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The influence of different types of loading on false brinelling
Wear 440–441 (2019) 203097
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The influence of different types of loading on false brinelling Khosro Fallahnezhad *, Osama Brinji, Ajay Desai, Paul A. Meehan University of Queensland, Brisbane, Australia
A R T I C L E I N F O
A B S T R A C T
Keywords: False brinelling Finite element Fretting wear False brinelling test rig Bearing damage
An experimental and numerical study was developed to investigate the influence of radial load and the amplitude of rotational and lateral vibrations on false brinelling damage in railway cylindrical roller bearings. For this objective, a novel false brinelling test-rig was designed and fabricated to conduct both linear vibration and rotational displacement tests. A reciprocating pin-on-cylinder wear test was also conducted to determine the friction and wear coefficients of the bearing, under different frequencies. These experimental results where then used to verify a developed finite element model for false brinelling of an individual roller. The reciprocating wear test results show that the friction coefficient is almost constant and does not signifi cantly, change, by changing the frequency. The wear coefficient, however, can be estimated by an exponential function of the frequency. The experimental and numerical results showed that reducing the bearing static radial load and increasing the amplitude of linear and rotational vibration, intensifies the false brinelling damage. It was also shown that by increasing the bearing radial load, the false brinelling wear profile changes from a Ushape to W-shape.
1. Introduction False brinelling is a type of fretting wear which occurs in the roller bearings, due to intentional and unintentional linear or rotational vi brations. Similar to fretting wear, false brinelling is caused by oscilla tory, low amplitude sliding that occurs at the roller-raceway interface [1,2]. This has been seen in several industrial applications, in which intentional oscillations [3,4] or unintentional vibrating oscillations [5, 6] occurs. Typical circumstances when a bearing may experience false brinelling are when the bearing is in transportation or when being stored in an environment exposed to vibrations [2,7–9]. The previous experi mental studies, conducted on oscillating bearings [10,11], highlighted the complexity of the degradation scenarios, due to the small area of contact and small amplitude of oscillation, role of the rheology of third body at the contact area and the influence of the system kinematics and dynamics on the local behavior at contact surfaces. Therefore, to un derstand the wear process, the tribological analysis needs to be done at the contact scale, to consider correct boundary conditions [4,12]. Over the past decade, numerical tribology has become a powerful tool to investigate contact issues and to simulate the wear process. Recently, different numerical techniques, such as adaptive and explicit finite element methods and discrete element simulations has been used to investigate fretting wear processes including false brinelling [6,13,14].
Maruschak et al. [11] and Sotnykov et al. [15] investigated false brinelling damage in a roller bearing used in a continuous billet-casting machine (CBCM). They showed that the surfaces of the bearing races were damaged, due to false brinelling caused by a dynamic loading. They explained this mechanism by a multi-level description of defor mation and fracture processes that accompany the wear of a bearing’s surface. They concluded that several complex deformation and friction mechanisms at meso- and macro-levels contribute in the wear process. Massi et al. [12], proposed a model to predict false brinelling. They analyzed the influence of the aircraft engines vibrations on the contact stresses of rolling bearings of the bleed system valves. However, their FE model, just predicted the stress distribution at the contact area between ball and race rather than the wear damage, caused by imposed vibrations. The approaches that have been used to simulate fretting wear can be used to model false brinelling, such as in Refs. [16–18]. McColl et al. [19,20] presented a finite element model to simulate fretting wear in a pin-on-disc set up, based on Archard’s equation [21]. This model has been used to simulate fretting wear in different applications [20,22–25]. Fouvry proposed that, using the accumulated friction energy dissipated through the interface the wear volume can be estimated. This can be calculated by integrating the friction work in the wear analysis, [26]. He showed the linear relation between wear volume and dissipated energy
* Corresponding author. E-mail addresses: [email protected] (K. Fallahnezhad), [email protected] (O. Brinji), [email protected] (A. Desai), [email protected] (P.A. Meehan). https://doi.org/10.1016/j.wear.2019.203097 Received 23 July 2019; Received in revised form 8 October 2019; Accepted 18 October 2019 Available online 23 October 2019 0043-1648/© 2019 Elsevier B.V. All rights reserved.
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trains. A false brinelling monitoring system was designed and installed to record the vibration and rotational motion of the bearing, during the train’s transportation and used as input for a 2D FE model. It was found that the wear profile is highly dependent on the accumulated slip of the contact area, over the process of false brinelling. Based on the FE results, for a railway bearing, under the transportation condition, they showed that the existence of stick-slip regions in the contact area causes the development of W shape wear marks along the lateral and axial direc tion of the bearing depending on the amplitude of the normal load and vibration. The W-shape marks have been seen in the false brinelling marks of a damaged bearing, along the axial direction. At present, no research has systematically investigated, both numerically and experimentally the influence of external parameters, such as amplitudes of radial force, vibration and rotational displacement on the occurrence and severity of the false brinelling wear in a cylin drical bearing. To address this, in this study, a false brinelling experi mental test rig was developed to simulate false brinelling of a cylindrical roller bearing, during transportation. A set of reciprocating pin-oncylinder wear test was performed to determine the frictional and wear coefficients of the bearing alloy, for different frequencies. Moreover, a 3D FE model was developed and used to simulate false brinelling caused by vibration and rotational displacement. The experimental and modelling results were used to investigate the influence of lateral and rotational vibrations, and radial force, on the false brinelling wear damage.
Fig. 1. Cylindrical bearing and its local directions.
and proved that, different parameters, such as contact profile, amplitude and frequency of sliding, and normal force can influence the slope of this linear relation [27]. They also showed that the abrasive wear process requires the existence of oxygen at the interface of contact elements. F. Schwack et al. [14] developed an experimental and finite element study to investigate false brinelling in a wind turbine ball bearing. In their model, the frictional work density was considered as an indicator to estimate false brinelling damage. It was concluded that the bearing geometry has a major impact on the occurrence of false brinelling damage. Moreover reduction of the oscillation amplitude and friction coefficient (using grease) can effectively reduce the false brinelling damage. In the authors’ previous work [6], a field monitoring and modelling study was performed to investigate and predict false brinelling in a cy lindrical bearing of a train bogie, during the transportation of new
2. Methodology In this study, the sample is a railway cylindrical bearing (Fig. 1). Based on the results of the authors’ previous work [6], the bearing was under a three dimensional vibration and rotational oscillating displacement, during the train transportation. The bearing was tested under rotational and lateral vibrations (see Fig. 1) as these vibrations were found to be the main cause of false brinelling wear damage pre viously [6].
Fig. 2. (a) Housing and the loading system (b) Exploded view of the housing and the loading system (c) simplified free body diagram showing forces acting on the shaft and sample bearings. 2
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Fig. 3. Schematic view of the false brinelling test-rig.
The methodology of the false brinelling experimental tests, including the test-rig design, is described in the first part of this section. In the second part, the methodology of determination of wear coefficient (using a set of reciprocating wear test) is detailed (all the experiments in this study were performed in dry condition). Thirdly, the methodology of developing the 3D FE model is explained.
The housing, shaft and loading system were designed and fabricated to hold the bearing and apply the required radial force (Fig. 2a). As is shown in Fig. 2b, the test can be conducted for four bearings, at the same time. The loading system consists of a load screw, load bars and two side rods (Fig. 2b). By tightening the load screw, side rods will apply the required radial force to two side-bearings covered by bushes, at two ends of the shaft. Fig. 2c is the simplified free body diagram showing forces acting on the shaft and sample bearings. In this diagram, Ftot is the total load applied by the middle load screw, Fside1 and FSide2 represent the forces applied by the side rods to the two sides of the shaft and F1 and F2 are the radial (normal) forces applied to the bearings. In this study, just one bearing was tested at each experiment. A load cell is installed be tween the load screw and the bottom load bar to measure the applied radial load. To provide the required vibration of the false brinelling test, an EDP Series Electro Dynamic Platform Shaker (Controlled Vibration EDP1818) is used which has the load capacity of 900 N and can provide the frequency range of 5 Hz to 2 kHz. The platform is supported by four actuator (ED Shakers with neodymium permanent magnet structures). Actuators of the shaker platform are powered by two DSi-1000 class A/B power amplifiers with the input signal of 1.5 Vrms (analog) and maximum output power of 1400 Wrms. Amplifiers are controlled by a
2.1. False brinelling test-rig The false brinelling testrig equipment and methodology will be described in the following. 2.1.1. False brinelling testrig equipment The false brinelling test rig, includes three main parts: � Housing and loading system to hold the bearing and apply radial load. � Shaker table to provide required vibrations and rotational displacement � Monitoring system, including accelerometers, load cell, encoder and data acquisition system to monitor and record the experiment’s outputs.
Fig. 4. Encoder’s set-up (a) side view (b) front view. 3
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Fig. 5. (a) Schematic view of the normal vibration set-up (b) schematic view of the lateral vibration set-up (c) Actual lateral vibration set-up.
Fig. 6. (a) Schematic view of the rotational vibration set-up (b) Actual rotational vibration test set-up.
two channel signal generator (Rigol’s DG-1022) that can be used to control both amplifiers simultaneously (Fig. 3). This signal generator has a sample rate of 1000 MS/s, resolution of 1μHz and can produce
different standard wave forms, such as Sine, Square, Ramp, Triangle, Pulse and Noise. A programmable digital encoder (with the resolution freely
Fig. 7. (a) FAG NU1018 cylindrical roller bearing (b) inner race, press fitted to the shaft. 4
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Table 1 The parameters of the lateral vibration test. Test Number
Frequency
Static load
Amplitude of acceleration
Test duration
1 2 3 4
24 24 19 19
80 kg 80 kg 300 kg 300 kg
2g 1g 0.6 g 0.6 g
192 h 192 h 72 h 168 h
Table 2 The parameters of the rotational vibration test. Test Number
Frequency
Static load
Amplitude of rotation
Test duration
1 2 3 4
14 14 14 15
80 kg 170 kg 115 kg 250 kg
0.3 0.1� 0.1� 0.2�
240 h 240 h 240 h 72 h
�
programmable from 1 to 10,000) is installed at the end of the shaft (Fig. 4) to measure the relative rotational displacement between the shaft and housing (which is equal to the relative displacement between the bearing inner and outer races). A Labview code was written to read the encoder pulses and convert them to the rotational angle of the shaft. Based on the written Labview code, the precision of the encoder in this application was 0.009� . This code also displays the accelerometer and load-cell outputs. The false brinelling test rig is able to provide both lateral and normal vibrations, depending on how the housing is mounted to the shaker platform. Fig. 5, schematically shows the differences between lateral and normal vibration set-ups. Fig. 5c shows the lateral vibration set-up. The shaker table was also used to provide rotational displacement. In this design, vertical and horizontal links convert the linear vertical vi bration in the shaker platform to the rotational vibration in the shaft (Fig. 6 (a) and (b)).
Fig. 8. (a) Reciprocating pin-on-cylinder set-up.
2.2. Experimental determination of wear coefficient A set of reciprocating wear tests were performed to determine the wear and friction coefficients of the bearing steel alloy, within a range of frequencies. These tests were performed using Bruker’s UMT TriboLab. As it can be seen in Fig. 8, the test was a pin-on-cylinder test, using a similar bearing material to that of the train bearing with the same hardness. The material is 52100 high carbon bearing quality steel (ASTM A295) [28] with the Vickers Hardness of 848 [HV], elastic modulus of 230 GPa and Poisson’s ratio of 0.3. The chemical composi tion of this steel is shown in Table 3. In this test, the cylinder was fixed and the normal load and tangential displacement were applied to the pin. The test was performed for different frequencies of 1, 2, 4, 6, 8, 10 Hz. Due to the limitation of the testing machine, the pin on cylinder tests could not be performed, at higher frequencies. The applied normal load for different tests was 4 kg that was equivalent to 464 MPa (max Hertzian pressure) based on local contact radii of 5 mm. The friction coefficient time histories were determined for all cases directly from the apparatus based on the measured vertical and lateral loading. The wear coefficient α was determined from the exper P imental wear volume Vw and measured accumulated frictional energy Ed according to (Eq. (1)) [26], X X X Vw ¼ α Ed ¼ α ðFT � dÞ→hw ¼ α ðμ � P � dÞ (1)
2.1.2. False brinelling testrig procedure The false brinelling test-rig was used to conduct lateral and rota tional vibration tests. The bearing that was used in the false brinelling tests was a FAG NU1018 cylindrical roller bearing (Fig. 7 a). Before starting the test, the shaft was press-fitted into the bearing inner race by placing it in a freezer to cool for 3 h. The bearing’s inner races were washed with a degreaser to remove any dirt and oil and placed in an oven and heated up to 100 � C. Then, the shaft was press fitted in to the inner race. (Fig. 7b). The shaft and the bearings were held by the housing and the required radial load was applied by the loading system. According to the field measurement data, recorded during the train transportation [6], the maximum lateral acceleration and rotational displacement, were 0.1g and 0.03� , during the sea transportation and 0.5g and 0.6� , during the road transportation, respectively. The road and sea transportation duration were, 20 h and 14 days, respectively. However, for the moni tored transportation and the recorded circumstances, no damage was reported on the bearing. Hence, to create the false brinelling damage, on the bearing, so as to reduce the experiment time, the parameters were intensified. The exact static normal load applied to the bearing, during the shipping process was unknown. Hence, the simulation was per formed for a range of normal loads. The static loads were chosen within the estimated range of the load that is being applied to the bearing, based on its application in the train. Tables 1 and 2 show test parameters for different lateral vibration and rotational displacement cases. After each test, the false brinelling wear marks on the inner race surface were measured using a stylus Taylor Hobson Talysurf i5 surface profiler. The maximum wear depth of each case was defined and used as an indicator of false brinelling damage to compare with the other cases.
where, FT is the lateral force, α is energy wear coefficient, d is the relative displacement at the contact area, hw is the wear depth, μ is the friction P coefficient, P is the contact pressure and Ed is the accumulated fric tional energy. In particular, the area under the graph of the measured lateral force versus lateral displacement using a summation of all test cycles was measured as the dissipated frictional energy. The volume of the wear profiles were measured using a stylus profilometer (Talysurf I series 5). Before the measurement, the surfaces of the samples were cleaned to remove any oil and dirt. The wear coefficients of different cases (with different frequencies) were used to propose an equation (using regression) to estimate the wear coefficient, as a function of frequency.
5
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Table 3 Chemical composition of material (mass %). C
Mn
P
S
Si
Ni
Cr
Cu
Mo
0.93–1.05
0.25–0.45
0.025
0.015
0.15–0.35
0.25
1.35–1.60
0.30
0.1
Fig. 9. 2D bearing model (a) lateral vibration loading structure (b) rotational vibration loading structure (c) meshing structure.
2.3. Finite element (FE) model for false brinelling
surface of the outer race was fixed to have no motion. The radial load was applied to the centre of the inner race which is coupled to the inner surface (Fig. 9 (a)). In this figure, FN is the normal static load and Wsh is the shaft’s weight (Fig. 9 (a)). Fig. 9 (c) shows the meshing structure of the model. The outer radius The outer radius of the inner race is 51.5 mm, the radius of the roller is 6 mm, the radius of the outer race is 70 mm and the bearing clearance is 0.07 mm [6].
A 2D FE model was developed to find the load distribution in the bearing. These results where then used in a 3D FE model to simulate the false brinelling process between the critical rollers and inner race. 2.3.1. 2D bearing model A 2D FE model of the bearing was developed to find the radial load, applied to each roller, under the test conditions. In this model, the outer
Fig. 10. 3D FE model and its meshing structure. 6
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To reduce the computational cost, the model was developed for a half single roller and a small part of the inner race. In this model, the small curvature along the inner race axis (Y-direction in Fig. 1) is considered in the model (the curvature is 0.0005 mm-1). Fig. 10 shows the meshing structure used in this model. The small contact patch of the inner race and roller are meshed with small structured break elements. These el ements need to be small enough (5 μm) to appropriately model the contact pressure and relative displacement, at the contact area. The rest of the model was meshed by tetrahedral elements which allows increased element sizes away from the contact area [14]. The modelling process includes two parts. The normal load (obtained from the FE 2D) model is applied to the roller, in the initial part. In the second part, the oscillating displacement/loading was applied. For the lateral vibration case, according to the dynamic model presented in the authors’ previous work, the lateral load applied to the roller is equal to the roller’s mass times vibration (acceleration) amplitude [6]. A python code is developed to calculate and extract the accumulated wear depth, for all nodes of the contact patch of the three dimensional FE model. This can provide a three dimensional profile of the wear profile.
Table 4 The results of the lateral vibration test. Test Number
Frequency
Static load
Amplitude of acceleration
Test duration
Wear depth
Wear profile
1
24
80 kg
2g
192 h
6 μm
2
24
80 kg
1g
192 h
2.7 μm
3 4
19 19
300 kg 300 kg
0.6 g 0.6 g
72 h 168 h
NA NA
Ushape Ushape
2.3.2. Three dimensional FE model A 3D FE model was developed to simulate false brinelling caused by lateral vibration and rotational displacement. To model false brinelling, a FORTRAN code that was presented in the authors’ previous work [6] was used in the false brinelling 3D FE model. This code updates the vertical position of each contact node (using Equation (1)) and accord ingly the contact stress of it, at each time increment. The new values are used to calculate the wear depth of each node, at the new time increment [6]. The algorithm of the FORTRAN code and the algorithm of inter action between the ABAQUS/CAE and the UMESHMOTION Code were presented in the authors’ previous work [6]. The assumption in this simulation is that the wear depth has a linear behaviour versus the number of wear cycles [6].
3. Results and discussions In the first part of this section, the results of the false brinelling tests are presented. In the second part, friction and wear coefficients are
Fig. 11. The wear marks of the first specimen of the lateral vibration test. 7
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Fig. 12. The wear marks of the first specimen of the rotational vibration test.
determined, based on the reciprocating wear tests results. In the last part, the 3d FE model is verified by the experimental results. This model was then used to investigate the influence of the lateral and rotational
vibrations, and normal load on the false brinelling damage.
Fig. 13. The wear marks of the second specimen of the rotational vibration test. 8
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Table 5 The results of the rotational experiments. Test Number
Frequency
Static load
Amplitude of rotation
The distance of the rotation
Test duration
Maximum wear depth
Wear profile
1 2 3 4
14 14 14 15
80 kg 170 kg 115 kg 250 kg
0.3 0.1� 0.1� 0.2�
0.27 mm 0.09 mm 0.09 mm 0.18 mm
240 h 240 h 240 h 72 h
2.5 μm 1.9 μm 1.6 μm NA
U-shape W-shape W-shape NA
�
3.1. Experimental tests
displacement, due to the very small amplitude of relative displacement and having no access to the contact area, during the experiment). However, this value is determined using the FE model that will be pre sented in the next sections. It can be seen from the experimental results, in Table 4 that by reducing the static load and increasing the acceleration, the false brin elling damage increases. Fig. 12 shows the wear marks, in the position of the two critical rollers for the first specimen of the rotational tests. These two bearings burden the largest portions of the static load. It can be found from the profilometery results that the false brinelling wear marks of this case have U-shape profiles along the bearing lateral direction (X-axis). The maximum wear depth of this specimen was 2.5 μm. The wear non-central marks may indicate that there has been some misalignment during assembly. Fig. 13 shows the results of the second specimen of the rotational test. The profilometery results are related to the position of the two most
For the two last cases of the lateral vibration test (Table 4), no sig nificant wear mark was seen. Although the trace of the marks could be seen, visually, profilometer measurements showed that the wear depth is within the surface roughness range and therefore is not measureable. However, for the Tests 1 and 2, the surfaces of the bearing’s races were significantly damaged. Fig. 11 shows the wear marks on the inner race surface, in the positions of the two critical rollers, for Test 1. These two rollers were burdened with the largest portions of the static load and were under the maximum lateral vibration. The profilometery results show that the marks have the U-shape profile, along the lateral direction (the direction of vibration). Table 4 represents the maximum wear depth of each lateral vibration test. The lateral false brinelling tests, in this study, are force controlled and the relative displacements (slip) between the rollers and races are not measured (it is very difficult/impossible to measure the lateral relative
Fig. 14. Reciprocating wear test results for the test with the frequency of 1 Hz (a) friction coefficient versus time (b) Frictional force versus lateral displacement (c) wear volume profile (d) wear coefficient versus frequency. Using this equation (Fig. 14d), the wear coefficient of the lateral vibration test (frequency of 24 Hz) and rotational vibration test (frequency of 15 Hz) were estimated to be 2.1E-15 Pa-1 and 7.3E-15 Pa-1, respectively. 9
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Fig. 15. Comparison between the experimental and FE false brinelling wear profiles, for the first specimen of the lateral vibration test.
critical rollers (on the inner race surface). The profilometery results showed that the false brinelling marks had W-shape profiles, for the second and third rotational tests. Such a profile shape was also seen for the marks of the third specimen of the rotational test. This profile shape is due to the existence of the stick and slip areas in the contact patch which has been reported in previous studies [6,27]. Table 5 represents the maximum wear depth for different rotational displacement tests. The distance of the rotation, in this table, represents the distance of the rotation, on the outer surface of the inner race. Table 5 shows that the amplitude of the rotational displacement plays an important role in the false brinelling damage intensity. It can also be seen that by increasing the radial load, the wear profile shape changes from U-shape to W-shape. Such a behavior has been reported in previous studies who have investigated shape of the fretting wear pro files in different applications [27]. The reason of this behavior will be explained in Section 3.3.
the same and about 0.6. Fig. 14a shows the friction coefficient for the test with the frequency of 1 Hz. The accumulated frictional energy of the reciprocating wear test were calculated for each case. Fig. 14b shows the lateral force-lateral displacement graph, by which the accumulated frictional energy was calculated. Fig. 14d represents the variation of the wear coefficient by changing frequency. The trend of the wear coeffi cient can be well approximated with an exponential function of fre quency. This trend has been previously reported by other researchers [27,29]. This can be explained based on the influence of contact tem perature on the debris ejection. At higher frequencies, the contact temperature will be significantly increased. At lower frequencies, debris is ejected from the contact, but at higher frequencies the debris is retained in the contact area (adhered debris bed), due to the high tem perature at the interface, and results in a reduction in wear rate [29,30]. The influence of the frequency on the wear coefficient can also be explained by the formation of the oxide debris. The increase in fre quency will reduce the time between asperity interactions in the contact, which will serve to limit oxygen penetration into the interface and accordingly limits the oxidation process which in turn reduces the wear rate [29,31].
3.2. Determination of wear coefficient The friction coefficient for all cases of the reciprocating wear test was
Fig. 16. Comparison between the experimental and FE false brinelling wear profiles, for the first specimen of the rotational vibration test. 10
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Fig. 17. Comparison between the experimental and FE false brinelling wear profiles, for the second specimen of the rotational vibration test. Table 6 Test parameters of each wear mark, for the rotational vibration specimens. Case Test 1- mark Test 1- mark Test 2- mark Test 2- mark Test 3- mark Test 3- mark
1 2 1 2 1 2
Table 7 Test parameters of each wear mark, for the lateral vibration specimens.
Static load on the roller
Amplitude of rotation
Case
Static load on the roller
Amplitude of acceleration
130 63 252 237 205 175
0.3� 0.3� 0.1� 0.1� 0.1� 0.1�
Test 1- mark 1 Test 1- mark 2 Test 2- mark 1 Test 2- mark 2
150 110 150 110
2g 2g 1g 1g
force, lateral vibration and rotational displacement of each mark, based on the position of the rollers, during the test. These parameters were used as an input in the FE model to simulate false brinelling, for each case. Fig. 18 compares the maximum wear depth of experimental specimens and the FE model. It can be seen that the FE model can predict the trend of the wear damage caused by different radial loads and lateral and rotational vi brations to within 85% error. This error can be mainly due to simplifi cations and assumptions that were made to determine the wear coefficient. In this study, the assumption is that changing the wear co efficient is not dependent on the contact pressure. This assumption has been made by many researchers, before [19,24,26,32,33]. However, based on the Fouvry’s results [27], wear coefficient can be a function of the contact pressure and contact profile. In this study, the same wear coefficient was used for different normal pressures. Moreover, due to the wear tester’s limitations, the reciprocating wear test could be performed for the frequencies up to 10 Hz and the wear coefficient of the lateral vibration test (frequency of 24 Hz) and rotational vibration test (fre quency of 15 Hz) were estimated using the proposed equation, based on the reciprocating wear test. This can also be another source of error.
3.3. Finite element model In the first part of this section, the FE results are compared to the experimental results to verify the FE model. In the second part, the in fluence of the variation of radial force and the amplitude of lateral and rotational vibrations on the false brinelling wear damage is investigated. 3.3.1. Verification Figs. 15–17 show three different cases, for which the experimental and modelled false brinelling wear profiles are compared. In the 2D cross section graphs, the FE profile is laterally shifted to better compare with the experiment wear profile. These figures confirm that the 3D FE model can predict the shape of the wear profile. Fig. 17 shows that the shape of the wear profile, along the X-axis can be well-predicted by the FE model, when the wear mark has a W-shape profile. According to Equation (1), the wear depth is depended on the contact pressure and the relative displacement (slip), at the contact area. When the tangential load is significantly smaller compared to the normal load, the magnitude of slip is zero at the middle part of the contact surface, where the contact pressure is largest, and as a result, the surface is divided into stick and slip areas. The existence of the stick and slip areas, at the interface can result in the creation of the W shape wear profile [6,26]. However, Fig. 17 shows that the wear depth is insignificant, in the middle of the experimental wear profile, along the Y-axis which is not predicted by FE model. This is likely, due to the lack of oxygen con centration, in the middle part (along Y-axis) [27]. The Finite element model is not able to include the oxygen concentration variable, in the modelling process. 3D Finite element model were used to determine the maximum wear depth for the critical rollers of each case. Tables 6 and 7 show the radial
3.3.2. Sensitivity analysis of static load and vibration levels on false brinelling The FE model was used to investigate the influence of the radial force and amplitude of the lateral and rotational vibrations on the wear damage of false brinelling. The maximum wear depth of each case is presented as the representative of the false brinelling wear damage. It should be noted that the radial (normal) load in this section, refers to the normal load that is applied to the bearing ie set of rollers. Fig. 19a shows the maximum wear depth versus normal load for two different ampli tudes of lateral vibration. Fig. 19b shows the wear depth versus lateral vibration, for two different normal loads of 80 and 120 kg. Fig. 19c 11
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Fig. 18. Comparison between the experimental and modelling maximum wear depth, for the rotational and lateral vibration cases.
Fig. 19. (a) Wear depth versus Normal load (b) wear depth versus lateral vibration (c) wear depth versus rotational displacement.
shows the maximum wear depth versus lateral vibration (acceleration), for two different normal loads (applied to the bearing). Fig. 19a shows that by increasing the normal load, in a constant amplitude of vibration, the wear depth, nonlinearly, reduces. This reduction is particularly significant, when the bearing static normal load is less than 100 kg. Where by increasing the normal load from 10 kg to 80 kg the wear depth reduces by 51%, when the lateral vibration is 2 g. This change can be explained based on the role of normal pressure and relative displacement on the magnitude of the wear depth. Equation (1) shows that the wear depth has a direct relation with the normal pressure and the relative displacement. Fig. 20 shows the maximum contact pressure and maximum accumulated slip (relative displacement) in the contact area, versus normal load, for one cycle of fretting wear, under the lateral vibration of 2 g, in the position of the critical roller. According to Fig. 20, it can be seen that the normal pressure increases (by power of
0.38), by increasing the normal load. However, by increasing the normal load, there is a substantial reduction in the amplitude of the relative displacement (by power of 0.95) which overcomes the effect of normal load increases and in turn reduces the wear depth. Fig. 19b shows that increasing the lateral vibration, while the bearing is under the constant radial load, increases the wear depth. This increase is more significant for smaller normal loads. Where, increasing the lateral vibration from 1.5 g to 2 g, increases the wear depth by 64%, when the bearing is under the normal load of 80 kg. In this case, increasing the lateral vibration, increases the lateral force, and accord ingly the lateral slip, under the constant normal pressure which in creases the wear depth, based on Equation (1). Fig. 19c shows that increasing the rotational displacement, significantly increases the wear depth. Increasing the rotational displacement from 0.42 to 0.6� , in creases the wear depth by 82%. This is because increasing the rotational 12
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Fig. 20. Contact pressure and maximum accumulated slip (relative displacement) versus normal load for one cycle of fretting wear, under the lateral vibration of 2 g, in the position of the critical roller.
displacement, increases the relative displacement between roller and inner race, under the constant contact pressure, which increases the wear depth, based on Equation (1).
the lateral vibration from 1.5 g to 2 g, and increasing the totational displacement from 0.42 to 0.6� , increased the maximum wear depth by 64% and 82%, respectively, when the bearing was under the normal load of 80 kg. In this case, increasing the lateral vibration, increases the lateral force, and accordingly the lateral slip, while the normal pressure is constant which increases the wear depth. Experimental results showed that by increasing the lateral vibration from 1g to 2g, when the bearing was under the normal load of 80 kg, the maximum wear depth of the inner race increased from 2.7 μm to 6 μm moreover, for the rotational vibration test, by increasing the bearing normal load from 80 kg to 170 kg and decreasing the rotational displacement from 0.3 to 0.1� , the maximum wear depth reduced from 2.5 to 1.6 μm (36%). This is because increasing the rotational displacement, increases the relative displace ment between roller and inner race, under the constant contact pressure, which increases the wear depth.
4. Conclusion In this study, a novel false brinelling test rig was used to recreate false brinelling in a controlled laboratory environment. A set of recip rocation wear tests was developed to determine the wear and friction coefficients at different excitation frequencies. The 3D FE model was developed and verified with the experimental results, in terms of pre dicting the false brinelling wear profile shape and the maximum wear depth. This model was then used to investigate the effect of the normal load and vibration amplitudes on the false brinelling damage. The graphs of maximum wear depth versus bearing radial load, lateral vi bration and rotational displacement were produced to show the influ ence of external parameters on the bearing false brinelling damage. The reciprocating wear test results show that the friction coefficient in this case was constant at about 0.6 for different vibration frequencies. The wear coefficient, however, can be estimated by an exponential function of the frequency. Using this function, the wear coefficient of the false brinelling lateral vibration test (frequency of 24 Hz) and rotational vibration test (frequency of 15 Hz) were estimated to be 2.1E-15 Pa-1 and 7.3E-15 Pa-1, respectively. This is due to the debris retention in the contact area, caused by temperature increasing, at high frequencies. Reduction of the oxygen penetration into the interface, at higher fre quencies, is another reason of wear coefficient reduction. This can limit the formation of the oxide debris, at the interface and reduce the wear rate [27,29–31]. Experimental and modelling results showed that increasing the normal force, reduces the false brinelling wear depth. This reduction is particularly significant, when the bearing static normal load is less than 100 kg. Where by increasing the normal load on the bearing from 10 kg to 80 kg the maximum wear depth reduces by 51%, when the lateral vibration is 2 g. Wear depth has a direct relation with the normal pres sure and the relative displacement. Normal pressure increases by increasing the normal load. However, by increasing the normal load, there is a substantial reduction in the amplitude of the relative displacement which in turn reduces the wear depth. It was also shown that increasing the lateral vibration and rotational displacement significantly increases the false brinelling damage. Where, increasing
Acknowledgments The authors greatly appreciate the financial support from the Rail Manufacturing Cooperative Research Centre (funded jointly by partici pating rail organisations and the Australian Federal Government’s Business Cooperative Research Centres Program) through Project “Monitoring and Control of False Brinelling”. References [1] D. Godfrey, Fretting corrosion or false brinelling? Tribol. Lubr. Technol. 59 (12) (2003) 28–30. [2] M. Eckels, M.N. Kotzalas, G.L. Doll, Attaining high levels of bearing performance with a nanocomposite diamond-like carbon coating, Tribol. Trans. 56 (3) (2013) 410–416. [3] F. Schwack, M. Stammler, G. Poll, A. Reuter, Comparison of life calculations for oscillating bearings considering individual pitch control in wind turbines, J. Phys. Conf. Ser. 753 (2016) 112013. [4] F. Massi, N. Bouscharain, S. Milana, G. Le Jeune, Y. Maheo, Y. Berthier, Degradation of high loaded oscillating bearings: numerical analysis and comparison with experimental observations, Wear 317 (1) (2014) 141–152. [5] H. Pittroff, Fretting corrosion caused by vibration with rolling bearings stationary, J. Basic. Eng. 87 (3) (1965) 713–723. [6] K. Fallahnezhad, S. Liu, O. Brinji, M. Marker, P.A. Meehan, Monitoring and modelling of false brinelling for railway bearings, Wear 424-425 (2019) 151–164. [7] R. McElveen, J. Hillhouse, K. Miller, Electric Motor Storage: Protecting Your Investment, Record of Conference Papers - Annual Petroleum and Chemical Industry Conference, 2011.
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[8] F. Massi, J. Rocchi, A. Culla, Y. Berthier, Coupling system dynamics and contact behaviour: modelling bearings subjected to environmental induced vibrations and ’false brinelling’ degradation, Mech. Syst. Signal Process. 24 (4) (2010) 1068–1080. [9] J.L.H. Silva, A.J.M. Cardoso, Bearing failures diagnosis in three-phase induction motors by extended Park’s Vector approach, in: IECON Proceedings (Industrial Electronics Conference), 2005, pp. 2591–2596. [10] Y. Berthier, D. Play, Wear mechanisms in oscillating bearings, Wear 75 (2) (1982) 369–387. [11] P.O. Maruschak, S.V. Panin, I.M. Zakiev, M.A. Poltaranin, A.L. Sotnikov, Scale levels of damage to the raceway of a spherical roller bearing, Eng. Fail. Anal. 59 (2016) 69–78. [12] F. Massi, J. Rocchi, A. Culla, Y. Berthier, Coupling system dynamics and contact behaviour: modelling bearings subjected to environmental induced vibrations and ‘false brinelling’ degradation, Mech. Syst. Signal Process. 24 (4) (2010) 1068–1080. [13] T. Slack, F. Sadeghi, Explicit finite element modeling of subsurface initiated spalling in rolling contacts, Tribol. Int. 43 (9) (2010) 1693–1702. [14] F. Schwack, F. Prigge, G. Poll, Finite element simulation and experimental analysis of false brinelling and fretting corrosion, Tribol. Int. 126 (2018) 352–362. [15] O. Sotnykov, M. Rodionov, P. Maruschak, J. Brezinov� a, A. Guzanov� a, Y.J. S. Apostol, Fracture, complexity, failure analysis of the hinge-lever mould oscillator bearings of the continuous casting machine 8 (3) (2014) 135–143. [16] A.R.S. Ponter, A.D. Hearle, K.L. Johnson, Application of the kinematical shakedown theorem to rolling and sliding point contacts, J. Mech. Phys. Solids 33 (4) (1985) 339–362. [17] K.L. Johnson, Contact mechanics and the wear of metals, Wear 190 (2) (1995) 162–170. [18] A. Kapoor, Wear by plastic ratchetting, Wear 212 (1) (1997) 119–130. [19] I.R. McColl, J. Ding, S.B. Leen, Finite element simulation and experimental validation of fretting wear, Wear 256 (11–12) (2004) 1114–1127. [20] J. Ding, S.B. Leen, E.J. Williams, P.H. Shipway, Finite element simulation of fretting wear-fatigue interaction in spline couplings, Tribol. Mater. Surf. Interfaces 2 (1) (2008) 10–24. [21] J.F. Archard, Contact and rubbing of flat surfaces, J. Appl. Phys. 24 (8) (1953) 981–988.
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Contents lists available at ScienceDirect
Wear journal homepage: http://www.elsevier.com/locate/wear
The influence of different types of loading on false brinelling Khosro Fallahnezhad *, Osama Brinji, Ajay Desai, Paul A. Meehan University of Queensland, Brisbane, Australia
A R T I C L E I N F O
A B S T R A C T
Keywords: False brinelling Finite element Fretting wear False brinelling test rig Bearing damage
An experimental and numerical study was developed to investigate the influence of radial load and the amplitude of rotational and lateral vibrations on false brinelling damage in railway cylindrical roller bearings. For this objective, a novel false brinelling test-rig was designed and fabricated to conduct both linear vibration and rotational displacement tests. A reciprocating pin-on-cylinder wear test was also conducted to determine the friction and wear coefficients of the bearing, under different frequencies. These experimental results where then used to verify a developed finite element model for false brinelling of an individual roller. The reciprocating wear test results show that the friction coefficient is almost constant and does not signifi cantly, change, by changing the frequency. The wear coefficient, however, can be estimated by an exponential function of the frequency. The experimental and numerical results showed that reducing the bearing static radial load and increasing the amplitude of linear and rotational vibration, intensifies the false brinelling damage. It was also shown that by increasing the bearing radial load, the false brinelling wear profile changes from a Ushape to W-shape.
1. Introduction False brinelling is a type of fretting wear which occurs in the roller bearings, due to intentional and unintentional linear or rotational vi brations. Similar to fretting wear, false brinelling is caused by oscilla tory, low amplitude sliding that occurs at the roller-raceway interface [1,2]. This has been seen in several industrial applications, in which intentional oscillations [3,4] or unintentional vibrating oscillations [5, 6] occurs. Typical circumstances when a bearing may experience false brinelling are when the bearing is in transportation or when being stored in an environment exposed to vibrations [2,7–9]. The previous experi mental studies, conducted on oscillating bearings [10,11], highlighted the complexity of the degradation scenarios, due to the small area of contact and small amplitude of oscillation, role of the rheology of third body at the contact area and the influence of the system kinematics and dynamics on the local behavior at contact surfaces. Therefore, to un derstand the wear process, the tribological analysis needs to be done at the contact scale, to consider correct boundary conditions [4,12]. Over the past decade, numerical tribology has become a powerful tool to investigate contact issues and to simulate the wear process. Recently, different numerical techniques, such as adaptive and explicit finite element methods and discrete element simulations has been used to investigate fretting wear processes including false brinelling [6,13,14].
Maruschak et al. [11] and Sotnykov et al. [15] investigated false brinelling damage in a roller bearing used in a continuous billet-casting machine (CBCM). They showed that the surfaces of the bearing races were damaged, due to false brinelling caused by a dynamic loading. They explained this mechanism by a multi-level description of defor mation and fracture processes that accompany the wear of a bearing’s surface. They concluded that several complex deformation and friction mechanisms at meso- and macro-levels contribute in the wear process. Massi et al. [12], proposed a model to predict false brinelling. They analyzed the influence of the aircraft engines vibrations on the contact stresses of rolling bearings of the bleed system valves. However, their FE model, just predicted the stress distribution at the contact area between ball and race rather than the wear damage, caused by imposed vibrations. The approaches that have been used to simulate fretting wear can be used to model false brinelling, such as in Refs. [16–18]. McColl et al. [19,20] presented a finite element model to simulate fretting wear in a pin-on-disc set up, based on Archard’s equation [21]. This model has been used to simulate fretting wear in different applications [20,22–25]. Fouvry proposed that, using the accumulated friction energy dissipated through the interface the wear volume can be estimated. This can be calculated by integrating the friction work in the wear analysis, [26]. He showed the linear relation between wear volume and dissipated energy
* Corresponding author. E-mail addresses: [email protected] (K. Fallahnezhad), [email protected] (O. Brinji), [email protected] (A. Desai), [email protected] (P.A. Meehan). https://doi.org/10.1016/j.wear.2019.203097 Received 23 July 2019; Received in revised form 8 October 2019; Accepted 18 October 2019 Available online 23 October 2019 0043-1648/© 2019 Elsevier B.V. All rights reserved.
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trains. A false brinelling monitoring system was designed and installed to record the vibration and rotational motion of the bearing, during the train’s transportation and used as input for a 2D FE model. It was found that the wear profile is highly dependent on the accumulated slip of the contact area, over the process of false brinelling. Based on the FE results, for a railway bearing, under the transportation condition, they showed that the existence of stick-slip regions in the contact area causes the development of W shape wear marks along the lateral and axial direc tion of the bearing depending on the amplitude of the normal load and vibration. The W-shape marks have been seen in the false brinelling marks of a damaged bearing, along the axial direction. At present, no research has systematically investigated, both numerically and experimentally the influence of external parameters, such as amplitudes of radial force, vibration and rotational displacement on the occurrence and severity of the false brinelling wear in a cylin drical bearing. To address this, in this study, a false brinelling experi mental test rig was developed to simulate false brinelling of a cylindrical roller bearing, during transportation. A set of reciprocating pin-oncylinder wear test was performed to determine the frictional and wear coefficients of the bearing alloy, for different frequencies. Moreover, a 3D FE model was developed and used to simulate false brinelling caused by vibration and rotational displacement. The experimental and modelling results were used to investigate the influence of lateral and rotational vibrations, and radial force, on the false brinelling wear damage.
Fig. 1. Cylindrical bearing and its local directions.
and proved that, different parameters, such as contact profile, amplitude and frequency of sliding, and normal force can influence the slope of this linear relation [27]. They also showed that the abrasive wear process requires the existence of oxygen at the interface of contact elements. F. Schwack et al. [14] developed an experimental and finite element study to investigate false brinelling in a wind turbine ball bearing. In their model, the frictional work density was considered as an indicator to estimate false brinelling damage. It was concluded that the bearing geometry has a major impact on the occurrence of false brinelling damage. Moreover reduction of the oscillation amplitude and friction coefficient (using grease) can effectively reduce the false brinelling damage. In the authors’ previous work [6], a field monitoring and modelling study was performed to investigate and predict false brinelling in a cy lindrical bearing of a train bogie, during the transportation of new
2. Methodology In this study, the sample is a railway cylindrical bearing (Fig. 1). Based on the results of the authors’ previous work [6], the bearing was under a three dimensional vibration and rotational oscillating displacement, during the train transportation. The bearing was tested under rotational and lateral vibrations (see Fig. 1) as these vibrations were found to be the main cause of false brinelling wear damage pre viously [6].
Fig. 2. (a) Housing and the loading system (b) Exploded view of the housing and the loading system (c) simplified free body diagram showing forces acting on the shaft and sample bearings. 2
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Fig. 3. Schematic view of the false brinelling test-rig.
The methodology of the false brinelling experimental tests, including the test-rig design, is described in the first part of this section. In the second part, the methodology of determination of wear coefficient (using a set of reciprocating wear test) is detailed (all the experiments in this study were performed in dry condition). Thirdly, the methodology of developing the 3D FE model is explained.
The housing, shaft and loading system were designed and fabricated to hold the bearing and apply the required radial force (Fig. 2a). As is shown in Fig. 2b, the test can be conducted for four bearings, at the same time. The loading system consists of a load screw, load bars and two side rods (Fig. 2b). By tightening the load screw, side rods will apply the required radial force to two side-bearings covered by bushes, at two ends of the shaft. Fig. 2c is the simplified free body diagram showing forces acting on the shaft and sample bearings. In this diagram, Ftot is the total load applied by the middle load screw, Fside1 and FSide2 represent the forces applied by the side rods to the two sides of the shaft and F1 and F2 are the radial (normal) forces applied to the bearings. In this study, just one bearing was tested at each experiment. A load cell is installed be tween the load screw and the bottom load bar to measure the applied radial load. To provide the required vibration of the false brinelling test, an EDP Series Electro Dynamic Platform Shaker (Controlled Vibration EDP1818) is used which has the load capacity of 900 N and can provide the frequency range of 5 Hz to 2 kHz. The platform is supported by four actuator (ED Shakers with neodymium permanent magnet structures). Actuators of the shaker platform are powered by two DSi-1000 class A/B power amplifiers with the input signal of 1.5 Vrms (analog) and maximum output power of 1400 Wrms. Amplifiers are controlled by a
2.1. False brinelling test-rig The false brinelling testrig equipment and methodology will be described in the following. 2.1.1. False brinelling testrig equipment The false brinelling test rig, includes three main parts: � Housing and loading system to hold the bearing and apply radial load. � Shaker table to provide required vibrations and rotational displacement � Monitoring system, including accelerometers, load cell, encoder and data acquisition system to monitor and record the experiment’s outputs.
Fig. 4. Encoder’s set-up (a) side view (b) front view. 3
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Fig. 5. (a) Schematic view of the normal vibration set-up (b) schematic view of the lateral vibration set-up (c) Actual lateral vibration set-up.
Fig. 6. (a) Schematic view of the rotational vibration set-up (b) Actual rotational vibration test set-up.
two channel signal generator (Rigol’s DG-1022) that can be used to control both amplifiers simultaneously (Fig. 3). This signal generator has a sample rate of 1000 MS/s, resolution of 1μHz and can produce
different standard wave forms, such as Sine, Square, Ramp, Triangle, Pulse and Noise. A programmable digital encoder (with the resolution freely
Fig. 7. (a) FAG NU1018 cylindrical roller bearing (b) inner race, press fitted to the shaft. 4
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Table 1 The parameters of the lateral vibration test. Test Number
Frequency
Static load
Amplitude of acceleration
Test duration
1 2 3 4
24 24 19 19
80 kg 80 kg 300 kg 300 kg
2g 1g 0.6 g 0.6 g
192 h 192 h 72 h 168 h
Table 2 The parameters of the rotational vibration test. Test Number
Frequency
Static load
Amplitude of rotation
Test duration
1 2 3 4
14 14 14 15
80 kg 170 kg 115 kg 250 kg
0.3 0.1� 0.1� 0.2�
240 h 240 h 240 h 72 h
�
programmable from 1 to 10,000) is installed at the end of the shaft (Fig. 4) to measure the relative rotational displacement between the shaft and housing (which is equal to the relative displacement between the bearing inner and outer races). A Labview code was written to read the encoder pulses and convert them to the rotational angle of the shaft. Based on the written Labview code, the precision of the encoder in this application was 0.009� . This code also displays the accelerometer and load-cell outputs. The false brinelling test rig is able to provide both lateral and normal vibrations, depending on how the housing is mounted to the shaker platform. Fig. 5, schematically shows the differences between lateral and normal vibration set-ups. Fig. 5c shows the lateral vibration set-up. The shaker table was also used to provide rotational displacement. In this design, vertical and horizontal links convert the linear vertical vi bration in the shaker platform to the rotational vibration in the shaft (Fig. 6 (a) and (b)).
Fig. 8. (a) Reciprocating pin-on-cylinder set-up.
2.2. Experimental determination of wear coefficient A set of reciprocating wear tests were performed to determine the wear and friction coefficients of the bearing steel alloy, within a range of frequencies. These tests were performed using Bruker’s UMT TriboLab. As it can be seen in Fig. 8, the test was a pin-on-cylinder test, using a similar bearing material to that of the train bearing with the same hardness. The material is 52100 high carbon bearing quality steel (ASTM A295) [28] with the Vickers Hardness of 848 [HV], elastic modulus of 230 GPa and Poisson’s ratio of 0.3. The chemical composi tion of this steel is shown in Table 3. In this test, the cylinder was fixed and the normal load and tangential displacement were applied to the pin. The test was performed for different frequencies of 1, 2, 4, 6, 8, 10 Hz. Due to the limitation of the testing machine, the pin on cylinder tests could not be performed, at higher frequencies. The applied normal load for different tests was 4 kg that was equivalent to 464 MPa (max Hertzian pressure) based on local contact radii of 5 mm. The friction coefficient time histories were determined for all cases directly from the apparatus based on the measured vertical and lateral loading. The wear coefficient α was determined from the exper P imental wear volume Vw and measured accumulated frictional energy Ed according to (Eq. (1)) [26], X X X Vw ¼ α Ed ¼ α ðFT � dÞ→hw ¼ α ðμ � P � dÞ (1)
2.1.2. False brinelling testrig procedure The false brinelling test-rig was used to conduct lateral and rota tional vibration tests. The bearing that was used in the false brinelling tests was a FAG NU1018 cylindrical roller bearing (Fig. 7 a). Before starting the test, the shaft was press-fitted into the bearing inner race by placing it in a freezer to cool for 3 h. The bearing’s inner races were washed with a degreaser to remove any dirt and oil and placed in an oven and heated up to 100 � C. Then, the shaft was press fitted in to the inner race. (Fig. 7b). The shaft and the bearings were held by the housing and the required radial load was applied by the loading system. According to the field measurement data, recorded during the train transportation [6], the maximum lateral acceleration and rotational displacement, were 0.1g and 0.03� , during the sea transportation and 0.5g and 0.6� , during the road transportation, respectively. The road and sea transportation duration were, 20 h and 14 days, respectively. However, for the moni tored transportation and the recorded circumstances, no damage was reported on the bearing. Hence, to create the false brinelling damage, on the bearing, so as to reduce the experiment time, the parameters were intensified. The exact static normal load applied to the bearing, during the shipping process was unknown. Hence, the simulation was per formed for a range of normal loads. The static loads were chosen within the estimated range of the load that is being applied to the bearing, based on its application in the train. Tables 1 and 2 show test parameters for different lateral vibration and rotational displacement cases. After each test, the false brinelling wear marks on the inner race surface were measured using a stylus Taylor Hobson Talysurf i5 surface profiler. The maximum wear depth of each case was defined and used as an indicator of false brinelling damage to compare with the other cases.
where, FT is the lateral force, α is energy wear coefficient, d is the relative displacement at the contact area, hw is the wear depth, μ is the friction P coefficient, P is the contact pressure and Ed is the accumulated fric tional energy. In particular, the area under the graph of the measured lateral force versus lateral displacement using a summation of all test cycles was measured as the dissipated frictional energy. The volume of the wear profiles were measured using a stylus profilometer (Talysurf I series 5). Before the measurement, the surfaces of the samples were cleaned to remove any oil and dirt. The wear coefficients of different cases (with different frequencies) were used to propose an equation (using regression) to estimate the wear coefficient, as a function of frequency.
5
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Table 3 Chemical composition of material (mass %). C
Mn
P
S
Si
Ni
Cr
Cu
Mo
0.93–1.05
0.25–0.45
0.025
0.015
0.15–0.35
0.25
1.35–1.60
0.30
0.1
Fig. 9. 2D bearing model (a) lateral vibration loading structure (b) rotational vibration loading structure (c) meshing structure.
2.3. Finite element (FE) model for false brinelling
surface of the outer race was fixed to have no motion. The radial load was applied to the centre of the inner race which is coupled to the inner surface (Fig. 9 (a)). In this figure, FN is the normal static load and Wsh is the shaft’s weight (Fig. 9 (a)). Fig. 9 (c) shows the meshing structure of the model. The outer radius The outer radius of the inner race is 51.5 mm, the radius of the roller is 6 mm, the radius of the outer race is 70 mm and the bearing clearance is 0.07 mm [6].
A 2D FE model was developed to find the load distribution in the bearing. These results where then used in a 3D FE model to simulate the false brinelling process between the critical rollers and inner race. 2.3.1. 2D bearing model A 2D FE model of the bearing was developed to find the radial load, applied to each roller, under the test conditions. In this model, the outer
Fig. 10. 3D FE model and its meshing structure. 6
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To reduce the computational cost, the model was developed for a half single roller and a small part of the inner race. In this model, the small curvature along the inner race axis (Y-direction in Fig. 1) is considered in the model (the curvature is 0.0005 mm-1). Fig. 10 shows the meshing structure used in this model. The small contact patch of the inner race and roller are meshed with small structured break elements. These el ements need to be small enough (5 μm) to appropriately model the contact pressure and relative displacement, at the contact area. The rest of the model was meshed by tetrahedral elements which allows increased element sizes away from the contact area [14]. The modelling process includes two parts. The normal load (obtained from the FE 2D) model is applied to the roller, in the initial part. In the second part, the oscillating displacement/loading was applied. For the lateral vibration case, according to the dynamic model presented in the authors’ previous work, the lateral load applied to the roller is equal to the roller’s mass times vibration (acceleration) amplitude [6]. A python code is developed to calculate and extract the accumulated wear depth, for all nodes of the contact patch of the three dimensional FE model. This can provide a three dimensional profile of the wear profile.
Table 4 The results of the lateral vibration test. Test Number
Frequency
Static load
Amplitude of acceleration
Test duration
Wear depth
Wear profile
1
24
80 kg
2g
192 h
6 μm
2
24
80 kg
1g
192 h
2.7 μm
3 4
19 19
300 kg 300 kg
0.6 g 0.6 g
72 h 168 h
NA NA
Ushape Ushape
2.3.2. Three dimensional FE model A 3D FE model was developed to simulate false brinelling caused by lateral vibration and rotational displacement. To model false brinelling, a FORTRAN code that was presented in the authors’ previous work [6] was used in the false brinelling 3D FE model. This code updates the vertical position of each contact node (using Equation (1)) and accord ingly the contact stress of it, at each time increment. The new values are used to calculate the wear depth of each node, at the new time increment [6]. The algorithm of the FORTRAN code and the algorithm of inter action between the ABAQUS/CAE and the UMESHMOTION Code were presented in the authors’ previous work [6]. The assumption in this simulation is that the wear depth has a linear behaviour versus the number of wear cycles [6].
3. Results and discussions In the first part of this section, the results of the false brinelling tests are presented. In the second part, friction and wear coefficients are
Fig. 11. The wear marks of the first specimen of the lateral vibration test. 7
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Fig. 12. The wear marks of the first specimen of the rotational vibration test.
determined, based on the reciprocating wear tests results. In the last part, the 3d FE model is verified by the experimental results. This model was then used to investigate the influence of the lateral and rotational
vibrations, and normal load on the false brinelling damage.
Fig. 13. The wear marks of the second specimen of the rotational vibration test. 8
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Table 5 The results of the rotational experiments. Test Number
Frequency
Static load
Amplitude of rotation
The distance of the rotation
Test duration
Maximum wear depth
Wear profile
1 2 3 4
14 14 14 15
80 kg 170 kg 115 kg 250 kg
0.3 0.1� 0.1� 0.2�
0.27 mm 0.09 mm 0.09 mm 0.18 mm
240 h 240 h 240 h 72 h
2.5 μm 1.9 μm 1.6 μm NA
U-shape W-shape W-shape NA
�
3.1. Experimental tests
displacement, due to the very small amplitude of relative displacement and having no access to the contact area, during the experiment). However, this value is determined using the FE model that will be pre sented in the next sections. It can be seen from the experimental results, in Table 4 that by reducing the static load and increasing the acceleration, the false brin elling damage increases. Fig. 12 shows the wear marks, in the position of the two critical rollers for the first specimen of the rotational tests. These two bearings burden the largest portions of the static load. It can be found from the profilometery results that the false brinelling wear marks of this case have U-shape profiles along the bearing lateral direction (X-axis). The maximum wear depth of this specimen was 2.5 μm. The wear non-central marks may indicate that there has been some misalignment during assembly. Fig. 13 shows the results of the second specimen of the rotational test. The profilometery results are related to the position of the two most
For the two last cases of the lateral vibration test (Table 4), no sig nificant wear mark was seen. Although the trace of the marks could be seen, visually, profilometer measurements showed that the wear depth is within the surface roughness range and therefore is not measureable. However, for the Tests 1 and 2, the surfaces of the bearing’s races were significantly damaged. Fig. 11 shows the wear marks on the inner race surface, in the positions of the two critical rollers, for Test 1. These two rollers were burdened with the largest portions of the static load and were under the maximum lateral vibration. The profilometery results show that the marks have the U-shape profile, along the lateral direction (the direction of vibration). Table 4 represents the maximum wear depth of each lateral vibration test. The lateral false brinelling tests, in this study, are force controlled and the relative displacements (slip) between the rollers and races are not measured (it is very difficult/impossible to measure the lateral relative
Fig. 14. Reciprocating wear test results for the test with the frequency of 1 Hz (a) friction coefficient versus time (b) Frictional force versus lateral displacement (c) wear volume profile (d) wear coefficient versus frequency. Using this equation (Fig. 14d), the wear coefficient of the lateral vibration test (frequency of 24 Hz) and rotational vibration test (frequency of 15 Hz) were estimated to be 2.1E-15 Pa-1 and 7.3E-15 Pa-1, respectively. 9
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Fig. 15. Comparison between the experimental and FE false brinelling wear profiles, for the first specimen of the lateral vibration test.
critical rollers (on the inner race surface). The profilometery results showed that the false brinelling marks had W-shape profiles, for the second and third rotational tests. Such a profile shape was also seen for the marks of the third specimen of the rotational test. This profile shape is due to the existence of the stick and slip areas in the contact patch which has been reported in previous studies [6,27]. Table 5 represents the maximum wear depth for different rotational displacement tests. The distance of the rotation, in this table, represents the distance of the rotation, on the outer surface of the inner race. Table 5 shows that the amplitude of the rotational displacement plays an important role in the false brinelling damage intensity. It can also be seen that by increasing the radial load, the wear profile shape changes from U-shape to W-shape. Such a behavior has been reported in previous studies who have investigated shape of the fretting wear pro files in different applications [27]. The reason of this behavior will be explained in Section 3.3.
the same and about 0.6. Fig. 14a shows the friction coefficient for the test with the frequency of 1 Hz. The accumulated frictional energy of the reciprocating wear test were calculated for each case. Fig. 14b shows the lateral force-lateral displacement graph, by which the accumulated frictional energy was calculated. Fig. 14d represents the variation of the wear coefficient by changing frequency. The trend of the wear coeffi cient can be well approximated with an exponential function of fre quency. This trend has been previously reported by other researchers [27,29]. This can be explained based on the influence of contact tem perature on the debris ejection. At higher frequencies, the contact temperature will be significantly increased. At lower frequencies, debris is ejected from the contact, but at higher frequencies the debris is retained in the contact area (adhered debris bed), due to the high tem perature at the interface, and results in a reduction in wear rate [29,30]. The influence of the frequency on the wear coefficient can also be explained by the formation of the oxide debris. The increase in fre quency will reduce the time between asperity interactions in the contact, which will serve to limit oxygen penetration into the interface and accordingly limits the oxidation process which in turn reduces the wear rate [29,31].
3.2. Determination of wear coefficient The friction coefficient for all cases of the reciprocating wear test was
Fig. 16. Comparison between the experimental and FE false brinelling wear profiles, for the first specimen of the rotational vibration test. 10
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Fig. 17. Comparison between the experimental and FE false brinelling wear profiles, for the second specimen of the rotational vibration test. Table 6 Test parameters of each wear mark, for the rotational vibration specimens. Case Test 1- mark Test 1- mark Test 2- mark Test 2- mark Test 3- mark Test 3- mark
1 2 1 2 1 2
Table 7 Test parameters of each wear mark, for the lateral vibration specimens.
Static load on the roller
Amplitude of rotation
Case
Static load on the roller
Amplitude of acceleration
130 63 252 237 205 175
0.3� 0.3� 0.1� 0.1� 0.1� 0.1�
Test 1- mark 1 Test 1- mark 2 Test 2- mark 1 Test 2- mark 2
150 110 150 110
2g 2g 1g 1g
force, lateral vibration and rotational displacement of each mark, based on the position of the rollers, during the test. These parameters were used as an input in the FE model to simulate false brinelling, for each case. Fig. 18 compares the maximum wear depth of experimental specimens and the FE model. It can be seen that the FE model can predict the trend of the wear damage caused by different radial loads and lateral and rotational vi brations to within 85% error. This error can be mainly due to simplifi cations and assumptions that were made to determine the wear coefficient. In this study, the assumption is that changing the wear co efficient is not dependent on the contact pressure. This assumption has been made by many researchers, before [19,24,26,32,33]. However, based on the Fouvry’s results [27], wear coefficient can be a function of the contact pressure and contact profile. In this study, the same wear coefficient was used for different normal pressures. Moreover, due to the wear tester’s limitations, the reciprocating wear test could be performed for the frequencies up to 10 Hz and the wear coefficient of the lateral vibration test (frequency of 24 Hz) and rotational vibration test (fre quency of 15 Hz) were estimated using the proposed equation, based on the reciprocating wear test. This can also be another source of error.
3.3. Finite element model In the first part of this section, the FE results are compared to the experimental results to verify the FE model. In the second part, the in fluence of the variation of radial force and the amplitude of lateral and rotational vibrations on the false brinelling wear damage is investigated. 3.3.1. Verification Figs. 15–17 show three different cases, for which the experimental and modelled false brinelling wear profiles are compared. In the 2D cross section graphs, the FE profile is laterally shifted to better compare with the experiment wear profile. These figures confirm that the 3D FE model can predict the shape of the wear profile. Fig. 17 shows that the shape of the wear profile, along the X-axis can be well-predicted by the FE model, when the wear mark has a W-shape profile. According to Equation (1), the wear depth is depended on the contact pressure and the relative displacement (slip), at the contact area. When the tangential load is significantly smaller compared to the normal load, the magnitude of slip is zero at the middle part of the contact surface, where the contact pressure is largest, and as a result, the surface is divided into stick and slip areas. The existence of the stick and slip areas, at the interface can result in the creation of the W shape wear profile [6,26]. However, Fig. 17 shows that the wear depth is insignificant, in the middle of the experimental wear profile, along the Y-axis which is not predicted by FE model. This is likely, due to the lack of oxygen con centration, in the middle part (along Y-axis) [27]. The Finite element model is not able to include the oxygen concentration variable, in the modelling process. 3D Finite element model were used to determine the maximum wear depth for the critical rollers of each case. Tables 6 and 7 show the radial
3.3.2. Sensitivity analysis of static load and vibration levels on false brinelling The FE model was used to investigate the influence of the radial force and amplitude of the lateral and rotational vibrations on the wear damage of false brinelling. The maximum wear depth of each case is presented as the representative of the false brinelling wear damage. It should be noted that the radial (normal) load in this section, refers to the normal load that is applied to the bearing ie set of rollers. Fig. 19a shows the maximum wear depth versus normal load for two different ampli tudes of lateral vibration. Fig. 19b shows the wear depth versus lateral vibration, for two different normal loads of 80 and 120 kg. Fig. 19c 11
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Fig. 18. Comparison between the experimental and modelling maximum wear depth, for the rotational and lateral vibration cases.
Fig. 19. (a) Wear depth versus Normal load (b) wear depth versus lateral vibration (c) wear depth versus rotational displacement.
shows the maximum wear depth versus lateral vibration (acceleration), for two different normal loads (applied to the bearing). Fig. 19a shows that by increasing the normal load, in a constant amplitude of vibration, the wear depth, nonlinearly, reduces. This reduction is particularly significant, when the bearing static normal load is less than 100 kg. Where by increasing the normal load from 10 kg to 80 kg the wear depth reduces by 51%, when the lateral vibration is 2 g. This change can be explained based on the role of normal pressure and relative displacement on the magnitude of the wear depth. Equation (1) shows that the wear depth has a direct relation with the normal pressure and the relative displacement. Fig. 20 shows the maximum contact pressure and maximum accumulated slip (relative displacement) in the contact area, versus normal load, for one cycle of fretting wear, under the lateral vibration of 2 g, in the position of the critical roller. According to Fig. 20, it can be seen that the normal pressure increases (by power of
0.38), by increasing the normal load. However, by increasing the normal load, there is a substantial reduction in the amplitude of the relative displacement (by power of 0.95) which overcomes the effect of normal load increases and in turn reduces the wear depth. Fig. 19b shows that increasing the lateral vibration, while the bearing is under the constant radial load, increases the wear depth. This increase is more significant for smaller normal loads. Where, increasing the lateral vibration from 1.5 g to 2 g, increases the wear depth by 64%, when the bearing is under the normal load of 80 kg. In this case, increasing the lateral vibration, increases the lateral force, and accord ingly the lateral slip, under the constant normal pressure which in creases the wear depth, based on Equation (1). Fig. 19c shows that increasing the rotational displacement, significantly increases the wear depth. Increasing the rotational displacement from 0.42 to 0.6� , in creases the wear depth by 82%. This is because increasing the rotational 12
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Fig. 20. Contact pressure and maximum accumulated slip (relative displacement) versus normal load for one cycle of fretting wear, under the lateral vibration of 2 g, in the position of the critical roller.
displacement, increases the relative displacement between roller and inner race, under the constant contact pressure, which increases the wear depth, based on Equation (1).
the lateral vibration from 1.5 g to 2 g, and increasing the totational displacement from 0.42 to 0.6� , increased the maximum wear depth by 64% and 82%, respectively, when the bearing was under the normal load of 80 kg. In this case, increasing the lateral vibration, increases the lateral force, and accordingly the lateral slip, while the normal pressure is constant which increases the wear depth. Experimental results showed that by increasing the lateral vibration from 1g to 2g, when the bearing was under the normal load of 80 kg, the maximum wear depth of the inner race increased from 2.7 μm to 6 μm moreover, for the rotational vibration test, by increasing the bearing normal load from 80 kg to 170 kg and decreasing the rotational displacement from 0.3 to 0.1� , the maximum wear depth reduced from 2.5 to 1.6 μm (36%). This is because increasing the rotational displacement, increases the relative displace ment between roller and inner race, under the constant contact pressure, which increases the wear depth.
4. Conclusion In this study, a novel false brinelling test rig was used to recreate false brinelling in a controlled laboratory environment. A set of recip rocation wear tests was developed to determine the wear and friction coefficients at different excitation frequencies. The 3D FE model was developed and verified with the experimental results, in terms of pre dicting the false brinelling wear profile shape and the maximum wear depth. This model was then used to investigate the effect of the normal load and vibration amplitudes on the false brinelling damage. The graphs of maximum wear depth versus bearing radial load, lateral vi bration and rotational displacement were produced to show the influ ence of external parameters on the bearing false brinelling damage. The reciprocating wear test results show that the friction coefficient in this case was constant at about 0.6 for different vibration frequencies. The wear coefficient, however, can be estimated by an exponential function of the frequency. Using this function, the wear coefficient of the false brinelling lateral vibration test (frequency of 24 Hz) and rotational vibration test (frequency of 15 Hz) were estimated to be 2.1E-15 Pa-1 and 7.3E-15 Pa-1, respectively. This is due to the debris retention in the contact area, caused by temperature increasing, at high frequencies. Reduction of the oxygen penetration into the interface, at higher fre quencies, is another reason of wear coefficient reduction. This can limit the formation of the oxide debris, at the interface and reduce the wear rate [27,29–31]. Experimental and modelling results showed that increasing the normal force, reduces the false brinelling wear depth. This reduction is particularly significant, when the bearing static normal load is less than 100 kg. Where by increasing the normal load on the bearing from 10 kg to 80 kg the maximum wear depth reduces by 51%, when the lateral vibration is 2 g. Wear depth has a direct relation with the normal pres sure and the relative displacement. Normal pressure increases by increasing the normal load. However, by increasing the normal load, there is a substantial reduction in the amplitude of the relative displacement which in turn reduces the wear depth. It was also shown that increasing the lateral vibration and rotational displacement significantly increases the false brinelling damage. Where, increasing
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