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The 14th IFToMM World Congress, Taipei, Taiwan, October 25-30, 2015 DOI Number: 10.6567/IFToMM.14TH.WC.OS12.009
The Reliability of Assembly Steel Wheels With Using FEM Analysis
I. Demiyanushko1
E. Loginov2
V. Mironova3
Moscow Automobile and Road Moscow Automobile and Road Moscow Automobile and Road
Construction State Technical Construction State Technical Construction State Technical
University (MADI), Russia University (MADI), Russia University (MADI), Russia
Abstract: The subject of the following article is the
problem of predicting fatigue strength and durability of
wheels constructed as an assembly of a rim and a disc, for
large dimension wheels. Such wheels are widely applied
to supersize cars, tractors, combine harvesters and other
agricultural and road machines Considered are the main
problems occuring when creating a FEA model for
various loading conditions, including bench test and
technological ones.
3 versions of the item production, depending on the
contact conditions of the disc and the rim during the
interference fit assembly followed by welding, have been
analyzed. Recommendations on decreasing of stress-strain
state in the most unsafe points of the construction have
been given. Keywords: Wheels of a modular design, Reliability, Fatigue
I. Introduction
The experience of automotive and tractor wheels
operation shows necessity of predicting fatigue strength
depending on the materials, loads applied, and production
technology [1,2]. Depending on the driving conditions,
certain testing methods for evaluating wheel durability
have been standardized. As regarded to the construction
operation mode under alternating loads (e.g. bending with
rotation), the fatigue strength evaluation is performed via
rotary bending fatigue tests (dynamic cornering fatigue
tests, as referred in EUWA), which are considered to be
the most informative fatigue tests.
In order to minimize testing and further construction
optimization costs, it is offered to perform FEM analysis
[2] and determine wheel stress-strain state, occurred under
the action of loads which correspond to dynamic
cornering fatigue tests performed in quasi-static problem
statement. When evaluating fatigue strength, the material
fatigue characteristics are examined, taking into account
the dispersion occurred due to the technology of
processing the interference fit, and welding between the
disc and the rim. The examination is performed by testing
the samples cutout from the wheel.
II. Problem statement
The chosen research object is a typical design tractor
wheel of high dimensionality, 26”, which is produced as
an assembly (Fig. 1). During the assembly process the disc
is fixed into the rim under interference fit with the
welding followed.
[email protected] [email protected] [email protected]
During the operation and fatigue bench testing of
separate items, fatigue cracks in the welding joint have
been frequently detected, which is unacceptable according
to EUWA ES 3.12 [3] standards
(standards covering tests
for agricultural vehicles’ wheels). One of the features of
wheels of given type is rather rough production
technology which may lead to significant fatigue
characteristics dispersion of the construction and decrease
of reliability.
Fig. 1. Fatigue crack initiation in the wheel
Investigation of the defect appearance reasons and
analysis of the wheels’ fatigue strength and reliability was
performed by combination of up-to-date methods: FEA
stress-strain state analysis, and fatigue strength analysis
based on experimental research data [4]. In order to
perform FEA stress-strain state analysis MSC. Software
instruments have been used [5-7]. The analysis has been
performed for the case of loading the wheel on a vertical
rotary bending moment stand. In order to create a FEA-
model required it is necessary to create a model not only
for the wheel itself, but also for the stand load-applying
units.
Quasi-static stress-strain state analysis under various
assembly versions allows evaluation of stress amplitudes
σa in unsafe regions of the wheel under bending loads
applied during rotation. Evaluation of stress-strain state of
the wheel under influence of the interference fit between
the disc and the rim allows determination of the static
component σm of the loading cycle depending on the value
of the interference closure. Received parameters of the
stress cycle have been compared with the results of the
templates fatigue tests. The templates were cut out of the
wheel and included the welding joint. Comparative
analysis allows evaluating the parameters of fatigue
strength and durability of the wheels, detecting the reasons
of fatigue damage initiation. This analysis allows to
evaluate the reliability of the wheel during operation [4]
Fatigue crack
initiation zone
and provide recommendations on improving the
technology of wheel production.
III. Dynamic cornering fatigue test procedure
Fatigue strength bench testing under bending loads
applied during rotation reproduce the combined influence
of the moments which occur under vertical load and side
force applied during turns or motion along an inclined
surface. The value of the vertical load applied to the wheel
is constant. And the vector of the moment applied, is
rotated relative to the wheel according to such pattern that
all the wheel spots are consecutively loaded by moments
with the values changing from one extreme to another.
Load appliance scheme is given on Fig. 2.
Fig. 2. Dynamic cornering fatigue test stand
The cyclic form of bending moment action is created
by rotating the wheel. When carrying out tests, the wheel
rim is fixed to the rotating stand bench. A cantilever arm
is fixed to the wheel via standard mounting holes, which
allows simulating the fastening of the wheel to the hub.
The load is applied to another end of the arm. During the
tests the wheel is rotated around the axis together with the
arm.
Depending on the arm position and the direction of
load application, necessary conditions of loading the
wheel relative to the respective axes are achieved.
Appearance of the testing stand is given on Fig. 3.
Fig. 3. Fixing the wheel to the dynamic cornering fatigue testing stand
IV. Modeling the test and fatigue strength evaluation
The process of creating a wheel model in assembly with
testing stand loading elements consists of several stages.
Due to construction symmetry the initial FEA model is
created being based on 1/8 part of the assembly. The
whole model is acquired by symmetrical mirroring of the
initial FEA mesh.
A. Creation of the wheel FEA model
The process of creating a FEA-mesh of a stamped wheel
is not complicated. Certain difficulties appear when
meshing the nipple hole zone. In order to receive proper
mesh, it is necessary to merge all surfaces with linear
dimensions less than the size of the element. As regarded
to the other surfaces, good quality mesh can be received
by using an automatic mesher.
Fig. 4 shows a transitional result for a 90˚ sector
directly after the first mesh mirroring against the
symmetry axis. The disc and the rim are created separately
and have no jointed nodes. It is accepted for an
insignificant amount of nodes to be coincident only. In
addition, it is recommended for the disc mesh to be of
greater size as compared to the rim mesh, in order to
ensure high quality of contact recognition.
Fig. 4. Wheel 90˚ segment FEA model
B. Creation of the testing stand FEA model
The bearing surface for the disc is the hub with given
parameters: height H = 40 mm; diameter D = 318 mm.
When creating the hub model, it requires a mesh seed
around the circumference with a diameter equal to the
diameter of the cantilever arm.
When creating the bolts model, the size of the
elements should be chosen 1,3 times smaller than the size
for the hub. The difference in the mesh size ensures better
quality contact detection between the parts.
Fig. 5. Hub and cantilever arm connection
Hereafter, 1 m cantilever arm simulation is performed.
In order to facilitate the analysis, the model is created by
10 Beam elements. The end of the arm coincident with
central hub node, is connected with the hub nodes located
within the closest surface to the arm. The connection is
performed via rigid RBE2 elements and includes the
nodes located within the circumference of a diameter
equal to the actual diameter of the arm (Fig. 5).
FEA model of the wheel assembled with the testing
stand is shown on Fig. 6. Then material properties data
with elastic-plastic constitutive model and stress-strain
curves are applied to all elements of the construction
(different properties for the rim and the disc). As regarded
to the Beam elements there should be additional
parameters specified, in particular cross-section
parameters with the circumference diameter.
Fig. 6. Assembled wheel and test stand FEA model
C. Loads & Boundary conditions
When simulating the load the following sequence of load
application shall be considered:
(1) Fixing the external rim flange and applying the bolts
tightening torque.
(2) The previous step is complemented by the force,
applied to the end of the testing stand cantilever arm.
In the pre-postprocessor software the stepwise loading
is simulated via a special “Load Cases” function. Since
the arm length is equal to 1 m, the force applied is equal
by absolute value to the bending moment and totals 16,14
kN.
The contact bodies defined are the disc, the rim, the
upper and lower bolt heads (16 contact bodies for the bolts
total).
The nodes which are in the immediate vicinity to the
transition edge from the bolt head to its body are excluded
from contact since the original construction includes a
washer between the disc and the bolt. Thus, contact
actually takes place at insignificant distance from the hole
which is considered to be a stress concentrator.
Bolts tightening torque is simulated by applying the
load equal to 78,45 kN via 3D Bolt Preload function. The
action of this force is equivalent to the tightening torque
of 600 Nm.
Fig. 7. Defining bolts as contact bodies
D. Solver options
The analysis has been performed in the elastic-plastic
constitutive model using Sol 400 [6] solver. The friction
model chosen in the solver contact task options is Bilinear
Coulomb model.
Contact pairs are determined on a condition that the
body with greater-size mesh is considered Master, and the
body with coarser mesh is considered Slave. Contact
search is performed from Slave to Master.
E. Results analysis and post processing
3 possible versions of item production under various
conditions of the technological assembly of the rim and
the disc have been considered for stress-strain state
analysis:
(1) Diametric dimensions of the disc and the rim equal to
nominal dimensions. Neither interference fit, nor
clearance is formed.
(2) The construction is assembled with a clearance
between the disc and the rim.
(3) The construction is assembled with an interference fit
between the disc and the rim. Analysis is performed
for 2 interference closure values: 0,25 mm and 0,4
mm.
In consequence of the wheel stress-strain state analysis
it has been determined that maximal stress in the bolting
zone is significant (Fig. 8). But since the bolted
connection during the analysis under conditions of stand
testing is chosen conventionally, the stress distribution in
the bolting zone is not of concern, and it shall not be
considered during the fatigue strength evaluation. In this
case the most loaded zone for the wheel is the rim in the
region of the rim well close to the welding joint.
Force
Cantilever
arm
Fig. 8. Von Mises stress distribution around bolt holes
Under conditions of tight contact between the disc and
the rim without a clearance or interference fit (Case 1),
maximum equivalent von Mises stress σi in the welding
joint zone result in σi = σa =73 MPa (Fig. 9).
During loading the construction according to “bending
during rotation” testing stand layout according to Case 2,
the model is created suggesting initial absence of contact
between the contiguous surfaces of the disc and the rim,
except for the welding zone (Fig. 10). Thus, faces of the
welding joint are the only surfaces transferring loads from
the disc to the rim.
Fig. 9. Von Mises stress distribution around the rim under the conditions
of no clearance or interference fit
.
Fig. 10. Clearance between the disc and the rim (scaled model)
The calculation has been performed in order to
evaluate maximal stress in the welding joint zone without
any interference fit. Fig. 11 shows the stress distribution in
this calculation round the rim surface. Maximal von Mises
stress equals σi = σa= 172 MPa.
Fig. 11. Von Mises stress distribution around the rim under conditions of
non-zero clearance
It should be mentioned that though the analysis has
been performed in the elastic-plastic constitutive model,
the stress-strain state in the welding joint zone under
“bending with rotation” load layout is elastic. This
provides a possibility to analyze stress-strain state
occurring independently from cyclic load to determine
stress amplitudes σa and from interference fit (Case 3) to
determine a static component of the stress cycle σm.
In order to evaluate the construction behavior under
the conditions of an interference fit, the wheel stress-strain
state FEA analysis under two values of interference
closure has been performed: 0,4 mm (maximum value as
referred to engineering documentation) and 0,25 mm.
The analysis of the outcomes shows that under greater
interference closure of 0,4 mm great stress occurs in the
welding joint zone. Besides, maximum stress, equals to
σi = σm = 228 MPa, provided distributed contact is
displayed (please refer to Fig. 12).
Considering that the yield strength of the material
equals 255 MPa, it should be considered that under cyclic
load of the disc during bending with rotation, the static
component of the stress resulting from interference fit,
may in some unfavorable cases achieve the values, close
to the yield strength.
Fig. 12. Von Mises stress distribution around the rim under conditions of
0,4 mm interference fit
The analysis performed at smaller value of
interference closure of 0,25 mm reveals that the stress
around the welding joint zone decreases up to the value of
σi = σm = 136 MPa (Fig. 13).
Welding
joint
Fig. 13. Von Mises stress distribution around the rim under conditions of 0,25 mm interference fit
V. Wheel templates fatigue testing
Since the main problem area is the junction of the disc and
the rim, special templates considering the welding
technology have been manufactured to determine fatigue
parameters of the material in the construction. The
templates have been cut out of the finished wheel via 2
parallel cross-sections, normal to the wheel plane.
Template solid model is shown on Fig. 14.
Fig. 14. DW20Ax26 tractor wheel template sketch
Applying bending momentum to the template allows
evaluating the endurance limit of the material used in the
construction, considering structural and technological
factors, determining the peculiarities of the rim cross-
section and its junction with the disc. It should be
mentioned that under these tests, the static load
component occurring as a result of interference fit
influence, is not reproduced.
As opposed to standard methods of fatigue testing, the
following method is based on the template forced
oscillation. The main advantage of such method lies in the
simplicity of load application and sufficient reduction in
test time[8]
.
The tests have been performed by using an
electrodynamics vibration stand with cantilever template
fixation. Equipment overview is shown on Figure 15. The
template (3) is fixed on a mobile stand of the oscillator (1)
by means of a special screw clamp (2).
Stand oscillation parameters (frequency and excitation
amplitude) have been measured with the use of an
accelerometer (7), installed on a vibration stand, and an
optical displacement controller (5).
The template’s rim oscillations have been measured by
means of an optical measuring device (6). Stresses have
been measured by resistance strain gauges (4), installed
close to the zone of disc-to-rim junction (Figure 16).
Fig. 15. Overview of electrodynamics vibration stand with a template mounted
Calibration of the stress initiated in the template has
been run with the use of strain-gaging, measuring the
propelling force with the oscillation frequency
corresponding with the greatest deformations in the
junction zone between the disc and the rim, and measuring
oscillations spread by means of an optical displacement
controller. Before running the tests all the elements of the
measuring circuit have been calibrated on the basis of test
signals (with known values of amplitudes and stress).
To achieve maximum oscillation amplitudes and,
respectfully, maximum stresses, the template oscillation
has been performed with a frequency, equal to the
frequency of its main mode, which has been preliminary
determined via free oscillations method and equals 690 Hz.
Fig. 16. Mounting resistance strain gauges to the template
In order to evaluate stress-strain state of the template
and choose the locations for the resistance strain gauges, a
template FEA analysis using MSC. Nastran has been
performed.
The first mode oscillations analysis with simulating
the template fixation on the vibration stand has shown
(Fig. 17) that the stress distribution of the FEA model
coincides with the one received within the experiment.
Fig. 17. Stress distribution during the template oscillations under 1st mode (FEA analysis using MSC. Software).
The maximal stress is detected in the fatigue crack
initiation zone around the welding joint, which allows
determining the resistance strain gauges mounting layout
(Fig. 16).
Templates testing on a vibration stand have been
performed via a step-by-step load increase method under
various values of the excitation amplitude.
During the test runs gauges #1 and #3 have been
mounted in the places of maximal stress initiation
according to the earlier performed analysis. The control
has been performed in terms of measuring the template’s
corner point oscillations amplitude by means of optical
displacement controller.
The base quantity of load cycles totals 2 х106
cycles.
The results are shown on Fig. 18 in the form of an S-N
curve. There is a distinct linear pattern of stress amplitude
decrease with the increasing quantity of cycles observed. Average value of the templates’ endurance limit on the
basis of 2 х106 cycles totals σv =160 MPa with the
minimal value being σv =150 MPa and the maximal value
being σv =180 MPa.
Fig. 18. S-N curve for templates tested
The location of the fatigue crack is shown on Fig. 19.
The crack is distributed from the leg of the welding joint
deep into the rim well. The number of cycles prior to the
damage was set to as amount of cycles prior to a 10%
decrease in the loading frequency.
Fig. 19. Fatigue crack in the template tested
VI. Fatigue strength evaluation
As a result of bending during rotation under conditions of
stand testing, cyclic harmonic stress alteration. Besides,
when the interference fit occurring as a result of the
assembly between the disc and the rim is not considered,
the stress alteration is executed via asymmetric cycle.
Given the presence of interference fit as a result of an
assembly, interference fit stress is considered constant
average cycle stress, and the loading cycle itself changes
to asymmetric. The influence of cycle asymmetry on the
endurance limit can be considered by using the
Goodman’s criterion (1):
(1)
To evaluate the durability of the wheel the value of в
has been taken according to the reference data and equals
в = 420 MPa. The endurance limit has been evaluated
from the experimental diagram on the basis of 106 cycles
considering the dispersion and cycle asymmetry under
various interference closure values (Figure 20).
An
aly
sis
cond
itio
ns
Str
ess
amp
litu
de
а
Av
erag
e
inte
rfer
ence
fit
stre
ss
m
En
du
tan
ce l
imit
con
sid
erin
g c
ycl
e
asy
mm
etry
аv
Res
ult
Units MPa MPa MPa -
Clearance
between the disc
and the rim.
Contact via
welding joint only
172 0 150-
180
Possible
breakdown in
the welding
joint zone
Interference
closure between
the disc and the
rim =0,25 mm
73 136 125-
105
Endurance
margin ca. 1,7
Interference
closure between
the disc and the
rim =0,4 mm
73 228 70-90
Possible
breakdown in
the welding
joint zone
TABLE I. Wheel fatigue strength analysis results
Listed in the table are the results of the expected wheel
endurance according to the data from the wheel stress-
strain state analysis and template testing experimental data.
Fatigue Crack
𝜎𝑎𝜎𝑣
+𝜎𝑚
𝜎в
= 1
average values
Fig. 20. Endurance limits evaluation considering cycle asymmetry
It should be considered that semiautomatic welding
process and insufficient margin of durability (Table 1), as
well as contact absence or maximal interference closure,
lead to crack initiation after smaller amount of cycles.
VII. Conclusions
In order to increase the reliability of the wheels
manufactured, strict control of diametric dimensions of
the discs and rims is required. Considering the production
volumes it is possible to group discs and rims into pairs in
order to ensure a secure minimal interference fit and
absence of a clearance. It is recommended to production
engineers to pay special attention to tolerances
specification process in items production. Therewith,
automatic welding technology ought to be supplied in
order to minimize fatigue characteristics dispersion for the
given construction.
Acknowledgment
Authors are grateful to their colleagues, i.e.
Doct. Alexander M. Vakhromeev and Eng. Iliya A.
Karpov for participation in this work.
References [1] Demiyanushko I.V., Cast aluminum wheels for cars: development,
manufacture, design, Demiyanushko I.V, Esenovsky Y.K.,
Vakhromeev A.M., Avtomobilnaya Promyshlennost, Moscow,
No.9, 2002, p.35 - 39. [2] Demiyanushko I.V., Yudin M.N., Information technologies and
creation of automobile wheels designs, Avtomobilnaya
Promyshlennost, No.9, 2003, p.3 - 5. [3] EUWA ES 3.12. Test requirements for agricultural wheels. 2004
[4] Irina V. Demiyanushko, 'State-of-the-Art and Trends of
Development of Reliability of Machines and Mechanisms', Mechanisms and Machine Science, 2011, pp. 173-183.
http://dx.doi.org/10.1007/978-94-007-1300-0_14
[5] Zienkewich О. The Finite Element Method. Moscow Mir
publishing, 1975. 544 pages.
[6] MSC.Patran 2012 User’s Guide. www.mscsoftware.com
[7] MSC.Nastran 2012 Quick Reference Guide. www.mscsoftware.com.
[8] Batrak N.I., Vakhromeev A.M. Methodical aspects of fatigue
testing for passenger car wheels // Questions of structural mechanics and construction reliability: Collection of MADI
scientific works. – Moscow, MADI, 2010. – p. 5-19.