh with a traction motor at start up illustrates such a case.
This additional torsional moment would be described as 𝑀𝑦′′. Similarly, traction generates moments
about the x and y-axes, denoted as 𝑀𝑥′′ and 𝑀𝑧
′′ , respectively. For the particular case of the
unpowered trailer axle, traction moments are not included.
Buckling under combined bending and torsion at the middle section of the axle is discounted as the
slenderness ratio (length/diameter) of the axle will be less than 10 and the wall of the axle is
relatively thick compared to the outer diameter (27 mm:169 mm).
The Standard is clear that both load case 1 and 2 require consideration and the worst load case is
used for the axle design.
3.1 LOAD CASE 1
Load case 1 represents a condition where the axle loading is distributed equally on each journal.
Asymmetric loading can occur when un-sprung elements such as brake discs or pinion gears are
attached to the axle. This, in combination with accentuated dynamic effects at high speeds, can
result in load case 1 being the worst-case loading condition.
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For the benchmark hollow steel axle (Figure 3), the moments are provided by Lucchini at the critical
sections listed in Table 2. Between the loading planes, position 𝐷 to 𝐷’, the axle is in pure bending
and bending moment is greatest. As a worst-case, a resultant moment, 𝑀𝑅, is used to combine
the moments about the x and z-axes. Generically, the term bending moment is used for 𝑀𝑅 within
this document particularly where associated axle deflections are discussed. 𝑀𝑅 is calculated as
follows:
𝑀𝑅 = √(𝑀𝑥 + 𝑀′𝑥)2 + 𝑀′𝑧
2
It is noted that this calculation of the resultant moment, 𝑀𝑅, differs from the Standard [1] in that it
does not include the moment about the y-axis, 𝑀𝑦′ .
For the benchmark steel axle under load case 1, the maximum resultant moment, 𝑀𝑅 , is
19,392,335 Nmm with a notional torque, 𝑀𝑦′ , of 6,533,460 Nmm. The static bending about the x-
axis, 𝑀𝑥, occurs, as expected, between loading planes with a magnitude of 15,419,135 Nmm.,
Table 2. Moment values at the critical sections along the axle for load case 1.
Position 𝑀𝑥 (N·mm) 𝑀𝑥′ (N·mm) 𝑀𝑧
′ (N·mm) 𝑀𝑅 (N·mm) 𝑀𝑦′ (N·mm)
A 0 0 0 0 6,533,460
B 6,275,229 1,617,000 751,686 7,927,945 6,533,460
C 8,068,152 2,079,000 966,454 10,193,073 6,533,460
D 15,419,135 3,973,200 1,847,001 19,392,335 6,533,460
E 15,419,135 3,973,200 1,847,001 19,392,335 6,533,460
F 15,419,135 3,973,200 1,847,001 19,392,335 6,533,460
3.2 LOAD CASE 2
Load case 2 occurs infrequently and relates to low-speed curving where dynamic effects are less
pronounced. In this case, the back of the flange of one wheel is constrained laterally by the check
rail. This causes the train to tilt outward and the outside journal (LHS) becomes more heavily loaded
than the inside one.
For the benchmark steel axle, the moments are provided by Lucchini at the critical sections given
in Table 3. At the LHS loading plane, Position 𝐷, the journal is most heavily loaded, and the
resultant moment is greatest. Unique to load case 2, an external load is generated outboard of the
running surface, Position A, so that 𝑀𝑥 is greater than zero at that location.
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For the benchmark hollow steel axle under load case 2, the maximum resultant moment, 𝑀𝑅, is
22,283,141 Nmm with a notional torque, 𝑀𝑦′ , of 6,533,460 Nmm. Note that the torque, 𝑀𝑦
′ , is
unaffected by the non-symmetrical resultant moment and is equivalent to that in load case 1. The
static bending about the x-axis, 𝑀𝑥, is maximum at the loading plane on the LHS, Position 𝐷, with
a magnitude of 18,233,262 Nmm.,
Table 3.3. Moment values at the critical sections along the axle for load case 2.
Position 𝑀𝑥 (Nmm) 𝑀𝑥′ (Nmm) 𝑀𝑧
′ (Nmm) 𝑀𝑅 (Nmm) 𝑀𝑦′ (Nmm)
A 5,597,281 0 0 5,597,281 6,533,460
B 10,739,831 1,617,000 751,686 12,379,673 6,533,460
C 12,209,131 2,079,000 966,454 14,320,779 6,533,460
D 18,233,262 3,973,200 1,847,001 22,283,141 6,533,460
E 18,169,423 3,973,200 1,847,001 22,219,522 6,533,460
F 17,993,660 3,973,200 1,847,001 22,044,372 6,533,460
3.3 FINAL LOAD CASE
As the resultant moment, 𝑀𝑅, is greatest under load case 2, this is used as the worst-case load
condition for the design of an HMC railway axle as a replacement for the benchmark hollow steel
axle. Although load case 2 produces the maximum resultant moment at the LHS loading plane
(Position 𝐷), for the analysis, an 𝑀𝑅 of 22,283,141 Nmm is applied equally at the journal loading
planes on both sides of the axle (Positions 𝐷 and 𝐷′). This will produce pure bending between the
loading planes so that the resultant moment at Position 𝐷 will be the same as that at Positions 𝐸,
𝐹 and 𝐷’. Furthermore, although the resultant moment combines braking loads around the x- and
z-axes, the moment will be applied singularly about the x-axis. This will provide a worst-case
deflection at the centre span in the z-direction (downward) and simplifies conceptualisation of the
axle behaviour. As previously explained, the resultant moment, 𝑀𝑅, is referred to generally as the
bending moment. Under this application of 𝑀𝑅 there is no shear force, 𝑉, in the HMC railway axle.
As a result, there is no transverse shear developed under this condition between the running and
loading planes.
The static load case is defined by the greatest static moment (load case 2), 𝑀𝑥, of 18,233,262
Nmm being resolved into a point load, 𝑃, acting at the journal loading planes on both sides of the
axle (Positions 𝐷 and 𝐷′ ) multiplied by the distance between the running and loading planes
(Positions 𝐴 and 𝐷) of 172 mm. As a result, 𝑃 has a magnitude of 106,007 N, with a corresponding
reaction, 𝑄, at each wheel (Positions 𝐴 and 𝐴′). Under this static loading condition, a constant shear
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force, 𝑉, develops in the HMC axle between the running and loading planes (Positions 𝐴 and 𝐷).
As a result, transverse shear developed under this condition between the running and loading
planes.
For completeness, the clockwise moment, 𝑴𝒚′ , is applied to the axle such that a constant
magnitude of 6,533,460 Nmm developed. This moment about the y-axis, 𝑴𝒚′ , is referred to simply
as the torque or torsional moment.
4. LOADING CONDITIONS AND STRUCTURAL PERFORMANCE PARAMETERS OF THE WHEELSET
For analysis of the wheelset, the resultant moment, 𝑀𝑅 is applied at the loading planes, Positions
𝐷 and 𝐷’ for the bending case. The static load, 𝑃, is used for calculation of the transverse shear.
For torsional loading, the moment, 𝑀𝑦′ , is applied about the y-axis, although this is not done in
combination with the bending moment, 𝑀𝑅, or the static load, 𝑃.
The global loading diagram is shown in Figure 5.
Figure 5. A typical railway wheelset with the resultant moment, 𝑴𝑹, applied at the loading planes, 𝑫
and 𝑫’, causing the greatest bending about the x-axis. The static load, 𝑷, is used for calculation of
transverse shear, is applied separately at the same position. The torsional moment, 𝑴𝒚′ , is applied
uniformly about the y-axis.
A A’
D D’
My’
MR
My’
MR
P P
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The corresponding shear and moment diagrams are shown in Figure 6.
For the static load case, under load 𝑃 the shear force, 𝑉, is constant and positive between the LHS
running surface (Position 𝐴) and LHS loading plane (Position 𝐷). Between the LHS and RHS
loading planes (Positions 𝐷 and 𝐷’, respectively), the shear force reduces to zero. Between the
RHS loading plane (Position 𝐷’) and the RHS running surface (Position 𝐴’) the shear force is
constant and negative, being equal and opposite to the simple shear on the LHS. The static
moment, 𝑀𝑥, is zero at the LHS running surface (Position 𝐴) and increases linearly to the maximum
value at the LHS loading plane (Position 𝐷). The axle is in pure bending and the moment is constant
between the LHS and RHS loading planes (Positions 𝐷 and 𝐷’ , respectively). The resultant
moment reduces from the maximum to zero between the RHS loading plane (Position 𝐷’) and the
RHS running surface (Position 𝐴’).
For the case where the resultant moment, 𝑀𝑅, is applied, the shear force, 𝑉, is zero across the
entire axle. The moment is zero between Positions 𝐴 and𝐷. At this position the moment is applied
and is constant up to Position 𝐷′. Beyond Position 𝐷′ the moment returns to zero to Position 𝐴′.
The clockwise positive torsional moment, 𝑀𝑦′ , is constant across the axle from the LHS running
surface (Position 𝐴) to the RHS running surface (Position 𝐴’).
Figure 6. Axle loaded with the resultant moment, 𝑴𝑹. The static load, 𝑷, is superimposed for
calculation of transverse shear. The torsional moment, 𝑴𝒚′ , is constant across the axle. (a) Shear
diagram (b) Moment diagram.
A A’D D’
= 106,007 N
= 22,283,141 Nmm
= 6,533,460 Nmm
Static
Loading
Resultant
Loading
= 18,233,262 Nmm
= 106,007 N
0 N
0 Nmm
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Reference to the shear and moment diagrams, Figures 6a and b respectively, along with the critical
sections diagram, Figure 4, allows identification of the positions of maximum stress within the axle.
4.1 POSITION OF MAXIMUM BENDING STRESS
The maximum bending stress, 𝜎𝑅, occurs between the loading planes 𝐷 to 𝐷’ where the resultant
moment, 𝑀𝑅, is constant and at a maximum. The stress is defined as:
𝜎𝑅 =𝑀𝑅 ∙ (
𝐷𝑜2 )
𝐼
The hollow tube has an outer diameter, 𝐷𝑜, and an inner diameter, 𝐷𝑖, and the second area moment
of inertia, 𝐼, is as follows:
𝐼 =𝜋
64(𝐷𝑜
4 − 𝐷𝑖4)
By inspection, the maximum bending stress occurs at the position where the tube is thinnest. This
relates to Position 𝐸 on the axle.
4.2 POSITION OF MAXIMUM DEFLECTION
Associated with the maximum bending moment is the maximum deflection, 𝛿𝑚𝑎𝑥, in the axle that
results. This occurs at the centre of the span, Position 𝐹, and is calculated as:
𝛿𝑚𝑎𝑥 =𝑃 ∙ 𝑎
24 ∙ 𝐸 ∙ 𝐼(3 ∙ 𝐿2 − 4 ∙ 𝑎2)
Where the journal load at Position 𝐷 is denoted as 𝑃 and 𝑎 is the distance between Positions 𝐴
and 𝐷. The length between the running surfaces is indicated by 𝐿. The Young’s modulus is 𝐸 and
𝐼 is calculated as for the maximum bending stress (Section 4.1).
4.3 ANGULAR MISALIGNMENT AT THE JOURNALS
The extent of axle bending leads to an angular misalignment with the bearings. The degree of
angular misalignment, 𝜃, at the loading plane, 𝐷, is important for specifying the bearings that can
be used on the axle. As a guide, a deep groove ball bearing can sustain an angular misalignment
between 4° and 7° [3]. The angular misalignment is the angular distance between the straight axis
of the undeflected axle and the tangent to the curved axis of the deflected axle as depicted in Figure
7.
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Figure 7. Diagram showing the amount of angular misalignment, 𝜽, at the journal for the axle undergoing bending.
The angular misalignment is calculated as:
𝜃 =𝑃 ∙ 𝑎 ∙ (𝐿 − 𝑎)
2 ∙ 𝐸 ∙ 𝐼
4.4 BACK-TO-BACK DISTANCE BETWEEN WHEEL FLANGES
Axle deflection also affects the back-to-back distance between wheel flanges at rail level (Figure
8). The requirement for the allowable back-to-back distance is stated in TSI Loc & Pass 1302 /
2014 (Technical Specification of interoperability “Loc & Pass”), clause 4.2.3.5.2.1 [4]. As a guide,
the back-to-back distance (at rail level) should remain within a 6 mm tolerance in both crush and
tare conditions. As the axle deflects downwards, the wheels splay outwards on each side by
(∆𝐿𝐵𝑡𝐵)/2) so that the total increase in the back-to-back distance is ∆𝐿𝐵𝑡𝐵.
Figure 8. Back-to-back distance, 𝑳𝑩𝒕𝑩, as measured between flanges at rail level. As the axle
deflects downwards, the overall back-to-back distance increases by ∆𝑳𝑩𝒕𝑩.
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4.5 FIRST CRITICAL SPEED
The flexural rigidity of the axle, 𝐸𝐼, influences stability in terms of the critical speed. At the critical
speed, the deflections in the rotating axle would increase to an unbounded limit without restraint by
the bearings. Assuming a maximum trains speed of 200 mph running on a wheel of diameter 850
mm, equates to an angular velocity of 209 rad/s, or 33 Hz. The first critical speed is expressed as:
𝜔1 = (𝜋
𝐿)
2
∙ √𝐸 ∙ 𝐼
𝑚𝑙
Where 𝑚𝑙 is the axle mass per unit length and all other variables are as defined
previously.Standard BS EN 61373 [5], indicates a bending frequency of 90 – 110Hz, a reserve
factor, RF, of 3. For the analysis, the distance between the loading planes, Positions 𝐷 to 𝐷’ is
used for the length, 𝐿.
4.6 POSITION OF MAXIMUM TRANSVERSE STRESS
For the static load case, shear stress occurs between the running surfaces and loading planes (for
example, between Positions 𝐴 and 𝐷, respectively).
The average shear stress, 𝜏𝑎𝑣𝑔, across the diameter of an axle section in this region is calculated
as:
𝜏𝑎𝑣𝑔 =𝑉
𝐴
Where 𝐴 is the cross-sectional area of the hollow axle and is expressed as:
𝐴 =𝜋 ∙ (𝐷𝑜
2 − 𝐷𝑖2)
4
However, the maximum shear stress across the axle section is a transverse stress due to bending
occurring at the neutral axis and is calculated as:
𝜏𝑚𝑎𝑥 =𝑉 ∙ 𝑄
𝐼 ∙ 𝑡
Referring to Figure 9, the first area moment of inertia, 𝑄, for a hollow tube at the neutral axis where
it is greatest can be calculated by subtracting an inner (negative area) semi-circular section from
an outer (positive area) semi-circular section as:
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Figure 9. Calculation of the first moment area of inertia, 𝑸, for a hollow tube at the neutral axis of the axle.
So
𝑄 = 𝑄𝑂𝑢𝑡𝑒𝑟 − 𝑄𝐼𝑛𝑛𝑒𝑟 =1
2∙ 𝜋 (
𝐷𝑜
2)
2
∙4
3𝜋(
𝐷𝑜
2) −
1
2∙ 𝜋 (
𝐷𝑖
2)
2
∙4
3𝜋(
𝐷𝑖
2)
And the thickness of the transverse shear plane, 𝑡, is the total wall thickness along the neutral axis
as shown in Figure 9.
𝑡 = 𝐷𝑜 − 𝐷𝑖
It is clear that for a constant wall thickness, 𝜏𝑚𝑎𝑥 will be greatest where the diameter of the hollow
axle is the least. Within region 𝐴 to 𝐷 this occurs in the stress relief groove at Position 𝐶.
4.7 POSITION OF MAXIMUM TORSIONAL STRESS
The torsional moment, 𝑀𝑦′ , produces a shear stress, 𝜏𝑡𝑜𝑟𝑠𝑖𝑜𝑛, which reaches a maximum at the
outer diameter of the tube and is calculated as:
𝜏𝑡𝑜𝑟𝑠𝑖𝑜𝑛 =𝑀𝑦
′ ∙ (𝐷𝑜2
)
𝐽
Where the polar moment of inertia, 𝐽, for a hollow tube is defined as:
𝐽 =𝜋
2∙ [(
𝐷𝑜
2)
4
− (𝐷𝑖
2)
4
]
Generally, the torsion is constant across the axle from Position 𝐴 to 𝐴′. However, the loading
scenario is taken as a seized bearing at Position 𝐷. Under this condition, the region between
Positions 𝐴 and 𝐷 is subject to 𝑀𝑦′ and the maximum torsional stress would occur at the thinnest
point, Position 𝐶.
4.8 MAXIMUM ANGULAR TWIST
The maximum angular twist, 𝜑, arises due to the torsional moment, 𝑀𝑦′ . As with the torsional
shear stress (Section 4.7) the condition is taken whereby the bearing is seized at Position 𝐷 so
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that the twist occurs between Positions 𝐴 and 𝐷, with a maximum at Position 𝐷. The amount of
twist is calculated as:
𝜑 =𝑀𝑦
′ ∙ 𝐿
𝐽 ∙ 𝐺
The shear modulus is defined as 𝐺 and the other variables are as defined previously. The angular
twist increases per unit increase in axle length.
5. FINITE ELEMENT ANALYSIS (FEA) OF THE WHEELSET MODEL
The benchmark, hollow steel and HMC axles are modelled individually using ABAQUS 2018 [6].
The same loading and boundary conditions are used, defined as a quasi-static analysis, with non-
linearity assumed. For both the steel and HMC axles two finite element approaches are adopted to
assess the structural response against the applied bending moments. These are a 3D continuum
model (Model 1), as well as a separate axisymmetric analysis (Model 2), to assess the axle to hub
interaction. To provide verification, a further beam element model (Model 3) was employed to
confirm the system configuration and accuracy of the 3D stress model. The following section
outlines the modelling approach used for both the hollow steel and HMC axles. To reduce
duplication, the HMC axle is used as a representation.
5.1 MODELLED AXLE SYSTEMS
For the 3D model (Model 1), the wheelset is modelled with only half symmetry along the y-axis.
The axle is modelled as two individual parts. The first part is the composite axle comprising the
primary and secondary tubes. The second part is the steel collar with one at each end of the axle.
The collars are modelled as eight node, linear solid elements (C3D8), with full integration and an
isotropic material definition. The primary composite tube is modelled as four node, linear,
conventional shell elements (S4), with full integration. To allow the use of shell elements, the
secondary tube is simplified to neglect the end tapers. The representative mesh for both the collar
and composite axle is given in Figure 10a with an average element size of 10mm.
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Figure 10. HMC axle model element mesh. (a) Model 1-3D solid model, showing element mesh for the composite axle with the RHS collar attached. The LHS collar is removed to show cohesive elements beneath representing adhesive. (b) Model 2-Axisymmetric model, with element mesh for the primary composite tube, collar and interfacing wheel.
The primary composite tube is defined as a laminate material section, with a single integration point
at the midpoint of each ply through the thickness. The contact and interaction between the primary
tube and the collar is modelled using cohesive elements, with a continuum, isotropic material
response. These solid elements of 0.2 mm thickness represent adhesive and are offset from the
primary tube surface, with the orphan mesh sharing the connected nodes of the base of the shell
elements.
For the interference analysis a separate axisymmetric model (Model 2) is created to perform a
localised detailed assessment of contact interaction between the wheel hub and axle. The
wheelset, shown in Figure 10b, with the axle, consisting of the collar and primary composite tube,
is modelled with 4 node, bilinear, axisymmetric, linear elements (CAX4), with full integration.
Cohesive elements with linear, continuum response (COHAX4) and 0.2 mm height are defined
between the collar and tube to represent the adhesive. To account for the stiffness properties in
the composite tube, classical laminate theory (CLT), developed in MATLAB [7], is used to calculate
the inter-ply (E3) stiffness modulus (17.23 GPa), accounting for the sectional properties of laminate
thickness and ply fibre stacking sequence.
The beam element verification model (Model 3), for both axles, is modelled using three node,
quadratic elements (B32). This approach is used to confirm the boundary conditions and application
of loads by comparing the observed locational displacements and bending moment. The axle is
defined as a thick-walled pipe cross section, with varying representative sectional and material
properties along its length. The effective material properties of the composite tube are calculated
using the same CLT approach to determine the axial tensile stiffness modulus. Using the
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Timoshenko (thick wall) formulation, the B32 element allows for transverse shear deformation, with
the stiffness assumed, calculated by default, to be linear elastic with a fixed modulus [6].
The finite element modal analysis is conducted to confirm initial investigation of the critical axle
speed by analysis the first modal frequency using both the 3D element (Model 1) and beam element
(Model 3) models. Both models are defined for the axle profile considering only the unsupported
length between the journals, D to D’, without any external force, constraint or inertial masses being
considered. The first eigenvalue is evaluated using a linear frequency analysis, with the Lanczos
solver.
5.2 LOADING CONDITIONS
The resultant moment, 𝑀𝑅, and the torsional moment, 𝑀𝑦′ , are applied at the axle journal Positions
𝐷 and 𝐷’, the loading planes. The loads are applied in the 3D model (Model 1) to the surface of the
journal seats using a coupling, defined as kinematic. This coupling types adds rotational degrees
of freedom at the journal surface so that angular (misalignment) values can be extracted. The
surface nodes constrain both the translational and rotational degrees of freedom (DOF) to a single
reference point at the centre line of the bearing where the coordinate x=z=0. Utilising this constraint,
a single moment load is applied to the control node and distributed to the seat surface.
For the axisymmetric model (Model 2), the loading is defined as an interference fit between the
axle and the wheel hub. The surface contact and interaction properties are defined between the
hub and collar edges, with a nodal overlap and finite-sliding, ‘hard’, contact-overclosure. The
interaction tangential behaviour coefficient is given as 0.8. Alternative values in the range 0.5 to 1
showed little sensitivity in the stress result field.
For the beam model, bending moments are simply applied to a single node located at the centre
line point of each journal, where coordinates y=z=0.
5.3 BOUNDARY CONDITIONS
To confirm the back-to-back deflection, the axle is required to be modelled as a wheelset, where
the axle collar is connected to the wheel at the forged hub. Boundary conditions for the wheelset,
annotated in Figure 11, are defined for both wheels. Note that u represents displacement with 1, 2,
and 3 relating to the x, y and z directions, respectively. Furthermore, ur represents rotation with 1,
2, and 3 relating to the x, y, and z axes. The left wheel is constrained along the centre of the wheel
at the running surface, Position 𝐴, with displacement u3=ur2=0 and at a single node where the
wheel rim and rail intersect as u2=0. For the right wheel, the centre line is constrained at the running
surface, Position 𝐴’, in the vertical direction with u3=ur2=0.
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Figure 11. Boundary conditions for the wheelset model applied to the running surfaces where the rail and wheel contact. At Position 𝑨, u3=u2=ur2=0 and Position 𝑨’, u3=ur2=0.
For simplicity and to reduce computational time, when not considering the back-to-back deflection,
the axle was modelled without the wheels. Representative boundary conditions employed through
a kinematic coupling between the axle hub contact surface and a reference point. Here, both
translational and rotational degrees of freedom (DOF) are constrained. The control node located
at the centre line of on the hub (z=x=0) is then constrained as u2=u3=ur2=0 and u3=ur2=0 for the
left and right conditions, respectively.
Both the wheelset and axle configurations adopt symmetry boundary conditions on the half model
in the yz-plane (xsymm) as u1=u3=ur2=0.
For the beam element model, boundary conditions are applied as simply supported, four-point
bending for the axle only. A single node located at the hub centre line, is constrained with z=y=0
and z=0 for the left and right sides, respectively.
5.4 MODEL VERIFICATION
To confirm the boundary conditions and applied bending moments, a simple comparative
verification study was done for the comparisons of the maximum deflection of the wheelset against
both the axle (defined without the wheels) and beam element model. For both comparative results
studies, there was an error percentage difference of less than 0.1 % and 3.2 % for the steel and
HMC axle respectively.
A second verification comparison for the deflection results was made to assess the maximum
central deflection imposed by MR, loaded in the x direction, compared against the individual
application of the bending moments 𝑀𝑥, 𝑀𝑥′ , and 𝑀𝑧
′ in the corresponding axial planes. The MR
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results gave percentage increase in the maximum vertical deflection of 0.45 %. This concludes that
the resultant moment, as defined in BS 8535 [1], is a more conservative approach.
5.5 ASSUMPTIONS FOR THE FEA WHEELSET MODELLING
A number of assumptions are made in the analysis of the benchmark hollow steel axle and
subsequent HMC axle. These include:
• The analysis is assumed to be a quasi-static, linear elastic analysis only, with no dynamic
effects being considered.
• The primary and overwrapped secondary composite tubes are to be manufacture by co-
curing and considered as one component in the model.
• While a 0.2mm adhesive layer is included within the model, the adhesive results are not
considered within the analysis.
• High cycle fatigue will reduce the ultimate strength of the steel and composite materials by
50%.
• Environmental and adiabatic effects, caused by material expansion and contraction, are not
considered.
• Failure analysis, where a linear first point of failure causes the evolution of composite
damage is not considered.
6. STRUCTURAL CHARACTERISATION OF THE BENCHMARK, HOLLOW STEEL AXLE
The FEA model of the hollow steel axle is characterised in relation to the loading conditions defined
Section 5.2 with the boundary condition set out in Section 5.3.
Specific material property inputs to the FEA model are required. The axle is manufactured from
EA1N grade steel (approximated as AISI 1030 steel) with mechanical properties listed in Appendix
A, Table A1. The properties of the wheel are taken as AISI 1050 grade steel to approximate ER7
grade steel and listed in Appendix A, Table A2.
The structural performance parameters of the wheelset identified within Chapter 4 are investigated.
Results from the FEA model of the benchmark hollow steel axle are presented in Table 4.
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Table 4. Structural performance of the benchmark hollow steel axle.
Parameter Position
Figure 4
Simplifying
Equation
FEA Value
Benchmark
Hollow Steel
Axle
(Model 1)
Mass - 𝑚 = 𝜌 ∙ 𝑉 196.3 kg*
Maximum interference stress at
wheelseat, von Mises
A 319.20 MPa
(Model 2)
Maximum bending stress, von
Mises, 𝜎𝑅
E
𝜎𝑅 =𝑀𝑅 (
𝐷𝑜2
)
𝐼
(Section 4.1)
73.64 MPa
MR
Reserve Factor in bending after 107
cycles
E 𝑅𝐹 =𝜎𝑆𝑡,𝑓𝑎𝑡 107
𝜎𝑅
=270 𝑀𝑃𝑎
73.64 𝑀𝑃𝑎
3.7
Maximum deflection, 𝛿𝑚𝑎𝑥 F 𝛿𝑚𝑎𝑥 =
𝑃𝑎
24𝐸𝐼
∙ (3𝐿2 − 4𝑎2)
(Section 4.2)
1.123 mm
MR
Angular misalignment at bearings, 𝜃 D 𝜃 =
𝑃𝑎 ∙ (𝐿 − 𝑎)
2𝐸𝐼
(Section 4.3)
0.134°
MR
Back-to-back displacement, ∆𝐿𝐵𝑡𝐵 Between
wheel
flanges at rail
level
(Section 4.4) 2.017 mm
MR
Maximum transverse shear, 𝜏𝑚𝑎𝑥 C 𝜏𝑚𝑎𝑥 =
𝑉 ∙ 𝑄
𝐼 ∙ 𝑡
(Section 4.6)
14.82 MPa
𝑀𝑥
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Maximum torsional stress, 𝜏𝑡𝑜𝑟𝑠𝑖𝑜𝑛 C 𝜏𝑡𝑜𝑟𝑠𝑖𝑜𝑛
=𝑀𝑦
′ ∙ (𝐷𝑜2
)
𝐽
(Section 4.7)
10.20 MPa
𝑀𝑦′
Maximum angular twist, 𝜑
At D from A
𝜑 =𝑀𝑦
′ ∙ 𝐿
𝐽 ∙ 𝐺
(Section 4.8)
0.008 °
𝑀𝑦′
First critical axle speed, 𝜔1
D to D’
𝜔1 = (𝜋
𝐿)
2
∙ √𝐸𝐼
𝑚𝑙
(Section 4.5)
233.79 Hz
*Mass supplied by Lucchini is 198 kg
7. HMC RAILWAY AXLE DESIGN
Definition of the structural performance parameters of the benchmark, hollow steel axle as
characterised within Table 4 establishes conformance criteria for the design of a replacement HMC
railway axle.
The parametric approach to size this concept shown in Figure 1 was overly simplistic as bulk
strength properties were used for the CF reinforced epoxy laminate. Furthermore, geometric
features were not taken into account. In elevating the design fidelity of the concept, the composite
is treated as a laminae stack (a laminate) and analysed using classical laminate theory (CLT).
Abaqus FEA includes numerical methods for a full CLT analysis to be undertaken. The loading,
boundary conditions and assumptions are applied as used for the benchmark, hollow steel axle
described in Chapter 5. The aim is to achieve conformance with the structural performance of the
hollow steel axle set out in Table 4. The composite material used is a conventional, unidirectional
carbon fibre reinforced epoxy prepreg (UCHM450 SE 84LV) supplied by Gurit. While this prepreg
incorporates high modulus carbon fibre, it can be treated as a generic material whose equivalent
could be sourced from other suppliers. The HMC railway axle resulting from the Abaqus CLT
analysis is presented in Figure 12.
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Figure 12. HMC railway axle comprising a full length, primary composite tube, a secondary composite tube and metallic collars as introduced in Figure 1. Abaqus 2018 has been used to size the primary and secondary composite tubes as well as the metallic collars.
The design methodology for the HMC railway axle is as follows:
• Design the metallic collars so that the wall thickness is sufficient to carry the external
pressure load imposed by the interference fit of the wheel onto the collar.
• Design the primary composite tube of the axle so that the outer diameter is coincident with
the inner diameter of the metallic collar. Specify the ply layup and tube thickness to meet
the maximum bending, torsional and transverse shear stress conditions.
• Design the secondary composite tube so that the inner diameter is coincident with the outer
diameter of the primary composite tube. Specify the ply layup so that the centre deflection
of the axle is minimised. In reducing the deflection of the axle, the secondary composite
tube will serve to further reduce the bending stresses within the primary composite tube,
hence the overall HMC axle.
These design sequences are considered in more detail in the following sections.
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7.1 DESIGN OF THE METALLIC COLLARS AND PRIMARY COMPOSITE TUBE DUE TO
EXTERNAL PRESSURE LOADING AT THE INTERFERENCE FIT, POSITION 𝑨
The requirement is to use the existing wheels and bearings on the HMC railway axle. The axle
diameter at the journal is necessarily larger than that of the wheel seat so that the inboard bearing
arrangement can be assembled. In addition, the interference fit of the rolling element bearing on to
the axle is less than that of the wheel against the axle. Hence, the critical diameter relating to the
interference fit is at Position 𝐴 on the loading plane. A cross section through the axle at this location
is shown in Figure 13.
Figure 13. Cross section through the HMC axle at the running surface (Position 𝑨) showing the diameters of the metallic collar and the primary composite tube.
The outer diameter of the collar is 177 mm and is aligned with the inner diameter of the wheel hub.
The thickness of the collar is modelled as either 17.5 mm when no adhesive is considered and as
17.3 mm when adhesive is present, a 0.2 mm bond line. The overall collar thickness dictated by a
necessity to maintain an existing geometric feature in the end of the axle.
The primary composite axle tube has an outer diameter of 142 mm and inner diameter of 115 mm.
The wall thickness is 13.5 mm. The layup is balanced with 30 plies (see Figure 12). The layup is
apportioned as 40% 0° fibres, 40% +/-45° fibres and 20% 90° fibres.
Figure 14 shows a global representation of the von Mises stresses within the steel collar and
primary composite tube due to the external pressure load introduced by the interference fit between
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the wheel hub and the axle collar. In this case, the resultant moment, 𝑀𝑅, and torque, 𝑀𝑦′ , are not
applied to the model.
Figure 14. von Mises stress at the wheelseat from external pressure loading due to the interference fit between the wheel hub and steel collar. The resultant stresses within the primary composite tube are minimal. Note that the adhesive is not included as a worst case.
The maximum stress occurs within the collar near the interface with the primary composite tube. It
is noted that the adhesive bond (0.2 mm thick) has not been included in the analysis as a worst
case. This indicates that while the radial stress reduces from the outer diameter to the inner
diameter of the collar, the circumferential stress increases and becomes the dominate stress in the
collar. However, at 358.50 MPa the maximum stress is less than the yield strength of the collar
(EA1N grade steel) at 440 MPa. The conclusion is that collar could be further reduced in thickness
from 17.3 mm. However, the required geometric feature within the axle end prevents further
thinning.
Analysis of the primary composite tube at the same location shows a maximum compressive von
Mises stress of 13.65 MPa occurring at the outer diameter of the tube where contact occurs with
the collar. This stress is driven predominately by the circumferential stress imparted by the collar
into the primary composite tube, although a component of radial stress arises as the inner diameter
of the collar deflects inward. The 20% proportion of 90° fibres are aligned with the circumferential
stresses within the tube and provide support due to the compressive strength.
7.2 DESIGN OF THE METALLIC COLLAR AND PRIMARY COMPOSITE TUBE DUE TO
STATIC LOADING, 𝑴𝒙, AT POSITION 𝑪
Application of the static load, 𝑃, at the loading planes, Position 𝐷 and 𝐷′, introduces an internal
shear force, 𝑉. This produces transverse stress within the HMC axle. The shear force is constant
over the region from Positions 𝐴 to 𝐷. For a round, hollow tube, the transverse stress is maximum
at the neutral axis of the cross section.
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The transverse stress will be highest at Position 𝐶 in the collar where the wall thickness is the least.
The same location is chosen to assess the transverse shear stress in the primary composite tube.
Figure 15 shows the values of the transverse stress through the axle cross section at that location.
The 40% proportion of +/-45° fibres are aligned to provide support to the transverse stress within
the tube. The maximum surface shear stress in the primary composite tube is 1.72 MPa at the
outer ply
Figure 15. A cross section through the HMC railway axle at Position C showing the absolute maximum value of transverse the shear stress in the primary composite tube.
7.3 DESIGN OF THE PRIMARY COMPOSITE TUBE DUE TO THE RESULTANT MOMENT, MR, AT POSITION 𝑬
The maximum bending moment arises at the loading plane, Position 𝐷, and is maintained at a
constant value of 𝑀𝑅 between loading planes. The primary composite axle gains bending support
in regions beneath the collar. However, at Position 𝐸, the collar ends and the diameter of the axle
increases due to the additional 13.5 mm thickness of the secondary composite tube. The HMC axle
is analysed at Position 𝐸 just before the diameter increases. As the moment is applied about the
x-axis and purely within the yz-plane, deflection is downward in the negative z direction. This results
in the “top” of the axle being in compression while the “bottom” is in tension (Figure 16). Of
importance is that as the axle rotates, the configuration changes and the axle is subject to fully
reversed bending for each cycle.
A DC
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Figure 16. (a) Maximum von Mises stress (170.00 MPa) in the composite axle at Position 𝑬, ply 4,
bottom of primary composite tube, due to the moment, 𝑴𝑹. (b) Damage field for Hashin failure criterion highlighting fibre compression in the primary composite tube at Position 𝑬. The secondary composite tube is included in the analysis, but not shown here for clarity.
The maximum stress is at Position E and is a combination axle bending coupled with a contact
stress on the outer surface of the axle. The highest tensile stress (170.00 MPa) in the laminate due
to bending by MR is in the 0° fibres near the outer diameter of the primary composite tube at the
bottom (Figure 16, ply 4). The 40% proportion of 0° fibres are aligned to provide strength resisting
this load.
Figure 17. (a) von Mises stress at Position 𝑬, ply 27, top of primary tube, due to the moment, 𝑴𝑹, showing the peak stress of 528.10 MPa due to penetration of the collar on the top surface of the primary composite tube. (b) Damage field for Hashin failure criterion highlighting fibre compression in the primary composite tube at Position 𝑬. The secondary composite tube is included in the analysis, but not shown here for clarity.
A D
E
T
T
Top
Section T
z
x
Bottom
(a) (b)
A D
E
T
T
Top
Section T
z
x
Bottom
(a) (b)
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The peak stress in the HMC axle (528.10 MPa) is at Position 𝐸, shown in Figure 17, occurs where
the collar penetrates the outer surface of the primary composite tube at the top, shown here for ply
27. A refinement study of the mesh around the penetration of the collar and primary tube showed
little variation in the stress field when a finer mesh is adopted.
Figure 18, shows the maximum von Mises stress at Position E for each ply through the thickness
in both the primary (a) and secondary composite (b) tubes. This illustrates that the peak
compressive stress (528.10 MPa) is localised on the outer surface of the primary tube (higher ply
number), and diminishes through the tube thickness towards the inner diameter. The greatest
stress on the adjacent secondary composite tube also occurs in the outer plies (b), however, the
magnitude is less than 100 MPa as there is no collar penetration.
Figure 18. von Mises stress, Position 𝑬, at each ply of the primary composite tube (a) and secondary composite tube (b), due to the moment, MR. The high peak stress in the primary composite tube is due to penetration by the collar.
The Hashin failure criterion is applied to the composite axle at Position 𝐸. Maximum values of 0.44
and 0.39, for matrix tension (HSNMTCRT) and fibre compression (HSNFCCRT) failure,
respectively, suggest that no failure is like to occur in this region.
7.4 DESIGN OF THE PRIMARY COMPOSITE AXLE DUE TO TORSION, 𝑴𝒚′ , AT POSITION
𝑪
Application of torsion, 𝑀𝑦′ , to the HMC railway axle produces torsional stress within the system.
Generally, the torsion is constant across the axle from Position 𝐴 to 𝐴′. However, the loading
(a) (b)
Primary composite tube Secondary composite tube
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scenario is taken as a seized bearing at Position 𝐷. Under this condition, the region between
Positions 𝐴 and 𝐷 is subject to 𝑀𝑦′ and the maximum torsional stress would occur at the thinnest
point, Position 𝐶 . Figure 19 shows the torsional stress at the outer diameter of the primary
composite tube in the first 45° ply (ply 2) with a maximum torsional stress of 7.93 MPa. The 40%
proportion of +/-45° fibres are aligned to provide support to the torsional stress within the tube. The
maximum torsional stress occurring in the steel collar at Position 𝐶 is 17.88 MPa.
Figure 19. (a) Torsional stress at the outer diameter, ply 2, of the primary composite at Positions 𝑪,
due to the torsional moment, 𝑴𝒚′ . (b) Damage field for the Hashin failure criterion highlighting
matrix compression in the primary composite tube at Positions 𝑪. The secondary composite tube is included in the analysis, but not shown here for clarity.
The notional torque, 𝑀𝑦′ , also produces twist in the axle, 𝜑. The maximum angle of twist occurs at
Position 𝐷 under the scenario of a seized bearing at this location and has a value of 0.011°.
7.5 DEFLECTION CHARACTERISTICS OF THE HMC COMPOSITE AXLE DUE TO THE
BENDING MOMENT, 𝑴𝑹
Associated with the bending moment, 𝑀𝑅 , is the deflection of the axle and the angular
misalignment at the journal shown in Figure 20. The deflection is downward bending (z direction)
in the plain section of the HMC axle where the primary composite tube is reinforced by the
secondary composite tube. At Position 𝐹, the deflection is greatest, 𝛿𝑚𝑎𝑥, reaching a value of 1.702
mm. For reference, the maximum deflection of the HMC axle with the primary composite tube only
(secondary composite tube not included) is 4.190 mm. Therefore, including the secondary
composite tube decreases the deflection by 59%.
A DC
Top
Section T
z
x
Bottom
(b)(a)
T
T
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Figure 20. HMC axle under the bending moment, 𝑴𝑹. (a) Vertical displacement field plot compared against the undeformed state, with a scale factor of 20 applied showing maximum deflection, 𝜹𝒎𝒂𝒙,
at Position 𝑭. (b) Angular misalignment angle 𝜽 at Position 𝑫 caused by the axle deflection at the journal seat, with a scale factor 10 applied.
The deflection also increases the back-to-back distance by ∆𝐿𝐵𝑡𝐵 between the wheel flanges at rail
level (Figure 8). For the HMC railway axle, the change in the back-to-back distance increases by
3.212 mm which is within the accepted tolerance of 6 mm [4].
The rolling element bearings can tolerate limited angular misalignment (4-7° for a deep groove ball
bearing) for normal operation [3]. This value is taken as the degree of rotation, 𝜃, (Figure 20b)
calculated from the rotational degree of freedom around the x-axis at the surface nodes of the
journal seat for Position 𝐷. This maximum rotation, 𝜃𝑚𝑎𝑥 is equivalent to 0.212° when subject to
the moment, 𝑀𝑅.
The first critical speed, 𝜔1,of the HMC railway axle as calculated between the loading planes,
Positions 𝐷 and 𝐷′ is 388.93 Hz.
7.6 STRUCTURAL PERFORMANCE PARAMETERS
The structural performance parameters of the wheelset identified within Chapter 4 are investigated.
Results from a the full FEA model of the benchmark hollow steel axle are compared to the HMC
axle and presented in Table 5.
(a) (b)
F
Angular misalignment (b)
Maximum vertical
deflection
Angular
misalignment
D
D
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Table 5. Structural performance of the benchmark hollow steel axle vs the HMC axle.
Parameter Position
Figure 4
Simplifying
Equation
FEA
Value
Benchmark
Hollow Steel
Axle
(Model 1)
FEA
Value
HMC Axle
(Model 1)
Mass - 𝑚 = 𝜌 ∙ 𝑉 196.3 kg* 74.0 kg Total
Collars = 26 kg each
Primary composite tube =
14 kg
Secondary composite
tube = 8 kg
Maximum
interference
stress at
wheelseat, von
Mises
A 319.20 MPa
In collar
(Model 2)
358.80 MPa
In collar
13.65 MPa
In primary composite tube
(Model 2)
Maximum
bending stress,
von Mises, 𝜎𝑅
E
𝜎𝑅 =𝑀𝑅 (
𝐷𝑜
2)
𝐼
(Section 4.1)
73.64 MPa
MR
170.00 MPa
In primary composite tube
528.10 MPa
Collar penetration
MR
Reserve Factor in
bending after 107
cycles
E 𝑅𝐹 =
𝜎𝑆𝑡,𝑓𝑎𝑡 107
𝜎𝑅
3.7
=270 𝑀𝑃𝑎
73.64 𝑀𝑃𝑎
2.5
=421.7 𝑀𝑃𝑎
170.00 𝑀𝑃𝑎
0.8
=421.7 𝑀𝑃𝑎
528.10 𝑀𝑃𝑎
Hashins Criterion Pass
Maximum
deflection, 𝛿𝑚𝑎𝑥
F 𝛿𝑚𝑎𝑥 =
𝑃𝑎
24𝐸𝐼
∙ (3𝐿2 − 4𝑎2)
(Section 4.2)
1.123 mm
MR
1.702 mm
MR
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Angular misalign-
ment at bearings,
𝜃
D 𝜃 =
𝑃𝑎 ∙ (𝐿 − 𝑎)
2𝐸𝐼
(Section 4.3)
0.134°
MR
0.212°
MR
Back-to-back
displacement,
∆𝐿𝐵𝑡𝐵
Between
wheel flanges
at rail level
(Section 4.4) 2.017 mm
MR
3.212 mm
MR
Maximum
transverse shear,
𝜏𝑚𝑎𝑥
C 𝜏𝑚𝑎𝑥 =
𝑉 ∙ 𝑄
𝐼 ∙ 𝑡
(Section 4.6)
14.82 MPa
𝑀𝑥
23.17 MPa
In collar
1.72 MPa
In primary composite tube
𝑀𝑥
Maximum
torsional stress,
𝜏𝑡𝑜𝑟𝑠𝑖𝑜𝑛
C
𝜏𝑡𝑜𝑟𝑠𝑖𝑜𝑛 =𝑀𝑦
′ ∙ (𝐷𝑜
2)
𝐽
(Section 4.7)
10.20 MPa
𝑀𝑦′
17.88 MPa
In collar
7.93 MPa
In primary composite tube
𝑀𝑦′
Maximum
angular twist, 𝜑
At D from A 𝜑 =
𝑀𝑦′ 𝐿
𝐽𝐺
(Section 4.8)
0.008 °
𝑀𝑦′
0.011°*
𝑀𝑦′
First critical shaft
speed, 𝜔1
D to D’
𝜔1 = (𝜋
𝐿)
2
∙ √𝐸𝐼
𝑚𝑙
(Section 4.5)
233.79 Hz 388.93 Hz
*Mass supplied by Lucchini is 198 kg
7.7 DISCUSSION - STRUCTURAL PERFORMANCE THE OF HMC RAILWAY AXLE
A hollow, steel railway axle having inboard bearings has been designed to Standard BS 8535 [1].
The structural performance of this axle has been assessed in relation to a number of critical
sections along the axle (Figure 4) and the results are presented in Table 4. An HMC railway axle
has been designed as a direct replacement for the benchmark hollow steel axle. The performance
of the HMC axle relative to the hollow steel axle is provided within Table 5.
The aim in replacing the steel axle with the HMC axle was to reduce the overall axle mass. The
hollow steel axle has a mass of 198 kg. The HMC railway axle has a mass of 74 kg and is 63%
lighter than the hollow steel axle. The mass of the primary and secondary composite tubes of the
HMC axle is modest at 22 kg, representing 30% of the total HMC axle mass. The steel collars, at
52 kg, account for 70% of the total mass of the HMC axle. Substituting titanium for the steel collars
indicated that a collar mass of 15 kg rather that 26 kg each could be achieved. This would result
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in an overall axle mass of 52 kg, or savings of 74% compared to the benchmark, i.e., a hollow steel
axle. Furthermore, a reduction in the collar wall thickness may be possible if the existing axle end
feature could be removed, thereby making and additional mass savings.
The structural performance of the HMC railway axle compared favourably against the benchmark
hollow steel axle. The maximum deflection of the HMC axle is 1.702 mm. While this was 52%
greater than the steel axle the deflection occurs over a 1156 mm span and is considered small. In
addition, the back to back wheel deflection is 3.312 mm and remains within the 6 mm tolerance for
this parameter. The angular misalignment at the bearings is limited to 0.212°, so the requirement
to use the existing bearings is satisfied. Further reduction in these deflection driven parameters
could be achieved by increasing the thickness of secondary composite tube. While this would add
mass to the HMC axle, the increase is estimated to be no more than 5 kg.
The maximum bending stress in the HMC axle is 170.00 MPa occurring at Position 𝐸 where the
primary composite tube is most affected by the maximum bending moment and the collar. This
results in a reserve factor (RF) of 2.5 for the HMC axle versus 3.7 for the steel axle under the
condition of high cycle (107) reversed bending fatigue. As a reference, the steel axle generally
operates with an RF of at least 2 across the axle. While bending is the predominant load case, the
effect of torsion at Position 𝐶 is also presented. This reflects the case where the bearing has seized
and the torque is driven through the collar and primary composite tube. Here the stress in the HMC
axle (7.93 MPa) is less than that for the steel axle, although the torsional stress in the collar is
greater at 17.88 MPa. The maximum transverse shear occurring in the primary composite tube at
the relief groove between the wheelseat and journal (Position 𝐶) is significantly less for the HMC
axle (1.72 MPa) than the steel axle (14.82 MPa), although the stress level in the collar is higher at
23.12 MPa. The Hashin criterion has been used to assess the likelihood of failure of the HMC axle
and values less than 45% of allowable were determined for the worst case of bending at position
𝐸. While the Hashin criterion provides an acceptable measure of composite laminate failure,
treatment of the stress transfer through the thickness (interlaminar shear stress) may be unreliable.
For this reason, the Tsai-Wu criterion is favoured and the HMC axle would benefit from an analysis
using this failure technique.
A clear area for further study is in the design of the metallic collars. The purpose of the collars is
to support the interference fit of the wheel and bearing onto the axle as well as provide the interface
geometry for attachment of those element. This has been achieved with maximum stresses of
358.50 MPa and 13.65 MPa within the collar and primary composite tube, respectively at the
running surface, Position 𝐴. However, the adhesive bond between the collar and the primary
composite tube requires an engineered solution. As presented, the stress within adhesive exceeds
the allowable. Furthermore, the end feature of the collar imparts a penetrating stress (528.10 MPa)
into the outer surface of the primary composite tube under bending. A discussion of the bonded
collar solution is provided in Chapter 9 of this report.
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8. ASSESSMENT OF THE MANUFACTURABILITY AND COMPARISON BETWEEN VARIOUS MANUFACTURING METHODS
The Wheelset Axle is manufacturable following two different processes: manual roll wrapping (RW)
or filament winding (FW).
In this chapter these processes are described in detail. The typical workflow of each method is
shown along with its pros and cons.
This assessment evaluates the feasibility of the Design Concept 3 of the axle, where the composite
part is formed by a primary tube (PT) and a secondary tube (ST), while the metallic collars are
assembled on the ends of the primary tube.
8.1 ROLL WRAPPING
Making the axle with a manual roll wrapping can be carried out following these steps:
1. Prepreg cutting
The prepreg material is cut into layers with appropriate fiber orientation.
2. Roll wrapping
The prepreg layers, regarding the primary and secondary tube, are rolled by hand on a cylindrical rod, known as mandrel, following the appropriate layup
3. Curing
The wrapped tube is placed in a vacuum bag and cured in an autoclave. Once curing is complete, the mandrel is removed from the tube.
4. Milling of the tube
The primary tube ends are milled on the outer side, in order to provide an accurate cylindrical coupling with the collars
5. Bonding of collars
The two metallic collars are bonded on the tube ends with an epoxy adhesive.
6. NDI
Nondestructive inspection of the bonding interface and composite laminate is carried out to find possible defects like delaminations or debonded areas.
7. Finishing
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The axle is finished by removing burrs and coated (if needed)
The roll wrapping provides the ability to make the stacking sequence more customizable, for
example, it allows the placing of layers with fibers aligned with the tube axis, which are the most
suitable for withstanding pure bending loads. The wrapping of the secondary tube can be done with
a good precision, ensuring the removal of material belonging only to the primary tube during the
milling phase and the clearance gap between the secondary tube and the stub axles.
Figure 21 - Section of a tube end.
Manually placing the layers will inevitably generate a butt joint for each layer. This means that there
is a fiber discontinuity for each layer of the composite tube, that cause a loss of performance of the
axle. Efforts should be made to stagger this butt joint around the circumference of the tube for
subsequent layers.
Figure 22 - butt joint generation during the mandrel wrapping.
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8.2 FILAMENT WINDING
Making the axle with a filament winding process can be carried out following these steps:
1. Machine setting
The bobbins of tow preg material is placed on the rack of filament winding machine.
2. First Winding
Winding of the primary tube on a mandrel following the appropriate layup. An extra layer shall be wounded as to be sure not to damage the fibers of the outermost layer of the primary tube.
3. Curing
The wounded tube is placed in a vacuum bag and cured in an autoclave. Once curing is complete, the mandrel is removed from the tube.
4. Milling of the tube
The primary tube ends are milled on the outer side, in order to provide an accurate cylindrical coupling with the metallic collars.
5. Bonding of collars
The two metallic collars are bonded on the tube ends with an epoxy adhesive.
6. NDI
Nondestructive inspection of the bonding interface is carried out to evaluate the voids quantity and dimensions.
7. Second Winding
The primary tube with bonded collars is the new mandrel on which the secondary tube is wounded.
8. Curing The wounded tube is placed in a vacuum bag and cured in an autoclave.
9. Finishing
The axle is finished by removing burrs and coated (if needed)
In the proposed workflow there are two winding steps because it is not possible to wind the
secondary tube with a precise length over the first winding, so the most practical method is to wind
the secondary tube after bonding the collars. Note that this process involves covering the inner
ends of the collars, eliminating the clearance gap, as modelled in Chapter 9.
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This method has a constraint on winding, i.e. it is not possible to place the fibres on the mandrel at
an angle of less than 10° to the tube axis. Moreover, the thicknesses of the single layers are
different than the plies applied during roll wrapping.
Basically, it is not possible to apply the same layup as used for roll wrapping, so dedicated analyses
are carried out.
Once adoption of filament winding as manufacturing route is discussed in technological terms, it
shall also be studied in terms of resulting mechanical performances. More specifically, because of
the manufacturing constraint presented above, it would require a completely different stacking
sequence with respect to the one proposed for roll-wrapping.
The goal is therefore that of quantitatively determine the mass variation caused by adoption of
filament winding and such analysis requires the development of an alternative and concurrent layup
sequence that performs the same as the proposed roll-wrapped layup sequence.
When aiming at mass reduction, it is easy to state that this latter activity shall be implemented
following an optimality approach: thus, the outcome won’t be an alternative layup but the best
performing alternative layup in terms of mass reduction.
An additional point is considered when switching from roll wrapping to filament winding; this latter
process generates an intertwining among tows being wound in different winding strokes.
Consequently, very local variations of ply thickness, orientation angle and, therefore, lamination
law can be observed. Despite such local variation are relatively small, their summation over the
whole wound item might leverage non-negligible global stiffness losses that shall be quantified.
Obviously, the process relies on a set of material properties describing the elastic behaviour of
each layer and determining the overall tubes stiffnesses; as a consequence, the engineering
constants of the base wound lamina in the principal material directions shall be used as input data
during the optimization process.
Summing up, the following points must be considered when developing the best stacking sequence
that can be manufactured by filament winding and that performs the same as the roll wrapped
tubes:
• Re-orientation of plies at 0 deg to ±10 deg;
• Introduction of orientation-dependant minimum ply thickness;
• Estimation of the stiffness loss due to the winding pattern;
• Determination of engineering constants in the principal material directions generated by
filament winding process.
The optimization flow chart is schematically reported:
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Figure 23 Filament winding layup optimization routine
The starting point is the stacking sequence proposed for the roll wrapping process. The final output
shall be a concurrent layup that can be manufactured by filament winding and that ensures the
same performance in terms of torsional and bending stiffness.
Design constraints for the studied application are stiffness-driven ones, since maximum allowed
deformation (displacements/rotations) are drivers for the presented problem; such a statement
appears self-evident because of the higher specific strength pointed out by laminated composite
items if compared to steel ones. Therefore, it is reasonable to adopt the performances of the
laminated tubes in terms of maximum allowed displacement and rotation as indexes of global
stiffness.
Hence, the first step is the evaluation of the performances of the base roll wrapping layup.
Such preliminary activity is implemented in the same Finite Element environment in which the
optimization of the equivalent filament winding layup is defined, to prevent possible errors or results
misalignment due to the adoption of different solvers. For this reason, the chosen FE solver is
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HyperWorks X, containing the OptiStruct suite; this latter allows for the numerical optimization of
composite laminates both in terms of ply thickness and stacking sequence.
Separate primary and secondary tube are modelled in a simplified bending/torsion loading and
constraint condition and their maximum static displacement and rotation are derived:
• 𝛿𝑗,𝑡𝑎𝑟𝑔𝑒𝑡 = maximum vertical displacement of the roll-wrapped PT or ST
• 𝜑𝑗,𝑡𝑎𝑟𝑔𝑒𝑡 = maximum rotation about the axis of the roll-wrapped PT or ST
• 𝑗 = PT (Primary Tube) or ST (Secondary Tube)
These quantities are relevant for mass optimization process of the FW layup, since they act as
optimization constraints.
Once the preliminary activity regarding the reference RW layup is terminated, the optimization
process begins. It shall be fed with few input data, among which of crucial relevance are:
• Objective function: a quantity to be maximized or minimized according to the design
requirements and which is dependent on design variables. According to the purposes of the
analysis, mass shall be minimized.
• Constraint functions: non-negotiable conditions that the outcome of optimization process
shall respect to be considered acceptable. Indeed, these conditions are highlighted by the
sentence written above: “[…] layup that […] performs the same in terms of bending and
torsional stiffness” which translated in quantitative terms below.
𝛿𝐹𝑊𝑗,𝑖 ≤ 𝐾𝐷𝑗,𝑖, 𝛿 ∙ 𝛿𝑗,𝑡𝑎𝑟𝑔𝑒𝑡
𝜑𝐹𝑊𝑗,𝑖 ≤ 𝐾𝐷𝑗,𝑖,𝜑 ∙ 𝜑𝑗,𝑡𝑎𝑟𝑔𝑒𝑡
Where:
o 𝑗 = Primary tube (PT) or secondary tube (ST) index
o 𝛿𝐹𝑊𝑗,𝑖 = max. vertical displacement of the filament-wound PT or ST (i-th iteration);
o 𝜑𝐹𝑊 𝑗,𝑖 = max. rotation about the axis of the filament-wound PT or ST (i-th iteration);
o 𝐾𝐷𝑗,𝑖,𝛿 = Knock-Down factor for bending stiffness due to fiber intertwining during the
winding process for PT or ST (i-th iteration);
o 𝐾𝐷𝑗,𝑖,𝜑 = Knock-Down factor for torsional stiffness due to fiber intertwining during the
winding process for PT or ST (i-th iteration);
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The definition of these coefficients is needed because fibers weaving during the winding
process could be detrimental for global laminate stiffness. They are directly attributed to the
optimization constraints to implicitly compensate for these stiffness losses during the
optimization process by imposing constraints that are more stringent than the target values by
themselves. Their estimation requires an iterative process since their values are assumed to
be stacking sequence-dependent; their values at the first iteration are set to 1 (i.e. fiber
patterning is initially assumed to have no effect on stiffness).
• Minimum ply thickness: such an information is adopted by the solver to discretize the domain
of the thicknesses that could be assigned to a ply: thus, the solver can assign to a certain ply
only manufacturable thicknesses that are integer multiples of the minimum one. In case of
filament winding, these thicknesses are orientation dependent: different deposition angles carry
out different extent of superposition of fibers and, therefore, slightly different thickness for each
ply. CadWind software has been used to determine these ply thicknesses by simulating the
winding process over the mandrel; the software is fed with material properties coming from a
SigmaPreg datasheet referring to a towpreg with the following properties:
- Flame retardant resin system
- Tape width of 6mm
- 24 K carbon fibers
- Fiber mass content: 67%
- TEX: 1600 g/km
Figure 24 Simulation of 45° helical winding
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Plies at ±10 and ±45 deg are featured by a minimum thickness of 0.29 mm whilst hoop-wound
plies by 0.30 mm. For sake of simplicity, 0.3 mm is assumed for all of the orientation angles.
Concerning the FW layup to be determined, the starting point is the generation of an
overconservative layup that can be manufactured by filament winding manufacturing. Such
operation is carried out referring to the layup proposed for RW by re-orienting plies originally
deposed at 0 deg to ±10 deg, and by increasing the number of plies themselves.
Figure 25 Overconservative initial guess for the FW layup
This latter point is needed because re-orientation of axial plies inescapably harms bending stiffness
and it would probably cause violation of optimization constraint on maximum vertical displacement
for the initial layup guess. Conversely, an excessively conservative initial guess would not harm
the validity of the outcomes since useless plies (providing poor contribution to the overall laminate
stiffness) are assigned of zero thickness and erased during the process. Thus, number of plies is
augmented to let the optimization solver starts from a feasible design (i.e. respecting the
constraints).
Then, according to the routine described in Figure 23, the optimization solver is launched. Once
the algorithm stops its iterations, a trial filament winding layup is proposed; the next step, according
to the routine, is the estimation of the KD factors describing the winding pattern detrimental effect
on overall laminate stiffness. These latter can be estimated thanks to CadWind Software, which
allows for the simulation of the whole winding process of the trial stacking sequence determined in
the previous step. Cadwind also enables the extraction of a meshed finite element shell model
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whose peculiarity is that it accounts for the very local thickness and material orientation variations
due to fibres intertwining and causing the losses of global stiffness mentioned above.
Hence, the strategy to estimate the knockdown factors relies in the comparison of the performances
of the model exported from CadWind with another one, being identical in terms of geometry, mesh
and loading conditions but with global thickness and material orientation assignments.
o 𝐾𝐷𝑗,𝑖,𝛿 = 𝛿𝐿,𝑗,𝑖
𝛿𝐺,𝑗,𝑖⁄
o 𝐾𝐷𝑗,𝑖,𝜑 = 𝜑𝐿,𝑗,𝑖
𝜑𝐺,𝑗,𝑖⁄
Where:
o 𝛿𝐿,𝑗,𝑖 = max. vertical displacement of the “local” PT or ST model (i-th iteration);
o 𝛿𝐺,𝑗,𝑖 = max. vertical displacement of the “global” PT or ST model (i-th iteration);
o 𝜑𝐿,𝑗,𝑖 = max. rotation about the axis of the “local” PT or ST model (i-th iteration);
o 𝜑𝐺,𝑗,𝑖 = max. rotation about the axis of the “global” PT or ST model (i-th iteration);
These KD factors can be defined as relative coefficient expressing the expected stiffness decay
that the laminated tube would experience because of the way it is manufactured.
They are attributed to the target deformation values for the next iteration, and, therefore, to update
the design constraints as they reduce the absolute values of the allowed deflection and rotations.
Indeed, the outcome of the optimization process is a function of the value of the knock-down
factors; however, these coefficients cannot be assumed to be universally valid, being that their
values are probably a product of a specific stacking sequence. Because of such a mutual
dependence, an iterative process on the knock-down factors is issued.
The iterations are stopped when, assuming a certain tolerance, two consecutive iterations point out
the same value of knock-down coefficients, because an additional iteration would have the same
result, since the optimization process would be issued with the same constraint boundary values
for deflections and rotations. A tolerance of 2.00% is assumed.
Another condition causing the interruption of the iterative process consists of output trial stacking
sequences whose stiffness performances (transverse vertical deflection and rotation) already fall
within the range of allowed vertical displacement and rotation for next iteration, updated with the
knock down; in such conditions, in fact, an additional iteration would provide the same output
stacking sequences.
At the end of the proposed concept routine, the equivalent stacking sequence for filament winding
is eventually derived.
• Primary tube: [90/±452/(±10/±45)7/±453]s (23.4 mm thick)
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• Secondary tube: [902/±454/±107]s (14.4 mm thick)
Once the presented method generates a mass-optimized stacking sequence, its validity is checked
against the one developed for roll wrapping with an independent analysis tool. Two complete
wheelset models containing the concurrent roll-wrapped tubes and the filament-wound tubes
respectively are therefore produced in Abaqus CAE; they are subjected to the same loading and
constraint condition and their stiffness performances are compared in terms of maximum vertical
deflection, gauge length increase and rotation about the axis.
Results are displayed and summarized:
Figure 26 Maximum vertical displacement of the roll-wrapped solution [mm]
Figure 27 Maximum rotation about the axis of the roll-wrapped solution [rad]
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Figure 28 Maximum vertical displacement of the filament-wound solution [mm]
Figure 29 Maximum rotation about the axis of the filament-wound solution [rad]
Table 5 Summary of Rw and FW comparison.
Property RW- Layup FW – Layup % variation
massPT 13.65 kg 21.83 kg +59.93%
massST 8.28 kg 8.88 kg +7.25%
U2max 2.582 mm 2.491 mm -3.52%
UR3max 12.3 mrad 8.360 mrad -32.03 %
gauge 4.520 mm 4.360 mm -3.54%
Tsai-Hill FI 0.3512 0.4761 +35.56%
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The total mass increase pointed out by the FW solution is of 8.28 kg; however, the assembly of
primary and secondary tube generates a solution that is still much lighter than traditional EA1N
steel axle. Consequently, in spite of its larger mass with respect to the roll-wrapped solution,
filament winding could provide advantages from the manufacturing point of view that may worth
such mass increment. Therefore, final conclusions are entrusted to a comparison over the two
concurrent manufacturing technologies.
8.3 COMPARISON AMONG ROLL WRAPPING AND FILAMENT WINDING PROCESS
The main difference between the two processes is the performance they provide to the component.
It is not possible to evaluate the effect of the layer butt joints (roll wrapping) during the analysis
since it is not possible to quantify accurately the loss of performance due to fibres discontinuities
without making a test campaign or numerically estimating it with relative coefficient as for the KD
factors for the winding pattern effect. Moreover, filament winding generates a pre-tension in the
fibres whose effect it is not included in the presented simulation and which can be relevant for
overall elastic behaviour of the axle.
Indeed, no conclusion based on the expected mechanical behaviour of the concurrent design (RW
and FW) solutions can be drawn without experimental validation of the models.
However, they can still be compared by the manufacturing point of view. A relevant factor that
differentiates the two processes can be found in repeatability: filament winding is an automated
process, so all the tubes produced with such a technology are expected to have identical
performances and characteristics. Tubes produced by roll wrapping with a manual process,
conversely, will inescapably have operator-dependent quality and, therefore, slightly different
output mechanical performances, since more errors could be expected for this kind of manual
process.
The performances obtained with adoption of filament winding process are higher in terms of
mechanical response because of its better repeatability with respect to the performances that would
probably be obtained with the manual roll wrapping.
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9. ANALYSIS OF THE BONDED JOINTS
In this chapter, the feasibility of a bonded joint between the metal collar and the composite tube is
assessed by FEA, with reference to its fatigue strength for 100 million cycles. First, a brief overview
of the literature about multi-material, adhesive joints is presented, and a structural adhesive is
proposed. Then, the bonded joint between the collar and the tube without modifications of the
geometries shown in Figure 12 is studied. Based on the results of this preliminary analysis, a
refined solution is analysed and discussed.
9.1 SELECTION OF THE ADHESIVE AND MECHANICAL CHARACTERIZATION
The use of adhesive joints in structural applications is particularly suitable for joining dissimilar
materials without adding weight (compared to mechanical joints), achieving good fatigue resistance
and design flexibility [8-16]. Nevertheless, joining multi materials can be a challenging task in the
design and manufacturing steps of these new lightweight structures, becoming even more
important to know/study the effects of dissimilar materials used as substrates, the mechanical
behaviour and environmental resistance of adhesive joints in order to guarantee their safety and
reliability [17,18]. G. Sun et al., 2018, studied the effects of adherend thickness and substrate
material type (Q235 steel, 5182 aluminium alloy and woven of carbon fibre reinforced plastic -
CFRP) in the tensile behaviour of the dissimilar adhesively bonded joints. M. D. Banea et al., 2018,
analysed the mechanical properties of similar and multi material adhesive joints by means of
experimental and numerical tests. For this study three different types of substrates were used: hard
steel, carbon fibre reinforced plastic and aluminium. A. H. Khawaja et al., 2016, studied different
methods for the joining of carbon fibre composite materials and aluminium 6061 T6: double-lap
adhesively bonded joints, hybrid joints (adhesive + rivets) and the use of adhesive pins. For the
analysis tensile and fatigue tests were performed.
A summary of the adhesive types found in these references and the most relevant characteristics
are reported in Table 6. The results of the tests reported in the references are summarized in Table
7.
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Table 6. Adhesives’ mechanical properties.
Reference Adhesive type
Shear
modulus
(MPa)
Shear yield
strength
(MPa)
Shear
strength
(MPa)
Shear
failure
strain (%)
Young's
modulus
(MPa)
[8] Sikaflex 256 1.351 ±
0.04 8.26 ± 0.30
8.26 ±
0.30 330 ± 27 -
AV138-HV998 1559 ± 11 25 ± 0.55 30.2 ±
0.40
5.50 ±
0.44 -
[9]
AV138-HV998 1560 ± 11 26 ± 0.55 30.2 ±
0.41
5.50 ±
0.45 -
Araldite 2015 487 ± 77 17.9 ± 1.80 17.9 ±
1.80
43.9 ±
3.40 -
[10]
AS1805 RTV
silicone rubber
0.68 ±
0.03 -
1.47 ±
0.02 332 ± 17 -
RTV 106 0.55 ±
0.05 -
1.97 ±
0.03 408 ± 21 -
[11] FM 73 - - - - 2160
[12] Araldite 420 A/B - - 27 - 1850
[13] AV138-HV998 1559 ± 11 25.1 ± 0.33 30.2 ±
0.41 7.8 ± 0.7 4890 ± 810
[14] AV138-HV999 1560 ± 10 - - - 4890 ± 810
[15] Betamate 4601 - - - - 2860
[16] SikaForce 7888 - - 22 - 2530 ± 160
[17] Araldite 2015 1000 - - - 1850
[18]
[19] 3M 9323 B/A 2600
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Table 7:The mechanical properties of the studied adhesive joints.
Reference Adhesive
type
Adherend type Overlap
(mm)
Lap shear
strength
(MPa)
Ultimate
tensile
strength
(MPa)
Tensile
failure
Loads
(N)
Impact
failure
loads -
SLJ (N)
Fatigue life equation
(SLJ)
[8] Sikaflex
256
Mild steel 25 - 12 914 around
5500
normalized load = -
0.048* ln (number of
cycles) + 1.0456
AV138-
HV998
25 - 41 2554 around
7000
normalized load = -
0.045* ln (number of
cycles) + 1.0555
[9] AV138-
HV998
Aluminium alloy
AA6082
25 - - around
4250
- 1000000 cycles at
2761 N
Araldite
2015
25 - - 9375 - -
[10] AS1805
RTV
silicone
rubber
Steel and
aluminium alloy
6082-T651
12.5 1.25 ±
0.08
- around
500
- normalized load = -
0.0496* ln (number
of cycles) + 1.0963
25 - - around
900
- -
50 - - 1500 - -
RTV 106 12.5 1.65 ±
0.13
- around
500
- normalized load = -
0.0491* ln (number
of cycles) + 1.0379
25 - - 1000 - -
50 - - 2500 - -
[11] FM 73 Alluminium
alloy
12.5 - - - - At 2000000 of cycles
the maximum tensile
strength of the joint
is around 60 MPa
[12] Araldite
420 A/B
Docol 1000
high strength
steel
12.5 - 35 around
6000
- -
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[13] AV138-
HV998
7075 T76
aluminium alloy
and Cr. D steel
12.5 - 39.45 ±
3.18
4825 - vibration cycle
134784 - peak load
of 4254N; vibration
cycle 67392 - peak
load of 4370N and
vibration cycle 0 -
peak load of 4847N
[14] AV138-
HV999
7075 T76
aluminium alloy
and Cr. D steel
12.5 - - - - vibration cycle
49259 - Young's
modulus of 5.054
MPa; vibration cycle
27462 - Young's
modulus of 9.142
MPa and vibration
cycle 0 - peak load
of 4890 MPa
[15] Betamate
4601
A5754-O
aluminium alloy
12.7 - 64 6500 - Variation of
J=1129.2*(number
of cycles) ^-0.1359
[16] SikaForce
7888
Hard steel (HS) 12.5 - 31.12 ±
1.17
5000 - -
Composite
(CFRP)
25 - 31.12 ±
1.17
15000 - -
Alluminium (Al) 50 - 31.12 ±
1.17
30000 - -
[17] Araldite
2015
Q235 steel,
5182 aluminium
alloy and woven
carbon fibre
reinforced
plastic (CFRP)
25 - 17.9 around
7000
- -
[18] KSR-177 6061-T6
aluminium and
USN 125
carbon epoxy
prepreg
40 80.8 4.86 around
5000
- endurance limit of
1.23 kN
[19] 3M 9323
B/A
40
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From the analysis of the literature, it appears that two-part epoxies are usually employed for the
manufacturing of hybrid metal-CFRP joints. The chosen adhesive for the feasibility analysis of the
metal collar to composite tube on is the epoxy adhesive 3M 9323 B/A studied in [19].
For this adhesive, fatigue test results are available for various joint types and in [19] a local stress
approach is presented. It was shown that the shear stress amplitude constitutes a parameter able
to correlate the fatigue lives for different joint configurations, as shown in Figure 30. The same
approach is proposed for the analysis of the joint between the metal collar and the composite tube.
It has to be pointed out that the range of cycles explored in [19] does not exceed one million cycles,
therefore an extrapolation is needed to obtain the admissible shear stress amplitude for 100 million
cycles. The extrapolation allowed evaluation of an allowable shear stress amplitude of 13 MPa for
a probability of failure of 10%, 16 MPa for a probability of failure of 50%.
Figure 30. Fatigue S-N diagram of the 3M 9323 B/A adhesive [19]
To complement the data reported in the technical data sheet of the chosen adhesive and in [19],
additional tests were performed in the framework of this project. They consisted of the evaluation
of the tensile properties of the bulk adhesive, conducted according to ISO 527 standard using
specimens manufactured according to the French standard NF T 76 – 142, and of mode I fracture
toughness tests, conducted according to ISO 25217 using double cantilever beam tests.
By tensile testing, the value of the Young’s modulus E and of the ultimate tensile strength of the
3M 9323 adhesives were obtained and added to Table 6 and Table 7, respectively.
Based on these tests, the coefficients of a triangular traction separation law were derived, as
reported in Table 8. Finite element simulations of the mode I fracture tests allowed assessment of
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the accuracy of the evaluation of these coefficients. Figure 31 showcases the superposition of the
numerical force-opening curve onto the experimental one.
Figure 31. The tensile stress-strain curve of the bulk adhesive 9323 B/A
Table 8. Coefficients of the proposed traction separation law for the 3M 9323 B/A adhesive
GnC(N/mm) GS
C(N/mm) tI0(MPa) tII
0(MPa) eI0(MPa/mm) eII
0(MPa/mm)
2.8 5.42 30.69 42 8564.3 6117.36
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Figure 32. results of mode I fracture test, with FE analysis results superimposed, showing the accuracy of cohesive modelling.
9.2 FEA OF THE ADHESIVE JOINT
The adhesive joint between the steel collar and the primary composite tube was modelled using
the partial model shown in Figure 33. It consists of one collar (ivory), a portion of the primary (inner)
tube (light gray) and the corresponding portion of the secondary (outer) tube (dark gray).
The wheels were not introduced into the model. Instead, a kinematic coupling between the surface
of the stub axle originally in contact with the inner surface of the wheel’s rim and a reference point
(RP2) was used to simulate the presence of a wheel and the corresponding constraints on the
displacements. The RP2 was constrained not to displace in the z and y directions.
Similarly, a kinematic coupling was used to simulate the presence of a bearing and simulate the
constraints imposed by it onto the displacements and the rotations of the surface of the axle
originally in contact with the bearing. Reference point 3 (RP3) was created and constrained not to
displace along x, y and z directions. Rotational degrees of freedom were left free.
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Figure 33. the portion of the composite wheelset used for modelling of the adhesive joint
A third reference point (RP1 in Figure 34) was used to apply the bending moment. The reference
point was linked to the free end’s cross section of the composite tubes on the right by a kinematic
coupling as well.
The outer tube and the inner tube were connected by another kinematic constraint of the “tie” type,
to simulate the achievement of a monolithic structure by overwrapping and co-curing of the two
tubes.
Figure 34. kinematic couplings, reference points and boundary conditions
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Between the inner surface of the collar and the outer surface of the inner composite tube, a thin
layer of cohesive elements was placed, to simulate the presence of the adhesive, as shown in
Figure 35. The adhesive layer was modelled using 0.3 mm thick cohesive elements of 2 mm edge
length. These elements were connected to the mating surfaces of the inner tube and the stub axle
by tie constraints. An additional layer of cohesive element was placed between the end surfaces
of the secondary tube and the collar, creating a sort of butt joint between them.
Figure 35. kinematic couplings, reference points and boundary conditions
Material properties were assigned to the parts as listed below. The mechanical properties of the
materials are listed in Table 9.
• Steel collar: homogeneous isotropic section, material: steel
• Outer tube: homogeneous orthotropic cross section, material: composite outer layup
• Inner tube: homogeneous orthotropic cross section, material: composite inner layup
• Adhesive: cohesive section; in this case, two definitions of the mechanical behaviour of the
adhesive were used: cohesive continuum formulation, to evaluate elastic stresses only, and
cohesive traction separation law, to assess the static damage induced by the external loads.
The choice of homogenizing the properties of the composite laminates through the thickness was
dictated by the need of modelling tapers with reasonable mesh size and the impossibility of defining
a composite laminate cross section in the presence of tapers. The only feasible option would have
been modelling each single ply as a layer of element stacked on one another, but this would have
increased the number of elements beyond the maximum number that it is possible to handle with
the workstation used for this project. A mesh size of 5 mm average length was defined for the metal
stub axle and for the composite tubes. Quadratic elements were used. Tetrahedral elements were
preferred for the more complex geometry of the stub axle, whereas more regular hexahedra were
employed for the composite tubes.
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The properties of the composite materials were derived from the layups proposed in Chapter 7, by
homogenization of the layup along the thickness, to derive the equivalent properties (engineering
constants) of an orthotropic material. Homogenization was conducted by the partner Bercella using
the software package Autodesk Helius.
Table 9. Elastic properties of the materials
Inner layup
Ex (MPa) 101796,00 xy 0,32
Ey (MPa) 63818,90 yx 0,20
Ez (MPa) 6390,00 xz 0,16
Gxy (MPa) 23654,90 zx 0,01
Gxz (MPa) 3742,00 yz 0,10
Gyz (MPa) 3548,00 zy 0,01
Outer Layup
Ex (MPa) 137328,00 xy 0,32
Ey (MPa) 45958,40 yx 0,11
Ez (MPa) 6390,00 xz 0,22
Gxy (MPa) 17146,60 zx 0,01
Gxz (MPa) 3871,33 yz 0,07
Gyz (MPa) 3418,67 zy 0,01
Adhesive
E 2600 0.35
Steel
E 206000 0.3
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The analysis consisted of a static step, with an applied bending moment equal to the resultant
bending moment of 22,283 Nm. This corresponds to the loading at any instant during one revolution
of the axle. If the conditions for a linear response are satisfied, the stress at the highly stressed
point under static loading should correspond to the maximum stress experienced during one
revolution by any point having the same radial coordinates (with respect to a cylindrical reference
system, having the Z axis coincident with the axle’s axis). This allows for assessing the fatigue
strength of the joint under rotating bending loading without simulating one full revolution. To perform
this assessment, the continuous response of cohesive elements is sufficient. However, it is
necessary to verify that the response can be linear. To verify this, a nonlinear analysis with a
cohesive formulation by a traction separation law was run. Results are presented in Figure 36,
where it clearly appears that the adhesive, in the previously defined butt joint, fails (MAXSCRT
damage variable reaches the limit value of 1, indicating that complete fracture occurs). This causes
a peak stress of 75 MPa (von Mises) in the adhesive layer between the collar and the inner tube,
which corresponds to a shear stress amplitude (out of plane shear stress) exceeding 25 MPa, as
shown in Figures 37 and 38. This largely exceeds the fatigue strength estimated for 100 million
cycles and therefore the nucleation of a crack in the adhesive layer cannot be excluded.
Figure 36. contour plot of the values of the MAXSCRT variable in the adhesive layers
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Figure 37. contour plot of the values of the von Mises stress in the adhesive layer
Figure 38. contour plot of the out of plane shear stresses in the adhesive layer
Moreover, the failure of the butt adhesive joint is likely to propagate during the first loading cycle
over the entire annular surface and therefore the real stress distribution would be obtained with a
model without the butt adhesive joints. The stress distribution obtained with this model is shown in
Figure 39. The out of plane shear stress amplitude is 66 MPa, which significantly exceeds the static
strength of the adhesive.
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Figure 39. contour plot of the out of plane shear stresses in the adhesive layer
The results obtained with the joint configuration of Figure 33 suggested a revision of the detail of
the overlap between the steel collar and the composite tubes. The original geometry of the joint
corresponds to a single lap joint. Other geometries are known to be more efficient in terms of stress
peak reduction, and among them the scarf joint is known to be allow the smoothest stress transfer
between dissimilar materials. A new, improved joint configuration was then proposed, inspired by
scarf joints. It is reported in Figure 40. The detailed drawing of the stub axle with dimensions is
reported in Figure 41.
Figure 40. the improved joint between the stub axle and the composite tubes
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Figure 41. shape and dimensions of the modified stub axle
From the manufacturing point of view, this solution requires careful identification of a suitable
sequence of assembly. A paste adhesive for the joint between the stub axle and the outer tube
does not seem to be the right choice anymore. Instead, a film adhesive seems to be more
appropriate, as the outer tube would be overwrapped onto the stub axle and the cured together
with the already assembled inner tube.
At this stage, two analyses were conducted, one without modifications in the constitutive model of
the adhesive, to check if the proposed solutions allow the stresses to be reduced below the fatigue
strength at 100 million cycles estimated for the 3M 9323 B/A adhesive. Then, a second analysis
was conducted, assigning to the adhesive layer the elastic properties of the 3M AF 163-2 film
adhesive, which appears to be a good candidate, but lacks specific experimental tests.
The new adhesive layer is shown in Figure 42. It covers the tapered part of the collar and it is
modelled like the adhesive layer between the inner tube and the collar. Cohesive elements of 2
mm size are used also in this case. The mesh size for the steel collar and the outer composite tube
was refined and an average element edge of 2 mm was defined in the composite tube and in the
region of the tapered overlap region of the collar. This time, a linear analysis step was defined, and
the constitutive model for the adhesive was elastic (selecting a continuum formulation for the
cohesive elements, without any traction separation law).
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Figure 42. Detail of the adhesive layer of the improved joint between the stub axle and the composite tubes
Results are shown in Figure 43. Shear stress amplitudes are now below 16 MPa and the von Mises
stress does not exceed 28 MPa (Figure 44). The shear stress amplitude is still 3 MPa higher than
the estimated fatigue strength at 100 million cycles, but in the adhesive between the inner
composite tube and the steel collar, stresses are now far below the estimated fatigue strength at
100 million cycles, as show in Figure 45.
Figure 43. contour plot of the values of the out of plane shear stress in the adhesive layers of the improved joint
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Figure 44. contour plot of the values of the von Mises stress in the adhesive layers of the improved joint
Figure 45. contour plot of the values of the shear stress amplitude in the adhesive layers between the inner composite tube and the steel axle
Results were then updated, assigning to the adhesive layer between the stub axle and the outer
tube the properties of the 3M AF 163-2 film, whose Young’s modulus is equal to 1100 MPa.
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Results, reported in Figure 46, show that shear stress amplitude is 13 MPa, a lower value than that
obtained by keeping the properties of the 3M 9323 B/A adhesive, thanks to the reduction of the
elastic modulus of the adhesive. However, for this adhesive, no extensive fatigue characterization
is available, and the only available data in terms of stress-life data are reported in [20]. Based on
the coefficients of the SWT parameter reported in [20], for a fatigue life of 100 million cycles, an
allowable shear stress amplitude of 21 MPa can estimated. However, it must be noted that the
experimental data used to derive the coefficients refer to test durations that do not exceed one
million cycles and therefore a specific test programme should be conducted.
Figure 46. contour plot of the values of the shear stress amplitude in the adhesive layers between the inner composite tube and the steel axle, for the 3M AF-163-2 adhesive
The analysis of the stress distribution in the steel collar, shown in Figure 47, confirms that the new
proposed geometry does not raise the stresses in the collar beyond the fatigue limit of the EA1N
steel of 166 MPa [21]. Moreover, further improvements of the local geometry of the collar are still
possible.
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Figure 47. contour plot of the values of the von Mises stress in the stub axle
9.3 DISCUSSION
The finite analysis of the adhesive joint between the steel collar (stub axle) and the composite tube
in the configuration proposed in Chapter 4 leads to the conclusion that the joint needs modification
to lower the stresses in the adhesive below the fatigue strength of the adhesive for 100 million
cycles of rotating bending.
A new geometry is proposed, which allows to reduce the stresses in the adhesive layer between
the steel collar and the inner tube, below the fatigue strength. In the second adhesive layer between
the stub axle and the outer tube, stresses still exceed the fatigue strength of the 9323 B/A adhesive,
but if the 3M AF 163-2 film adhesive is used, the applied stresses fall below the estimated fatigue
strength. However, the fatigue properties of the AF 163-2 adhesive are not known in depth as those
of the paste 9323 B/A adhesive initially proposed. Therefore, an extensive characterization of the
adhesive is required before proceeding to the approval of a final design of the joint.
Moreover, the accuracy of the estimation of applied stress at the end of the overlap between the
outer tube and the new adhesive layer is affected by the simplification made when the composite
layup was homogenized through the thickness. Coupon specimens and full-scale tests would be
required for both assessing the fatigue performances of the adhesives and calibrating the numerical
models. Development of improved modelling techniques based on fatigue crack growth data is
needed, and models should be refined, considering the layered structure of the composite parts
and the possible phenomena of delamination, particularly in the proximity of the ends of the overlap
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in the adhesive joints, where peel stresses arise. Finally, the environmental effect on the fatigue
behaviour of the chosen adhesives should also be considered for future activities and electrical
insulation between the steel stub axle and the carbon fibre reinforced polymer tubes must be
ensured to avoid corrosion due to the mismatch in the electric potential of the different materials in
contact. An electrically insulating glass fibre woven mat on the outer surface of the tubes would
probably solve the problem.
Being the highly stressed bond-line region the end of the overlap on the upper adhesive layer,
towards the steel collar, the site appears to be appropriate for NDT and/or structural health
monitoring, as fatigue cracks are likely to first appear there, and not in the underlying adhesive
layer between the inner composite tube and the steel collar. More details about this point are
reported in Chapter 10.
It is worth mentioning that the possibility of substituting the adhesive joint with a mechanical joint,
or the combined used of adhesive and mechanical joints has not been investigated thoroughly in
this project. For load bearing applications, like the connection between the wind turbine blades and
the rotor, mechanical joints are often applied [22], as shown in Figure 48.
Figure 48. Four different types of mechanical joints between composite and metal parts in wind turbine blades, from [21]
A preliminary analysis of a mechanical joint inspired by the solution (a) reported in Figure 48 was
conducted. Figure 49 showcases the model of a flanged joint between the stub axle and the outer
composite tube, with a cross section presented in Figure 50. The inner composite tube is meant to
be bonded to the stub axle using the 3M 9323 B/A adhesive. The bolts and the counter-flange
shown in Figure 48 (a) were not modelled. Instead, a simplified tie interaction was established
between the flange on the tube and that on the axle, to assess the effect of this type of connection
onto the stresses in the adhesive layer (Figure 51). As shown in Figure 52, it appears that stresses
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are lower than the estimated fatigue strength at 100 million cycles for the 3M 9323 B/A paste
adhesive. Nevertheless, more refined models should be built to confirm the feasibility of this
solution. At present, the adhesively bonded joint still constitutes the preferred solutions, particularly
because it does not add mass, as a bolted flange would do.
Figure 49. Simplified model of the flanged joint
Figure 50. Cross sectional view of the flanged joint
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Figure 51. Detail of the “tie” constraint between the flanges
Figure 52. contour plot of the von Mises stress distribution in the adhesive layers
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10. ASSESSEMENT OF THE FEASIBILITY OF NDT AND SHM
The assessment of the feasibility of NDT and SHM applied to the composite axle is here carried
out considering the specific axle geometry and configuration named “HMC axle” in the previous
Chapters.
From the point of view of NDT and SHM, the composite axle can be broken down into three different
constituent regions: the central one, characterized by the superposition of two coaxial CFRP
composite tubes, the lateral one, characterized by the inner (primary) CFRP tube and the outer
metallic collar bonded together by an epoxy adhesive, and the bonded joint located between the
central and the lateral regions (the bonded joint considered in the present part of the report is the
scarf joint shown in Figure 40). Due to the features characterizing the three different regions, each
of them requires the application of specific NDT methods and procedures and, possibly, of SHM
approaches.
Generally, the application of NDT to axles adopts different inspection procedures for the
manufacturing stages or for in-service maintenance. This because the accessibility to the inspected
parts is usually different (higher during manufacturing) and because typical manufacturing defects
have different nature, shape and size with respect to those typically originating during service. Here,
it is assumed to be in a scenario related to in-service maintenance.
10.1 FEASIBILITY OF NDT METHODS
During in-service maintenance, the traditional approach (common practice) to employ NDT
inspection of railway axles made of steel is based on the synergic application of three different NDT
methods ([23-24]): visual testing (VT), magnetic particle testing (MT) and ultrasonic testing (UT).
All the three are focused on the detection of service defects (fatigue cracks, corrosion pits and
corrosion fatigue cracks, fretting fatigue cracks, ballast impacts, …) mainly originating at the
surfaces of the inspected axles. Recently, a fourth method (eddy current testing, ET) has been
added in the relevant standards [24] with the same scope.
Considering the application of VT to the composite axle, no relevant or substantial differences can
be highlighted with respect to the case of steel axles. This is because VT is usually applied to get
a first general feedback about the conditions of the inspected part and, possibly, to evaluate local
situations by means of direct (for the external surfaces) or remote (for the internal surfaces by, for
example, endoscopy) visual approaches. The scope and methodology of application, then, remain
the same for all the three regions (central, lateral and the bonded joint) of the composite axle, but
the personnel must be trained to detect the typical defects of composites and adhesive bonding,
along with those of steel.
The possible application of MT to the composite axle is, instead, very limited because composite
parts are not ferromagnetic and, consequently, the method cannot be applied. MT would still remain
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effective for the accessible surface of the metallic collar, but just after the disassembly of wheels
and axle boxes. Possible alternatives could be:
1. liquid penetrant testing (PT): this method can be theoretically applied to the accessible surface
of any materials, provided they are not too porous (and this is not a problem for composite
parts) and they are chemically inert with respect to the products used for inspection. This
second point has to be experimentally and carefully checked, because liquid penetrants are
based on organic derivatives of petroleum and could react with the polymeric resin of the
composites adopted for the axle or with the epoxy adhesive used for manufacturing the bonded
joint. Moreover, the inspection time required by PT is much longer than the one by MT and this
must be considered along with the fact that the presence of coatings is not allowed, on the
inspected surfaces, in order to effectively apply PT. Summarizing: given successful checks on
applicability, PT could be effective for the internal surface of the bore, for the external surface
of the collar (provided the wheels and axle boxed are disassembled), for the external surface
of the central region (provided no coatings prevent accessibility to the base material) and for
the external CFRP-metal tip of the bonded joint (provided no coatings prevent accessibility);
2. eddy current testing (ET): this method has been very recently introduced into the relevant
standards, so its application is not yet very widespread and some technical details, in the
application to axles, have to be still understood. Since this method requires an electrically
conductive material, its applicability to the composite axle depends on the volume fraction of
carbon fibres and this detail has to be experimentally checked. Nevertheless, with respect to
MT and PT, it is more expensive because it requires a more refined equipment, but it can be
very fast and totally automatized. Finally, its sensitivity is typically higher than MT and PT.
Summarizing: given successful checks on applicability, ET could be effective for the internal
surface of the bore, for the external surface of the collar (provided the wheels and axle boxes
are disassembled) and for the external surface of the central region (provided no coatings
prevent accessibility to the base material);
3. tap testing: this method was used, in the past (decades ago), on steel axles, but it was
abandoned in order to introduce more performant NDT methods. On the other hand, today it is
a very effective and widespread method for inspecting the surface and sub surface regions of
composite parts and coatings, so it could be reintroduced for composite axles. With respect to
MT, PT and ET, maybe it is the fastest and cheapest one, but, at the same time, it is not the
most sensitive. Summarizing: tap testing could be effective for the internal surface of the bore,
for the external surface of the central region and for the external CFRP-metal tip of the bonded
joint.
UT is theoretically applicable to composite axles, but, being one of the most complicated NDT
methods, it requires careful design and validation, the latter possibly based on experimental
activities. Section 10.2 presents and describes a detailed feasibility analysis, based on numerical
simulations, of UT applied to the central and lateral regions of the composite axle: anticipating the
results, it seems feasible, but, at the same time, a clear and definitive statement, on the feasibility
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of UT, is not possible without some kind of experimental validation. On the other hand, UT does
not seem to be suitable for application to the bonded scarf joint due to its very complex tapered
geometry and alternation of materials. Possible alternatives to UT for the bonded joint could be, as
described above, PT and tap testing, while for the central and lateral regions:
1. radiographic testing (RT) or computed tomography (CT): these methods could be considered
as a volumetric alternative to UT for the composite parts of the composite axle, but not for the
metallic ones, due to the high thickness value of the involved steel, which could not be
penetrated by the radiation generated by the most powerful commercial radiographic tubes
available today. This is the real reason why, today, RT/CT are not an option for traditional steel
axles, but these methods could gain some attractiveness in the case of a composite axle due
to the higher penetrable thickness values. It remains that RT/CT show some drawbacks with
respect to UT: they are much more expensive, the inspection time is much longer and radio
safety issues arise. As for many other possibilities described in this Chapter, an experimental
activity should be carried out in order to clearly understand the real feasibility of RT/CT applied
to the composite axle.
Concluding, in the case of the considered composite axle, some of the traditional NDT possibilities
for axles seem to be unfeasible, but new ones seem to be worth investigating. It remains that,
generally speaking, the reliability of NDT applied to the considered composite axle seems to be
lower than the one of traditional steel axles. This is because MT cannot be systematically applied
and UT shows lower sensitivity, while the possible alternatives must be still evaluated by suitable
experimental activities. A possible alternative, to NDT, is a shift of paradigm to SHM: a short
discussion on this topic, with the proposal of a possible solution, is give in Section 10.3.
10.2 FEASIBILITY OF UT: RESULTS OF THE SIMULATIONS USING CIVANDE
SOFTWARE
As stated in the previous Section, UT seems to be the most promising volumetric NDT method for
the composite axle. The feasibility of its application was, then, evaluated by means of the specific
software package CIVAnde 2020 SP2 [25], which is a simulation tool for different NDT methods (UT,
ET, RT/CT, …).
It is worth remarking that the main hypothesis assumed in the present feasibility analysis is that the
composite axle is going be inspected, by UT, just from the surface of the longitudinal internal bore.
This is reasonable because such a surface is a smooth cylindrical one, so suitably regular for the
application of the inspecting UT probes, while the external surface of the axle is going to be
characterized by a more complex geometry, by the presence of coatings and wrappings, which
would be detrimental for the application of the inspecting probes, and by the presence of press-
fitted and assembled parts.
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Analyses were carried out considering two different regions of the composite axle: the central one,
characterized by the superposition of the inner (primary) and outer (secondary) composite tubes,
and the lateral one, characterized by the superposition of the inner composite tube, the metallic
collar and an adhesive layer. Each region was evaluated considering both perpendicular incidence
of longitudinal sound waves and angled incidence of shear waves.
Feasibility analysis of UT within the central section of the composite axle
Figure 53 shows the detail of the considered region of the composite axle, characterized by the
superposition of the inner and outer composite tubes. The two tubes are assumed to be joined by
a co-curing process of their matrices, without the help of any adhesive.
Figure 53. Geometry of the central region of the composite axles considered for UT numerical simulations.
The CFRP composite lay-ups of the inner and outer tubes were modelled, treated and implemented
as homogenized orthotropic materials characterized by the same elastic properties and stiffness
matrixes already adopted for structural simulations and analyses (see Section 9.2). For the sake
of completeness, Figure 54 shows the implementation of the stiffness matrices of the inner and
outer composite tubes.
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Inner tube
Outer tube
Figure 54. Stiffness matrices of the inner and outer composite tubes.
The abovementioned stiffness matrices, along with the density of the materials (here assumed to
be equal to 1.75 g/cm3 [26] for both CFRP lay-ups), allows the sound speeds to be determined
within the materials themselves and the slowness curves (Figure 55) representing the anisotropy
of sound propagation. Finally, the structural attenuation of sound pressure during propagation is
the last very important parameter for the application of UT to resin-based materials (plastics or
composites): for both the inner and outer tubes and for both longitudinal and shear waves, the
structural attenuation coefficient was assumed to be, according to the literature [27], equal to 0.8
dB/mm at 4 MHz.
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Inner tube Outer tube
Figure 55. Slowness curves for the inner and outer composite tubes.
Considering, first, the inspections based on the perpendicular incidence of longitudinal sound
waves, Figure 56 shows the modelled probe. Specifically, a conventional circular ultrasonic
transducer, characterized by diameter equal to 10 mm and nominal frequency equal to 4 MHz, was
chosen because it is the typical one adopted for inspecting traditional steel axles. In order to
guarantee a good contact between the transducer and the curvilinear surface of the bore, a
cylindrical convex wedge, made of rexolite, was modelled. Coupling between the probe (wedge)
and the inspected piece was ensured by simulating the presence of a thin layer of mineral SAE oil.
The same figure shows the purely geometrical expected sound beam in terms of a ray-tracing
representation. Such a representation has no real physical meaning, because it is just a qualitative
indication of the sound path.
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Figure 56.Model of the adopted UT probe for perpendicular incidence of longitudinal waves in the central region of the composite axle.
The result of the simulation of the physical sound beam propagating into the inner and outer
composite tubes is shown in Figure 57. As can be seen, the sound beam can be effectively
transmitted from the inner tube to the outer one even if, due to the slight mismatch of acoustic
impedance between the two lay-ups, a discontinuity in sound pressure is evident at the interface
between the two.
Transducer
Wedge
Inner tube
Inner tube
Outer tube
Outer tube Expected geometrical (ray
tracing) sound beam
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Figure 57.Simulation of the physical sound beam for perpendicular incidence of longitudinal sound waves in the central region of the composite axle.
The following step was to introduce circular defects into the inner tube (exemplified in Figure 58),
into the outer one and at their interface. Such defects lay in planes perpendicular to the acoustic
axis of the sound beam, so to represent possible delaminations in the composite materials, and
were characterized by a diameter equal to 5 mm, according to the common practice for traditional
steel axles. Their ultrasonic response, i.e. the amount of sound pressure sent back to the probe
according to a pulse-echo inspection technique, was evaluated.
Figure 58. Circular defect representing a delamination in the composite material.
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Defect within the inner tube
Defect at the interface between the inner and the outer tubes
Defect within the outer tube
Figure 59. Ultrasonic responses of the central region of the composite axle inspected by normal incidence of longitudinal waves.
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Figure 59 gathers the obtained results in terms of B-Scan, i.e. a mapping of the ultrasonic response
along the thickness of the inspected piece, and of the A-Scan, i.e. a section of the B-Scan,
corresponding to the maximum value of the response of the inspected defect. As can be seen, all
of the three defects can be clearly detected, even if, as expected, the farer the defect from the
probe, the lower is the amplitude of its response. Nevertheless, the interface seems not to be a
problem for defect detection and the total thickness of the part seems not to too high to prevent the
same detection due to the structural attenuation of the sound beam. On the other hand, the present
simulations are performed in ideal conditions (no background noise, no sound transfer losses, …)
and the outcome should be validated by suitable experiments.
Moving to the inspections based on the angled incidence of shear sound waves, Figure 60 shows
the modelled probe along with the ray tracing representation of the sound beam. In this case, a
conventional rectangular ultrasonic transducer, characterized by a size equal to 10x9 mm2 and
nominal frequency equal to 4 MHz, was chosen because it is similar to the ones adopted for
inspecting traditional steel axles.
Figure 60. Model of the adopted UT probe for angled incidence of shear waves in the central region of the composite axle; the inset image shows the probe from a different angle of view.
To guarantee a good match between the transducer and the curvilinear surface of the bore, a
cylindrical convex wedge, made of rexolite, was modelled. The same wedge was also used to
suitably incline the sound beam incident at the bore surface and to get, via Snell’s Laws, the shear
waves characterized by the proper refraction angles (Figure 61). It is worth noting that such
refraction angles get modified passing through the interface between the inner and outer tubes.
This is due to the slightly different composite lay-ups of the two tubes. Coupling between the probe
(wedge) and the inspected piece was ensured by simulating the presence of a thin layer of mineral
SAE oil.
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Figure 61. Refraction angles of the shear waves used in the central region of the composite axle.
The result of the simulation of the physical sound beam propagating into the inner and outer
composite tubes is shown in Figure 62. As can be seen, the sound beam can be effectively
transmitted from the inner tube to the outer one even if, due to the slight mismatch of acoustic
impedance between the two lay-ups, a discontinuity in sound pressure is evident at the interface
between the two and, due to the anisotropy of the involved materials, the sound beam is
significantly scattered along many different directions.
In the case of angled incidence of shear waves, the morphology of the inspected defects (Figure
63) consisted of a concave shape, representing a transverse crack in the composite material,
characterized by a 16x3 mm2 size. The different positions of the described defects were three: just
below the interface between the inner and outer tubes, just above the interface between the inner
and outer tubes and at the external surface of the outer tube. The obtained results are summarized
in Figure 64 in terms of S-Scan, i.e. a sectorial mapping of the ultrasonic response, and of the A-
Scan, i.e. a section of the S-Scan, corresponding to the maximum value of the response of the
inspected defect.
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Figure 62. Simulation of the physical sound beam for angled incidence of shear waves in the central region in the central region of the composite axle.
Figure 63. Concave defect representing a transverse crack in the composite material.
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Defect just below the interface between the inner and outer tubes
Defect just above the interface between the inner and outer tubes
Defect at the external surface of the outer tube
Figure 64. Ultrasonic responses of the central region of the composite axle inspected by angled incidence of shear waves.
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As can be seen, all of the three defects can be clearly detected, even if, as expected, the farer the
defect from the probe, the lower is the amplitude of its response. Nevertheless, in one case (defect
just below the interface between the inner and outer tubes), the defect tip diffraction is very well
highlighted, and this helps the possible sizing of the defect, while, in the other two cases (farer than
the interface between the inner and outer tubes), it is much less pronounced, even if the
detectability of the defect still remains relevant. On the other hand, the present simulations are
performed in ideal conditions (no background noise, no sound transfer losses, …) and the outcome
should be validated by suitable experiments.
Feasibility analysis of UT within the lateral section of the composite axle
Figure 65 shows the detail of the considered region of the composite axle, characterized by the
superposition of the inner composite tube, the metallic collar and an adhesive layer. In particular,
the two parts are assumed to be joined by adhesive bonding, adopting a 0.3 mm layer of 9323
epoxy adhesive (see Section 9.1 for details on the chosen adhesive).
Figure 65. Geometry of the lateral region of the composite axles considered for UT numerical simulations.
The involved materials were modelled as follows:
1. the composite CFRP inner tube was modelled exactly as described above;
2. the properties of the 3M 9323 epoxy adhesive were derived from the literature [27]. In particular,
it has density 1.23 g/cm3, longitudinal wave velocity equal to 2488 m/s and transverse wave
velocity equal to 1134 m/s. Structural attenuation is equal to 0.815 dB/mm (longitudinal wave
at 2 MHz) and to 3.885 dB/mm (transverse wave at 2 MHz);
3. the collar, made of carbon steel, has [27] density 7.8 g/cm3, longitudinal wave velocity equal to
5900 m/s and transverse wave velocity equal to 3230 m/s. Structural attenuation is equal to
0.006 dB/mm (longitudinal wave at 4 MHz) and to 0.006 dB/mm (transverse wave at 4 MHz).
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The probes, adopted for perpendicular and angled inspections, and their modelling were exactly
the same already described for the case of the central region of the composite axle. The result of
the simulation of the physical sound beam for perpendicular incidence of longitudinal sound waves
in the lateral region of the composite axle is shown in Figure 66. As can be seen, no big issues are
observed in the transmission of the acoustic energy from the composite inner tube to the adhesive,
while very few of the sound energy is actually transmitted from the adhesive to the metallic stub,
due to the strong mismatch of acoustic impedance between the two materials. This can be a real
trouble during real inspections and should be checked by suitable experiments.
The same can be concluded observing the result of the simulation of the physical sound beam for
angled incidence of shear sound waves in the lateral region of the composite axle shown in Figure
67. In this case, due to the anisotropy of the involved composite material, the sound beam is, again,
significantly scattered along many different directions, as well. Moreover, it is worth noting that
multiple refraction angles have to be taken in to account due to the presence of multiple interfaces.
Figure 66. Simulation of the physical sound beam for perpendicular incidence of longitudinal sound waves in the lateral region of the composite axle.
Inner tube
Steel
Adhesive
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Figure 67. Simulation of the physical sound beam for angled incidence of shear waves in the lateral region in the central region of the composite axle.
Steel
Adhesive
Inner tube
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Defect within the inner tube
Defect within the adhesive
Defect within the metallic stub
Figure 68. Ultrasonic responses of the lateral region of the composite axle inspected by normal incidence of longitudinal waves.
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Figure 68 gathers the results, obtained for perpendicular incidence of longitudinal sound waves in
the lateral region of the composite axle, in terms of B-Scan and of the A-Scan corresponding to the
maximum value of the response of the inspected defect. The adopted defect shape and size were
the same previously described for the central region of the axle. As can be seen, the defect within
the inner tube can be easily detected, the defect within the adhesive cannot be detected due to the
shadowing effect of the high impedance mismatch at the interface between the adhesive and the
metallic collar and the defect within the metallic collar can be detected, but with a very low entity of
reflected sound energy. Actually, the issue arising for the defect within the adhesive has no solution
and, consequently, it has to be considered in the preparation of inspection procedure and
maintenance plans or it requires the development of other approaches, probably based on SHM.
On the other hand, in the case of the defect within the metallic stub, the present simulations are
performed in ideal conditions (no background noise, no sound transfer losses, …) and the outcome
should be validated by suitable experiments.
Figure 69 gathers the results, obtained for angled incidence of shear sound waves in the lateral
region of the composite axle, in terms of S-Scan and of the A-Scan corresponding to the maximum
value of the response of the inspected defect. The adopted defect shape and size were the same
previously described for the central region of the axle. As can be seen, all of the three defects can
be clearly detected, even if the defect tip diffraction is very well highlighted, and this helps the
possible sizing of the defect, in just one case, while, in the other two cases, it is much less
pronounced, even if the detectability of the defect still remains relevant. On the other hand, the
present simulations are performed in ideal conditions (no background noise, no sound transfer
losses, …) and the outcome should be validated by suitable experiments.
Finally, due to the complicated morphology, characterized by the presence of many notched
sections, of the external surface of the metallic collar, a series of analyses were carried out in order
to understand if some of such notched sections could represent an issue for UT inspections. Figure
70 gathers the results of all the considered cases: the conclusion is that no relevant issues seem
to be actually present.
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Defect just below the interface between the inner tube and the metallic stub
Defect just above the interface between the inner tube and the metallic stub
Defect at the external surface of the metallic stub
Figure 69. Ultrasonic responses of the lateral region of the composite axle inspected by angled incidence of shear waves.
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Figure 70. Ultrasonic responses of the external surface of the metallic collar inspected by angled incidence of shear waves.
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Conclusions on the feasibility analysis of UT of the composite axle
Based on the results of the analyses presented so far, the following conclusions on the feasibility
of UT can be drawn:
• UT seems to be effectively applicable to the central and lateral regions, even if it shows
significantly different sensitivity levels: the central region seems to be more inspectable, by
UT, than the lateral one.
• The scarf bonded joint has not been investigated because its features (tapered geometry
and alternate materials) suggest, from the beginning, a very difficult application of UT.
• UT simulations were implemented considering ideal conditions (no background noise, no
transfer losses, …), so careful experimental validation should be considered.
• The optimization of UT set-up should be carried out in terms of Probability of Detection,
which, on the other hand, requires an experimental validation, as well.
10.3 POSSIBLE SOLUTIONS FOR SHM
In this Section, possible solutions for structural health monitoring (SHM) of the HMC axle are
discussed and results of a preliminary assessment of the feasibility of a strain based SHM system
for the bonded joint are presented. The focus is on the adhesively bonded joint, that appears to be
the region less suitable for UT inspections.
A large variety of sensors are available for SHM of bonded joints, like the one present in the HCM
axle studied in this project. These sensors can be divided in the following classes, according to the
physical principle that is exploited:
• Acoustic emission
• Elastic wave based methods (particularly, ultrasonic guided waves)
• Vibration monitoring
• Strain sensing
For the present application, a distributed strain sensing technique is proposed, as it does not
require continuous monitoring during operation, as some the other above-mentioned techniques
do (acoustic emission, vibration monitoring) and does not require additional research for the case
of bonds between dissimilar materials, as guided waves would require.
The principle of crack detection and monitoring based on distributed strain sensing consists of
measuring and recording strain patterns along predefined paths in the critical areas at fixed time
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intervals, under static loads, and compare them with values measured the beginning of the service
life. The expected variations of the strain pattern due to the presence of an advancing crack can
be obtained by FE simulations.
Distributed sensing can be achieved by means of an array of sensors, be them physical or virtual.
Physical sensors can be electrical strain gages or fiber optic sensors, like Fibre Bragg Gratings
[28]. Virtual sensors can be defined along fiber optics interrogated by Optical Backscatter
Techniques. In this case, a spatial resolution up to 0.7 mm can be achieved [29].
The back-face technique is often employed to monitor cracks in adhesively bonded joints, as the
strain values and distributions on the free surface of the adherends are modified by the presence
of an advancing front. The detection and tracking of features of the strain distributions associated
to the presence of a crack can allow to infer the shape and position of the crack front.
Figure 71. Schematic view of the installation of a strain sensing fiber optic
This principle is applied to the bonded joint between the metallic collar and the composite outer
tube. A distributed sensing method by optical fibres and an OBR distributed sensing technique is
designed to monitor the back face strain along longitudinal paths, originating from the beginning of
the overlap of the outer composite tube over the collar, in the configurations shown in Figure 71.
One fibre is bonded onto the surface of the composite tube, and strain can be read during
inspections under static loading. The wheelset needs to be rotated until the fibre coincides with the
highly stresses fibres of the composite tube under bending.
Path of the fiber optic
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Figure 72. Size and position of the simulated crack (10 mm crack length shown in this picture)
The feasibility of this SHM system is assessed by FE simulations. Three models were built, one
with an integer bond-line, and two with an artificial crack of 5 mm and 100 mm length. The crack is
assumed to stem from the beginning of the overall and run parallel to the bond-line. The crack front
is assumed uniform and perpendicular to the axle’s axis, as it can be expected in the case of crack
propagation under rotating bending conditions. Figure 72 showcases a schematic representation
of the crack inserted in the model. The presence of a crack was simulated by modifying the
dimensions and the shape of one slave surface in the surface to surface tie constrains that defines
the adhesion of the adhesive layer to the outer composite tube in the FE model.
Longitudinal strains were extracted from the FE models along the node path shown in Figure 73.
To define longitudinal strains, a local coordinate system was defined with its 1 axis coinciding with
the fiber optic axis. Figure 74 showcases the strain patterns for the three cases considered. It
clearly appears that the strain patterns are modified by the presence of the crack and that the
longitudinal strain pattern translates in the same direction of the advancing crack.
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Figure 73. The node path used for the extraction of the strain values
No crack 5 mm crack 10 mm crack
Figure 74. The different strain patterns (longitudinal, with reference to the 1 axis of the local coordinate system shown in yellow) for increasing simulated crack length.
Figure 75 showcases the three curves corresponding to the values of the longitudinal strains
extracted along the path. It clearly appears that the blue curve, corresponding to the strain values
of the joint without any crack, translate along the path defined to extract strain values by a distance
that is close to the increment of crack length. The relationship between crack length and
displacement of the strain curve does not appear to be linear. Nonlinearity is likely to be due to the
non-uniform thickness of the substrate (scarf joint). Moreover, strain values at the beginning of the
overlap in the integer joint and at a distance close to the position of the crack length are close to
zero as expected, but negative. This is likely to be due to the distortion of the elements, whose size
is too coarse with respect to the scale of the defect.
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Figure 75. Strain values along the longitudinal path, for different simulated crack lengths
In spite of these difficulties that could be overcome by more refined models, it seems that a SHM
technique based on strain values measured along the path identified in Figure 71, after appropriate
calibration based on refined simulations and experimentally validate, can constitute a feasible
solution for periodic SHM of the bonded joint at inspection intervals. The definition of the inspection
intervals would require experiments to define the crack propagation speed as a function of the
crack length and the critical length, i.e. the crack length corresponding to the failure of the joint.
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11. ANALYSIS OF THE IMPACT RESPONSE
To verify in detail the consequences of possible impacts onto the axle of stones raised from the
ballast during the passage of the train, a specific analysis campaign was implemented.
11.1 OBJECTIVE OF THE IMPACT ANALYSES
Impact represents a particularly severe condition for the axle design. The objective of the
implemented impact analyses is to identify potential criticalities in the system design and to suggest
possible countermeasures to be taken in possible following detailed design and optimization
phases. Regulatory scouting was performed to identify the impact characteristics of railway axles.
EN 13261:2009+A1 Railway applications - Wheelsets and bogies - Axles - Product requirements
standard defines axle characteristics, qualification procedures and delivery conditions of axles for
use on European networks. It defines characteristics of forged or rolled solid and hollow axles,
made from vacuum-degassed steel grade EA1-Normalized that is the most used grade on
European networks. For hollow axles, this standard applies only to those that are manufactured by
machining a hole in a forged or rolled solid-axle [30]. The standard foresees two different impact
test methodologies, namely:
- Paragraph 3.2.2 (Impact Test Characteristics) refers to EN 10045-1 Metallic materials-
Charpy impact test - Part 1: Test Method and regards some specific test samples taken
from axles.
- Annex C which analyzes the effect of the impact on the coating of the axle with a specific
described method.
11.1.1 EN 13261:2009+A1 - Paragraph 3.2.2 Impact Test Characteristics
Considering the axle design described in Chapter 2, the test methodology related to solid axles
described in Paragraph 3.2.2 of the abovementioned standard could be neglected, the focus should
be directed to the one related to the hollow axles.
Considering hollow axle design, test pieces for Charpy impact test shall be taken from three levels
in the largest axle section:
1) as near as possible to the external surface;
2) at mid-distance between external and internal surfaces, and near the internal surface of
hollow axles [30].
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Figure 76. Location of test pieces for hollow axles according to EN 13261 2009 +A 1 2010 [29]
The abovementioned test procedure is specifically designed for steel axles, as almost all the
existing axles for railway applications. Since the innovative axle design foresees the use of
composite material, which is non-uniform by definition, the test procedure seems to be hardly
applicable to the present design concept. Furthermore, according to axle design, composite tubes
should not be thick enough to extract specimens of correct dimensions.
11.1.2 EN 13261:2009+A1 – Annex C
Paragraph 3.9.1.4 of the standard describes resistance to impacts which is the ability of a coating
to protect the axle from damage due to impacts from projectiles, e.g. ballast (this characteristic
applies only to class 1 axles sections which are those subject to atmospheric corrosion and
mechanical impacts). The test piece shall be the axle or an axle section covered with the coating
to be evaluated and shall be tested by firing a projectile onto the protected surface following Annex
C of the same standard [30].
The test method is to fire a projectile perpendicular to the protected surface and then to study the
change to the coating and that of the test piece surface. A treated steel projectile (diameter: 32
mm; top angle: 105°; mass: 60 g Vickers hardness: 400) shall be fired by the expansion of a volume
of air compressed at 8 bar to ensure an exit speed of 19,4 m/s. The resistance to the impact is
assessed at – 25 °C and ambient temperature [30].
After the impact, the appearance of the coating surface shall be examined with the naked eye, as
well as the appearance of the test piece surface once the coating has been removed. Changes
shall be recorded and compared to the criteria given by this standard. No hole shall be found in the
coating, nor shall there be any alteration to the test piece surface [30].
Although also this test methodology is conceived for steel axles, especially class 1 axle sections,
it can be considered a first reference to evaluate the impact performance of the developed axle
design. FEM analyses has been set-up to reproduce, as accurately as possible, the test
methodology prescribed by Annex C of EN 13261:2009+A1 standard.
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11.2 SOFTWARE TOOL
The numerical model was set up using the Ansys© Workbench 2020 R2 suite, with the adoption of
the Ansys Composite PrepPost (ACP) tool for the definition of the two composite tubes stacking
sequence. The tool also allows performing the post-processing of results by evaluating the most
used failure criteria for composite materials.
Figure 77. Analysis workflow in Ansys© Workbench 2020 R2 suite.
11.3 GEOMETRICAL MODEL
The geometrical model considered for the analysis is based on the design described in Chapter 2
and comprises:
- the axle, made of two concentric composite tubes and two steel collars at its ends;
- the spherical projectile impacting the axle at its middle.
Figure 78. Simplified geometrical model considered for impact analyses.
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As the analysis objective was to investigate the behaviour of composite parts, the steel collars were
simplified as cylindrical parts in the analyses.
The projectile was considered spherical with a diameter equal to 32 mm. Trial analyses were
performed also with a pyramid-shaped projectile, but convergence problems were encountered due
to its sharp edges.
11.4 MATERIALS
The materials adopted are based on the library implemented in Ansys
- Side collars: Structural steel (E=200 GPa, δ= 7850 kg/m3)
- Spherical projectile: Structural steel with modified density to conform its mass with
requirements from Annex C.3: “Method to assess resistance to the impact of the coating”
(E=200 GPa, δ=3500 kg/m3)
- Composite material: Epoxy Carbon UD (UniDirectional) Prepreg, customized with the
properties included in the latest version of the design guidelines (Gurit UCHM450 SE84 –
UD)
Figure 79. Composite material properties table in Ansys© Workbench 2020 R2 suite.
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11.5 NUMERICAL MODEL
The numerical simulations required a particular fine-tuning for the setting of the composite layers
that constitute the two tubes of the axle, but also more generally for the numerical setup of the
analysis. The analysis is carried out in the form of an implicit transient structural simulation.
The methodology for defining composite layers adopted in Ansys ACP tool allows to:
- Define the fabric characteristics (thickness, material);
- Implement the stacking sequences;
- Define the modelling plies with relative deposition angles;
- Expand the layers to create 3D solid mesh starting from the surfaces of the tubes.
Concerning the axle design described in Chapter 2, the geometry and composite layers stacking
sequences considered in the analyses are those represented in Figure 80 (a restatement of Figure
12).
Figure 80. Composite layers stacking sequences considered in the analyses.
Both tubes are composed by a sequence of 30 plies each, with a ply thickness of 0.45 mm. To
optimize computational efficiency while maintaining adequate results accuracy, the solid mesh is
generated as follows:
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- Primary tube: 5 plies for each mesh layer, a single mesh layer thickness of 2.25 mm, 6
mesh layers in total
- Secondary tube: 3 plies for each mesh layer, a single mesh layer thickness of 1.35 mm, 10
mesh layers in total
Figure 81. Composite tubes mesh in radial and tangential direction
From a global point of view, hexahedral linear elements were adopted for meshing both the
composite tubes and the side collars, except for the spherical projectile, realized with pure
tetrahedrons. Since the area of interest was near the impact with the sphere, a gradual element
refinement from the ends to the centre of the axle was performed, starting from an average
longitudinal size of 10mm the elements, reaching 3mm in the impact area. The sphere represented
3mm tetrahedrons. The total amount of elements was almost 1.5 million.
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Figure 82. Discretized model of all components
Figure 83. Discretized model of all components (section view)
During the analysis set-up, the following assumptions were performed:
- General joints are applied to constrain the collars to the ground, leaving only the rotations
along the vertical axis free;
- Bonded contacts are applied between the metal collars and the composite tube as well as
between primary and secondary tube, as investigation on glued joints is reported in Chapter
8;
- Simple frictionless contact is applied between the secondary tube and the spherical
projectile.
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11.6 LOADING CONDITIONS
Two analyses were performed to evaluate sensitivity to impact angle, namely:
- The first analysis with a spherical projectile moving with adirection normal to the axle
surface (radially concerning the tubes axis), with an initial velocity of 19.4 m/s, as described
in Annex C.4 of [30];
- A second analysis, completely analogous to the previous one with spherical projectile
impacting onto the axle with 45° angle respect to axle surface.
Trial analyses were performed also with a pyramid-shaped projectile, but convergence problems
were encountered due to its sharp edges.
11.7 RESULTS
Post-processing of results was performed to evaluate the structural response of the proposed
design to the impact load previously described. The post-processing of results was performed
within the specific ACP module and was focused on the evaluation of possible occurrence of
failures in the composite material.
In particular, to evaluate the occurrence of a failure in the composite material, the Hashin criterion
was adopted, which is specifically designed for UD composite fabrics and is capable of identifying
the presence of:
- Fibre failure;
- Matrix failure;
- Delamination.
The following plots show the behaviour of the system in terms of damaged elements, the colour
scale does not represent a physical quantity, since it corresponds to a damage parameter which
only defines whether the composite layers present failure. In detail, blue areas indicate values close
to 0 and no occurrence of physical failure. Colours from light blue to orange represent values from
0 to 1, where no occurrence of physical failure is foreseen but safety coefficient reduces
proportionally as the parameter approaches 1. The red areas, which identifies the elements with a
value higher than one, are critical from the point of view of the structural performance and need to
be investigated.
For red coloured elements, ACP provides information about the failure criterion by identifying the
elements with the following code:
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- “hf” indicates fibre failure;
- “hm” indicates matrix failure;
- “hd” indicates delamination.
Furthermore, the software tool provides information about the ply number (in parenthesis) for each
element which is subjected to failure
11.7.1 Impact direction: normal to axle surface
The following plots show the damage contour plots for the load case in which the spherical projectile
impacts the axle surface with normal direction.
Figure 84. Damage plot in the nearby of the impact region - impact angle 90°
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Figure 85. Damage plot in the nearby of the impact region (section view) - impact angle 90°
As shown in Figure 84 and Figure 85, damage occurs only in the secondary tube near the impact
region, while no significant alteration is recorded in the remaining parts of the system.
In detail failure affects the 21 external plies underlying the impact region, corresponding to almost
a 10 mm depth, which is equal to the about the 70% of the thickness of the secondary tube. Failure
involves mainly the composite matrix, as expected, due to the high compression load. Delamination
occurs instead on the external surface of the secondary tube, in the nearby of the “perimeter” of
the impacted region.
11.7.2 Impact direction 45° to axle surface
The following plots show the damage contour plots for the load case in which the spherical projectile
impacts the axle surface with 45° angle respect to the axle surface itself.
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Figure 86. Damage plot in the nearby of the impact region - impact angle 45°
Figure 87. Damage plot in the nearby of the impact region (section view) - impact angle 45°
Also in this load case, as shown in Figure 86 and Figure 87, damage occurs only in the secondary
tube in the nearby of the impact region, while no significant alteration is recorded in the remaining
parts of the system. Damage plot is very similar to the previous load case, as expected damage
pattern is no more symmetric.
In detail failure affects all the 30 external plies underlying the impact region, corresponding to the
whole 13.5 mm thickness of the secondary tube. Failure involves mainly the composite matrix, as
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expected, due to the high compression load. Delamination occurs instead on the external surface
of the secondary tube, in the nearby of the “perimeter” of the impacted region.
11.8 MITIGATION MEASURES / FURTHER DEVELOPMENTS
Taking into account the previous results, it seems clear that the test procedure described in
Appendix C [30] results to be highly severe for the assembly, since it results in local failure, mainly
within the matrix, of a certain amount of plies belonging to the secondary tube. This behaviour
seems to be coherent with the type of load applied since the structure is subjected to a high
compressive load close to the impact point with the projectile. It is likely that the axle will not perform
properly, leading to safety and security problems, after such impact, which could be caused by
stones raised from the ballast during the passage of the train.
These kinds of phenomena indeed occur especially for high-speed trains, which could be the last
applications for composite axles, but mitigation measures shall be considered.
Mitigation measures comprise onboard sensors which record impacts and lead to a condition-
based maintenance approach as wells as, above all, an external protection system which can
absorb the highest amount as possible of impact energy. Due to the many challenges tackled within
the axle design phase, it has not been possible in the current project to perform a detailed design
of external protection systems which could solve this issue.
Among the possible solutions, some include the possibility to apply onto the axle surface an
additional external layer of material with high impact absorbing properties. Another approach could
be to create a fixed (not bonded to the axle) external shield. The following table summarizes the
pros/cons of the two different solutions:
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Table 10. Pros and Cons of the impact mitigation solutions
Solution Pros Cons
Additional layer bonded onto
axle surface
- Limited modifications to
axle and bogie designs
- Limited effect on train
aerodynamic
- Depending on material, it
could also provide fire
protection
- Difficulties in inspection
and maintenance on axles
- Additional rotating and
unsprung mass
Fixed shield - Ease of inspection and
maintenance on axles
- No additional rotating and
unsprung mass
- Aerodynamic drag
- Modifications could be
requested to integrate into
bogie design
To reduce the effect of an impact on the system it could be interesting to implement the effect of a
protective coating on the secondary tube. If adequately thick, an additional external layer could
absorb part of the impact energy, reducing the damaged area in the composite material.
For steel axles, Lursak® is the solution developed by LRS to the increasing demand to guarantee
the total protection of railway axle against corrosion and damages derived from ballast impacts. It
is an epoxy combination reinforced by synthetic fibres applied normally with a thickness of 5mm.
In case of damage to the Lursak surface due to very heavy impact, the coating can be easily and
quickly repaired [32]. As it was conceived for denting protection of steel axles, it should be
investigated its capacity to absorb high impact energy and limit damages to underlying composite
layers. However, it should be removed to inspect the composite secondary tube and therefore it is
not deemed feasible.
Among the various possible alternative solutions, two are promising and worthy of further study:
- Additional composite layer with Kevlar® fibres: Kevlar® is an organic fibre in the
aromatic polyamide family, with a unique combination of high strength, high modulus,
toughness and thermal stability. It was developed for demanding industrial and advanced-
technology applications [31]. The considerable resistance to shear stresses, typical of
Kevlar fibres, could allow a significant increase in terms of impact resistance, limiting the
overall dimensions of the system and ensuring good protection of the underlying layers. An
alternative to Kevlar fibres could be ultra-high molecular weight polyethylene fibres (e.g.
Dyneema®). It is worth pointing out that if tests confirm that ballast impact would result in
matrix damage as shown by simulation, a more compliant protective layer could offer more
protection.
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- Additional foam layer: Metallic (e.g. aluminum) or polymeric foams to be positioned onto
the axle surface which can absorb the most of impact energy. Other compliant materials
could be also considered. An additional metallic thin layer should be positioned onto the
foam layer to protect it from the high shear stress caused by the impact with a sharp ballast
stone. This solution is the most complex, but probably the most effective.
Concerning the approach of fixed shields, it regards the creation of a structure to be fixed to the
bogie frame which protects the axle from the impact of ballasts. This structure could be composed
by metallic (e.g. steel) sheets or a textile layer fixed to a beam metallic structure. Concerning the
latter, RINA-C, in the framework of FLY-BAG2 project (Grant agreement ID: 314560) developed a
high strength and impact resistant multi-layer textile to contain blast and fragments produced by an
explosion. A preliminary feasibility study has been already proposed to an Italian industrial
company in the railway sector to adapt this solution to protect systems located in the lower part of
train vehicles against impacts from ballast.
The aforementioned solutions result to be necessary, especially if the results of the numerical
simulations are considered. It is important to notice that all the mitigation measures previously
described require periodical integrity checks, to ensure the overall structural condition and identify
possible damaged areas, that would need a restoration of the protective structure.
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12. ANALYSIS OF THE DYNAMIC BEHAVIOUR
The wheelset is a component of a railway vehicle; in which it is integrated. Therefore, its running
behaviour can only be considered in a realistic way by simulating the behaviour of the entire vehicle.
12.1 VEHICLE MODEL
The wheelset, which is analysed in this project, is designed for the use in metro vehicles. Therefore,
the multibody system used for the simulation of the running behaviour should represent a vehicle
of such type. Unfortunately, relatively few data, which is required for setting up a multibody model
of a metro vehicle, is publicly available. In several works e.g. by Pombo and Ambrosio [33] and by
Marques [34] the data set for the vehicle of the type ML95 operated by the Lisbon metro company
(Metropolitano de Lisboa) has been published. Unfortunately, the bogie design of this vehicle uses
outboard axle boxes instead of inboard axle boxes as chosen for the design of the wheelset used
in the present project. Nevertheless, this is the publicly available data, which seems to come the
closest to the present application case. Therefore, these parameters are used; the essential
modifications are the adaptation of the lateral distances of the axle boxes and of the primary
suspension to the inboard design and the adaptation of the inertia of the wheelsets, which will be
discussed in the following Section. It should also be noted that each axle box is modelled as a
separate body. The following illustration shows a drawing of the vehicle’s bogie.
Figure 88. Bogie of the ML95 vehicle (source [34])
The wheelset is interacting with the track via the wheel-rail contact, which possess a high stiffness.
Therefore, the running on a completely rigid track may lead to unrealistic results so that at least an
approximate description of the track flexibility and dynamics is required. Such a description can be
implemented by using a substitution track model, which consists of “standard multibody system
elements” like bodies, springs and dampers. Their parameters are chosen in such a way that the
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substitution model reproduces the motions of the rail head as a reaction to a force acting on it.
Usually, such a substitution model supports one wheelset and moves together with it along the
trajectory of the track. A family of such substitution track models has been developed and presented
by Chaar and Berg [35]. In the present project, the track model A presented in this paper has been
implemented into the simulation model, but an extension to more complex models can be done in
a relatively easy way. This model is shown in the following illustration.
Figure 89. Substitution track model by Chaar and Berg [35]
The interaction between a railway vehicle and its infrastructure strongly depends on the trajectory
of the track including e.g. curves and on track irregularities, which are inevitable in real operation.
In the present project, data for the trajectory and for the irregularities of a metro line was provided
by Metro de Madrid. The data for the trajectory includes the curvature, i.e. the reciprocal value of
the curve radius, and the cant or superelevation, i.e. the vertical distance between the outer and
the inner rail in a curve; the data for the irregularity describes the vertical and lateral deviation of
each rail from its ideal position. The wheel profile, which is specific for Metro de Madrid, and the
track geometry using UIC54 rail with an inclination of 1:20 were also provided by Metro de Madrid,
although in the present case the standard gauge of 1435 mm was applied.
The entire vehicle model was developed and created in the multibody system software SIMPACK,
which is widely used in the analysis of the dynamics of railway vehicles. The following image, Figure
90, shows the multibody model. It should be noted that in this model the axle boxes, which are
represented as yellow cuboids, are installed between the wheels.
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Figure 90. SIMPACK model of the investigated vehicle
12.2 WHEELSET INERTIA
The goal of the present investigation is to evaluate the advantages of the new wheelset design.
This is done by simulating the same scenarios for two types of wheelsets, here a wheelset of
conventional design and the wheelset of the new design, and by comparing the results.
In a “classical” multibody system, bodies are elements, which are rigid, i.e. undeformable, and
possess an inertia. Therefore, in the present investigation the two different designs of the wheelsets
are represented by different inertia properties. It should be noted that both wheelsets considered
in this investigation have a reflection symmetry to their middle cross plane, i.e. the xz-plane, and a
rotational symmetry around the 𝑦-axis. As a result, the centre of gravity is located in the geometrical
centre of symmetry. Furthermore, as a result of the rotational symmetry, the moment of inertia with
respect to the centre of gravity is equal for each transversal axis so that the inertia moments 𝐼𝑥𝑥
and 𝐼𝑧𝑧 are equal and no deviation moments occur.
For the new wheelset, the original steel axle is replaced by new axle, while the same wheels are
used. The wheelset axle has the same symmetry properties as the entire wheelset, i.e. the
reflection symmetry to the 𝑥𝑧-plane and the rotational symmetry around the 𝑦-axis, and therefore
also the same position of the centre of gravity.
The inertia data for the conventional steel axle was provided by Lucchini RS. After correcting some
inevitable very small numerical errors, the inertia is described by the following parameters:
• Mass: 𝑚Axle,steel = 197.882 kg
• Mass moment of inertia for transversal axis: 𝐼𝑥𝑥,Axle,steel = 𝐼𝑧𝑧,Axle,steel = 52.8686 kg ∙ m2
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• Moment of inertia for axis of symmetry: 𝐼𝑦𝑦,Axle,steel = 0.893713 kg ∙ m2
For the HMC axle, the following parameters were calculated based on data provided by the
University of Nottingham
• Mass: 𝑚Axle,comp = 78.7489 kg
• Moment of inertia for transversal axis: 𝐼𝑥𝑥,Axle,comp = 𝐼𝑧𝑧,Axle,comp = 27.2336 kg ∙ m2
• Moment of inertia for axis of symmetry: 𝐼𝑦𝑦,Axle,comp = 0.473088 kg ∙ m2
The inertia data for the conventional steel wheelset, which serves as the reference case, was
provided by Lucchini RS. Also here, some inevitable very small numerical errors have been
corrected, so that the inertia is described by the following parameters:
• Mass: 𝑚WS,steel = 859.524 kg
• Moment of inertia for transversal axis: 𝐼𝑥𝑥,WS,steel = 𝐼𝑧𝑧,WS,steel = 457.740 kg ∙ m2
• Moment of inertia for axis of symmetry 𝐼𝑦𝑦,WS,steel, = 73.2372 kg ∙ m2
The inertia parameters of the new wheelset are obtained by subtracting the inertia parameters of
the steel axle from the conventional steel wheelset and adding the inertia parameters of the
composite axle. For instance, the mass of the new wheelset is obtained by:
𝑚WS,comp = 𝑚WS,steel − 𝑚Axle,steel + 𝑚Axle,comp
The moments of inertia are treated in the same way. Since the centres of gravity of the entire
wheelset and of the wheelset axle coincide, no further adaptations are required. Based on this, the
following inertia parameters of the new wheelset are obtained:
• Mass: 𝑚WS,comp = 740.391 kg
• Moment of inertia for transversal axis: 𝐼𝑥𝑥,WS,comp = 𝐼𝑧𝑧,WS,comp = 432.105 kg ∙ m2
• Moment of inertia for axis of symmetry: 𝐼𝑦𝑦,WS,comp = 72.8166 kg ∙ m2
The replacement of the steel axle by the HMC axle mainly affects the mass of the wheelset, which
is reduced from 𝑚WS,steel = 859.524 kg to 𝑚WS,comp = 740.391 kg, i.e. by approximately 14%. In
contrast to this, the wheelset’s rotational inertia described by the moments of inertia is hardly
affected. This can be explained by considering the equations for the moments of inertia:
𝐼𝑥𝑥 = ∫(𝑦2 + 𝑧2)𝑑𝑚 , 𝐼𝑦𝑦 = ∫(𝑥2 + 𝑧2)𝑑𝑚 , 𝐼𝑧𝑧 = ∫(𝑥2 + 𝑦2)𝑑𝑚
A mass particle having a larger distance to the reference point makes a higher contribution to the
moment of inertia. Therefore, in the case of the wheelset the highest contribution to the moments
of inertia results from the wheels, which have a larger radius than the axle and are mounted in a
lateral distance to the wheelset’s centre.
One important motive for using other materials than steel for the wheelset is the reduction of the
unsprung mass, since a reduction of the unsprung mass usually reduces the dynamic forces acting
between the wheel and the rail. However, it has to be noticed that the axle boxes also contribute
to the unsprung mass and to the moment of inertia, which is relevant for the wheelset’s yaw motion.
For the vehicle used in the present case, each axle box has a mass of 𝑚AB = 88 kg. As a result,
the two wheelsets have the following unsprung masses:
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• Steel wheelset: 𝑚unspr,steel = 𝑚WS,steel + 2 ∙ 𝑚AB = 1035.524 kg
• HMC wheelset: 𝑚unspr,comp = 𝑚WS,comp + 2 ∙ 𝑚AB = 916.391 kg
Thereby, the use of the composite axle instead of the steel axle reduced the unsprung mass by
11.5% of the original value. This order of magnitude should be kept in mind with regard to the
evaluation of the running behaviour.
12.3 SCENARIO “RUNNING ON A CURVED MEASURED TRACK”
In the first scenario, the running of the vehicle on a measured track is considered. The measured
data, which were provided by Metro de Madrid, describe the track layout and the track irregularities.
The parameters for the track layout are the curvature, i.e. the reciprocal value of the curve radius,
and the superelevation, i.e. the vertical distance between the outer and the inner rail in the curve.
The irregularities are indicated by the lateral and vertical deviation of each rail from the ideal
position. All these parameters were provided as functions of the distance along the track. Also, the
wheel-rail geometry including the profiles of wheel and rail and the rail inclination were provided by
Metro de Madrid.
The following results were calculated for a running speed of 𝑣0 = 54 km/h. This speed was chosen,
because it permitted the passing through the curves of the track without exceeding the limits for
operation. The maximum absolute value of the curvature is max |1
𝑅𝐶| = 0,0052 m−1 , which is
equivalent to a minimum curve radius of 𝑅𝐶,min = 192.3 m. The ideal superelevation ℎ0, for which
the lateral acceleration is fully compensated, is approximated by
ℎ0 ≈𝐸 ∙ 𝑣2
𝑅𝐶 ∙ 𝑔
Here, the sign of the curvature 1
𝑅𝐶, where positive and negative values describe right and left curves,
respectively, has to be taken into account so that in the present case the ideal superelevation is
positive for right curves and negative for left curves. For the standard track gauge, the lateral
distance between the contact points is 𝐸 ≈ 1.5 m, and the gravitational acceleration is 𝑔 = 9.81 m
s2.
The cant deficiency Δℎ = ℎ0 − ℎ is calculated as the difference between the ideal superelevation
ℎ0 and the real superelevation ℎ, whereby the signs of ℎ0 and ℎ are taken into account. For a
running speed of 𝑣 = 54km
h= 15
m
s the absolute value |Δℎ| of the cant deficiency does not exceed
0.15 m, i.e. |Δℎ| < 0.15 m, which is in accordance with the usual limits for operation. The following
diagrams show the curvature 1
𝑅𝐶 and the superelevation ℎ of the used metro line and the cant
deficiency Δℎ, which is calculated for the running speed of 𝑣0 = 54 km/h and the contact point
distance of 𝐸 = 1.5 m, as functions of the track length 𝑠.
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Figure 91: Parameters of the used metro line: Curvature 𝟏/𝑹𝑪 (upper diagram), superelevation 𝒉
(middle diagram), cant deficiency 𝚫𝒉 for 𝒗𝟎 = 𝟓𝟒 𝐤𝐦/𝐡 and 𝑬 = 𝟏. 𝟓 𝐦 (lower diagram).
The simulation of a relatively complex multibody system provides a lot of data. In the present case,
some quantities will be considered, which characterize the running behaviour of the wheelset and
its interaction with the infrastructure. These quantities are:
• The dynamic vertical contact force Δ𝑄 acting in a wheel-rail contact
• The sliding mean value Σ𝑌2m of the resulting lateral force Σ𝑌 between wheelset and rail over
a distance of Δ𝑠 = 2
• The 𝑇𝛾 value, also known as the wear number, for a wheel-rail contact
The wheelsets are numbered in the scheme that the first digit indicates the bogie and the second
digit indicates the wheelset within the bogie, i.e. the wheelsets 11 and 12 are the leading and the
trailing wheelsets of the leading bogie, respectively, and the wheelsets 21 and 22 are the leading
and the trailing wheelsets of the trailing bogie, respectively. In the analysis, the following colour
code will be used:
• The blue curves denote the results calculated for the conventional steel wheelset.
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• The orange curve denote the results calculated for the new HMC wheelset.
First, the dynamic vertical contact force Δ𝑄 shall be considered. This force is defined in the
following way:
Δ𝑄(𝑡) = 𝑄(𝑡) − 𝑄0
Here, 𝑄(𝑡) denotes the current vertical wheel-rail contact force at the time 𝑡. The static vertical
wheel-rail force, which is constant, is denoted by 𝑄0. This formulation is chosen, because due to
different masses of the two different wheelset types the static force 𝑄0 depends on the used
wheelset type. The values of the static vertical wheel-rail force 𝑄0 are:
• Steel wheelsets: 𝑄0 = 23.725 kN
• HMC wheelsets: 𝑄0 = 23.040 kN
First, the dynamic vertical contact force Δ𝑄 shall be considered for the four wheel-rail contacts of
the leading bogie, i.e. for the contacts of the wheelsets 11 and 12. In the following diagrams, the
dynamic vertical contact force Δ𝑄 is displayed as a function of the curved track-length coordinate
𝑠.
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Figure 92. Comparison of the dynamic vertical wheel-rail forces 𝚫𝑸 at the leading bogie; 𝒗𝟎 =𝟓𝟒 𝐤𝐦/𝐡.; blue: steel wheelset; orange: HMC wheelset.
The orange curves (HMC wheelsets) cover the blue curves (steel wheelsets) nearly completely;
from the blue curves, only the peaks are visible. This indicates that for the new composite wheelsets
the dynamic vertical contact force Δ𝑄 is slightly lower than for the conventional steel wheelsets.
Very few blue peaks are visible; in these cases, the lower mass of the new HMC wheelsets distinctly
reduces the dynamic vertical contact force Δ𝑄. However, in total, the effect of the lower wheelset
mass is rather weak.
The dynamic vertical contact force Δ𝑄 obtained for the wheel-rail contacts of the trailing bogie, i.e.
for the contacts of the wheelsets 21 and 22 are displayed in the following diagrams.
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Figure 93. Comparison of the dynamic vertical wheel-rail forces 𝚫𝑸 at the trailing bogie; 𝒗𝟎 =𝟓𝟒 𝐤𝐦/𝐡; blue: steel wheelset; orange: HMC wheelset.
The diagrams for the wheel-rail contacts indicate a very similar result: The lower mass of the HMC
wheelset slightly reduces the dynamic vertical contact force Δ𝑄, but the effect of the reduced mass
is rather weak.
Next, the sliding mean value Σ𝑌2m of the resulting lateral force Σ𝑌 between wheelset and rail over
a distance of Δ𝑠 = 2 m is considered. It is calculated based on the following equation:
Σ𝑌2m = ∫ Σ𝑌(𝑠) 𝑑𝑠s0+2 m
s0
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Originally, this expression has been developed in order to evaluate the risk of lateral track shifting.
Here, the sliding mean value Σ𝑌2m must not exceed the following limit Σ𝑌max,lim:
Σ𝑌max,lim = 𝑘1 ∙ (10 kN +2 𝑄0
3)
Here, 2 𝑄0 is the static axle load of for each wheelset of the vehicle. In the present case of a
passenger vehicle, a factor of 𝑘1 = 1 has to be used. In the present case, the vehicle has the
following static axle loads for the two types of wheelsets:
• Steel wheelsets: 2 𝑄0 = 47.250 kN ⇒ Σ𝑌max,lim = 25.750 kN
• HMC wheelsets: 2 𝑄0 = 46.081 kN ⇒ Σ𝑌max,lim = 25.360 kN
Besides the evaluation of the risk of track shifting, the sliding mean sliding mean value Σ𝑌2m is also
helpful to obtain an impression of the level of the lateral forces Σ𝑌; these forces can sometimes
reach very high values, but for extremely short periods of time, so that these high values have
relatively little effect.
The following diagrams show the sliding mean values Σ𝑌2m for the four wheelsets.
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Figure 94. Comparison of the sliding mean values 𝚺𝒀𝟐𝐦 at the four wheelsets; 𝒗𝟎 = 𝟓𝟒 𝐤𝐦/𝐡; blue: steel wheelset; orange: HMC wheelset.
For all four wheelsets, the sliding mean values Σ𝑌2m stay distinctly below the limit values of
Σ𝑌max,lim = 25.750 kN (steel wheelsets) and Σ𝑌max,lim = 25.360 kN (HMC wheelsets). Generally, for
the leading wheelsets 11 and 21 higher values are obtained than for the trailing wheelsets 12 and
22. This is plausible, since for the curve entry the guiding force acting at the leading wheelset,
which enters the curve first, has to change the direction of motion of the bogie. The highest values
are observed at the leading wheelset 11. Also here, the blue lines (steel wheelsets) are nearly
completely covered by the orange lines (HMC wheelsets) so that just the blue peaks are visible.
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This indicates that the reduction of the unsprung mass in fact reduces the lateral guiding forces,
but also here the reduction is rather small.
Next, the 𝑇𝛾 value, also known as the wear number, is considered. The 𝑇𝛾 value describes the
energy per track length, which is dissipated in the wheel-rail contact. Therefore, it is an indicator
for the strength of the wear occurring in the wheel-rail contacts.
First, the 𝑇𝛾 values for the wheel-rail contacts of the leading bogie shall be considered. The
following diagrams show the 𝑇𝛾 values for the wheel-rail contacts of the wheelsets 11 and 12. Since
it can be expected that higher friction forces occur in curves, the track curvature is shown for
comparison.
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Figure 95. Comparison of 𝑻𝜸 values (wear numbers) at the leading bogie; 𝒗𝟎 = 𝟓𝟒 𝐤𝐦/𝐡; blue: steel wheelset; orange: HMC wheelset; magenta: track curvature.
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At the wheel-rail contacts of the leading wheelset 11, higher 𝑇𝛾 values are observed than at the
contacts of the trailing wheelsets 12. In the diagrams, only the peaks of the blue curves (steel
wheelsets) are visible, indicating that the 𝑇𝛾 values are lower for the HMC wheelsets than for the
steel wheelsets. The reduction of the 𝑇𝛾 values due to the reduced wheelset mass is slightly
greater than the reduction of the Σ𝑌2m values.
The following diagrams display the 𝑇𝛾 values for the wheel-rail contacts of the trailing bogie, i.e. for
the wheel-rail contacts of the wheelsets 21 and 22. Also here, the track curvature is shown for
comparison,
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Figure 96. Comparison of 𝑻𝜸 values (wear numbers) at the trailing bogie; 𝒗𝟎 = 𝟓𝟒 𝐤𝐦/𝐡; blue: steel
wheelset; orange: HMC wheelset; magenta: track curvature.
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The results are very similar to those obtained for the contacts of the leading bogie. Again, higher
𝑇𝛾 values occur in the contacts of the leading wheelset, here the wheelset 21, than in the contacts
of the trailing wheelset, here the wheelset 22. Also here, the 𝑇𝛾 values obtained for the composite
wheelsets are slightly lower than those obtained for the steel wheelsets.
In total, the comparison qualitatively confirms that a reduction of the unsprung mass reduces the
dynamic vertical contact forces, the lateral guiding forces and the energy dissipated in the wheel-
rail contacts due to friction. Quantitatively, the effect is rather weak, i.e. the values obtained for the
lighter composite wheelsets are only slightly lower than those obtained for the heavier steel
wheelsets.
12.4 SCENARIO “RUNNING ON A STRAIGHT TRACK WITH MEASURED IRREGULARITIES”
In the analysis presented in the previous Section, a running speed of 𝑣0 = 54 km/h was chosen
because of the curvature of the trajectory. The comparison of the results has shown that the
reduction of the unsprung mass reduces the dynamic vertical contact forces, the guiding forces and
the energy dissipated in the contact. It can be expected that the reduction of the unsprung mass
has a stronger effect at higher running speeds, since at higher speeds stronger dynamic
interactions can be expected. Therefore, the running behaviour shall now be investigated at a
higher running speed of 𝑣0 = 90 km/h. However, in order to do so, a straight track is used for the
trajectory, while the same irregularities are applied to the track. In this simulation, the first kilometre
of the track had to be excluded from the calculation because of numerical problems.
The analysis in the previous Section has shown that both bogies show qualitatively the same
behaviour. Therefore, for the sake of brevity, only the wheelsets 11 and 12 of the leading bogie
shall be considered here.
First, the dynamic vertical wheel-rail force Δ𝑄 is considered for the four wheel-rail contacts of the
leading bogie, i.e. the contacts of the wheelsets 11 and 12. It should be pointed out that these
diagrams cover a wider range up to 150 kN for the dynamic vertical wheel-rail force Δ𝑄, while in
the previous Sthis range could be limited to 30 kN.
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Figure 97. Comparison of the dynamic vertical wheel-rail forces 𝚫𝑸 at the leading bogie; 𝒗𝟎 =𝟗𝟎 𝐤𝐦/𝐡; blue: steel wheelset; orange: HMC wheelset.
Also here, the dynamic vertical wheel-rail force Δ𝑄 is generally lower for the new HMC wheelset
than for the conventional steel wheelset. Several peaks of the blue curve, which are not covered
by the orange curve, are clearly visible. This indicates that in these points the lower mass of the
HMC wheelset strongly reduced the dynamic force.
Next, the sliding mean value Σ𝑌2m is considered in order to evaluate the level of the guiding forces.
The results are displayed in the following diagrams.
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Figure 98. Comparison of the sliding mean values 𝚺𝒀𝟐𝐦 at the leading bogie; 𝒗𝟎 = 𝟗𝟎 𝐤𝐦/𝐡 blue: steel wheelset; orange: HMC wheelset.
With the exception of very few peaks occurring at the leading wheelsets 11 and 21, the values for
Σ𝑌2m occur stay far below the limit values limit values Σ𝑌max,lim = 25.750 kN (steel wheelsets) and
Σ𝑌max,lim = 25.360 kN (HMC wheelsets) also for the higher running speed. This can also be seen
as an indicator that the running stability is not yet a critical issue at this higher running speed.
Although in this scenario the running on a straight line is considered, also in this case higher values
Σ𝑌2m occur at the leading wheelset 11 than at the trailing wheelset 12. However, also here, the
peaks of the blue curves (steel wheelsets) hardly exceed those of the orange curve (HMC
wheelsets), so that also here the effect of the reduced un-sprung mass is relatively low.
Finally, the 𝑇𝛾 values, which are displayed in the following diagrams, shall be considered. It should
be pointed out that due to the higher level of the 𝑇𝛾 values the considered range, which has been
limited to 𝑇𝛾 ≤ 500 N, is extended here to 1000 N.
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Figure 99. Comparison of 𝑻𝜸 values (wear numbers) at the leading bogie; 𝒗𝟎 = 𝟗𝟎 𝐤𝐦/𝐡.; blue: steel wheelset; orange: HMC wheelset.
Again, higher 𝑇𝛾 values occur at the wheel-rail contacts of the leading wheelset 11. In these
diagrams, in particular those for the leading wheelset 11, the blue curves (steel wheelsets) are
more visible. This indicates that the reduction of the un-sprung mass mostly affects the energy
dissipated by the friction in the contact.
The results indicate that for higher running speeds in fact a stronger dynamic interaction between
the wheelset and the track can be observed. This becomes particularly evident from the dynamic
vertical wheel-rail forces Δ𝑄 and from the 𝑇𝛾 values. Regarding the lateral guiding forces described
by Σ𝑌2m, it has to be noted that in this scenario a straight line instead of a curved trajectory is used
so that the guiding forces required for curve running are eliminated.
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Of course, the behaviour of the vehicle is strongly influenced by the irregularity profile. In order to
estimate this influence, the scenario of running at 𝑣0 = 90 km/h on a straight track shall also be
considered for a different irregularity profile. In this case, the irregularities are taken from a section
of an upgraded mainline between Dortmund and Hannover in Germany. This upgraded line is
adapted to a regular operational speed of 200 km/h. For this line, only data for a section of 2 km
were available. Again, for the following results, an actual running speed of 𝑣0 = 90 km/h is used
for the metro vehicle. Also, the contact geometry defined by the profiles of wheel and rail and by
the rail inclination is kept unchanged.
Also in this case, the leading bogie shall be considered. In the following diagrams, the dynamic
vertical wheel-rail forces Δ𝑄 are compared for the steel wheelset and for the HMC wheelset.
Figure 100. Comparison of the dynamic vertical wheel-rail forces 𝚫𝑸 at the leading bogie; 𝒗𝟎 =𝟗𝟎 𝐤𝐦/𝐡; mainline irregularity profile; blue: steel wheelset; orange: HMC wheelset.
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Since the higher admissible speed on the upgraded line requires a higher track quality, i.e. a lower
level of irregularities, the dynamic vertical forces are far lower than those obtained for the metro
line. Therefore, a different scaling is applied here. Nevertheless, the diagrams show that many
peaks of the blue lines (steel wheelset) are not covered by the orange lines (HMC wheelset), but
clearly visible. This indicates that the percentage, by which the dynamic vertical forces are reduced
for the HMC wheelset, is higher in this case.
Next, the sliding mean values Σ𝑌2m of the lateral forces acting between the wheelsets 11 and 12
and the track shall be considered; they are displayed in the following diagrams.
Figure 101. Comparison of the sliding mean values 𝚺𝒀𝟐𝐦 at the leading bogie; 𝒗𝟎 = 𝟗𝟎 𝐤𝐦/𝐡; 𝒗𝟎 =𝟗𝟎 𝐤𝐦/𝐡; mainline irregularity profile. ; blue: steel wheelset; orange: HMC wheelset.
The absolute values for Σ𝑌2m hardly exceed 2 kN indicating a very low level of guiding forces. The
blue curves are hardly visible so that the impact of the reduced wheelset mass on the guiding forces
is rather weak.
Finally, the 𝑇𝛾 values for the four wheel-rail contacts of the leading bogie’s wheelsets shall be
considered. The results obtained for the two wheelset types are compared in the following
diagrams.
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Figure 102. Comparison of 𝑻𝜸 values (wear numbers) at the leading bogie; 𝒗𝟎 = 𝟗𝟎 𝐤𝐦/𝐡; mainline irregularity profile; blue: steel wheelset; orange: HMC wheelset.
Here, the 𝑇𝛾 values hardly exceed 0.8 N, which indicates an extremely low level. Again, great parts
of the blue curves are covered by the orange ones so that also here the impact of the reduced
wheelset mass is very weak.
Of course, a mainline, which is adapted to a regular operational speed of 200 km/h, requires a high
track quality in the form a very low levels of track irregularities, while for a metro line with a lower
operational speed higher levels of irregularities may be admissible. Therefore, applying these
mainline irregularities to a metro vehicle, which is operated at lower speeds, may appear a bit
arguable; this also explains the extremely low values for Σ𝑌2m and 𝑇𝛾. Nevertheless, the results
obtained for these irregularities clearly show that use of the HMC wheelsets distinctly reduces the
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dynamic vertical force Δ𝑄. For future work, it may therefore be worthwhile to consider also other
vehicle types as application cases for the HMC wheelset.
12.5 CONCLUSIONS
Based on the results of multibody simulations performed considering a metro vehicle in which the
wheelset with composite axle could be realistically used, the following conclusions can be drawn:
• The results of multi-body simulations confirm that the reduction of the un-sprung mass
offered by the HMC axle provides benefits in terms of reduced dynamic vertical wheel-rail
forces Δ𝑄, track shift forces Σ𝑌2m and wear number 𝑇𝛾. This means less impact forces, less
wear and a reduction of rolling contact fatigue damage can be expected for both the rails
and the rolling surfaces of the wheels. Furthermore, a reduction of track damage related to
metal fatigue of rails and to permanent settlement in the ballast + embankment can be
expected as a positive outcome of using the wheelset with HMC in place of the benchmark
one. Additionally, the reduction of un-sprung mass will have an effect on vibrations
transmitted to the ground.
• The benefits mentioned above will be much higher when the vehicle speed is increased,
whereas they are limited at low speed, e.g. the case when the vehicle negotiates a short
radius curve. The fact that 90 km/h was chosen was to be consistent with the wheelset that
has been designed (metro vehicle). Higher benefits are expected in case the HMC axle is
used in a high-speed vehicle, for which service speeds would be much higher than the ones
considered here.
• When assessing the positive impact provided by the use of the HMC axle, it should be borne
in mind that the axle takes a relatively small share of the total un-sprung mass, so even a
design of the HMC axle providing a strong reduction of the axle mass like concept 3
considered in this study leads to a relatively small reduction of the total un-sprung mass
(11.5% approximately in the case considered here). This is the reason why in some of the
results presented in this Chapter only a rather slight reduction of the vertical and lateral
forces and of the wear number is observed.
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13. CONCLUSIONS
The objective of Task 3.2 of the NEXTGEAR project was to assess the feasibility of a HMC
wheelset. In Task 3.1, a composite axle of a trailer bogie, with integrated connections with wheel
rims, brake discs and bearings, was identified as the best candidate for substituting a steel axle,
reaching the desired TRL level of 2.
The aim to reduce the mass of the hollow steel trailer axle by replacement with a HMC equivalent
axle has been achieved. The mass of the HMC axle is 74 kg, a reduction of 63% over the steel axle
at 198 kg. There is the potential to further reduce the mass by altering the collar material and
potentially reducing the wall thickness.
The HMC railway axle permits the existing wheels and bearings to be used. The interference fits
between these components and the axle are met by the metallic collars. There is little load
transmission through the collars to the primary composite tube.
The maximum bending stress in the HMC axle is 170.00 MPa as compared to 73.64 MPa in the
steel axle representing safety factors of 2.5 and 3.7 respectively. A safety factor of 2 was the
threshold being maintained in the design so the higher stress within the HMC axle was considered
acceptable. The maximum torsional stress in the HMC axle (7.93 MPa) is less than that of the steel
axle (10.20 MPa), although the torsional stress in the collar is greater at 17.88 MPa . Maximum
transverse shear stress in the HMC axle is less than in the steel axle at 23.12 MPa (collar).
Maximum deflection in the HMC axle is 1.702 mm versus 1.119 mm for the steel axle over a span
of 1156 mm. The deflection in the HMC axle could be reduced by increasing the thickness of the
secondary composite tube. As the HMC axle remained within tolerance for the allowable back to
back deflection (<6 mm) no further stiffening was proposed.
In the current configuration the metallic collar imparts a high contact stress (528.10 MPa) into the
primary composite tube. An improved solution for the collar has been proposed to reduce the
stresses in the adhesive and increase the fatigue life of the joint. Reaching a higher TRL would
require a comprehensive characterization of the chosen adhesives, particularly under fatigue
loading and in different environmental conditions. Mechanical joining is not an option that has been
considered in this project because of the mass increment involved, but it could be a valid alternative
to adhesive bonding, should future tests demonstrate the unfeasibility of an adhesively bonded
joint.
The feasibility of the manufacturing process has been assessed for roll wrapping and filament
winding, by finite element simulations combined with process simulations. Both processes allow
similar mechanical performance to be achieved, although filament winding offers the potential for
an automated process, characterized by a high level of repeatability of the results. To reach higher
TRL levels, the need of a comprehensive experimental characterization of the materials used in
the different processes has been pointed out.
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The proposed design has been checked against requirements for inspection during maintenance
service interruption. The feasibility of NDT has been assessed, focussing particularly on the use of
ultrasonic testing (UT), by simulation. Some limitations of UT have been identified with respect to
the possibility of detecting cracks in the adhesive layer, whereas UT would allow to detect cracks
in the composite tubes and in the metallic collar. Simulations assumed ideal conditions, therefore,
to switch to higher TRL, experimental verification would be needed to optimize the setup. To
overcome the limitations of inspection of the bond line by UT, a possible structural health monitoring
approach has been proposed, based on strain profile monitoring, using fibre optic strain sensors
allowing for distributed sensing.
Dynamic analyses have shown the effect of impact loading by a foreign object (.e.g ballast stone)
Damage consists mainly in matrix failure of the external surface of outer tube due to high
compressive stresses. Although this would not impair the overall structural integrity of the axle,
solution like a protective coating and the installation of sensors capable to detect severe impacts
should be identified in future works.
Finally, the analysis of the dynamical forces at the interaction between rail and wheels has shown
that the proposed HMC axle can contribute to reduce the dynamic forces that are responsible of
wear mechanisms of the wheels and the rails, particularly at high speeds, thus confirming the
potential positive impact on maintenance costs offered by a lighter wheelset.
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APPENDIX A. MATERIAL PROPERETIES USED AS INPUT TO THE FEA
Material properties used as input to the FEA model of the hollow, steel railway axle (Table A1) and wheel
(Table A2).
Table A1. Mechanical properties of AISI 1030 Plain Carbon 0.3% Steel normalised representing EA1N steel used for the benchmark hollow railway axle (Source: Cambridge Engineering Selector Database).
Mechanical property Symbol Value Unit
Young’s modulus 𝐸𝑆𝑡 200 GPa
Yield strength 𝜎𝑆𝑡,𝑦 440 MPa
Poisson’s ratio 𝑣𝑆𝑡 0.285 -
Density 𝜌𝑆𝑡 7850 kg/m3
Average fatigue strength at 107 cycles 𝜎𝑆𝑡,𝑓𝑎𝑡 107 270 MPa
Average fatigue strength at 109 cycles 𝜎𝑆𝑡,𝑓𝑎𝑡 109 200 MPa
Table A2. Mechanical properties of AISI 1050 steel representing ER7 steel used for the wheels (Source: Cambridge Engineering Selector Database).
Mechanical property Symbol Value Unit
Young’s modulus 𝐸𝑇𝑖 115 GPa
Yield strength 𝜎𝑇𝑖,𝑦 850 MPa
Poisson’s ratio 𝑣𝑇𝑖 0.340 -
Density 𝜌𝑇𝑖 4450 kg/m3
Table A3. Mechanical properties of Gurit UCHM450 SE 84LV unidirectional (0°) laminate (Source: Gurit).
Mechanical property Symbol Value Unit
Fibre volume fraction 𝑣𝑓 56 %
Ply thickness 𝑡𝑝𝑙𝑦 0.45 mm
Ply weight 𝑊𝑝𝑙𝑦 683 g/m2
Density 𝜌 1498 kg/m3
Longitudinal tensile modulus 𝐸11,𝑡 208.26 GPa
Longitudinal tensile strength 𝜎11,𝑡 1562 MPa
Fatigue strength at 107 cycles (estimated) 𝜎11,𝑡,𝑓𝑎𝑡 107 781 MPa
Longitudinal compressive modulus 𝐸11,𝑐 187.43 GPa
Longitudinal compressive strength 𝜎11,𝑐 843.40 MPa
Fatigue strength at 107 cycles (estimated) 𝜎11,𝑐,𝑓𝑎𝑡 107 421.7 MPa
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Transverse tensile modulus 𝐸22,𝑡 6.39 GPa
Transverse tensile strength 𝜎22,𝑡 28.80 MPa
Transverse compressive modulus 𝐸22,𝑐 6.39 GPa
Transverse compressive strength 𝜎22,𝑐 83.1 MPa
Interlaminar shear modulus 𝐸13 4.31 GPa
Interlaminar shear strength 𝜎13 64.70 MPa
In-plane shear modulus 𝐸12 4.31 GPa
In-plane shear strength (estimated) 𝜎12 64.70 MPa
Poisson’s ratio – longitudinal strain 𝑣12 0.337 -