Asymmetry characteristic of tilting-pad thrust bearing

Industrial Lubrication and Tribology Asymmetry characteristic of tilting-pad thrust bearing during the start-up and shut-down process Zhanchao Wang, Fei Guo, Ying Liu, Xiangfeng Liu, Yuming Wang,

Article information: To cite this document: Zhanchao Wang, Fei Guo, Ying Liu, Xiangfeng Liu, Yuming Wang, (2018) "Asymmetry characteristic of tilting-pad thrust bearing during the start-up and shut-down process", Industrial Lubrication and Tribology, https://doi.org/10.1108/ILT-11-2017-0351 Permanent link to this document: https://doi.org/10.1108/ILT-11-2017-0351

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Asymmetry characteristic of tilting-pad thrust bearing during the start-up and shut-down process Zhanchao Wang Tsinghua University, Beijing, China

Fei Guo State Key Laboratory of Tribology, Beijing, China

Ying Liu Mechanical Engineering, State Key Laboratory of Tribology, Beijing, China

Xiangfeng Liu Tsinghua University, Beijing, China, and Downloaded by Mr Zhanchao Wang At 23:21 27 September 2018 (PT)

Yuming Wang State Key Laboratory of Tribology, Tsinghua University, Beijing, China Abstract Purpose – This aim of this paper has been to investigate the squeeze effect of a water-lubricated tilting-pad thrust bearing during start-up and shutdown periods. Design/methodology/approach – In this paper a numerical model with a squeeze and slippage effect was adopted to analyse the asymmetry characteristic of a tilting-pad thrust bearing during start-up and shut-down periods. A test rig was built to verify numerical results, which were a combined measurement method in which acceleration sensor and torque sensor were used simultaneously to determine the angle change of the thrust pad. Findings – It was found that as the velocity gradient increased, the difference of the minimum dimensionless film Hmin could be ignored in the startup process. But in the shut-down process, as the velocity gradient increased, the value of Hmin also increased, which showed that there was an asymmetry characteristic of the tilting bearing in two processes. This phenomenon was verified by measuring the friction torque curve in the test. Originality/value – The results of the studies demonstrated that the velocity gradient could be designed to reduce the friction of the thrust bearing, which would be beneficial to the working life of the tilting-pad thrust bearing. Keywords Asymmetry, Tilting-pad thrust bearing, Squeezed effect, Start up and Shut down Paper type Research paper

1. Introduction In the industrial application of tilting-pad thrust bearings, the start-up and shut-down process times are usually short. The velocity gradient of the bearing speed during this process is an important factor in the operation of the tilting-pad thrust bearing. During these periods, the thrust pad swings around the pivot cause the film thickness to change quickly, which causes the squeezed effect in the gap between the thrust pad surface and the thrust disc. Therefore the squeezing effect should be considered in this process, and the velocity gradient of the speed plays an important role (Kettleborough, 1974). In the early stages of the study of the squeezed effect, scholars mainly studied the rolling bearing with the point contact model. The current issue and full text archive of this journal is available on Emerald Insight at: www.emeraldinsight.com/0036-8792.htm

Industrial Lubrication and Tribology © Emerald Publishing Limited [ISSN 0036-8792] [DOI 10.1108/ILT-11-2017-0351]

An interesting attribute of squeezed films – the second sharp pressure peak – was revealed using a thin-film pressure transducer in the centre of contact (Safa and Gohar, 1986). Theoretical evidence of this phenomenon was presented in the literature (Larsson and Hoglund, 1994; Dowson and Wang, 1994; Larsson and Hoglund, 1995) together with a broad description of EHL (elastohydrodynamic lubrication) contacts subject to impact loadings where a time lag between the occurrence of the maximum force and the minimum film thickness was analysed as a result of the damping and elasticity of the lubricating film. The related works (Chu et al., 2006a, 2006b; Guo et al., 2007) investigated the pressure and film thickness distributions under squeeze motions. The biggest boom of experimental studies in this research field took place at

This work was supported by the National Basic Research Program of China (973) (Grant No. 2015CB057303) and Natural Science Foundation of China (Grant No.51735006). Received 4 January 2018 Revised 31 March 2018 Accepted 3 May 2018

Asymmetry characteristic of tilting-pad thrust bearing

Industrial Lubrication and Tribology


Zhanchao Wang et al.

the end of 1990s, mainly due to the affordability of high-speed cameras at this time. Chu et al. (2004) and Martini and Bair (2010) focused on the pure squeeze action that showed, as well as the previous contributions did, that a central dimple film shape, with the minimum thickness at the peripheral region of contact, was formed and a pressurised lubricant was entrapped between the approaching surfaces for a long time after the impact. For lubricant entrapment under the conditions of the sudden halting of a rolling/sliding motion, acceleration together with the rheological properties of lubricants has proved experimentally (Sugimura et al., 1998; Glovnea and Spikes, 2000, 2001a, 2001b; Sugimura, 2002; Ohno and Yamada, 2007) and theoretically (Glovnea and Spikes, 2001a, 2001b; Holmes et al., 2003; Zhao and Sadeghi, 2003) important for the squeezed film phenomenon. Furthermore, if the rolling/ sliding conjunction was subjected to sudden changes in load, a squeezed film of lubricant was generated at the inlet of the contact and was entrained through it without a change in thickness or shape (Nishikawa and Kaneta, 1993; Sakamoto et al., 2003). Fryza et al. (2017) studied the film thickness behaviour of lubricant entrapment under diverse conditions including initial impact gaps, initial approach speeds, loading speeds and a variety of lubricants during the introductory part of the impact loading. The results showed that the entrapped film shape directly depends on loading speed and that the central film thickness was mainly determined by the approach speed and lubricant viscosity and could be approximated by the power law where the influence of impact times/speeds could be estimated from the basic rheological properties of the lubricants. In recent years EHL squeezed film behaviour has been investigated, mainly theoretically. For very thin films under 5 nm, it was shown in theoretical analyses (Chu et al., 2010, 2013) that both pressure and film thickness oscillate during the squeeze action due to the action of the surface forces. However, those studies mainly focused on point contact conditions. There are many contact conditions such as seal and sliding bearings in face-to-face contact in industrial applications, which needed be researched. Bo (2002) established a dynamic simulation numerical model considering the influence of the squeezing effect on the gas lubrication spiral groove seal. Lu et al. (2015) studied the thermal transient mixed lubrication characteristics of the angular contact bearing during start-up and shut-down periods. It was shown that the squeezing effect was introduced due to the decrease in the film thickness during shut-down. The thickness of the oil film was higher than the corresponding thickness during start up at the same speed. Liu et al. (2016) analysed the transient characteristics and the squeezing effect of the fluid lubrication film during acceleration and deceleration by a slider-disc test system. During acceleration and deceleration, the film thickness alteration and velocity sustained the lag phenomenon. Meng and Hou (2010) used the modified transient Reynolds, thermal energy and working oil temperature–viscosity equations to study the effect of oil film squeezing on the start-up process, and were solved simultaneously by the finite element method. The results showed that the effect of oil film squeezing was very small in the earlier stages of the start-up process. In the later stages, the effect of oil film squeezing became more and more significant with the decrease of the thickness of the oil film.

From previous studies, it can be concluded that the squeeze effect affected the fluid pressure and film thickness, which can impact the friction torque of the thrust bearing. Compared to other operating environments, the motion of the thrust pad is complicated during the start-up and shut-down processes. In this paper, a transient model of a tilting-pad thrust bearing has been proposed, and a verification test rig was designed to verify the numerical model and results. The swing of the thrust pads was monitored by the acceleration sensors. The results of the influence of the velocity gradient on the tilting-pad thrust bearing performance were obtained.

2. Numerical model Based on the water-lubricated tilting-pad thrust bearing during start-up and shut-down periods, a transient model under the mixed lubrication condition was presented. The squeezing effect during start-up and shut-down periods was considered in the PC flow equation (Patir and Cheng, 1978, 1979): ! ! 1 @ rUr h3 @p 1 @ Uu h3 @p 1 2 r @r 12 m @r r @ u 12 m @ u ¼ Uc

v 1 v s @h h @ ðv 1 v s Þ v v s @Us @h 1 1s 1 Uc 2 @t @u 2 @u 2 @u (1)

where: Ur, Uu , Us = flow factors, when h > 3s , the value is equal to 1; Uc = contact factor; h = film thickness, m; vs = sliding angular speed, rad/s; s = synthetic roughness. The non-dimensional equation (1) is shown as equation (2), with dimensionless parameters that have been determined in equations (3)-(7): @ 1 @ 3 @P 3 @P Rf r H 1 fuH @R @R R @u @u ¼ f c 1s

v 1 v s @H H @ ðv 1 v s Þ 1 @u @u 2 2

v vs @f s @H 1fc @j 2 @u

(2)

H ¼ h=s ;

(3)

R ¼ r=ro ;

(4)

ps 2 ; 6 mv ro 2

(5)

v ; v0

(6)

j ¼ v t;

(7)

P¼

v ¼

The CEB (Chang, Etsion and Bogy) contact model (Chang et al., 1987) was adopted for the tilting-pad thrust bearing start-




up and shut-down numerical model. Consequently whether the deformation of interference roughness was elastic or plastic was determined by: 2 p KHa vc ¼ Ra (8) 2E


where: v c = the parameter to determine whether the deformation of interference roughness was elastic or plastic; Ha = hardness or yield strength of the soft material; E = relative elastic modulus, Pa; K = constant (approximately 0.6). When h < v c, the two rough contact surfaces will result in elastic contact; when h = v c, the two rough contact surfaces will begin to yield; when h > v c, plastic deformation of the two rough contact surfaces is produced; and when h > 6s , the deformation caused by surface roughness can be ignored. In the PC and CEB models, the full film lubrication condition was determined by the film thickness. In the PC model, when the film thickness was 6s > h > 3s , the bearing Figure 1 Flow chart of the transient numerical model

ran in full film lubrication (Chang et al., 1987). However, at this time, a contact force still existed in the CEB model. When h < 3s , the bearing ran in mixed lubrication and the friction torque would be reduced as the rotational speed increased. After the bearing began running in full film lubrication (h > 6s ), the friction torque gradually increased as the rotational speed increased; therefore, the friction torque had a minimum value when the film thickness was 6s > h > 3s . Based on the PID (proportion, integration and differentiation) method (Wang et al., 2017a, 2017b), the flow chart for Matlab programming has been presented in Figure 1. The parameters of the tilting-pad thrust bearing discussed in this paper have been shown in Table I.

3. Numerical results and analysis Four velocity gradients were adopted in the numerical simulations and experiments as the operation curve, as shown in Figure 2. In these four speed curves, the maximum speed of the thrust bearing was 600 r/min. For this speed, the bearing was assumed





Table I Main parameters of the tilting-pad thrust bearing Feature

Unit

Value

Inner diameter Outer diameter Wrap angle Circumferential eccentricity coefficient Radial eccentricity coefficient Environment temperature Material of thrust plate Material of thrust pad Elastic modulus of pivot E1 Elastic modulus of pivot seat E2 Radius of pivot R1 Radius of pivot seat R2 Roughness of pad Roughness of thrust plate Number of thrust pads

mm mm ° — — °C —

60 140 50 0.5 0.5 25 Cemented carbide Graphite 204 204 16 25 0.8 (Ra) 0.4 (Ra) 6 (each set of bearing has 3 pads)

GPa GPa mm mm mm mm —

Figure 2 Velocity gradient of tilting-pad thrust bearing during start-up and shut-down periods

to be open and the lubrication of the thrust bearing was EHL. The value of h and the angle of the pad were zero, when the speed was zero. However, at low speed, usually less than 10 rpm, the speed of the motor cannot be accurately controlled by the converter. Therefore, the lubrication condition within the 0- to 10-rpm speed range has not been studied in this paper. From Speed Curve 1 to Speed Curve 4, the velocity gradient of the four speed curves gradually increased. The calculation results of the performance of the tilting pad thrust bearing, such as hmin, angle of the pad and the friction torque, have been shown in Figure 3. In Figure 3(c), the friction torque value was small between No. 15 to No. 23 of the start-up and shut-down sequences, and it is hard to distinguish the four friction torque curves; therefore, this part of the curve has been magnified, as shown in Figure 3(d). To compare the results for the same speed, the start-up and shut-down sequence has been chosen as the abscissa axis in the figures. The speed of the four speed curves was the same for the same serial number of the start-up and shut-down sequence.

3.1 Film thickness As shown in Figure 3(a), the dimensionless film thicknesses Hmin were asymmetrical during start-up and shut-down periods. The four Hmin curves were approximately the same in the start-up stage; during the shut-down stage, the four Hmin curves were different. For the same speed, Hmin increased as the velocity gradient increased. At the beginning of the shut-down stage, the Hmin curves suddenly increased when the operation curve chose Speed Curves 2 to 4, and the saltation disappeared when the operation curve was Speed Curve 1. There is a squeeze item (@h/@t) in the right of equation (1). From the definition of the squeeze effect, when @h/@t > 0 during the start-up period, the squeeze effect was zero; in the shut-down stage, @h/@t < 0, the squeeze effect was raised. The degree of influence increased as the velocity gradient of the speed curves increased. When the bearings were operated under Speed Curve 1, the Hmin curve was symmetric in the second stage. Because the velocity gradient of Speed Curve 1 was small, the effect of the velocity gradient can be ignored. 3.2 Angle of the thrust pad In Figure 3(b), the angle of the thrust pad (a, drawn in Figure 4) curves was also asymmetric during the start-up and shut-down stages. The four a curves were approximately the same in the start-up stage; but, in the shut-down stage, the four a curves were different. For the same speed, a decreased as the velocity gradient increased. At the beginning of the shut-down stage, the a curves suddenly decreased when the operation curve chose Speed Curves 2 to 4, the saltation disappeared when the operation curve was Speed Curve 1. The speed of the system began to decrease, the thrust plate fell down and the squeeze effect appeared in the gap, as shown in Figure 4(a). The hydrodynamic pressure on the left pad (F1) was more than that on the right pad (F2), and there was a torque value (M) around the pivot which made the thrust pad rotate. Therefore, as the angle a decreased, hmin increased. When the speed decreased from V to V’, the torque value M could rotate the angle of the pad from a to a”, as shown in Figure 4(c). The LCC (load-carrying capacity) of the pad depended on the film thickness h and the angle a of the pad, as shown in equation (9): 00 00 FLCC ¼ f h ; a (9) As M increased, for example M’(M’ > M), the pad would rotate from a to a’ (a’ < a”, Da = a” a’) . Therefore, Da increased as the velocity gradient increased. According to equation (9), the LCC of the pad will be: 0 0 0 FLCC ¼ f h ; a (10) However, the thrust bearing needs to provide FLCC (>F’LCC) to balance the load of the bearing, so the angle of the pad would rotate to a”, as shown in Figure 4(b). This is the reason why there was a sudden drop and then rise in the curves of the angle of the pad at the beginning of the shutdown stage. The Hmin curves also had a sudden rise and then





Figure 3 Numerical results in the start-up and shut-down stages

Figure 4 Tilting-pad thrust bearing motion schematic diagram at the beginning of the shut-down stage

drop. The amplitude value of the change increased as the velocity gradient increased, as shown in Figures 3(a) and (b). 3.3 Friction torque As shown in Figure 3(c), the friction torque of the tilting pad thrust bearing approximately overlapped during the start-up stage curves. However, the four friction torque curves were different during the shut-down stage. When the speed curve chose Speed 1, the friction torque values were the same for the same speed. When the Speed Curves 2 to 4 were chosen, the friction torque curves were asymmetric. In this figure, the friction torque decreased as the velocity gradient increased during the shut-down period. After No. 23, the friction torque values were smaller than that for the same speed during the start-up period, the value of the friction torque decreased as the velocity gradient increased. The value of Hmin during shut-down period was greater than that during the start-up period, so the flow shear stress decreased. At the beginning of the shut-down stage (from No. 15 to No. 20), the flow field was EHL, and the friction torque was mainly affected by the fluid shear force. Therefore, the friction torque during the shut-down period was smaller





than that during the start-up period. The differences of the four friction torque values have been shown in Table II. The velocity gradient of the speed curve affected the film thickness, the angle of the pad and the friction torque of the tilting-pad bearing during the shut-down stage, but there was no effect during the start-up stage. The curves will be asymmetric when the velocity gradient is large enough. The degree of asymmetry of the curves increased as the velocity gradient increased. Furthermore, the results of the numerical analysis were consistent with that of Lu et al. (2015). The influence of the velocity gradient on the pad and the friction torque was the opposite. An increase in the velocity gradient can result in a decrease in the friction torque, which can improve the life of the bearing. However, an increase in the velocity gradient can result in the angle of the pad saltate increasing which can damage the pad. Therefore, in order to improve the life of the bearing as much as possible, the velocity gradient of the speed curve should choose a balanced value.

4. Verification experiment 4.1 Test rig To verify the numerical model, the experiment was executed with a test rig for the water lubricated tilting-pad thrust bearing (Zhang et al., 2017), as shown in Figure 5. Test cavity include torque sensor, loading device, thrust plate and tilting-pad thrust bearing, as shown in Figure 6. The torque sensor was used to measure the friction torque which would affect the performance and life of the tilting-pad thrust bearing. The error of the system friction torque caused by the friction torque of the ball bearing, which should be reduced in Table II Comparison of friction torque values of the four speed curves with the value of Speed Curve 1 Speed 600 540 480 420 360 300 240 180 120 60 10

T1 (%) 100 100 100 100 100 100 100 100 100 100 100

Relative error T2 (%) T3 (%) 100 94 95 95 95 95 96 96 98 88 68

100 89 89 90 90 91 91 92 96 70 41

T4 (%) 100 83 84 84 85 86 87 88 94 51 21

Note: Ti: friction torque value when system chose the Speed Curve i; i = 1, 2, 3, 4.

Figure 5 Schematic diagram of the water-lubricated tilting-pad thrust bearing shrinkage ratio test rig

Figure 6 Internal schematic diagram of the body of the test rig

the measurement results, can be evaluated before the test. The loading device was a hydraulic cylinder connected to a hydraulic station to provide a constant load to the thrust pad. A pair of symmetric tilting-pad thrust bearings was arranged face to face to balance the axial force. To prevent the temperature of the lubrication medium from getting too hot, the external water circulation system was introduced. The reader can find more pictures and information about this test rig in the related literature (Wang et al., 2017a, 2017b). Thermocouples monitored the temperature variation of the water. In the test rig, three acceleration sensors on the pads (Figure 7) were able to get acceleration signals when the angle of the pad changed. 4.2 Experimental results and analysis In the verification experiment, the parameters of the inverter and electric motor were changed to ensure the speed of the test rig followed the curves in Figure 2. The film thickness and angle of the pad could not be measured directly, instead acceleration sensors were adopted to monitor the changing angle of the tilting-pad thrust bearing, and the friction torque was measured by the torque sensor. The relationship between the acceleration curves and film thickness has been shown in Figure 8. As shown in Figure 8(a), when the operation chose the Speed Curve 1, there were no major changes in the three acceleration curves, and the amplitude of the swing of the thrust pad was small, less than 0.5 m/s2 which showed that the swing of the thrust pad was very small. When the operation chose the Speed 2 to 4 curves, as shown in Figure 8(b)-(d), the single acceleration curve decreased significantly. As the velocity gradient of the speed curves increased, the single acceleration Figure 7 Schematic diagram of the acceleration sensor installation position





Figure 8 Relationship between the thrust pad acceleration curves and the film thickness (simulation value)

curve increased in the beginning of the shut-down stage, and the absolute value of the accelerations were more than the value in Figure 8(a). The change of the acceleration curves can also analyse the motion of the pad. In Figure 8(a), the value of the acceleration was a positive number during start-up and a negative number during shut-down. The positive acceleration meant the angle of the pad increased, and the negative acceleration meant the angle of the pad decreased. In Figure 8(b)-8(d), the accelerations were negative during the beginning of the shut-down period (No. 15-No. 17.5), and changed to be positive after No. 17.5, until the end of the shut-down period. In the experimental results, the sign of the acceleration value changed two times, which illustrated the angle of pad first decreasing and then increasing. Those test results were in agreement with the theoretical results shown in Figures 3(a) and 3(b). As shown in Figure 9, the friction torque of the thrust bearing was asymmetric, and it decreased as the velocity gradient of the speed curves increased during the shut-down process. These results were in accordance with the results in Figure 3(c). Therefore, the experimental results were consistent with the results from the numerical model.

Figure 9 Experimental results of the friction torque in the start-up and shut-down stages





5. Conclusion A transient model under mixed lubrication conditions has been presented in this paper, and the analysis results were verified by the test rig. The following conclusions were obtained: The tilting-pad thrust bearings have some asymmetrical characteristics during the start-up and shut-down processes, such as the distribution of film thickness, angle of the pad and the friction torque. As the velocity gradient of the speed increased, the oscillation amplitude of the thrust pad increased, which is harmful to the tilting-pad thrust bearing; but the friction torque of the tilting-pad thrust bearings decreased, which is beneficial to the tilting-pad thrust bearing. Therefore, the velocity gradient of the speed should be selected to be an appropriate value. The acceleration sensor can be adopted to monitor the motion and changing angle of the thrust pad. The direction of the swing of the pad can be judged by the positive or negative value of the acceleration, and the impact force can be judged by the amplitude of the acceleration signal. Of course, there is more work needed to be done in the further research, such as the measurement of the film thickness and the performance of the tilting pad thrust bearing under low-speed conditions (0-10 rpm).

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Corresponding author Ying Liu can be contacted at: [email protected]


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