GEARBOX NOISE AND VIBRATION INFLUENCE OF BEARING PRELOAD

GEARBOX NOISE AND VIBRATION INFLUENCE OF BEARING PRELOAD Mats Åkerblom * and Ulf Sellgren *KTH Dep. of Machine Design SE-100 44 Stockholm Sweden *Volvo CE Component Division, SE-631 85 Eskilstuna, Sweden, mats.akerblom@volvo.com KTH Dep. of Machine Design SE-100 44 Stockholm Sweden, ulfs@md.kth.se Abstract The influence of bearing preload or endplay on gearbox noise and vibrations was investigated using a test gearbox consisting of a helical gear pair, shafts, tapered roller bearings, and housing. Vibration measurements were carried out at 140 Nm and 400 Nm torque, with 0.15 mm and 0 mm bearing endplay, and 0.15 mm bearing preload. The results show that the bearing endplay or preload influences the gearbox vibrations. For the test gearbox, it seems that in comparison with endplay, bearing preload decreases vibrations at speeds below 2000 rpm and increases vibrations at speeds over 2000 rpm. Finite element simulations show the same tendencies as the measurements. The literature was reviewed in order to find earlier work investigating the influence of bearing properties on gearbox noise. Introduction In recent years there have been increased legal and customer demands for lower noise levels for construction machinery. In wheel loaders and articulated haulers, the gearbox is sometimes the dominant source of noise. Even though gear whine is not the loudest source, its pure tone, which consists of frequencies that correspond to the gear mesh frequency and multiples thereof, is easily distinguished from other noise sources. It is often perceived as highly unpleasant. Furthermore, this type of gear noise creates an impression of poor quality. A general design requirement is to keep gear whine noise at least 15 db lower than the noise from other sources, such as the engine. Consequently any reduction in noise from these other sources necessitates a simultaneous reduction in the gear whine. Gear whine originates from vibrations that are considered to be primarily excited by transmission error (TE). TE is defined by Welbourn [1] as the nonconjugacy of a gear pair, that is, the motion error defined by the difference between the output gear's actual position and its position if the gear teeth were perfect in shape and infinitely stiff. TE is defined as: TE R N g θ p θ (1) N p = bp g where θ p and θ g are the rotations of the pinion and gear shafts, and N p and N g are the number of teeth on the pinion and gear, respectively. R bp is the base radius of the pinion. 1

The major causes of TE are manufacturing and assembly imperfections as well as elastic deformation of gear teeth, shafts, bearings, and the housing. Figure 1 shows a recorded TE and its low frequency runout and high frequency tooth-to-tooth components. Total TE Combined gear and pinion runout 0 1 2 Gear rev. 0 1 2 Gear rev. TE with runout removed 0 10 20 No. of mesh cycles Figure 1. Recorded TE and its runout and tooth-to-tooth component, Houser [2] The TE-induced vibrations are transmitted to the housing via the gears, shafts, and bearings. The housing vibrates and radiates noise. The level and frequency content of the gear noise can be influenced by changing any one of the following highly complex mechanisms: excitation, transmission, or radiation. In earlier work by Åkerblom and Pärssinen [3] and Åkerblom [4] a test rig was used to investigate the effect of different gear-finishing methods and gear deviations on the gearbox noise at different torque levels. The test rig principle is shown in Figure 2 and a photo of the test rig is shown in Figure 3. Hydraulic Cylinder Slave or Master Gearbox Electric Motor Load Sensor Test Gearbox Microphone Articulated Attachment Accelerometer Figure 2. Test rig principle, Åkerblom [5] 2

The test rig is of the circulating power type, which means that it consists of two identical gearboxes, each containing a single gear pair that represents the average gears in a wheel loader transmission. Tapered roller bearings are used in the test gearboxes in order to make them as similar as possible to a wheel loader gearbox. The two gearboxes are connected to each other by universal joint shafts. Torque is applied by a hydraulic cylinder connected to the slave gearbox, which is tilted around one of its shafts. The test rig is described in more detail in Åkerblom [5]. Technical data for the test gears are given in Table 1. Figure 3. Gear test rig, Åkerblom [5] Most but not all of the tested gear pairs showed a strong correlation between TE and noise. The measurements also revealed that disassembly and reassembly of the gearbox with the same gear pair could significantly change the housing vibration and gearbox noise levels. Three different noise measurements are shown in Figure 4. The gearbox was disassembled and reassembled using the same parts after each measurement. The rebuild variation was sometimes the same order of magnitude as the variations obtained when testing gear pairs with different topography and surface structure. Oswald et al. [6] also reported rebuild variations of the same order of magnitude when noise-testing gears in a test rig. Further efforts to control gear whine require a proper explanation of the observed rebuild variations. The aim of this work is to find the cause of the variations and thereafter decrease the rebuild variations. Pinion Gear Number of teeth 49 55 Normal module (mm) 3.5 3.5 Pressure angle (degrees) 20 20 Helix angle (degrees) -20 20 Center distance (mm) 191.9 191.9 Face width (mm) 35 33 Profile shift coefficient +0.038-0.529 Tip diameter (mm) 191 209 Table 1. Technical data for the test gears 3

Figure 4. Results of three different measurements of the sound pressure level (p ref = 2 10E-5 [Pa]) at 500 Nm torque. The gearbox was disassembled and reassembled with the same gears, shafts, bearings, and housing, Åkerblom and Pärssinen [3] Possible causes for the scatter in the recorded noise levels were studied by Sellgren and Åkerblom [7] by experimenting with variants of a gearbox FE model (Figure 5). The FE model of the gearbox consists of three sub models: Housing, Pinion System, and Gear System. These sub models interact at two composite interfaces, c 1 and c 2, and one elementary interface, i 8, that connects the cylindrical representations of the gear and pinion. Interface i 8 is represented by a single bar element with an axial stiffness equal to the gear teeth bending stiffness and the Hertzian contact stiffness of the gear pair. The effect of TE is modeled as a force pair applied at the two ends of the bar and acting in the contact direction. A second-level decomposition of the FE model of the gearbox means that each of the four bearing sub models can be further decomposed into two sub models and an interface feature. Gearbox Housing Gearbox # 1 2 3 Housing 1 m 1 c 1 c 2 PinionSystem PinionSystem 2 c 1 m 2 i 8 GearSystem 3 c 2 i 8 m 3 GearSystem Figure 5. Gearbox FE-model, Sellgren and Åkerblom [7] 4

Figure 6 shows the computed accelerations at the midpoint of the housing surface for four different model variants. The curve labeled Rigid shows the acceleration response to a harmonically varying excitation force at the pinion and gear interface. The force amplitude corresponds to a TE amplitude of 1 µm. A 1% overall relative damping was chosen for the model. The results for the soft gasket model variant show the limit case response of a gearbox with the two gearbox housing halves loosely interconnected. The all soft bearings curve shows the influence from four bearings with significantly reduced stiffness in all three spatial directions. The response curve in Figure 6 that is labeled 2 axially soft bearings emulates the effect of a frictionless shaft contact for two of the four bearings. On the basis of these and other simulations, it was hypothesized that the observed rebuild variations are caused by differences in the axial bearing preloading between different reassembly operations. If the hypothesis holds, the rebuild variations can be significantly reduced by using a more controlled reassembly procedure. Acceleration [db Re 1.e-5] 70 65 60 55 2 axially soft bearings all soft bearings Rigid soft gasket 50 1500 2000 2500 u [rpm] Figure 6. Housing vibrations in db (relative to 1 10-5 m/s 2 ) for four gearbox model variants, Sellgren and Åkerblom [7] Literature Review The literature was reviewed in order to find earlier research investigating the influence of bearing properties on gearbox noise. As early as 1969, Opitz [8] showed that different bearing types can influence gearbox noise levels. He compared the noise level from a gearbox with the same helical gear pair but with different bearing types and different axial preloads. The results showed that tapered roller bearings reduced the noise level (SPL) by 3 db compared to ball bearings. Axial preload reduced the noise level by approximately 1 db for both tapered roller bearings and ball bearings. Welbourn [1] states that Opitz [8] also shows that plain bearings reduce gearbox noise by 3 db compared to tapered roller bearings. 5

More recently, Young [9], Lin [10], and Rook [11] investigated the influence of bearing properties on gearbox vibrations and noise. Their results show that bearing properties can have a considerable influence on the gearbox vibrations and thus also on noise. However, it is necessary to consider the complete dynamic system, not only the bearings. In Young s bearing stiffness model [9] the geometry of the ball bearing was the input to the model. The result was a 3x3 stiffness matrix, including radial, axial, bending, and coupled stiffness. Damping was not included in the bearing model. Lin studied the dynamic force transmissibility through the bearings to the supporting housing [10]. A system consisting of a plate, a bearing, and a shaft was used to simulate a gearbox. Frequency response functions obtained by FE analysis were compared with experimental measurements. Different types of rolling element bearings were studied: ball bearings, cylindrical roller bearings, double row angular contact ball bearings, and spherical roller bearings. Rook [11] studied vibratory power flow through bearings. Two different approaches were compared: the mobility approach and the modal approach. Bearings were modeled as compliant and dissipative joints. He studied a simplified gearbox consisting of flexible shafts and a stiff housing on flexible mounts. He also studied a system consisting of a flexible plate, a bearing, and a shaft. The system was treated as a source path receiver system. The shaft was the source, the bearing was the path, and the plate the receiver. According to Rook power flow to the housing (i.e., the plate) can be reduced by adopting the following design criteria: 1) minimize the mobility of the receiving structure. 2) maximize the mobility of the joint (bearing). 3) enhance the mobility of the source (shaft) as much as possible. Due to possible misalignment of the gear, only the first design criterion is practically feasible. This means that the gearbox housing should be as stiff as possible. Fleming [12] used the similarities between rotor dynamics and gear dynamics to study a simple gear shaft bearing system. He investigated the influence of bearing stiffness and damping on dynamic transmission error and lateral gear vibrations. He concluded that dynamic transmission error could be decreased by 16 db if the damping is increased from typical values for rolling element bearings (3 kn sec/m) to the optimum value (350 kn sec/m). He noted that the required damping could be achieved using fluid film bearings or squeeze film dampers in combination with rolling element bearings. Fleming and Poplawski [13] used load-dependent non-linear bearing stiffness in transient rotor-dynamic calculations. Later they also included the dependence of rotational speed on ball bearing stiffness [14]. 6

Rebuilding of the test rig The test rig was rebuilt in order to avoid the risk of vibration from the slave gearbox influencing the vibration and noise from the test gearbox. The test rig was modified by changing from a circulating power principle to a test rig with only one gearbox, driven by the electric motor and braked by a hydraulic pump (Figure 7). The gears in the slave gearbox were removed and a hydraulic pump connected to the output shaft via a toothed belt and belt pulleys. A torque sensor at the input shaft was used to measure the torque applied to the gearbox. A check-valve in the output oil line from the hydraulic pump was used to control the torque. In this configuration the torque is limited to approximately 500 Nm due to limitations of the electric motor and the torque capacity of the toothed belt and hydraulic pump. Hydraulic Pump Tooth Belt Test Gearbox Microphone Electric Motor Torque Sensor Accelerometer Figure 7. Test rig operation after rebuilding of the rig (compare with Figure 2) The toothed belt and the hydraulic pump also create noise and vibration. However, the frequencies differ from the gear-induced vibrations, which consist mainly of the gear mesh frequency and multiples thereof. It is therefore possible to separate noise and vibration from the gearbox from noise and vibration from other parts of the test rig. 7

Instrumentation The instrumentation consists of a tachometer, three microphones, and three accelerometers. The three microphones are positioned in front of the gearbox, as shown in Figure 8. Three accelerometers are attached to the front of the gearbox (Figure 9). Accelerometer 1 registers vibrations in the axial direction. Accelerometer 2 measures vibrations in the radial direction, at an angle corresponding to the direction of the gear mesh contact force. Accelerometer 3 is at right angle to the direction of accelerometer 2. Microphone horisontal positions: Shaft no. 1 Shaft no. 2 Tacho Gearbox 29 cm 20 cm Mic. 1 40.5 cm Mic. 2 Mic. 3 Vertical positions: Microphone 1: 30 cm above table. Microphone 2: 45 cm above table. Microphone 3: 74 cm above table. 26.5 cm 37.5 cm Figure 8. Gearbox from above, showing tachometer and microphone positions, Åkerblom and Pärssinen [3] Acc. 2 Acc. 1 Shaft 1. Shaft 2. Acc. 3 Figure 9. Gearbox from the front, showing accelerometers attached to the gearbox. Arrows denote positive directions of accelerometers 2 and 3. Note that accelerometer 1 measures in the axial direction, Åkerblom and Pärssinen [3] 8

Measurements Table 2 shows the measurements made. Each measurement was made at pinion speeds from 500 to 2500 rpm. The speed steadily increases over 200 s. Order tracking was used to evaluate the noise and vibrations related solely to the gears. Reshimmed in place means that the bearing endplay or preload was changed without disassembling or removing the gearbox from the test rig. Measurement no. Pinion torque [Nm] Bearing endplay [mm] 1 140 0 2 400 0 Reshimmed in place 3 140 0.15 4 400 0.15 Reshimmed in place 5 140-0.15 6 400-0.15 Reshimmed in place 7 400 0.15 8 140 0.15 Gearbox completely rebuilt with same parts 9 140 0 10 400 0 Reshimmed in place 11 140-0.15 12 400-0.15 Table 2. Description of the measurements (negative endplay means preload) Results The results of two or three of the measurements are shown in each of the Figures 10 to 16. The figures show the vibrations at the gearbox housing measured by accelerometer 1 for the 49 th order of the pinion rotational frequency, corresponding to the gear mesh frequency. The torque at the pinion is 140 Nm for Figures 10 to 13 and 400 Nm for Figures 14 to 16. All measurements are made while increasing the speed from 500 to 2500 rpm over 200 s. 9

Figure 10 shows the reshim repeatability. After the first measurement, the gearbox bearing preload/endplay was changed (for another measurement), and then changed back to the same value as in the first measurement (0.15 mm endplay). This was done without disassembling the complete gearbox, and the gearbox was not removed from the test rig. Figure 10. Reshim repeatability for 0.15 mm bearing endplay and 140 Nm torque Figure 11 shows the rebuild repeatability. After the first measurement, the gearbox was completely disassembled and reassembled with the same parts and the bearing preload/endplay was set to the same value (0 mm) as in the first measurement. The differences between the two measurements are due to rebuild variations. Figure 11. Rebuild repeatability for 0 mm bearing endplay and 140 Nm torque 10

Figure 12 shows the influence of bearing preload. After the first measurement, the gearbox was not disassembled or removed from the test rig; only the bearing preload/endplay was changed from 0 mm to 0.15 mm preload. The differences between the two measurements are due to different bearing preloads and reshim variation. Figure 12. Influence of preload, for 0 and 0.15 mm bearing preload at 140 Nm torque Figure 13 also shows the influence of bearing preload on the vibration levels on the gearbox housing. As in Figure 12, the gearbox was not disassembled or removed from the test rig; only the bearing preload/endplay was changed from 0.15 mm endplay to 0 mm endplay and to 0.15 mm preload. The differences between the three measurements are due to different bearing preloads and reshim variation. The frequency is the 49 th order of the rotating frequency and the torque is 140 Nm at the pinion. Figure 13. Influence of preload, for 0.15 mm endplay, 0 and 0.15 mm bearing preload at 140 Nm torque 11

Measurements were also made at a torque level of 400 Nm at the pinion. Figure 14 shows the reshim variation. After the first measurement, the bearing preload/endplay was changed (for another measurement), and then changed back to the same value as in the first measurement, which was 0.15 mm endplay. This was done without disassembly of the complete gearbox, and the gearbox was not removed from the test rig. Figure 14. Reshim repeatability for 0.15 mm bearing endplay and 400 Nm torque Figure 15 shows the rebuild repeatability at 400 Nm torque. After the first measurement, the gearbox was completely disassembled and reassembled with the same parts and the bearing preload/endplay was set to the same value (0 mm) as in the first measurement. The differences between the two measurements are due to rebuild variations. Figure 15. Rebuild repeatability for 0 mm bearing endplay and 400 Nm torque 12

Figure 16 shows the influence of bearing endplay or preload on the vibration levels on the gearbox housing at 400 Nm torque. The gearbox was not disassembled or removed from the test rig; only the bearing preload/endplay was changed from 0.15 mm endplay to 0 mm endplay and to 0.15 mm preload. The differences between the three measurements are due to different bearing preloads and reshim variation. The frequency is the 49 th order of the rotating frequency and the torque is 400 Nm at the pinion. Figure 16. Influence of endplay or preload, for 0 and 0.15 mm endplay and 0.15 mm bearing preload and 400 Nm torque Conclusions Sellgren and Åkerblom [7] used finite element simulations to find reasons for the observed rebuild variations when noise-testing gears. Their simulations show that bearing stiffness significantly affects vibrations at the gearbox housing. Measurements show that for a gearbox with tapered roller bearings, the bearing endplay or preload influences the vibration level on the gearbox housing, and thus also the noise radiated from the gearbox. Figures 13 and 16 show that the difference is larger when changing from 0 to 0.15 mm preload than when changing from 0 to 0.15 mm endplay. Consequently, to minimize the rebuild variation when noise-testing gears, a small endplay is better than a small preload because the sensitivity to small variations in endplay is smaller than the sensitivity to variations in preload. It is more likely that it is preloading the bearings that changes the dynamics of the system rather than the excitation level. That is because the peaks corresponding to resonances in the system are moved to different frequencies. It is not only the amplitude that is changed. Amplitude changes would be expected if the excitation was different or if the damping was increased or decreased. 13

As a general conclusion for the test gearbox, it seems that in comparison with endplay, bearing preload decreases vibrations at speeds below 2000 rpm and increases vibrations at speeds over 2000 rpm, at least at a torque level of 140 Nm. The results of the simulations of housing vibration show the same tendency as the measurements. Rigid bearings result in higher levels of vibration over 1800 rpm and lower levels below 1800 rpm, compared to all soft bearings. The bearing endplay or preload influences the vibration more at 140 Nm than at 400 Nm. The reshim variations are also smaller at 400 Nm. This is probably because the bearing stiffness increases when the load increases. In addition, the relative difference in stiffness due to small variations in preload is smaller at higher loads. The influence of bearing preload on the noise level from a gearbox is therefore most likely to be an issue at low loads. Acknowledgements The work presented here was performed as part of the Interface Project and was financially supported by Volvo Construction Equipment and the Swedish Strategic Research Foundation. The authors would also like to acknowledge all colleagues at Volvo and at the Royal Institute of Technology who contributed to this work. References [1] Welbourn D.B., Fundamental Knowledge of Gear Noise A Survey, Proc. Noise & Vib. of Eng. and Trans., I Mech E., Cranfield, UK, July 1979, pp 9-14. [2] Houser D.R., Gleason Goulder single flank measurement system, http://gearlab.eng.ohio-state.edu/pages/teststand/subsites/gleason-goulder.htm, 2006. [3] Åkerblom M. and Pärssinen M., A study of Gear Noise and Vibration, TRITA-MMK 2002:8 / ISSN 1400-1179 / ISRN/KTH/ MMK/R-02/8-SE, Stockholm, 2002. [4] Åkerblom M., Gear Noise and Vibration Influence of Gear Finishing Method and Gear Deviations, Licentiate thesis, TRITA-MMK 2002:7 / ISSN 1400-1179 / ISRN/KTH/ MMK/R-02/7-SE, Stockholm, 2002. [5] Åkerblom M., Gear test rig for noise and vibration testing of cylindrical gears, Proceedings OST 99 Symposium on Machine Design, KTH, Stockholm, 1999. [6] Oswald F.B., Influence of Gear Design on Gearbox Radiated Noise, Gear Technology, January / February 1998, pp 10-15. [7] Sellgren U. and Åkerblom M., A Model-Based Design Study of Gearbox Induced Noise, International Design Conference Design 2004, Dubrovnik, May 18-21, 2004. [8] Opitz H., Noise of gears, Phil. Trans R. Soc., London Ser. A, Vol. 263, 1968-9, pp 369-380. [9] Young W.B., Dynamic Modelling and Experimental Measurements of a Gear Shaft and Housing System, M.S. Thesis, Ohio State University, 1988. [10] Lin J.S., Experimental Analysis of Dynamic Force Transmissibility Through Bearings, M.S. Thesis, Ohio State University, 1989. 14

[11] Rook T., Vibratory Power Flow Through Joints and Bearings with Application to Structural Elements and Gearboxes, Doctoral Thesis, Ohio State University, 1995. [12] Fleming D.P., Effect of Bearing Dynamic Stiffness on Gear Vibration, NASA/TM- 2002-211356, http://gltrs.grc.nasa.gov/, January 2002. [13] Fleming D.P. and Poplawski J.V., Transient Vibration Prediction for Rotors on Ball Bearings Using Load-Dependent Non-Linear Bearing Stiffness, NASA/TM-2002-211829, http://gltrs.grc.nasa.gov/, August 2002. [14] Fleming D.P. and Poplawski J.V., Unbalance Response Prediction for Rotors on Ball Bearings Using Speed and Load Dependent Nonlinear Bearing Stiffness, NASA/TM- 2003-212527, http://gltrs.grc.nasa.gov/, August 2003. 15