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Friction and wear of pivot jewel bearing in oil-bath lubrication for high rotational speed application
Wear 302 (2013) 1506–1513
Contents lists available at SciVerse ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
Short communication
Friction and wear of pivot jewel bearing in oil-bath lubrication for high rotational speed application Xingjian Dai n, Kai Zhang, Changliang Tang Department of Engineering Physics, Tsinghua University, Beijing 100084, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 August 2012 Received in revised form 2 January 2013 Accepted 11 January 2013 Available online 23 January 2013
Oil-lubricated pivot jewel bearings are used in the vertical support systems for small, high speed rotating machinery such as flywheels for energy storage, fabric spindles, and centrifuges. The friction and wear of a tool steel pivot tip spinning in a corundum jewel cup were studied experimentally. The contact stress conditions at the tip were analyzed by a finite element method. The friction coefficients of the pivot jewel varied from 0.10 to 0.05, which are typical of boundary lubrication. Wear tests of samples from three groups of bearings indicated that abrasive wear, fatigue wear and adhesive wear occurred in a sequence. The size of the damage of the contact surface varied form 1 mm to dozens of mm. Abrasive and fatigue wear were also observed on the harder jewel cup surface. A wear index based on surface appearance was used to categorize the wear process on the bearing. & 2013 Elsevier B.V. All rights reserved.
Keywords: Jewel bearings Sliding wear Wear testing Lubricated wear including scuffing Fatigue
1. Introduction Low speed jewel bearings are used as supports in electrical measuring instruments such as galvanometers, ammeters and energy measuring meters. A pivot jewel bearing consists of a ball or a shaft tip that spins on an axis perpendicular to the contact area. The bearing support element is usually a concave or plate surface of hard anti-wear material such as ruby or steel. Although jewel bearings have limited load-bearing capacity, it is possible to use them as flexible support for rotor systems such as small high speed flywheels and centrifuges. Pivot jewel bearings are usually used with permanent magnetic bearings, and thus only 5%–10% of the rotor’s weight is born on the jewel bearing. Unlike the low speed situation with dry friction in electrical measuring instruments, the pivot jewel bearings must be lubricated by oil for high speed application. The lubrication oil resists wear and extracts the friction heat of the bearing. The bearing life can last as long as 5–10 years for small high speed rotating machinery. The tribological behavior of jewel bearings in high speed machinery needs investigating for its proper design and application. For the high spinning vertical shaft bearing application in small rotating machinery such as hard disks [1], centrifuges, flywheels [2] and fabric spindles, the commonly used mechanical bearings include small ball bearings, spiral groove hydrodynamic
n
Corresponding author. Tel.: þ86 1062784518; fax: þ86 1062798299. E-mail address: [email protected] (X. Dai).
0043-1648/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.wear.2013.01.032
film bearings and jewel bearings. Ball bearings have high stiffness and considerable friction loss. Spiral groove bearings have good load-bearing capacity and moderate stiffness, but lack stability due to oil film. Pivot jewel bearings have good stability but small load-bearing capacity and they have wear problems caused by contact friction. Pivot jewel bearings fall into three types depending on the curvature of the contact interaction surfaces. The traditional type is a small pivot tip and a large bearing cup with a point contact in Fig. 1(a). For the total contact type, the pivot tip and the bearing cup enjoy the same curvature in Fig. 1(b), and they share a spherical contact area. The line contact type is the case of a larger tip curve ratio and smaller cup curvature in Fig. 1(c). As manifested in the published papers, pivot jewel bearings were used as thrust bearings with dry friction [3,4]. In the hybrid magnetic bearing for a flywheel energy storage system, a synthetic ruby or sapphire ball on the flywheel and a stationary, flat sapphire plate were used as the axial support. The typical friction energy dissipation was 0.3 W at 100,000 rpm [3]. A Si3N4 ball held at the end of the shaft span against the stationary 440C stainless steel disk in the experimental study of the permanent magnetic bearings for spacecraft applications. In this case, the test rig with the jewel bearing as the axial support arrived at the speed of 5500 rpm [4]. Sankar and Tzenov presented a mechanical model for the jewel bearings to predict the errors and friction loss [5]. They also presented and modeled a jewel bearing with a free ball between the cup surface fixed to the rotor and the stationary cup to solve the concentrated wear due to the circular contact band of the
X. Dai et al. / Wear 302 (2013) 1506–1513
P Pb Pw Pm
Nomenclature
o do dt dE J
rotational speed of the flywheel a little decrease of the flywheel speed time interval energy loss of the spinning system rotational inertia of spinning system
deceleration power of the spinning system bearing loss power windage loss power motor loss power friction coefficient load of the bearing mean radius of the contact ring
m N r
spherical end of the rotor [6]. Their study indicated that the friction force between the steel tip and the cup sapphire surface had great effect on the rotor motion. The friction coefficient of the pivot jewel bearing in boundary lubrication was determined by experimental methods [7]. However, the wear details of the jewel bearings remain unclear. The current study was undertaken to analyze the contact stress and wear of pivot jewel bearings. The contact stress of the bearings was calculated by the finite element method. A test rig was built to investigate the friction coefficient, the wear types and wear mechanisms of the pivot jewel bearings. The wear tests of about 30 bearing samples were carried out for hundreds of hours to thousands of hours. A wear index was presented to describe the wear process of the bearing according to the damage on the pivot tip surface.
2. Contact stress analysis Stress distribution in contact area of a pivot jewel bearing may lead to the onset and deterioration of the fatigue crack of the pivot tip surface. The contact stress of all the three type bearings can be calculated by the finite element method. The three types of pivot jewel bearings have the same material parameters, as shown in Table 1. For the traditional type, the curvature radius of pivot tip r ¼1.95 mm, and curvature radius of bearing cup R¼2.0 mm. For the total contact type, r ¼R¼2.0 mm. For the line contact type, r ¼2.05 mm and R¼2.0 mm. The two-dimensional element Plane183 in ANSYS was chosen to model the pivot jewel bearing. The properties of the Plane183 were axisymmetric. The Targe69 and Conta172 in ANSYS were selected to establish contact pair. The load applied on the top of pivot was 10 N. The results were
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as follows: as shown in Fig. 2, the maximum Von Mises stress of the three types of pivot tips was significantly smaller than 630 MPa, the yield strength of the T10 steel. The stress of pivot tip was within the safe range according to the fourth strength theory. The maximum contact pressure and the maximum Von Mises stress of line contact type were 658 MPa and 368 MPa respectively, both of which were much higher than those of the traditional type and total contact type bearings. That could be explained by the non-smooth transition of the curvature radius of line contact type pivot bearings. A line contact type bearing had the maximum contact pressure and was prone to be worn. However, such bearings had a gap between the pivot tip and the bearing cup that was able to store abrasive particles, which helped prevent the more severe abrasive wear. The material of pivot tip surface lost continuously in runningin period, so geometric contours of the pivot tip changed constantly. Both the Hertz point contact and the line contact turned into conforming contact with growing contact area. It was hypothesized that the radius of circular abrasion area of the traditional contact type bearing was 160 mm and the divergence of outside radius and inner radius of annular abrasion area of the line contact type bearing was also 160 mm at the end of the
Table 1 Mechanical properties of materials. Parts
Material
Elasticity modulus /GPa
Pivot Jewel bearing
T10 steel 210 Corundum 407
Poisson’s ratio m
Yield strength / MPa
0.3 0.2
630 –
contact area
contact area
contact area
pivot
pivot
jewel R>r
pivot
jewel R=r
jewel R
Fig. 1. Three types of pivot jewel bearings. (a) Traditional, (b) total contact and (c) line contact.
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Fig. 2. Contact pressure and Von Mises stress of pivot jewel bearings: (a) traditional type, (b) total contact type, and (c) line contact type.
running-in period. 10 N was loaded on the top of the pivot. The contact stress analysis results are shown in Fig. 3. For traditional type pivots, the non-smooth transition of curvature radius of pivot tip produced a small stress concentration on the exterior margin. The pressure was about 31 MPa in most of the contact area and the corresponding von Mises stress was 16 MPa, with the peak contact pressure being 277 MPa and the corresponding Von Mises stress 142 MPa. For line contact type pivots, the pressure was 11 MPa in most of the contact area and the corresponding Von Mises stress was 7 MPa. The peak contact pressure and corresponding Von Mises stress were smaller (102 MPa and 67 MPa respectively) than those of the traditional total contact type bearings. It can be concluded that the running-in transforms pivot contact from Hertz point or line contact into conforming surface contact, which increases the contact area and reduces the contact stress. The contact stress of the line contact type bearings is about
half of the traditional contact type bearings after the running-in period. The pivot jewel bearings used in the following experimental study were line contact type ones.
3. Wear test of pivot jewel bearings 3.1. Test instrument As shown in Fig. 4, the wear test rig was built to investigate the tribological behavior of the pivot jewel bearings. The friction pair included the pivot tip and the jewel cup. The pivot was made from tool steel (T10) and the bearing was corundum (man-made stone Al2O3). The contact parts were immersed in oil bath to minimize friction and wear. The spherical radius of the jewel cup was 2.00 mm, a little bit smaller than that of the pivot tip (2.05 mm). The surface roughness of the tip and the cup was
X. Dai et al. / Wear 302 (2013) 1506–1513
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Fig. 3. Contact pressure and Von Mises stress after running-in: (a) traditional type, and (b) line contact type.
vacuum chamber flywheel motor rotor motor stator
pivot jewel bearing damper flexible shaft Fig. 4. Test rig.
very low (see SEM images in Fig. 5), with the roughness parameter Ra (arithmetic average) being smaller than 20 nm. The bearing was set on the damper with a slim shaft as the spring element of the bearing-damper vibration system. A flywheel was used to simulate the vertical load to the bearing. The motor rotor in disk shape produced the driving torque of the spinning system. The bearing vertical load was 5–10 N from the flywheel. The very low stiffness of the slim shaft made the flywheel pivot bearing damper system easily pass through the critical speed of the vibration system. Obviously the one-point support system was unstable in non-rotating state. An auxiliary support (usually being a small shaft inserted in the hole on the flywheel held by the operator) at the top of the flywheel was necessary to run up the flywheel pivot bearing system. The auxiliary support should be removed after the flywheel arrived at the speed of 40 r/s or above. After that, the top cap of the vacuum chamber was closed and the vacuum pump started
to work. The vacuum pump kept the pressure at 2–5 Pa in the chamber. The flywheel ran at the speed of several hundred rotations per second with very low aerodynamic drag loss because of the vacuum condition. The spinning system ran at high speeds for many hours and then decelerated to stop. The pivot tip surface was observed by the Scanning Electron Microscope (SEM). Fig. 6 shows the images of the pivot tip surface under wear after 150 h running at the speed of 800 r/s. The wear surface was a circular ring with a width of 150 mm, which indicated that the curvature radius of the tip was bigger than that of the cup. From Fig. 6, one can see that the plow grooves were obvious on the contact area. Local material loss track was observed as well. Some fatigue pits were also on the surface. Apart from the contact area, the tip surface within the scuffing ring remained intact without any wear. 3.2. Friction coefficient and friction loss A varying load method has been proposed to measure the friction coefficient of the high speed pivot jewel bearing in oil bath lubrication [7]. The heavy load was 7 N and the light load was 5 N, which were applied by using two load disk flywheels of the same size but of different metals (steel and aluminum alloy). The same size of the varying load disk flywheels guaranteed the same windage loss in the decelerating experiments. When the motor power is turned off, the flywheel (with rotational inertia of J including the motor rotor and the shaft) speed o decreases a little with do in dt, the energy loss is 1 dE ¼ J o2 ðodoÞ2 J odo ð1Þ 2
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Fig. 5. Surfaces under SEM of the intact pivot tip and jewel cup.
Fig. 6. Surfaces of the pivot tip after 150 h running.
The flywheel speed decreases because of the bearing friction, the windage, and the eddy current loss of the motor. The deceleration power of the flywheel is P¼
dE J odo ¼ ¼ Pb þ Pw þP m dt dt
ð2Þ
where, Pb is bearing loss power, Pw is windage loss power and Pm is motor loss. P b ¼ mN or
ð3Þ
where, m is the friction coefficient (including the friction between the pivot and the oil), N is the bearing load and r is the mean radius of the contact ring. In the decreasing test from o to o do in duration dt1, in the heavy load 7 N case, the decreasing power is P 1 ¼ mN1 or þ Pw þP m
ð4Þ
Re-do the decreasing test from o to o do in duration dt2, in the light load 5 N case, the decreasing power is P 2 ¼ mN2 or þ Pw þP m
ð5Þ
From Eqs. (4) and (5), the friction coefficient is deduced as P 1 P2 do J 1 J ¼ m¼ 2 ð6Þ orðN1 N2 Þ r dt 1 dt 2 J1 is the rotational inertia of the steel flywheel spinning system, and J2 is the rotational inertia of the aluminum alloy flywheel spinning system. Figs. 7 and 8 indicated that the friction coefficients became smaller when the running speed increased from 200 r/s to 800 r/s and the average measured values were between 0.10 and 0.05. The decrease of the friction coefficient with the increasing speed indicated that the hydro-dynamic effect in the boundary lubrication was augmented and the thin-film lubrication reduced the
Fig. 7. Friction coefficient of the pivot jewel bearing in oil-bath.
surface contact between the pivot and the jewel. The friction loss power of the bearing under 7 N load was 1.6 W at the running speed of 48,000 rpm. In Fig. 6, the nominal contact area was about 0.87 mm2, and the nominal contact pressure was 8 MPa. The linear velocity of the tip was 4.5 m/s. Therefore, the value of PV was 36 MPa m/s.
4. The wear types and mechanisms 4.1. Abrasive wear Abrasive wear occurs when asperities of a rough, hard surface or hard particles slide on a softer surface and damage the interface
X. Dai et al. / Wear 302 (2013) 1506–1513
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Fig. 8. Abrasive wear surfaces.
Fig. 9. Fatigue wear surfaces.
Fig. 10. Adhesive wear surfaces.
by plastic deformation or fracture [8]. Abrasive wear is most common in the wear of the pivot tip surface. A series of grooves parallel to the direction of sliding were observed in every test sample bearing at different wear test time durations. With the surface roughness being very low, the plowing was mainly attributed to the hard grits from wear. The grit materials included both steel (steel oxygen) and ceramics (Al2O3). The width of the plowing area along the direction vertical to the sliding increased as the experimental time became longer, which meant that more surface wore. The width of the grooves varied from 1 mm to several mm in the SEM graphs. Both the interval and the thickness of the grooves varied notably. The bulges swelled on the surface because of the plastic deformation. In the plowing process, material was displaced from a groove to the sides without being removed. Material removal might occur after the surface has been plowed several times. The plowed ridges became flattened, and eventually fractured after repeated loading and unloading cycles. 4.2. Fatigue wear Fatigue wear was also observed on the surface of the pivot tip. The contact pressure of the surface varied 200–800 times per second because of the rotation of the pivot. A million cycles
of the pressure varying occurred in 20–80 min. The repeated loading and unloading cycles to which the material is exposed may induce subsurface or surface cracks, which eventually, after a critical number of cycles, will result in the breakup of the surface with the formation of large fragments, leaving large pits on the surface [8]. The edge of the surface damage pits caused by material loss was irregular (see Fig. 9). The sizes of the pits varied form 1 mm to 10 mm or more. No dominant dimension of the pits, irregular pit edge and the random locations of the pits on the contact area were the three important characters of the fatigue wear of the bearing. 4.3. Adhesive wear Adhesion occurred at the steel asperity and the wear particles. The asperity-particle contacts were sheared by sliding, which resulted in detachment of a fragment from the steel surface. Unlike other metal–metal adhesion, the fragment from the pivot tip surface would not attach to the jewel cup surface but formed new wear particles or stuck back to the steel surface of the pit in most cases. The damage feature of adhesive wear was the pullout of the debris. Fig. 10 indicates that the pits by material loss were thick, long and located along the sliding direction, unlike the nondominant dimension and randomly located ones in fatigue wear.
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Fig. 11. Wear surfaces of jewel bearings.
Table 2 Wear process. Wear time Total (h) sample
Abrasive Fatigue Adhesive Adhesive occurring frequency
2000 4000 8000
4 13 6
4 13 6
4 13 6
1 6 5
1/4 6/13 5/6
The size of the damage along the sliding circular direction was much bigger than that of the radial direction. The long pits due to material loss in adhesion tended to form broken ditches which were different from the grooves with the bulges swelled on the surface in abrasive wear. Adhesion wear was more severe than abrasive wear and fatigue wear for the pivot jewel bearing. In some contact places, breaks occurred in the tip surface and a small fragment was ripped by the asperity peak. The break-offs of the material formed many long grooves along the sliding direction with rough edges. The grooves from material loss differed from the grooves due to the plastic deformation in abrasive wear. The abrasive grooves were continuous, smaller in both width and depth. In another mechanism of adhesive wear, the wear steel particles between the interaction surfaces bonded with the steel tip surface under great pressure in some contact points. The bonded particles became new peaks and were dropped off by the cup asperities. The plastic shearing of the bonded peaks of an asperity contact resulted in detachment of a wear fragment and the large rough discontinuous grooves. 4.4. Jewel wear surface The hardness of the jewel was about 1700 (Vickers diamond hardness), two times that of the pivot tip surface. The wear of the hard surface was slighter than that of the soft surface. The scratch grooves and the fatigue pits were found on the jewel surface. The jewel wear confirmed that the hard grits from wear contributed to the abrasive wear. The material transfer was observed on the surface (see the right picture of Fig. 11) in the adhesion in some cases.
5. Wear process analysis The test tip samples in three groups were observed under SEM after different test time durations as shown in Table 2 from which one can see that abrasive wear and fatigue wear always happened on the wear samples. Moreover, the adhesive wear happened more frequently when the wear time became longer. It is difficult to analyze the wear process in numerical quantities. Firstly, the manufacture error made the contact area
inconsistent. Secondly, the unbalance of the test flywheel had random impacts on the actual load on the bearing. Thirdly, the random performance of the roughness of the surface made the actual contact force distribute arbitrarily. However, it is possible and necessary to describe the wear process qualitatively. From the large number of SEM images of test samples, the damage index was presented to describe the wear process according to the wear type and damage severity. The damage index was set to 1, 2, 3 and 4. The severity of the damage on the tip surface and the typical wear behavior were illustrated in Table 3. The damage index escalated with the increasing running time. The wear rate was slow in the wear test in constant load and the worn pivot jewel bearing still worked properly. However, for the actual using in small high speed rotating machinery, with the material loss by wear in time as long as 5–10 years, the vertical size of the pivot will become shorter, which will increase the air gap of the magnet bearing in the rotor-bearing system. The lower attraction force of the magnet bearing due to larger air gap will increase the load of the pivot jewel bearing and accelerate the wear process.
6. Conclusions The contact pressure and stress of line contact type pivot bearings are significantly higher than those of traditional type and total contact type bearings due to the non-smooth transition of the curvature radius of the line contact type. The conforming surface contact in running-in state make the contact stress of the line contact type bearings about half of the traditional contact type, which means that the line contact type have better antiwear performance. The pivot jewel bearings displayed the tribological behavior of boundary friction in the experiments. The friction coefficients of the pivot jewel varied from 0.10 to 0.05 with the rising of the rotational speed from 200 r/s to 800 r/s. The pivot jewel bearing in oil-bath lubrication ran smoothly with low wear rate for the application of high speed and low load. All the abrasive, fatigue and adhesive wear occurred and demonstrated different surface damage features in the wear test time durations ranging from 2000 h to 8000 h. The typical width of the plowing groove was around 1 mm; the typical size of the fatigue pits was several mm and the typical size of the adhesive damage pits was dozens of mm. Moreover, the location and direction of the damage on the tip also helped categorize the wear type. The wear of jewel cup occurred in abrasive and fatigue wear but not adhesive wear. The wear tests on the 23 tip samples in three groups with different wear time durations showed that the abrasive and fatigue wear always happened. However, the adhesive wear happened more frequently for longer durations. According to the wear type and damage severity, the damage index was set
X. Dai et al. / Wear 302 (2013) 1506–1513
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Table 3 Index of surface damage on the pivot tip. Index of damage
1
2
3
4
Wear severity Wear behavior
Light Abrasive grooves some fatigue pits
Moderate Cutting grooves large fatigue pits
Fairly severe Much fatigue loss pits in large sizes
Severe Large fatigue pits adhesive grooves
o 2000
1000–3000
2000–6000
45000
Typical image
Typical wear time duration (h)
to 1, 2, 3 and 4 to describe the wear process. The damage index escalated with the increasing running time.
Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant no.: 11075087). References [1] K. Ono, S. Murashita, H. Yamaura, Stability analysis of a disk–spindle supported by a plain journal bearing and pivot bearing, Microsystem Technologies 11 (2005) 734–740.
[2] H. Wang, Sh. Jiang, Z. Shen, The dynamic analysis of an energy storage system flywheel system with hybrid bearing system, Journal of Vibration and Acoustics 131 (2009) 051006–1/9. [3] J.D. Stienmier, S.C. Thielman, B.C. Fabien, Analysis and control of a flywheel energy storage system with a hybrid magnetic bearing, Journal of Dynamic Systems, Measurement, and Control 119 (1997) 650–656. [4] W. Morales, R. Fusaro, A. Kascak, Permanent magnetic bearing for spacecraft applications, Tribology Transactions 46 (2003) 460–464. [5] T.S. Sankar, P.I. Tzenov, On friction and motion accuracy in jewel bearing, Tribology Transactions 37 (1994) 269–276. [6] T.S. Sankar, P.I. Tzenov, The steady-state dynamics of jewel bearing with a free ball, Tribology Transactions 37 (1994) 403–409. [7] X. Dai, Ch. Tang, Sh. Yu, Measuring friction coefficient of the high speed pivot bearing in oil-bath lubrication by a varying load method, Triboloy 31 (2011) 7–11. (in Chinese). [8] B. Bhushan, Introduction to Tribology, John Wiley & Sons, New York, 2002.
Contents lists available at SciVerse ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
Short communication
Friction and wear of pivot jewel bearing in oil-bath lubrication for high rotational speed application Xingjian Dai n, Kai Zhang, Changliang Tang Department of Engineering Physics, Tsinghua University, Beijing 100084, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 August 2012 Received in revised form 2 January 2013 Accepted 11 January 2013 Available online 23 January 2013
Oil-lubricated pivot jewel bearings are used in the vertical support systems for small, high speed rotating machinery such as flywheels for energy storage, fabric spindles, and centrifuges. The friction and wear of a tool steel pivot tip spinning in a corundum jewel cup were studied experimentally. The contact stress conditions at the tip were analyzed by a finite element method. The friction coefficients of the pivot jewel varied from 0.10 to 0.05, which are typical of boundary lubrication. Wear tests of samples from three groups of bearings indicated that abrasive wear, fatigue wear and adhesive wear occurred in a sequence. The size of the damage of the contact surface varied form 1 mm to dozens of mm. Abrasive and fatigue wear were also observed on the harder jewel cup surface. A wear index based on surface appearance was used to categorize the wear process on the bearing. & 2013 Elsevier B.V. All rights reserved.
Keywords: Jewel bearings Sliding wear Wear testing Lubricated wear including scuffing Fatigue
1. Introduction Low speed jewel bearings are used as supports in electrical measuring instruments such as galvanometers, ammeters and energy measuring meters. A pivot jewel bearing consists of a ball or a shaft tip that spins on an axis perpendicular to the contact area. The bearing support element is usually a concave or plate surface of hard anti-wear material such as ruby or steel. Although jewel bearings have limited load-bearing capacity, it is possible to use them as flexible support for rotor systems such as small high speed flywheels and centrifuges. Pivot jewel bearings are usually used with permanent magnetic bearings, and thus only 5%–10% of the rotor’s weight is born on the jewel bearing. Unlike the low speed situation with dry friction in electrical measuring instruments, the pivot jewel bearings must be lubricated by oil for high speed application. The lubrication oil resists wear and extracts the friction heat of the bearing. The bearing life can last as long as 5–10 years for small high speed rotating machinery. The tribological behavior of jewel bearings in high speed machinery needs investigating for its proper design and application. For the high spinning vertical shaft bearing application in small rotating machinery such as hard disks [1], centrifuges, flywheels [2] and fabric spindles, the commonly used mechanical bearings include small ball bearings, spiral groove hydrodynamic
n
Corresponding author. Tel.: þ86 1062784518; fax: þ86 1062798299. E-mail address: [email protected] (X. Dai).
0043-1648/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.wear.2013.01.032
film bearings and jewel bearings. Ball bearings have high stiffness and considerable friction loss. Spiral groove bearings have good load-bearing capacity and moderate stiffness, but lack stability due to oil film. Pivot jewel bearings have good stability but small load-bearing capacity and they have wear problems caused by contact friction. Pivot jewel bearings fall into three types depending on the curvature of the contact interaction surfaces. The traditional type is a small pivot tip and a large bearing cup with a point contact in Fig. 1(a). For the total contact type, the pivot tip and the bearing cup enjoy the same curvature in Fig. 1(b), and they share a spherical contact area. The line contact type is the case of a larger tip curve ratio and smaller cup curvature in Fig. 1(c). As manifested in the published papers, pivot jewel bearings were used as thrust bearings with dry friction [3,4]. In the hybrid magnetic bearing for a flywheel energy storage system, a synthetic ruby or sapphire ball on the flywheel and a stationary, flat sapphire plate were used as the axial support. The typical friction energy dissipation was 0.3 W at 100,000 rpm [3]. A Si3N4 ball held at the end of the shaft span against the stationary 440C stainless steel disk in the experimental study of the permanent magnetic bearings for spacecraft applications. In this case, the test rig with the jewel bearing as the axial support arrived at the speed of 5500 rpm [4]. Sankar and Tzenov presented a mechanical model for the jewel bearings to predict the errors and friction loss [5]. They also presented and modeled a jewel bearing with a free ball between the cup surface fixed to the rotor and the stationary cup to solve the concentrated wear due to the circular contact band of the
X. Dai et al. / Wear 302 (2013) 1506–1513
P Pb Pw Pm
Nomenclature
o do dt dE J
rotational speed of the flywheel a little decrease of the flywheel speed time interval energy loss of the spinning system rotational inertia of spinning system
deceleration power of the spinning system bearing loss power windage loss power motor loss power friction coefficient load of the bearing mean radius of the contact ring
m N r
spherical end of the rotor [6]. Their study indicated that the friction force between the steel tip and the cup sapphire surface had great effect on the rotor motion. The friction coefficient of the pivot jewel bearing in boundary lubrication was determined by experimental methods [7]. However, the wear details of the jewel bearings remain unclear. The current study was undertaken to analyze the contact stress and wear of pivot jewel bearings. The contact stress of the bearings was calculated by the finite element method. A test rig was built to investigate the friction coefficient, the wear types and wear mechanisms of the pivot jewel bearings. The wear tests of about 30 bearing samples were carried out for hundreds of hours to thousands of hours. A wear index was presented to describe the wear process of the bearing according to the damage on the pivot tip surface.
2. Contact stress analysis Stress distribution in contact area of a pivot jewel bearing may lead to the onset and deterioration of the fatigue crack of the pivot tip surface. The contact stress of all the three type bearings can be calculated by the finite element method. The three types of pivot jewel bearings have the same material parameters, as shown in Table 1. For the traditional type, the curvature radius of pivot tip r ¼1.95 mm, and curvature radius of bearing cup R¼2.0 mm. For the total contact type, r ¼R¼2.0 mm. For the line contact type, r ¼2.05 mm and R¼2.0 mm. The two-dimensional element Plane183 in ANSYS was chosen to model the pivot jewel bearing. The properties of the Plane183 were axisymmetric. The Targe69 and Conta172 in ANSYS were selected to establish contact pair. The load applied on the top of pivot was 10 N. The results were
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as follows: as shown in Fig. 2, the maximum Von Mises stress of the three types of pivot tips was significantly smaller than 630 MPa, the yield strength of the T10 steel. The stress of pivot tip was within the safe range according to the fourth strength theory. The maximum contact pressure and the maximum Von Mises stress of line contact type were 658 MPa and 368 MPa respectively, both of which were much higher than those of the traditional type and total contact type bearings. That could be explained by the non-smooth transition of the curvature radius of line contact type pivot bearings. A line contact type bearing had the maximum contact pressure and was prone to be worn. However, such bearings had a gap between the pivot tip and the bearing cup that was able to store abrasive particles, which helped prevent the more severe abrasive wear. The material of pivot tip surface lost continuously in runningin period, so geometric contours of the pivot tip changed constantly. Both the Hertz point contact and the line contact turned into conforming contact with growing contact area. It was hypothesized that the radius of circular abrasion area of the traditional contact type bearing was 160 mm and the divergence of outside radius and inner radius of annular abrasion area of the line contact type bearing was also 160 mm at the end of the
Table 1 Mechanical properties of materials. Parts
Material
Elasticity modulus /GPa
Pivot Jewel bearing
T10 steel 210 Corundum 407
Poisson’s ratio m
Yield strength / MPa
0.3 0.2
630 –
contact area
contact area
contact area
pivot
pivot
jewel R>r
pivot
jewel R=r
jewel R
Fig. 1. Three types of pivot jewel bearings. (a) Traditional, (b) total contact and (c) line contact.
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Fig. 2. Contact pressure and Von Mises stress of pivot jewel bearings: (a) traditional type, (b) total contact type, and (c) line contact type.
running-in period. 10 N was loaded on the top of the pivot. The contact stress analysis results are shown in Fig. 3. For traditional type pivots, the non-smooth transition of curvature radius of pivot tip produced a small stress concentration on the exterior margin. The pressure was about 31 MPa in most of the contact area and the corresponding von Mises stress was 16 MPa, with the peak contact pressure being 277 MPa and the corresponding Von Mises stress 142 MPa. For line contact type pivots, the pressure was 11 MPa in most of the contact area and the corresponding Von Mises stress was 7 MPa. The peak contact pressure and corresponding Von Mises stress were smaller (102 MPa and 67 MPa respectively) than those of the traditional total contact type bearings. It can be concluded that the running-in transforms pivot contact from Hertz point or line contact into conforming surface contact, which increases the contact area and reduces the contact stress. The contact stress of the line contact type bearings is about
half of the traditional contact type bearings after the running-in period. The pivot jewel bearings used in the following experimental study were line contact type ones.
3. Wear test of pivot jewel bearings 3.1. Test instrument As shown in Fig. 4, the wear test rig was built to investigate the tribological behavior of the pivot jewel bearings. The friction pair included the pivot tip and the jewel cup. The pivot was made from tool steel (T10) and the bearing was corundum (man-made stone Al2O3). The contact parts were immersed in oil bath to minimize friction and wear. The spherical radius of the jewel cup was 2.00 mm, a little bit smaller than that of the pivot tip (2.05 mm). The surface roughness of the tip and the cup was
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Fig. 3. Contact pressure and Von Mises stress after running-in: (a) traditional type, and (b) line contact type.
vacuum chamber flywheel motor rotor motor stator
pivot jewel bearing damper flexible shaft Fig. 4. Test rig.
very low (see SEM images in Fig. 5), with the roughness parameter Ra (arithmetic average) being smaller than 20 nm. The bearing was set on the damper with a slim shaft as the spring element of the bearing-damper vibration system. A flywheel was used to simulate the vertical load to the bearing. The motor rotor in disk shape produced the driving torque of the spinning system. The bearing vertical load was 5–10 N from the flywheel. The very low stiffness of the slim shaft made the flywheel pivot bearing damper system easily pass through the critical speed of the vibration system. Obviously the one-point support system was unstable in non-rotating state. An auxiliary support (usually being a small shaft inserted in the hole on the flywheel held by the operator) at the top of the flywheel was necessary to run up the flywheel pivot bearing system. The auxiliary support should be removed after the flywheel arrived at the speed of 40 r/s or above. After that, the top cap of the vacuum chamber was closed and the vacuum pump started
to work. The vacuum pump kept the pressure at 2–5 Pa in the chamber. The flywheel ran at the speed of several hundred rotations per second with very low aerodynamic drag loss because of the vacuum condition. The spinning system ran at high speeds for many hours and then decelerated to stop. The pivot tip surface was observed by the Scanning Electron Microscope (SEM). Fig. 6 shows the images of the pivot tip surface under wear after 150 h running at the speed of 800 r/s. The wear surface was a circular ring with a width of 150 mm, which indicated that the curvature radius of the tip was bigger than that of the cup. From Fig. 6, one can see that the plow grooves were obvious on the contact area. Local material loss track was observed as well. Some fatigue pits were also on the surface. Apart from the contact area, the tip surface within the scuffing ring remained intact without any wear. 3.2. Friction coefficient and friction loss A varying load method has been proposed to measure the friction coefficient of the high speed pivot jewel bearing in oil bath lubrication [7]. The heavy load was 7 N and the light load was 5 N, which were applied by using two load disk flywheels of the same size but of different metals (steel and aluminum alloy). The same size of the varying load disk flywheels guaranteed the same windage loss in the decelerating experiments. When the motor power is turned off, the flywheel (with rotational inertia of J including the motor rotor and the shaft) speed o decreases a little with do in dt, the energy loss is 1 dE ¼ J o2 ðodoÞ2 J odo ð1Þ 2
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Fig. 5. Surfaces under SEM of the intact pivot tip and jewel cup.
Fig. 6. Surfaces of the pivot tip after 150 h running.
The flywheel speed decreases because of the bearing friction, the windage, and the eddy current loss of the motor. The deceleration power of the flywheel is P¼
dE J odo ¼ ¼ Pb þ Pw þP m dt dt
ð2Þ
where, Pb is bearing loss power, Pw is windage loss power and Pm is motor loss. P b ¼ mN or
ð3Þ
where, m is the friction coefficient (including the friction between the pivot and the oil), N is the bearing load and r is the mean radius of the contact ring. In the decreasing test from o to o do in duration dt1, in the heavy load 7 N case, the decreasing power is P 1 ¼ mN1 or þ Pw þP m
ð4Þ
Re-do the decreasing test from o to o do in duration dt2, in the light load 5 N case, the decreasing power is P 2 ¼ mN2 or þ Pw þP m
ð5Þ
From Eqs. (4) and (5), the friction coefficient is deduced as P 1 P2 do J 1 J ¼ m¼ 2 ð6Þ orðN1 N2 Þ r dt 1 dt 2 J1 is the rotational inertia of the steel flywheel spinning system, and J2 is the rotational inertia of the aluminum alloy flywheel spinning system. Figs. 7 and 8 indicated that the friction coefficients became smaller when the running speed increased from 200 r/s to 800 r/s and the average measured values were between 0.10 and 0.05. The decrease of the friction coefficient with the increasing speed indicated that the hydro-dynamic effect in the boundary lubrication was augmented and the thin-film lubrication reduced the
Fig. 7. Friction coefficient of the pivot jewel bearing in oil-bath.
surface contact between the pivot and the jewel. The friction loss power of the bearing under 7 N load was 1.6 W at the running speed of 48,000 rpm. In Fig. 6, the nominal contact area was about 0.87 mm2, and the nominal contact pressure was 8 MPa. The linear velocity of the tip was 4.5 m/s. Therefore, the value of PV was 36 MPa m/s.
4. The wear types and mechanisms 4.1. Abrasive wear Abrasive wear occurs when asperities of a rough, hard surface or hard particles slide on a softer surface and damage the interface
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Fig. 8. Abrasive wear surfaces.
Fig. 9. Fatigue wear surfaces.
Fig. 10. Adhesive wear surfaces.
by plastic deformation or fracture [8]. Abrasive wear is most common in the wear of the pivot tip surface. A series of grooves parallel to the direction of sliding were observed in every test sample bearing at different wear test time durations. With the surface roughness being very low, the plowing was mainly attributed to the hard grits from wear. The grit materials included both steel (steel oxygen) and ceramics (Al2O3). The width of the plowing area along the direction vertical to the sliding increased as the experimental time became longer, which meant that more surface wore. The width of the grooves varied from 1 mm to several mm in the SEM graphs. Both the interval and the thickness of the grooves varied notably. The bulges swelled on the surface because of the plastic deformation. In the plowing process, material was displaced from a groove to the sides without being removed. Material removal might occur after the surface has been plowed several times. The plowed ridges became flattened, and eventually fractured after repeated loading and unloading cycles. 4.2. Fatigue wear Fatigue wear was also observed on the surface of the pivot tip. The contact pressure of the surface varied 200–800 times per second because of the rotation of the pivot. A million cycles
of the pressure varying occurred in 20–80 min. The repeated loading and unloading cycles to which the material is exposed may induce subsurface or surface cracks, which eventually, after a critical number of cycles, will result in the breakup of the surface with the formation of large fragments, leaving large pits on the surface [8]. The edge of the surface damage pits caused by material loss was irregular (see Fig. 9). The sizes of the pits varied form 1 mm to 10 mm or more. No dominant dimension of the pits, irregular pit edge and the random locations of the pits on the contact area were the three important characters of the fatigue wear of the bearing. 4.3. Adhesive wear Adhesion occurred at the steel asperity and the wear particles. The asperity-particle contacts were sheared by sliding, which resulted in detachment of a fragment from the steel surface. Unlike other metal–metal adhesion, the fragment from the pivot tip surface would not attach to the jewel cup surface but formed new wear particles or stuck back to the steel surface of the pit in most cases. The damage feature of adhesive wear was the pullout of the debris. Fig. 10 indicates that the pits by material loss were thick, long and located along the sliding direction, unlike the nondominant dimension and randomly located ones in fatigue wear.
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Fig. 11. Wear surfaces of jewel bearings.
Table 2 Wear process. Wear time Total (h) sample
Abrasive Fatigue Adhesive Adhesive occurring frequency
2000 4000 8000
4 13 6
4 13 6
4 13 6
1 6 5
1/4 6/13 5/6
The size of the damage along the sliding circular direction was much bigger than that of the radial direction. The long pits due to material loss in adhesion tended to form broken ditches which were different from the grooves with the bulges swelled on the surface in abrasive wear. Adhesion wear was more severe than abrasive wear and fatigue wear for the pivot jewel bearing. In some contact places, breaks occurred in the tip surface and a small fragment was ripped by the asperity peak. The break-offs of the material formed many long grooves along the sliding direction with rough edges. The grooves from material loss differed from the grooves due to the plastic deformation in abrasive wear. The abrasive grooves were continuous, smaller in both width and depth. In another mechanism of adhesive wear, the wear steel particles between the interaction surfaces bonded with the steel tip surface under great pressure in some contact points. The bonded particles became new peaks and were dropped off by the cup asperities. The plastic shearing of the bonded peaks of an asperity contact resulted in detachment of a wear fragment and the large rough discontinuous grooves. 4.4. Jewel wear surface The hardness of the jewel was about 1700 (Vickers diamond hardness), two times that of the pivot tip surface. The wear of the hard surface was slighter than that of the soft surface. The scratch grooves and the fatigue pits were found on the jewel surface. The jewel wear confirmed that the hard grits from wear contributed to the abrasive wear. The material transfer was observed on the surface (see the right picture of Fig. 11) in the adhesion in some cases.
5. Wear process analysis The test tip samples in three groups were observed under SEM after different test time durations as shown in Table 2 from which one can see that abrasive wear and fatigue wear always happened on the wear samples. Moreover, the adhesive wear happened more frequently when the wear time became longer. It is difficult to analyze the wear process in numerical quantities. Firstly, the manufacture error made the contact area
inconsistent. Secondly, the unbalance of the test flywheel had random impacts on the actual load on the bearing. Thirdly, the random performance of the roughness of the surface made the actual contact force distribute arbitrarily. However, it is possible and necessary to describe the wear process qualitatively. From the large number of SEM images of test samples, the damage index was presented to describe the wear process according to the wear type and damage severity. The damage index was set to 1, 2, 3 and 4. The severity of the damage on the tip surface and the typical wear behavior were illustrated in Table 3. The damage index escalated with the increasing running time. The wear rate was slow in the wear test in constant load and the worn pivot jewel bearing still worked properly. However, for the actual using in small high speed rotating machinery, with the material loss by wear in time as long as 5–10 years, the vertical size of the pivot will become shorter, which will increase the air gap of the magnet bearing in the rotor-bearing system. The lower attraction force of the magnet bearing due to larger air gap will increase the load of the pivot jewel bearing and accelerate the wear process.
6. Conclusions The contact pressure and stress of line contact type pivot bearings are significantly higher than those of traditional type and total contact type bearings due to the non-smooth transition of the curvature radius of the line contact type. The conforming surface contact in running-in state make the contact stress of the line contact type bearings about half of the traditional contact type, which means that the line contact type have better antiwear performance. The pivot jewel bearings displayed the tribological behavior of boundary friction in the experiments. The friction coefficients of the pivot jewel varied from 0.10 to 0.05 with the rising of the rotational speed from 200 r/s to 800 r/s. The pivot jewel bearing in oil-bath lubrication ran smoothly with low wear rate for the application of high speed and low load. All the abrasive, fatigue and adhesive wear occurred and demonstrated different surface damage features in the wear test time durations ranging from 2000 h to 8000 h. The typical width of the plowing groove was around 1 mm; the typical size of the fatigue pits was several mm and the typical size of the adhesive damage pits was dozens of mm. Moreover, the location and direction of the damage on the tip also helped categorize the wear type. The wear of jewel cup occurred in abrasive and fatigue wear but not adhesive wear. The wear tests on the 23 tip samples in three groups with different wear time durations showed that the abrasive and fatigue wear always happened. However, the adhesive wear happened more frequently for longer durations. According to the wear type and damage severity, the damage index was set
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Table 3 Index of surface damage on the pivot tip. Index of damage
1
2
3
4
Wear severity Wear behavior
Light Abrasive grooves some fatigue pits
Moderate Cutting grooves large fatigue pits
Fairly severe Much fatigue loss pits in large sizes
Severe Large fatigue pits adhesive grooves
o 2000
1000–3000
2000–6000
45000
Typical image
Typical wear time duration (h)
to 1, 2, 3 and 4 to describe the wear process. The damage index escalated with the increasing running time.
Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant no.: 11075087). References [1] K. Ono, S. Murashita, H. Yamaura, Stability analysis of a disk–spindle supported by a plain journal bearing and pivot bearing, Microsystem Technologies 11 (2005) 734–740.
[2] H. Wang, Sh. Jiang, Z. Shen, The dynamic analysis of an energy storage system flywheel system with hybrid bearing system, Journal of Vibration and Acoustics 131 (2009) 051006–1/9. [3] J.D. Stienmier, S.C. Thielman, B.C. Fabien, Analysis and control of a flywheel energy storage system with a hybrid magnetic bearing, Journal of Dynamic Systems, Measurement, and Control 119 (1997) 650–656. [4] W. Morales, R. Fusaro, A. Kascak, Permanent magnetic bearing for spacecraft applications, Tribology Transactions 46 (2003) 460–464. [5] T.S. Sankar, P.I. Tzenov, On friction and motion accuracy in jewel bearing, Tribology Transactions 37 (1994) 269–276. [6] T.S. Sankar, P.I. Tzenov, The steady-state dynamics of jewel bearing with a free ball, Tribology Transactions 37 (1994) 403–409. [7] X. Dai, Ch. Tang, Sh. Yu, Measuring friction coefficient of the high speed pivot bearing in oil-bath lubrication by a varying load method, Triboloy 31 (2011) 7–11. (in Chinese). [8] B. Bhushan, Introduction to Tribology, John Wiley & Sons, New York, 2002.