Available online at … · 2017. 1. 25. · b Carraro S.p.A., Via Olmo 37, 35010, Campodarsego (PD), Italy c OZ S.p.A., Via Monte Bianco 10, 35018, San Martino di Lupari (PD), Italy

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Structural Integrity Procedia 00 (2016) 000–000 www.elsevier.com/locate/procedia

2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016.

XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal

Thermo-mechanical modeling of a high pressure turbine blade of an airplane gas turbine engine

P. Brandãoa, V. Infanteb, A.M. Deusc* aDepartment of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,

Portugal bIDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,

Portugal cCeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,

Portugal

Abstract

During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data. © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016.

Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.

* Corresponding author. Tel.: +351 218419991.

E-mail address: [email protected]

Procedia Structural Integrity 2 (2016) 3185–3193

Copyright © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer review under responsibility of the Scientific Committee of ECF21.10.1016/j.prostr.2016.06.397

10.1016/j.prostr.2016.06.397


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2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21.

21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy

A twin disc test rig for contact fatigue characterization of gear materials

G. Meneghettia,*, A. Terrina,b, S. Giacomettic a University of Padova, Department of Industrial Engineering, Via Venezia 1, 35131, Padova, Italy

b Carraro S.p.A., Via Olmo 37, 35010, Campodarsego (PD), Italy c OZ S.p.A., Via Monte Bianco 10, 35018, San Martino di Lupari (PD), Italy

Abstract

Pitting on gear tooth flanks is one of the major causes of failure in power transmissions. Cracks originate at the surface and propagate at a small depth causing the detachment of material debris, which results in craters. Pitting is detrimental as it leads to vibration, noise, loss of efficiency and eventually to the gear un-serviceability. The contact fatigue characterization of gear materials requires a great number of endurance tests on reference gears and is rarely affordable for industries. For this reason, the ISO standard 6336 suggests that tests on rolling pair of disks may be performed in order to compare the pitting durability of either different materials or manufacturing processes. However, the standard does not provide guidance about the geometry of the specimens and the correlation between the results of disc tests and actual gears durability.

In this paper a twin-disc test rig is presented, that was conceived to reproduce the contact pressure and the sliding velocity of gears at one particular point along the tooth profile. A criterion for specimens design is also described. The discs were sized to resemble the working conditions experienced by sun gears mounted in the final drive of an axle for medium power Off-Highway vehicles. In particular, the Lower Point of Single Tooth Contact (LPSTC) was considered to design the tests, being the most favourable location for pitting occurrence because of the high contact pressures and unfavourable kinematic conditions.

© 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21.

Keywords: Pitting; Gears; Contact fatigue; Twin-Disc;

* Corresponding author. Tel.: +39-049-8276751; Fax: +39-049-8276785 E-mail address: [email protected]


ScienceDirect


2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21.

21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy

A twin disc test rig for contact fatigue characterization of gear materials

G. Meneghettia,*, A. Terrina,b, S. Giacomettic a University of Padova, Department of Industrial Engineering, Via Venezia 1, 35131, Padova, Italy

b Carraro S.p.A., Via Olmo 37, 35010, Campodarsego (PD), Italy c OZ S.p.A., Via Monte Bianco 10, 35018, San Martino di Lupari (PD), Italy

Abstract

Pitting on gear tooth flanks is one of the major causes of failure in power transmissions. Cracks originate at the surface and propagate at a small depth causing the detachment of material debris, which results in craters. Pitting is detrimental as it leads to vibration, noise, loss of efficiency and eventually to the gear un-serviceability. The contact fatigue characterization of gear materials requires a great number of endurance tests on reference gears and is rarely affordable for industries. For this reason, the ISO standard 6336 suggests that tests on rolling pair of disks may be performed in order to compare the pitting durability of either different materials or manufacturing processes. However, the standard does not provide guidance about the geometry of the specimens and the correlation between the results of disc tests and actual gears durability.

In this paper a twin-disc test rig is presented, that was conceived to reproduce the contact pressure and the sliding velocity of gears at one particular point along the tooth profile. A criterion for specimens design is also described. The discs were sized to resemble the working conditions experienced by sun gears mounted in the final drive of an axle for medium power Off-Highway vehicles. In particular, the Lower Point of Single Tooth Contact (LPSTC) was considered to design the tests, being the most favourable location for pitting occurrence because of the high contact pressures and unfavourable kinematic conditions.

© 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21.

Keywords: Pitting; Gears; Contact fatigue; Twin-Disc;

* Corresponding author. Tel.: +39-049-8276751; Fax: +39-049-8276785 E-mail address: [email protected]

Copyright © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of the Scientific Committee of ECF21.

http://creativecommons.org/licenses/by-nc-nd/4.0/

http://creativecommons.org/licenses/by-nc-nd/4.0/

http://crossmark.crossref.org/dialog/?doi=10.1016/j.prostr.2016.06.397&domain=pdf

3186 G. Meneghetti et al. / Procedia Structural Integrity 2 (2016) 3185–3193 G. Meneghetti/ Structural Integrity Procedia 00 (2016) 000–000 3

In the present paper, a twin disc test rig for contact fatigue test is presented along with the procedure adopted to design specimens geometry in order to recreate the working conditions of sun gears of a planetary gear set adopted in off highway axles.

2. Twin-Disc test rig

Test facilities where discs are used to resemble the contact conditions of gears date back to 1935 when Merrit developed the first twin-disc rig (Merritt 1935; Mihailidis et al. 2003). Generally speaking, specimens consist of two discs pressed one against the other to obtain the desired contact pressure. The rolling speeds and diameters may be chosen in order to generate a relative motion with different degrees of rolling and sliding between the specimens surface. Among the factors affecting the pitting durability, while material, lubricant and roughness can be easily transferred from the actual gears to the twin-disc tests, the task is not that simple concerning speed and geometry. In fact in a gear mesh the curvature radii of teeth, as well as the sliding speed, change continuously along the involute profile. In particular the sliding speed is null only at the pitch point and increases in module moving toward the tip and root of the tooth. Conversely, discs allow to reproduce only the rolling/sliding conditions at a specific point of the contact path of gears. Nevertheless, since it is much cheaper to use metal discs instead of actual gears and it is easier to inspect and analyse the surface of a disc than the recessed surface of a gear, twin-discs test rig have been widely used to simulate the working conditions responsible of the onset of pitting in gears (Kleemola & Lehtovaara 2009; Li & Kahraman 2013; Sukumaran et al. 2012; Ahlroos et al. 2009; Wilkinson & Olver 1999). However, while twin-disc tests are universally accepted to compare the surface fatigue performances of different materials relative to one another, correlation of disc test results with gears durability is still debated (Totten 2001; Wilkinson & Olver 1999; Flamand et al. 1981).

In this paper a twin-disc rig is presented. A schematic representation of the bench is given in Figure 1. The discs are mounted on a couple of spindles and rotate with the same angular velocity . The desired sliding speed is obtained by using two discs with different radii and :

(2)

The centre distance of the twin disc test rig was chosen equal to 70 mm (Rx1+Rx2=70 mm). One of the spindle is fixed, while the other one can perform small rotations around a pin and is loaded by means of a screw-spring system equipped with a load cell. The number of contacts elapsed by the start of the test is measured by a cycle counter.

Figure 1: Set-up of the twin-disc test rig.

The whole system is suspended by means of anti vibration mounts. A lubrication unit serves the gear box and the spindles bearings as well as a nozzle aimed to keep the contact area of the specimens wet.

The rig is provided with a vision system able to detect the onset of pitting on the specimens surface during the test. During completely automated periodical inspections, discs are rotated by angular steps of 36 degrees and the system grabs ten pictures for each disc through a digital microscope. To ensure cleanliness of the discs the residual lubricant

2 G.Meneghetti/ Structural Integrity Procedia 00 (2016) 000–000

1. Introduction

In couplings between components with non-conformal surfaces such a cams, bearings and gears, high contact pressure may origin even with moderate loads due to the small dimension of the contact area. In rolling contacts the material is subjected to multiple reversals of the shear stress, which may result in rolling contact fatigue (RCF) phenomena. Among these pitting is the most common and it produces craters on the surface of the parts, leading to vibrations, noise and efficiency loss.

In gears cracks usually initiates at the surface of the teeth and they are favoured by the presence of manufacturing furrows, by metal-to-metal contacts between roughness crests and by the pressure of lubricant which promotes their propagation. Driven by the repeated stress cycles generated by contact between the mating parts, cracks grow with small angles to the surface and, eventually, curve up causing the detachment of material debris and leaving craters.

The main factors influencing contact fatigue in gears may be summarized as follows:

Geometry: The curvature radii of the mating surfaces determine both shape and dimension of the contact area. Thus for a given force, the maximum contact pressure and the stress gradients are strongly influenced by the geometry of the contacting bodies (Johnson 1987; Stachowiak & Batchelor 2013).

Material: Composition (Redda et al. 2008), residual stresses (Batista et al. 2000), and microstructure (Hyde 2003) may play an important role in the pitting behaviour of gears. A crucial issue is the presence of defects or inclusions, which may act as stress raiser and become crack initiation sites.

Lubricant: Contact between asperities is particularly undesirable because it concentrates pressure stresses. If rolling speed is high enough, then an elastohydrodinamic (EHD) film of lubricant originates, providing separation between the mating surfaces. The capability of the lubricant to form an adequate EHD film is function of its viscosity, which depends on the composition as well as on the working temperature. High temperature and/or low viscosity lead to thinner lubricant films, making possible contacts between asperities and therefore promoting surface fatigue (Johnson 1987; Stachowiak & Batchelor 2013).

Speed: The rolling speed of the surfaces plays an important role in the development of the EHD film (AGMA 925-A03 2003; ISO-TR 15144 2014 ; Stachowiak & Batchelor 2013). On the contrary, high sliding velocities lead to lubricant overheating and reduction of its viscosity.

Surface finish: the higher is the surface roughness, the greater is the thickness of lubricant film required to avoid contacts between asperities.

The ISO 6336 standard (ISO 6336-Part 2, 2006) dedicated to the calculation of load carrying capacity of gears

analyses the contact between mating teeth assuming two cylinders with parallel axes having the same local radius of curvature of the real gears teeth at the considered point along the involute profile.

The criteria used to validate a gear pair is expressed by the standard in the form:

σ��σ�� (1)

Where the maximum stress �� acting on the tooth flank is compared to a permissible stress ��, which is calculated for the specific material and for the required service life and is based on contact fatigue curves provided by the standard for several different types of material. To evaluate the applied and permissible stresses several factors must be calculated to take into account the influencing factors defined above. The design fatigue curves according to the standard classification (ISO 6336-Part 5, 2006), cannot take into account the wide range of design solutions in terms of materials, treatments and manufacturing processes. Therefore, since tests on actual gears are expensive and time consuming, gear manufacturers need simpler methods to characterize materials and processes.

This work is part of a wider study on the development of simple methods for the evaluation of fatigue behaviour of gear materials with regards of both pitting and bending (Dengo et al. 2015) failures. Concerning contact fatigue, the standard merely mentions the possibility of using discs to analyse the pitting behaviour of gear materials, without providing any information about the geometry of the specimens and the correlation between the results of disc tests and actual gears durability.

G. Meneghetti et al. / Procedia Structural Integrity 2 (2016) 3185–3193 3187 G. Meneghetti/ Structural Integrity Procedia 00 (2016) 000–000 3

In the present paper, a twin disc test rig for contact fatigue test is presented along with the procedure adopted to design specimens geometry in order to recreate the working conditions of sun gears of a planetary gear set adopted in off highway axles.

2. Twin-Disc test rig

Test facilities where discs are used to resemble the contact conditions of gears date back to 1935 when Merrit developed the first twin-disc rig (Merritt 1935; Mihailidis et al. 2003). Generally speaking, specimens consist of two discs pressed one against the other to obtain the desired contact pressure. The rolling speeds and diameters may be chosen in order to generate a relative motion with different degrees of rolling and sliding between the specimens surface. Among the factors affecting the pitting durability, while material, lubricant and roughness can be easily transferred from the actual gears to the twin-disc tests, the task is not that simple concerning speed and geometry. In fact in a gear mesh the curvature radii of teeth, as well as the sliding speed, change continuously along the involute profile. In particular the sliding speed is null only at the pitch point and increases in module moving toward the tip and root of the tooth. Conversely, discs allow to reproduce only the rolling/sliding conditions at a specific point of the contact path of gears. Nevertheless, since it is much cheaper to use metal discs instead of actual gears and it is easier to inspect and analyse the surface of a disc than the recessed surface of a gear, twin-discs test rig have been widely used to simulate the working conditions responsible of the onset of pitting in gears (Kleemola & Lehtovaara 2009; Li & Kahraman 2013; Sukumaran et al. 2012; Ahlroos et al. 2009; Wilkinson & Olver 1999). However, while twin-disc tests are universally accepted to compare the surface fatigue performances of different materials relative to one another, correlation of disc test results with gears durability is still debated (Totten 2001; Wilkinson & Olver 1999; Flamand et al. 1981).

In this paper a twin-disc rig is presented. A schematic representation of the bench is given in Figure 1. The discs are mounted on a couple of spindles and rotate with the same angular velocity . The desired sliding speed is obtained by using two discs with different radii and :

(2)

The centre distance of the twin disc test rig was chosen equal to 70 mm (Rx1+Rx2=70 mm). One of the spindle is fixed, while the other one can perform small rotations around a pin and is loaded by means of a screw-spring system equipped with a load cell. The number of contacts elapsed by the start of the test is measured by a cycle counter.

Figure 1: Set-up of the twin-disc test rig.

The whole system is suspended by means of anti vibration mounts. A lubrication unit serves the gear box and the spindles bearings as well as a nozzle aimed to keep the contact area of the specimens wet.

The rig is provided with a vision system able to detect the onset of pitting on the specimens surface during the test. During completely automated periodical inspections, discs are rotated by angular steps of 36 degrees and the system grabs ten pictures for each disc through a digital microscope. To ensure cleanliness of the discs the residual lubricant


1. Introduction

In couplings between components with non-conformal surfaces such a cams, bearings and gears, high contact pressure may origin even with moderate loads due to the small dimension of the contact area. In rolling contacts the material is subjected to multiple reversals of the shear stress, which may result in rolling contact fatigue (RCF) phenomena. Among these pitting is the most common and it produces craters on the surface of the parts, leading to vibrations, noise and efficiency loss.

In gears cracks usually initiates at the surface of the teeth and they are favoured by the presence of manufacturing furrows, by metal-to-metal contacts between roughness crests and by the pressure of lubricant which promotes their propagation. Driven by the repeated stress cycles generated by contact between the mating parts, cracks grow with small angles to the surface and, eventually, curve up causing the detachment of material debris and leaving craters.

The main factors influencing contact fatigue in gears may be summarized as follows:

Geometry: The curvature radii of the mating surfaces determine both shape and dimension of the contact area. Thus for a given force, the maximum contact pressure and the stress gradients are strongly influenced by the geometry of the contacting bodies (Johnson 1987; Stachowiak & Batchelor 2013).

Material: Composition (Redda et al. 2008), residual stresses (Batista et al. 2000), and microstructure (Hyde 2003) may play an important role in the pitting behaviour of gears. A crucial issue is the presence of defects or inclusions, which may act as stress raiser and become crack initiation sites.

Lubricant: Contact between asperities is particularly undesirable because it concentrates pressure stresses. If rolling speed is high enough, then an elastohydrodinamic (EHD) film of lubricant originates, providing separation between the mating surfaces. The capability of the lubricant to form an adequate EHD film is function of its viscosity, which depends on the composition as well as on the working temperature. High temperature and/or low viscosity lead to thinner lubricant films, making possible contacts between asperities and therefore promoting surface fatigue (Johnson 1987; Stachowiak & Batchelor 2013).

Speed: The rolling speed of the surfaces plays an important role in the development of the EHD film (AGMA 925-A03 2003; ISO-TR 15144 2014 ; Stachowiak & Batchelor 2013). On the contrary, high sliding velocities lead to lubricant overheating and reduction of its viscosity.

Surface finish: the higher is the surface roughness, the greater is the thickness of lubricant film required to avoid contacts between asperities.

The ISO 6336 standard (ISO 6336-Part 2, 2006) dedicated to the calculation of load carrying capacity of gears

analyses the contact between mating teeth assuming two cylinders with parallel axes having the same local radius of curvature of the real gears teeth at the considered point along the involute profile.

The criteria used to validate a gear pair is expressed by the standard in the form:

σ��σ�� (1)

Where the maximum stress �� acting on the tooth flank is compared to a permissible stress ��, which is calculated for the specific material and for the required service life and is based on contact fatigue curves provided by the standard for several different types of material. To evaluate the applied and permissible stresses several factors must be calculated to take into account the influencing factors defined above. The design fatigue curves according to the standard classification (ISO 6336-Part 5, 2006), cannot take into account the wide range of design solutions in terms of materials, treatments and manufacturing processes. Therefore, since tests on actual gears are expensive and time consuming, gear manufacturers need simpler methods to characterize materials and processes.

This work is part of a wider study on the development of simple methods for the evaluation of fatigue behaviour of gear materials with regards of both pitting and bending (Dengo et al. 2015) failures. Concerning contact fatigue, the standard merely mentions the possibility of using discs to analyse the pitting behaviour of gear materials, without providing any information about the geometry of the specimens and the correlation between the results of disc tests and actual gears durability.


3. Specimens design

Among gear boxes, planetary gear sets are particularly critical concerning pitting resistance. Sun gears indeed mesh simultaneously with more planet gears and thus perform several load cycles for each revolution. Moreover they are usually small and therefore the contact area in the mesh is thin, resulting in an increased pressure. In vehicles for agricultural applications the working conditions of sun gears of planetary gear sets in the wheel hubs are even more demanding due to the low operating speeds which reduces the capability of the lubricant to form an adequate EHD film. The most critical point along the tooth profile of a sun gear is the Lower Point of Single Tooth Contact (LPSTC) for several reasons. First of all, this is the point with the smallest curvature radius in the region of the flank where the load is carried by a single pair of teeth. Secondly, the slide-to-roll ratio (SRR) is negative (

Figure 3) in the dedendum of both sun and planet gears, therefore the direction of friction forces (sliding direction) is opposite with respect to the motion of the counter surface (rolling direction).

The SRR is defined for each of the two mating bodies as the ratio between the relative speed of the counter surface

(sliding speed) and the average absolute tangential speed of the two surfaces in the contact point (rolling speed). As an example, considering the tangential speeds of the two points of contact of two mating bodies ��and ��, the SRR relative to body 1 is given by:

��

�� 2 (3)

The negative SRR in the dedendum of sun gears implies that being the contact stress of sun gear and planet gear

the same, the former tends to fail at a lower number of cycles than the latter. Indeed, friction forces stretch the top layers of the tooth flank before the passage of the contact. Thus, the lubricant tends to wedge between the free surfaces of initiated cracks and then to be pressurised by the rolling surfaces, promoting crack propagation. Conversely, in areas with rolling and sliding velocities in the same direction cracks are closed by compression of the top layers before the contact of mating surfaces occurs and hence have a lower tendency to propagate due to hydraulic pressure of the lubricant. Therefore, in the present work the contact conditions at the LPSTC of a sun gear of a medium power axle for agricultural application were taken as reference and recreated through an adequate design of discs according to the following.

The main design data of the planetary gear set are summarized in Table 1.

Table 1: Main features of the planetary gear set taken as reference for specimens design. Sun Planet Ring

Pressure Angle, α [deg] 20 20 20

Module, m [mm] 2.9295 2.9295 2.9295

Number of Teeth, z 15 31 81

Centre distance [mm] 72.05 72.05 72.05

Case Hardening Depth [mm]* 0.6÷1.1 0.6÷0.8 0.22÷0.45

Surface Hardness H.R.C. 58÷62 58÷62 62÷66

Core Hardness H.R.C. 36÷42 36÷42 22÷27

Residual Austenite (% max) 20 20 20

Material 17NiCrMo6-4 17NiCrMo6-4 20MnCr5

* Distance from surface to point where hardness is 550 HV

Figure 4 shows the nominal contact pressure along the sun gear tooth profile relevant to a wheel torque of 10320

Nm, which is the design value adopted by the manufacturer to perform endurance tests on the axle.


is removed from the surface by compressed air. The microscope and the specimens area are obscured from ambient light by means of a cover; a number of leds provides repeatable light conditions. However, the surface geometry originate undesired shadows on the image, which may cause malfunctions in the algorithm for pits recognition. In order to minimize the effect of different light conditions, the images are processed as follows:

1) A region of interest (ROI) is defined in the image and the gray level of each pixel is evaluated; 2) For each pixels row in the ROI, a moving average over the gray levels of 100 pixels is calculated; 3) The averaged frame is subtracted to the original image; 4) All pixels having a grey level greater than a predefined threshold are considered to belong to a damaged

area; 5) The damages may be filtered by shape and dimensions in order to discard all candidate defects which can

not be attributed to pitting damage; Finally the total extension of damaged area is compared with a target defined by the user and adopted as failure criterion to stop the test.

Figure 2: example of image acquisition and processing on a pair of cylindrical specimens with chamfered edges.

Figure 3 – Slide-to-Roll Ratio along the tooth profile.


3. Specimens design

Among gear boxes, planetary gear sets are particularly critical concerning pitting resistance. Sun gears indeed mesh simultaneously with more planet gears and thus perform several load cycles for each revolution. Moreover they are usually small and therefore the contact area in the mesh is thin, resulting in an increased pressure. In vehicles for agricultural applications the working conditions of sun gears of planetary gear sets in the wheel hubs are even more demanding due to the low operating speeds which reduces the capability of the lubricant to form an adequate EHD film. The most critical point along the tooth profile of a sun gear is the Lower Point of Single Tooth Contact (LPSTC) for several reasons. First of all, this is the point with the smallest curvature radius in the region of the flank where the load is carried by a single pair of teeth. Secondly, the slide-to-roll ratio (SRR) is negative (

Figure 3) in the dedendum of both sun and planet gears, therefore the direction of friction forces (sliding direction) is opposite with respect to the motion of the counter surface (rolling direction).

The SRR is defined for each of the two mating bodies as the ratio between the relative speed of the counter surface

(sliding speed) and the average absolute tangential speed of the two surfaces in the contact point (rolling speed). As an example, considering the tangential speeds of the two points of contact of two mating bodies ��and ��, the SRR relative to body 1 is given by:

��

�� 2 (3)

The negative SRR in the dedendum of sun gears implies that being the contact stress of sun gear and planet gear

the same, the former tends to fail at a lower number of cycles than the latter. Indeed, friction forces stretch the top layers of the tooth flank before the passage of the contact. Thus, the lubricant tends to wedge between the free surfaces of initiated cracks and then to be pressurised by the rolling surfaces, promoting crack propagation. Conversely, in areas with rolling and sliding velocities in the same direction cracks are closed by compression of the top layers before the contact of mating surfaces occurs and hence have a lower tendency to propagate due to hydraulic pressure of the lubricant. Therefore, in the present work the contact conditions at the LPSTC of a sun gear of a medium power axle for agricultural application were taken as reference and recreated through an adequate design of discs according to the following.

The main design data of the planetary gear set are summarized in Table 1.

Table 1: Main features of the planetary gear set taken as reference for specimens design. Sun Planet Ring

Pressure Angle, α [deg] 20 20 20

Module, m [mm] 2.9295 2.9295 2.9295

Number of Teeth, z 15 31 81

Centre distance [mm] 72.05 72.05 72.05

Case Hardening Depth [mm]* 0.6÷1.1 0.6÷0.8 0.22÷0.45

Surface Hardness H.R.C. 58÷62 58÷62 62÷66

Core Hardness H.R.C. 36÷42 36÷42 22÷27

Residual Austenite (% max) 20 20 20

Material 17NiCrMo6-4 17NiCrMo6-4 20MnCr5

* Distance from surface to point where hardness is 550 HV

Figure 4 shows the nominal contact pressure along the sun gear tooth profile relevant to a wheel torque of 10320

Nm, which is the design value adopted by the manufacturer to perform endurance tests on the axle.


is removed from the surface by compressed air. The microscope and the specimens area are obscured from ambient light by means of a cover; a number of leds provides repeatable light conditions. However, the surface geometry originate undesired shadows on the image, which may cause malfunctions in the algorithm for pits recognition. In order to minimize the effect of different light conditions, the images are processed as follows:

1) A region of interest (ROI) is defined in the image and the gray level of each pixel is evaluated; 2) For each pixels row in the ROI, a moving average over the gray levels of 100 pixels is calculated; 3) The averaged frame is subtracted to the original image; 4) All pixels having a grey level greater than a predefined threshold are considered to belong to a damaged

area; 5) The damages may be filtered by shape and dimensions in order to discard all candidate defects which can

not be attributed to pitting damage; Finally the total extension of damaged area is compared with a target defined by the user and adopted as failure criterion to stop the test.

Figure 2: example of image acquisition and processing on a pair of cylindrical specimens with chamfered edges.

Figure 3 – Slide-to-Roll Ratio along the tooth profile.


attain its highest value is proportional to the width 2a of the contact area, such depth is equal to 0.16 mm for the actual gears, while it would have been 0.4 mm in the case of cylindrical specimens. With a wider contact strip (up to 10m in absence of chamfers), lower value of 2a could have been obtained but the force necessary to develop the required contact pressure would have been too high for the bench set-up (in the case of 2b=10mm, 2a=0.52mm and the force needed to obtain a contact pressure of 1690 MPa is 13873N). Therefore, to reduce the relative curvature radius of the specimens, and consequently the contact area, one of the two discs was crowned (not both of them in order to facilitate their manufacturing). A good approximation of the actual stress field in sun gears was obtained with the specimens geometry shown in Table 2 and Figure 5, where the stresses under the point of contact were calculated for both discs and tooth using Hertz theory of contact between elastic bodies(Johnson 1987; Boresi & Schmidt 2003; Williams & Dwyer-Joyce 2001).

Table 2: Features of specimens and cylinders equivalent to the teeth profiles evaluated at the LPSTC of sun gear.

Sun-Planet Equivalent Cylinders Specimens

Symbol Value Symbol Value

Curvature radius along the x direction body 1 [mm] �� 9.13 �� 35.13

Curvature radius along the y direction body 1 [mm] �� ∞ �� 15


Curvature radius along the x direction body 2 [mm] �� ∞ �� ∞

Reduced curvature radius [mm] �′ 6.7 �′ 8.07

Rolling speed [m/s]* �� 0.21 �� 7.33

Sliding speed [m/s] * �� 0.05 �� 0.05

Contact area dimension in the x direction [mm] * 2a 0.40 2a 0.80

Contact area dimension in the y direction [mm] * 2b 49 2b 0.72

* Parameters are evaluated for a typical wheel speed of 30 rpm [m/s] in the case of gears and for a spindle speed of 2000 rpm in the case of specimens. The applied Hertzian pressure is 1690 MPa for both the cases.

Figure 5: Contact stress field beneath the surface of gears and specimens. Contact pressure in gears teeth is calculated at the LPSTC of sun gear for a wheel torque of 10320 Nm.


Figure 4: Nominal contact pressure and slide to roll ratio calculated along the tooth profile according to ISO-TR 15144 (2014) for the analysed

sun gear and planet with a wheel torque of 10320Nm.

The highest value of contact pressure obtained at the LPSTC, �� 1�� is accompanied by a negative value of SRR=-0.24.

The disc specimens were manufactured using the same material of the sun gear reported in Table 1 and, in order to reduce as much as possible the duration of the tests, specimens were rotated at 2000 rpm. Some authors (Sukumaran et al. 2012; Ahlroos et al. 2009; Li & Kahraman 2013) proposed to recreate the same slide to roll ratio of gears, with the aim to reproduce the lubrication conditions of the real gears under analysis. Indeed, according to the theory of elastohydrodynamic lubrication the thickness of the lubricant film depends mainly on the rolling speed of the mating bodies and on the viscosity of the fluid, which decreases the higher is the temperature increase due to the sliding velocity. However, in agricultural applications the operating speeds are very low and the EHD film of lubricant is not likely to form. As an example, in the present application the typical pitch line speed of the sun gear is 0.5 m/s, far below the range of validity of the method for film thickness calculation proposed by ISO/TR 15144 (2014), which is applicable for pitch line velocities greater than 2m/s. Despite the higher rolling speed of the discs, it is too small to allow the formation of an EHD film thick enough to prevent contact among asperities. Actually, to evaluate the EHD film thickness in the elliptical contact occurring in the discs, Hamrock and Dowson’s formula (Hamrock & Dowson 1978; Stachowiak & Batchelor 2013) would lead to a film thickness of 0.2 μm, while the disc roughness is �� 1��. In presence of such small ratios between the thickness of the lubricant film and the surface roughness, the rolling speed was thought to have poor influence on the test results. On the contrary, sliding speed was considered of paramount concern as it may influence friction-related mechanisms such as scuffing and surface distress. Therefore the radii of discs were chosen in order to obtain the same sliding speed observed at the LPSTC of sun gears. Since pitting is expected to manifest at first in the smaller disc, which is the one subjected to negative SRR, the lower diameter was assigned to the cylindrical disc because image processing is easier than for the crowned disc, as explained later on. Using n=2000 rpm and vs=0.05 m/s in Eq. (2), R1x and R2x were calculated and are reported in Table 2.

Attention was paid to recreate the field of the maximum shear stress (defined as semi-difference between the maximum and minimum principal stresses) beneath the point of contact, because it is often considered a driving parameter for contact fatigue failures (Boresi & Schmidt 2003; Hyde 2003):

�� 1 ��3

2 (4)

However, the curvature radii of sun and planet gears were too small to be recreated with two cylindrical discs because of the 70 mm centre distance of the twin disc test rig. The use of two cylindrical specimens would have led to a width 2a of contact area (see Fig. 5) too higher than that of the sun and planet gears and therefore to a stress field beneath the surface very different from the one of the actual gears. As an example, for a wheel torque of 10320 Nm, the width 2a of the contact area is 0.4 mm for the actual gears, as reported in Fig. 5, while it would have equalled 1mm for the same applied maximum contact stress z if specimens with chamfered edges and a cylindrical contact strip of width 2 mm (see Figure 2) would have been adopted. Moreover, since the depth at which the maximum shear stress


attain its highest value is proportional to the width 2a of the contact area, such depth is equal to 0.16 mm for the actual gears, while it would have been 0.4 mm in the case of cylindrical specimens. With a wider contact strip (up to 10m in absence of chamfers), lower value of 2a could have been obtained but the force necessary to develop the required contact pressure would have been too high for the bench set-up (in the case of 2b=10mm, 2a=0.52mm and the force needed to obtain a contact pressure of 1690 MPa is 13873N). Therefore, to reduce the relative curvature radius of the specimens, and consequently the contact area, one of the two discs was crowned (not both of them in order to facilitate their manufacturing). A good approximation of the actual stress field in sun gears was obtained with the specimens geometry shown in Table 2 and Figure 5, where the stresses under the point of contact were calculated for both discs and tooth using Hertz theory of contact between elastic bodies(Johnson 1987; Boresi & Schmidt 2003; Williams & Dwyer-Joyce 2001).

Table 2: Features of specimens and cylinders equivalent to the teeth profiles evaluated at the LPSTC of sun gear.

Sun-Planet Equivalent Cylinders Specimens

Symbol Value Symbol Value


Curvature radius along the y direction body 1 [mm] �� ∞ �� 15


Curvature radius along the x direction body 2 [mm] �� ∞ �� ∞

Reduced curvature radius [mm] �′ 6.7 �′ 8.07

Rolling speed [m/s]* �� 0.21 �� 7.33

Sliding speed [m/s] * �� 0.05 �� 0.05

Contact area dimension in the x direction [mm] * 2a 0.40 2a 0.80

Contact area dimension in the y direction [mm] * 2b 49 2b 0.72

* Parameters are evaluated for a typical wheel speed of 30 rpm [m/s] in the case of gears and for a spindle speed of 2000 rpm in the case of specimens. The applied Hertzian pressure is 1690 MPa for both the cases.

Figure 5: Contact stress field beneath the surface of gears and specimens. Contact pressure in gears teeth is calculated at the LPSTC of sun gear for a wheel torque of 10320 Nm.


Figure 4: Nominal contact pressure and slide to roll ratio calculated along the tooth profile according to ISO-TR 15144 (2014) for the analysed

sun gear and planet with a wheel torque of 10320Nm.

The highest value of contact pressure obtained at the LPSTC, �� 1�� is accompanied by a negative value of SRR=-0.24.

The disc specimens were manufactured using the same material of the sun gear reported in Table 1 and, in order to reduce as much as possible the duration of the tests, specimens were rotated at 2000 rpm. Some authors (Sukumaran et al. 2012; Ahlroos et al. 2009; Li & Kahraman 2013) proposed to recreate the same slide to roll ratio of gears, with the aim to reproduce the lubrication conditions of the real gears under analysis. Indeed, according to the theory of elastohydrodynamic lubrication the thickness of the lubricant film depends mainly on the rolling speed of the mating bodies and on the viscosity of the fluid, which decreases the higher is the temperature increase due to the sliding velocity. However, in agricultural applications the operating speeds are very low and the EHD film of lubricant is not likely to form. As an example, in the present application the typical pitch line speed of the sun gear is 0.5 m/s, far below the range of validity of the method for film thickness calculation proposed by ISO/TR 15144 (2014), which is applicable for pitch line velocities greater than 2m/s. Despite the higher rolling speed of the discs, it is too small to allow the formation of an EHD film thick enough to prevent contact among asperities. Actually, to evaluate the EHD film thickness in the elliptical contact occurring in the discs, Hamrock and Dowson’s formula (Hamrock & Dowson 1978; Stachowiak & Batchelor 2013) would lead to a film thickness of 0.2 μm, while the disc roughness is �� 1��. In presence of such small ratios between the thickness of the lubricant film and the surface roughness, the rolling speed was thought to have poor influence on the test results. On the contrary, sliding speed was considered of paramount concern as it may influence friction-related mechanisms such as scuffing and surface distress. Therefore the radii of discs were chosen in order to obtain the same sliding speed observed at the LPSTC of sun gears. Since pitting is expected to manifest at first in the smaller disc, which is the one subjected to negative SRR, the lower diameter was assigned to the cylindrical disc because image processing is easier than for the crowned disc, as explained later on. Using n=2000 rpm and vs=0.05 m/s in Eq. (2), R1x and R2x were calculated and are reported in Table 2.

Attention was paid to recreate the field of the maximum shear stress (defined as semi-difference between the maximum and minimum principal stresses) beneath the point of contact, because it is often considered a driving parameter for contact fatigue failures (Boresi & Schmidt 2003; Hyde 2003):

�� 1 ��3

2 (4)

However, the curvature radii of sun and planet gears were too small to be recreated with two cylindrical discs because of the 70 mm centre distance of the twin disc test rig. The use of two cylindrical specimens would have led to a width 2a of contact area (see Fig. 5) too higher than that of the sun and planet gears and therefore to a stress field beneath the surface very different from the one of the actual gears. As an example, for a wheel torque of 10320 Nm, the width 2a of the contact area is 0.4 mm for the actual gears, as reported in Fig. 5, while it would have equalled 1mm for the same applied maximum contact stress z if specimens with chamfered edges and a cylindrical contact strip of width 2 mm (see Figure 2) would have been adopted. Moreover, since the depth at which the maximum shear stress


Treatments. Tribology Transactions, 42(3), 503–510. Wilkinson, C.M.R., Olver, A. V., 1999. The Durability of Gear and Disc Specimens—Part II: Post Failure Examination and Gear-Disc Correlation.

Tribology Transactions, 42(3), 610–618. Williams, J.A., Dwyer-Joyce, R.S., 2001. Contact Between Solid Surfaces. In C. Press, ed. Modern Tribology Handbook. 121–162.


4. Conclusions

A twin-disc test rig for contact fatigue characterization of materials was developed. The device is aimed to reproduce the most influencing operating conditions of gears at the most critical point along the tooth profile with regard to pitting damage. To allow the execution of complete tests without the need for inspection by an operator, the rig has been provided with a vision system conceived to automatically detect the onset of pitting on the surface of specimens. The tests are stopped automatically when a given percentage of worn surface is obtained.

The criteria used to design specimens in order to recreate as much as possible the operating conditions of a specific planetary gear box have been as follows: the stress field below the most critical point of contact of gears with regard to pitting has been recreated by using a proper crown radius on one of the discs; moreover, since the low operating speed of gears prevents the formation of a EHD film, the absolute sliding speed was chosen as the main kinematic parameter to be recreated in discs. Such choice is in contrast with most of the existing literature which claims the SRR as the relevant parameter, but in applications where speeds are high enough to form an EHD film of lubricant, which is not the present case.

Although preliminary tests on specimens with different geometries showed encouraging results, a test campaign must be performed to prove the correlation between gears and specimens durability, the topic being still debated in the existing literature. It should be pointed out that durability is expected to be greater for disc specimens than for gears because of the regular geometry of the specimens that reduces the risk of geometric stress concentration due to local reduction of the curvature radius. Moreover, in twin-disc tests the expulsion of debris from the contact area is easier because of the smaller contact length in axial direction of disc with respect to gears, which should result in lower risks of indentation and then creation of possible sites for crack nucleation. Finally, the lubrication of discs surfaces might be favoured by the higher rolling speed, even if a full separation between the crests of asperities is not expected.

Acknowledgements

The authors would like to acknowledge Carraro S.p.a. for the financial support to the specimens manufacturing.

References

AGMA 925-A03 Effects of Lubrication on Gear Surface Distress, 2003. Ahlroos, T. et al., 2009. Twin disc micropitting tests. Tribology International, 42(10), 1460–1466. Batista, Dias, Lebrun, L.F. and I., 2000. Contact fatigue of automotive gears: evolution and effects of residual stresses introduced by surface

treatments. Fatigue, Fracture of Engineering Materials and Structures, 23(3), 217–228. Boresi, A.P., Schmidt, R.J., 2003. Advanced mechanics of materials J. W., Sons, ed., Dengo, C., Meneghetti, G., Dabalà, M., 2015. Experimental analysis of bending fatigue strength of plain and notched case-hardened gear steels.

International Journal of Fatigue, 80, 145–161. Flamand, L., Berthe, D., Godet, M., 1981. Simulation of Hertzian Contacts Found in Spur Gears with a High Performance Disk Machine. Journal

of Mechanical Design, 103(1), p.204. Hamrock, B.J., Dowson, D., 1978. Minimum film thickness in elliptical contacts for different regimes of fluid film lubrication. NASA Technical

Paper, 1342. Hyde, R.S., 2003. Contact fatigue of hardened steels. In ASM handbook, 19. Ohio, p. 1749. ISO 6336:2006 Calculation of load carrying capacity of spur and helical gears. ISO/TR 15144-1:2014 - Calculation of micropitting load capacity of cylindrical spur and helical gears -- Part 1: Introduction and basic principles. Johnson, K.L., 1987. Contact Mechanics, Cambridge University Press. Kleemola, J., Lehtovaara, A., 2009. Experimental simulation of gear contact along the line of action. Tribology International, 42(10), 1453–1459. Li, S., Kahraman, A., 2013. Micro-pitting fatigue lives of lubricated point contacts: Experiments and model validation. International Journal of

Fatigue, 48, 9–18. Merritt, H.E., 1935. Worm gear performance. ARCHIVE: Proceedings of the Institution of Mechanical Engineers 1847-1982 (vols 1-196),

129(1935), 127–194. Mihailidis, A. et al., 2003. Friction behavior of FVA reference mineral oils obtained by a newly designed two disk test rig. In Int. Conf. on Power

Transmissions. 32–37. Redda, D.T., NakanishI, T., Deng, G., 2008. Surface Durability of Developed Cr-Mo-Si Steel under Rolling-Sliding Contact. Journal of Advanced

Mechanical Design, Systems, and Manufacturing, 2(2), 214–221. Stachowiak, G., Batchelor, A.W., 2013. Engineering Tribology, Butterworth-Heinemann. Sukumaran, J. et al., 2012. Modelling gear contact with twin-disc setup. Tribology International, 49, 1–7. Totten, G.E. et al., 2001. Bench Testing of Industrial Fluid Lubrication and Wear Properties, ASTM International. Wilkinson, C.M.R., Olver, A. V., 1999. The Durability of Gear and Disc Specimens — Part I: The Effect of Some Novel Materials and Surface


Treatments. Tribology Transactions, 42(3), 503–510. Wilkinson, C.M.R., Olver, A. V., 1999. The Durability of Gear and Disc Specimens—Part II: Post Failure Examination and Gear-Disc Correlation.

Tribology Transactions, 42(3), 610–618. Williams, J.A., Dwyer-Joyce, R.S., 2001. Contact Between Solid Surfaces. In C. Press, ed. Modern Tribology Handbook. 121–162.


4. Conclusions

A twin-disc test rig for contact fatigue characterization of materials was developed. The device is aimed to reproduce the most influencing operating conditions of gears at the most critical point along the tooth profile with regard to pitting damage. To allow the execution of complete tests without the need for inspection by an operator, the rig has been provided with a vision system conceived to automatically detect the onset of pitting on the surface of specimens. The tests are stopped automatically when a given percentage of worn surface is obtained.

The criteria used to design specimens in order to recreate as much as possible the operating conditions of a specific planetary gear box have been as follows: the stress field below the most critical point of contact of gears with regard to pitting has been recreated by using a proper crown radius on one of the discs; moreover, since the low operating speed of gears prevents the formation of a EHD film, the absolute sliding speed was chosen as the main kinematic parameter to be recreated in discs. Such choice is in contrast with most of the existing literature which claims the SRR as the relevant parameter, but in applications where speeds are high enough to form an EHD film of lubricant, which is not the present case.

Although preliminary tests on specimens with different geometries showed encouraging results, a test campaign must be performed to prove the correlation between gears and specimens durability, the topic being still debated in the existing literature. It should be pointed out that durability is expected to be greater for disc specimens than for gears because of the regular geometry of the specimens that reduces the risk of geometric stress concentration due to local reduction of the curvature radius. Moreover, in twin-disc tests the expulsion of debris from the contact area is easier because of the smaller contact length in axial direction of disc with respect to gears, which should result in lower risks of indentation and then creation of possible sites for crack nucleation. Finally, the lubrication of discs surfaces might be favoured by the higher rolling speed, even if a full separation between the crests of asperities is not expected.

Acknowledgements

The authors would like to acknowledge Carraro S.p.a. for the financial support to the specimens manufacturing.

References

AGMA 925-A03 Effects of Lubrication on Gear Surface Distress, 2003. Ahlroos, T. et al., 2009. Twin disc micropitting tests. Tribology International, 42(10), 1460–1466. Batista, Dias, Lebrun, L.F. and I., 2000. Contact fatigue of automotive gears: evolution and effects of residual stresses introduced by surface

treatments. Fatigue, Fracture of Engineering Materials and Structures, 23(3), 217–228. Boresi, A.P., Schmidt, R.J., 2003. Advanced mechanics of materials J. W., Sons, ed., Dengo, C., Meneghetti, G., Dabalà, M., 2015. Experimental analysis of bending fatigue strength of plain and notched case-hardened gear steels.

International Journal of Fatigue, 80, 145–161. Flamand, L., Berthe, D., Godet, M., 1981. Simulation of Hertzian Contacts Found in Spur Gears with a High Performance Disk Machine. Journal

of Mechanical Design, 103(1), p.204. Hamrock, B.J., Dowson, D., 1978. Minimum film thickness in elliptical contacts for different regimes of fluid film lubrication. NASA Technical

Paper, 1342. Hyde, R.S., 2003. Contact fatigue of hardened steels. In ASM handbook, 19. Ohio, p. 1749. ISO 6336:2006 Calculation of load carrying capacity of spur and helical gears. ISO/TR 15144-1:2014 - Calculation of micropitting load capacity of cylindrical spur and helical gears -- Part 1: Introduction and basic principles. Johnson, K.L., 1987. Contact Mechanics, Cambridge University Press. Kleemola, J., Lehtovaara, A., 2009. Experimental simulation of gear contact along the line of action. Tribology International, 42(10), 1453–1459. Li, S., Kahraman, A., 2013. Micro-pitting fatigue lives of lubricated point contacts: Experiments and model validation. International Journal of

Fatigue, 48, 9–18. Merritt, H.E., 1935. Worm gear performance. ARCHIVE: Proceedings of the Institution of Mechanical Engineers 1847-1982 (vols 1-196),

129(1935), 127–194. Mihailidis, A. et al., 2003. Friction behavior of FVA reference mineral oils obtained by a newly designed two disk test rig. In Int. Conf. on Power

Transmissions. 32–37. Redda, D.T., NakanishI, T., Deng, G., 2008. Surface Durability of Developed Cr-Mo-Si Steel under Rolling-Sliding Contact. Journal of Advanced

Mechanical Design, Systems, and Manufacturing, 2(2), 214–221. Stachowiak, G., Batchelor, A.W., 2013. Engineering Tribology, Butterworth-Heinemann. Sukumaran, J. et al., 2012. Modelling gear contact with twin-disc setup. Tribology International, 49, 1–7. Totten, G.E. et al., 2001. Bench Testing of Industrial Fluid Lubrication and Wear Properties, ASTM International. Wilkinson, C.M.R., Olver, A. V., 1999. The Durability of Gear and Disc Specimens — Part I: The Effect of Some Novel Materials and Surface

Documents

Available online at … · 2017. 1. 25. · b Carraro S.p.A., Via Olmo 37, 35010, Campodarsego (PD), Italy c OZ S.p.A., Via Monte Bianco 10, 35018, San Martino di Lupari (PD), Italy