Wear 376-377 (2017) 920–930
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Inﬂuence of both friction and wear on the vibration of marine water lubricated rubber bearing Huanjie Wang a,b,n, Zhenglin Liu a, Li Zou a, Jun Yang a a b
School of Energy and Power, Wuhan University of Technology, Wuhan, Hubei, China Wuhan Institute of Shipbuilding Technology, Wuhan, Hubei, China
art ic l e i nf o
a b s t r a c t
Article history: Received 28 August 2016 Received in revised form 31 January 2017 Accepted 1 February 2017
Marine water-lubricated bearing is the key part of the thrust shafting of underwater vehicles and some surface vessels, that is currently made with rubber, Thordon, Feroform, nylon, lignumvitae materials etc. Because the performance of vibration and noise reduction of the rubber material is better than some materials so that it is usually applied in water-lubricated propeller shaft bearing of submarines and underwater vehicles to improve their stealth, security, performance and reliability. Although the rubber is of better damping effect, it is always easy to cause friction vibration and noise under low speed, heavy load and wear situation, especially at starting or stopping phases. Therefore, it is of important theoretical signiﬁcance and engineering value to enhance the mute level of the vehicles and alleviate friction vibration and noise. The tribological properties of water-lubricated rubber bearing such as friction and wear can affect the bearing vibration directly. So the research objective is to explore the inﬂuence of both friction and wear of water-lubricated rubber bearing on the bearing vibration under the different rubber materials of the bearing lining and working conditions. In the research, both theoretical analysis and test methods are applied. In theoretical analysis, the ﬁnite element model of the bearing is established and the deformation of the bearing lining is analyzed, and in test research, kinds of water-lubricated bearings with different rubber material were tested on the bearing test-bed under different shaft rotary speed, load and cooling water temperature. The research results show that both friction coefﬁcient and wear of waterlubricated rubber bearings are affected with the different rotary speed, load and cooling water temperature, which result in the bearing vibration status changed signiﬁcantly. With the increase of the load in some range, the deformation of the bearing lining is intensiﬁed and the speciﬁc pressure of the bearing is decreased due to the augment of contact area of between test shaft and bearing lining so that the friction coefﬁcient and vibration are declined. As cooling water temperature is enhanced, both wear and vibration are aggravated.The higher shaft rotary speed is, smaller friction coefﬁcient is in certain speed range so friction vibration is reduced. & 2017 Elsevier B.V. All rights reserved.
Keywords: Water lubricated rubber bearing Friction Wear Vibration Deformation
1. Introduction The friction vibration of marine water lubricated stern bearings is one of the bottleneck problems of underwater vehicles, which seriously affects the concealment, reliability, and occupant comfort of the underwater vehicles. Today's most quiet underwater vehicle isn't easy to be found more than 100 m far from it with the most sensitive acoustic equipment. If vibration noise radiation of the stern bearing is declined by 6 10 dB, the detecting range of the passive sonar of the enemy can reduce about 50%, and one of our part can increase 1 times or so, thus it can enhance the mute level n Corresponding author at: School of Energy and Power, Wuhan University of Technology, Wuhan, Hubei, China.
http://dx.doi.org/10.1016/j.wear.2017.02.006 0043-1648/& 2017 Elsevier B.V. All rights reserved.
and survival ability of the underwater vehicles to inhibit the friction vibration of the bearing. The frictional vibration of the water lubricated stern bearing is a very complex natural phenomenon, which has to do with the friction, wear and lubrication conditions closely. Practice has proved that the frictional vibration mainly appear in low speed (o0.5 m/s), overloading, and starting and stopping conditions. At this time, both shaft and bearing often operate under boundary lubrication or mixed lubrication status so that water ﬁlm is difﬁcult to establish, which can lead to the abnormal vibration and noise, the rapid wear of both shaft and bearing and the damage of sealing device. These affect the concealment of the underwater vehicle seriously. Kinkaid. N.M et al. [1–3] indicated that the friction vibration aroused by the water lubricated stern bearing mainly is self-excited
H. Wang et al. / Wear 376-377 (2017) 920–930
Fig. 1. Water lubricated rubber stern bearing.
vibration. At present, researchers have offered four kinds of the formation mechanism of friction self-excited vibration such as the stickslip movement, self-locking sliding, the negative slope of friction coefﬁcient-relative sliding velocity and the modal coupling. But the four kinds of friction vibration mechanism can't explain all of frictional vibration phenomena satisfactorily. SUN Di et al.  thought that Friction vibration can reﬂect the change of the running-in wear state of the friction pair, and presented that the change law of characteristic parameter K of vibration signal is consistent with one of friction coefﬁcient, so K can be used to identify the running-in wear state of the friction surface. Zhou Jianhui et al.  discussed the tribological mechanism of the marine water lubricated rubber stern bearings. The research results indicate that the friction coefﬁcient of the bearing is decreased with the increment of the shaft rotary linear speed. Zhao Shuhe et al.  pointed out that if there is the local interaction of the micro convex body in the working surfaces between the shaft and bearing, then the friction resistance between the shaft and bearing is jointly composed by the shear forces of both ﬂuid ﬁlm and the micro convex body of the contact surfaces, and the friction coefﬁcient is signiﬁcantly decreased with the increase of the relative sliding speed between friction surfaces. The friction vibration characteristic of ship shafting depends on the lubrication condition of the bearing. Sudan  pointed out that this friction vibration is not resonance phenomenon in linear vibration, but is the self-excited vibration by dry friction. In the nonlinear self-excited vibration caused by this kind of dry friction, now whole sliding motion and both hysteresis stopping and sliding motion can be analyzed [8–11]. Because self-excited vibration equation is much more complex, therefore, more studies are based on the numerical analysis, phase plane analysis and experimental research. R.A. Ibrahim et al.  discussed the friction self-excited vibration mechanism of water lubricated radial rubber bearing, and pointed out that under low speed, particularly at starting or stopping moment, the bearing is in dry friction state whose lubrication effect of is very poor, so it is easy to generate self-excited vibration and noise, but with the increase of rotary speed, both vibration and noise are obviously improved. Chen et al. [13,14] found in his experiment that friction vibration may only occur at a part of the test procedure, but it is possible to bring about throughout the whole test procedure, which depends on the test conditions, such as the structure stiffness of the friction system, normal contact force and relative sliding speed, friction pair material, abrasion and some unknown factors. The occurrence of friction vibration is not completely depending on the size of the friction resistance. Both friction and wear behavior characteristics on the rubber lining surface of water lubricated stern bearing are explored by the
experiments in this paper to reveal both friction vibration and noise mechanism and their forming process, performance variation law and implementation condition under low speed, overload and low viscosity (water) and to provide the theoretical support for reducing friction vibration and noise.
2. Test bearing and testing machine 2.1. Water lubricated rubber bearing The research object in this paper is marine water lubricated rubber bearings (hereinafter referred to as the bearing). This kind of bearing is different from oil lubricated one, especially its structure and lining material. In this paper, the rubber bearing only is the test specimen used to evaluate the tribological performance of kinds of rubber materials of the bearing such as friction coefﬁcient, wear and vibration. As long as the testing conditions of specimen is the same as one of the service use of marine bearing including speciﬁc pressure, shaft rotary speed, cooling water temperature and bearing lining material, and water slot structure is semblable, the size of the bearing such as diameter and length to diameter ratio is not be emphasized in general. 2.1.1. The structure and basic size of bearing Bearing samples are divided into 5 groups, a total of 15 pieces. Bearing inner diameter D is Ø150 mm, length L is 150 mm, and is decorated with 10 pieces of ﬂat rubber slats to form 10 sinks. The ﬂat slat can preferably improve lubricating performance than circular arc one. The slat thickness δ is 9.5 mm. In the test, one slat of the bearing is installed directly below the test shaft, as shown in Fig. 1. 2.1.2. Bearing material The bush material of the bearing is brass and the lining one is Buna-N rubber. The main component of Buna-N rubber are butadiene and acrylonitrile (20% 35%), and graphite or molybdenum disulﬁde etc. self-lubricating materials. In addition to different acrylonitrile in each bearing, the rest of components are the same. The performance index of the lining material includes tensile strength sb 416 MPa, Shore Hardness HA ¼7085. Although both structure and dimension of all of bearing samples are the same, the individual component ratio difference of the bearing lining material will cause the friction coefﬁcient and the critical speed varied to generate friction vibration and noise, which affect the friction vibration suppression of the bearing.
H. Wang et al. / Wear 376-377 (2017) 920–930
where W is normal load applied on the bearing. 2.2. Testing machine of water lubricated stern bearing
Fig. 2. Test shaft.
Water lubricated rubber stern bearing tests were proceeded on the SSB-100 marine stern bearing testing machine developed by Wuhan University of Technology, as shown in Fig. 4. The machine is mainly composed of 4 parts of driving, loading, controlling and testing. In tests, the middle radial loading method is accepted in order to ensure the pressure evenly exerted on the bearing rubber slats. The measurement equipment includes such as torque speed gauge, pressure gauge, etc. The torque speed meter is used to gain the friction torque M, rotary speed n and power consumption N of the test shaft; the pressure gauge of hydraulic system is applied to indicate the load W of hydraulic loading cylinder. BK pulse software and sensors are adopted in vibration test system. The vibration sensors are arranged at the top and ﬂank of the test bearing device to measure both vertical and lateral vibration of the bearing respectively.
Fig. 3. Assembly drawing of test shaft and bearing.
2.1.3. The structure and basic size of test shaft Test shaft is made with 45 steel, and the shaft journal is ﬁxed with ZCuSn10-2 bushing whose outside diameter is Ø150 mm and length is 175 mm, as shown Fig. 2. The elasticity modulus of the bushing is110 GPa, Poisson ratio is 0.34. The assembly of test shaft and bearing is as shown Fig. 3. 2.1.4. Test requirement Measurement requirement: The wear of a bearing means that the inside diameter D of the bearing is varied after test. The inside diameter D is indicated with the measured distance between two symmetrical slats to the center of a circle. The bearing is divided into 3 measuring cross sections (including front, middle and rear sections) along axial direction of the bearing, two symmetrical slats of each section are marked as Di (i ¼ 1, 2, 3… 5) according to clockwise order, as shown in Fig. 1. The measuring position of the outside diameter of the test shaft bushing is corresponding to the front, middle and rear measuring cross sections of the bearing. In general, the wear loss of the test shaft bushing is less, which isn't discussed in detail below. Key test parameters: speciﬁc pressure p, test shaft rotary speed v and water temperature T and so on. The speciﬁc pressure p is expressed as:
3. Friction vibration model of bearing Marine water lubricated stern bearing is easy to produce friction vibration and noise such as high-frequency whistlers and lowfrequency quaver. When the rotary linear speed of the propeller shaft of underwater vehicle is lower than 0.5 m/s, the whistlers of the stern bearing is easy to cause, and lower than 0.3 m/s, the quaver is prone to take place. This kind of noise is called singing in general, and considered related to the friction vibration. The friction vibration model of the shaft and bearing (lining with rubber slats) can be simplistically simulated with speed feedback pattern, as shown in Fig. 5. Assume that the test shaft quality is m1, spring constant is k1, damping constant is c1; the rubber slat quality of the stern bearing is m2, spring constant is k2, damping constant is c2. Under the effect of load W, the movement speeds of both shaft and the rubber slat of the stern bearing are x1̇ , x2̇ respectively, and the friction resistance between the shaft and slat is Ff. The motion equations of the friction pair of both shaft and slat of stern bearing are as follows:
m1x¨1 + c1x1̇ + k1x1 = Ff
m2 x¨2 + c2 x2̇ + k2 x2 = − Ff
Fig. 4. Testing machine of water lubricated stern bearing. 1- variable frequency motor; 2- coupling; 3, 5, 10- supporting baring; 4-torque speed meter; 6- seal device; 7vibration sensor 8- test bearing device; 9- test shaft; 11- cooling and lubricating system; 12- hydraulic system; 13- loading cylinder.
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lubrication status so that two sliding interaction surfaces can't keep uniform sliding speed and bring about intermittent movement, especially in starting or stopping moment and under the working condition of low speed. When the friction coefﬁcientspeed curve is a negative slope, the possibility of self-excited friction vibration and quaver or whistlers to bring about is increased, which produces serious wear, damages the ﬁt dimension between shaft and bearing and lowers the working quality. Practice shows that the main cause of the friction vibration and noise of the water lubricated bearing is the instability of friction coefﬁcient that is affected by material properties of the bearing lining, speciﬁc pressure, rotary speed, water temperature and wear, etc. The cause of the friction vibration and noise of the bearing is veriﬁed by both friction and wear tests as following. Fig. 5. Friction vibration model of shaft and bearing.
Where the relative sliding speed of the friction pair is x ̇, x ̇ = x2̇ − x1̇ ; x1, x2 are the displacement of m1, m2 respectively. Assume that friction resistance Ff is the function of both static and dynamic friction coefﬁcients (μ0, μ1) and x ̇ = x2̇ − x1̇ , so
Ff = Ff (ẋ) = W [μ1 + (μ 0 − μ1) e−α (ẋ2 − x1̇ ) ]
where α is constant. In general situation, assume Ff (x ̇) can be generated into power series near x ̇ = 0, so formula (3) can be expressed as
Ff (ẋ) = Ff (0) +
dFf (0̇ ) d2Ff (0¨ ) 2 ẋ + x¨ + ⋯ dẋ d2x¨
If it is only to judge the occurring condition of the friction selfexcited vibration in the system, and not to describe the whole process of both occurrence and development of the vibration, then in the formula (3), x ̇ can be thought very small, so the higher order terms of x ̇ can be missed. Meanwhile, the ﬁrst item Ff (0) is a constant force that can't effect the vibration of the system and can be omitted too. So formula (4) is shown as:
dF (0̇ ) dF (0̇ ) F (ẋ) = ẋ = − c′ẋ, − c′ = dẋ dẋ
Eq. (2) can be rewritten into the general form:
mx¨ + cẋ + kx = − c′ẋ mx¨ + (cẋ + c′ẋ) + kx = 0
dF f ( x )̇ Nearby x ̇ = 0, when dẋ < 0, and the relationship between friction resistance Ff (x ̇) and relative sliding speed x ̇ is negative slope, so the equivalent damping c′ is negative damping. When negative damping c′ is large enough and more than the system damping c, so c + c′ becomes negative damping, namely
c + c′ < 0 The system with negative damping is not stable and in a state of "explosive", which can't hinder the friction vibration of the system, but can promote the vibration of system. With the increase of the speciﬁc pressure of the bearing, the rise of the surface temperature and the change of relative sliding velocity, the friction surfaces between shaft and stern bearing rubber slat are likely in dry friction, boundary lubrication or mixed
4. Friction and wear tests of water lubricated rubber bearing Tribological properties of the water lubricated bearing, including friction, wear and lubrication, have greater inﬂuence on the friction vibration and noise of the bearing. The suppression level evaluation of the friction vibration and noise of the bearing is mainly based on both friction and wear tests, including friction coefﬁcient-speed, friction coefﬁcient-temperature characteristic tests and wear test. Main test parameters such as vibration amplitude (acceleration), friction coefﬁcient, rotary speed, water temperature, speciﬁc pressure etc. are measured, especially when bearing singing occurs. In engineering practice, the bearing singing has to be restricted in order to keep mute level of underwater vehicles, so the main object of the tests is to explore the friction coefﬁcient, rotary speed and other relative parameters at singing occurrence. 4.1. Friction test 4.1.1. Friction coefﬁcient-velocity characteristic test The inﬂuence of both friction coefﬁcient and rotary speed on the friction self-excited vibration of the water lubricated rubber stern bearing is studied under speciﬁc pressure, rotary speed, water temperature and cooling water ﬂow rate. Test conditions are as follows: 1) speciﬁc pressure p ¼0.10, 0.212 MPa; 2) rotary linear speed v ¼ 0.28 4.92 m/s; 3) water temperature T¼ 3571 °C; 4) cooling water ﬂow rate Q¼13 L/min. Bearing samples have A, B, C, D, E ﬁve groups, a total of 15 pieces. Before each bearing test, the original moment of the testing machine of water lubricated stern bearing is measured under noload, for example, the original moment of the testing machine of water lubricated stern bearing for one bearing is listed in Table 1. Then, a rubber bearing is installed on the machine and the total moment is measured under different load and liner speed etc. testing conditions. The different value between total moment and original moment is as the friction moment of the rubber bearing in corresponding load and linear speed etc., and the relative friction coefﬁcient of the rubber bearing is obtained. When speciﬁc pressure is 0.10, 0.212 MPa respectively, friction coefﬁcient-speed characteristics of the tests are shown in Fig. 6. From Fig. 6, it can be seen, that the friction coefﬁcient-speed characteristic curve of each bearing has similar change trend, and each curve has a the least extreme point (that is a turning point at
Table 1 Original moment of original moment of the testing machine for one bearing. Revolving speed/(r/min) Linear speed/(m/s) Original friction moment/(N m)
15 0.12 13.33
31 0.24 11.10
46 0.36 8.51
62 0.49 6.16
77 0.60 4.40
93 0.73 3.62
154 1.21 2.75
309 2.43 2.37
463 3.63 1.92
617 4.84 1.90
H. Wang et al. / Wear 376-377 (2017) 920–930
Fig. 6. Friction coefﬁcient-speed of A~E kinds of water lubricated bearings.
the lowest level of the curve), at which the friction coefﬁcient is minimum, so the corresponding rotary speed to the friction coefﬁcient is called the critical speed. When the speed is equal to or lower than the critical speed, the operating condition of the bearing may be in the mixed lubrication state or boundary lubrication state. At this time, the friction coefﬁcient is increased, bearing operation is not stable, and friction vibration and noise is easy to appear. When rotary speed is higher than the critical speed, operating condition of the bearing initiates to turn into hydrodynamic pressure lubrication status, and the contact state between both shaft and bearing is disappeared, water ﬁlm thickness increased and lubrication state improved so that operation condition is more steady, but friction coefﬁcient is slightly increased, which is characterized by slightly tilted upward curve. At this stage, friction vibration and noise disappear completely. In a general case, the kinetic characteristic of friction can be presented by the known Stribeck diagram that sets the friction coefﬁcient as a function of a complex parameter ηω/p; where η is dynamic viscosity; ω is angular rotation velocity of the shaft; p is speciﬁc pressure . Under general conditions, the more operation process of the bearing is in the mixed lubrication status. Assume that friction resistance of each bearing consists of two part of ones, one is the resistance hydrodynamic pressure lubrication ∫ τdsτ , the other is the resistance of boundary lubrication ∫ fd ⋅pd dsW (in dry friction and the half dry friction), so the friction resistance of the bearing can be expressed as:
F (ẋ) =
dx dsτ + ∫ fd ⋅pd dsW ∫ τdsτ + ∫ fd ⋅pd dsW = ∫ η dh ̇
where τ is the ﬂuid shear force; sτ is hydrodynamic pressure lubrication area; η is dynamic viscosity; pd is the contact pressure; sW is contact area; fd is dry friction coefﬁcient; h is the water ﬁlm thickness. It can be seen in formula (7), that in the region of the hydrodynamic pressure lubrication, friction resistance is related to dynamic viscosity η, the gradient of velocity and ﬂuid lubrication ﬁlm thickness dẋ and hydrodynamic pressure lubrication area sτ. In the dh region of the boundary lubrication, namely contact area between the shaft and bearing, the dry friction coefﬁcient of the region is related to both contact pressure pd and contact area sW. When the operation condition is in full dry friction status, the product of pd and sW is the normal load W of the bearing. The friction coefﬁcient f of the bearing is the ratio of the friction resistance F (x ̇) of the bearing and the normal load W applied on the bearing.
F (ẋ) W
In the friction test, sometimes the wear of the bearing samples was found, which indicates that the test is not in full ﬂuid lubrication state to be proceeded, so it is reasonable to assume that test procedure is in mixed lubrication status particularly under lower speed or overload conditions, which has local hydrodynamic pressure lubrication and local boundary lubrication conditions, but both proportion is still difﬁcult to determine quantitatively. Although the variation trend of the friction coefﬁcient-velocity characteristic curve of each bearing is similar (in Fig. 6), the inﬂection point positions of their curves are various and the critical speed and corresponding friction coefﬁcient are also different due
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to the component content difference of the rubber lining material of each bearing. This suggests that under the same speed, the smaller friction coefﬁcient of the bearing samples is, the more conducive to restrain frictional vibration. For an example, when speciﬁc pressure p¼ 0.212 MPa, the contrast between bearing sample C-03 with D-02 indicates that the critical speed and the friction coefﬁcient of the former (v ¼1.23 m/s, f¼ 0.011) is lower than the latter (v ¼2.46 m/s, f ¼0.031) separately, which suggests that the former is more conducive to restrain friction vibration and noise than latter. From the Fig. 6(a)~(d) contrast, it can be seen that with the enhancement of speciﬁc pressure (from p¼ 0.10 MPa to 0.212 MPa), the declining trend of the friction coefﬁcient of the bearing is taken place, and both critical speed and friction coefﬁcient to produce friction self-excited vibration and noise are decreased too. Taking an example of bearing sample D-02, under pressure p ¼0.212 MPa, both critical speed and the friction coefﬁcient are 2.46 m/s and 0.030 respectively, and under pressure p ¼0.10 MPa, both are 3.08 m/s and 0.045 separately, the critical speed and friction coefﬁcient of the former are fell by 20.1% and 31.4% than ones of the latter respectively. Thus, in the mixed lubrication state and within a certain speciﬁc pressure range, it can be explained that with the enhancement of the speciﬁc pressure, the deformation of lining rubber material is increased, the contact area between the shaft and bearing is widened, contact pressure declined, lubrication conditions improved and frictional resistance decreased so that critical speed and friction coefﬁcient are declined eventually. The deformation of the bearing lining is relative to the component content of rubber material, which is analyzed with ﬁnite element method. The ﬁnite element models of both shaft and bearing are established, therein the bearing contains 41580 nodes and 34560 units, and the test shaft contains 58969 nodes and 55600 units, as shown in Fig. 7. The deformation of a part of bearing samples including D-02 and C-03is shown in Fig. 8. In Fig. 8, it can be seen that the deformation trends of the bearings are increased with the enhancement of speciﬁc pressure, the deformation size of each bearing is related to itself component content such as acrylonitrile. For example, the deformation of bearing sample D-02 (acrylonitrile content 20%) is larger than bearing sample C-03 (acrylonitrile content 30%), which can make the contact area between shaft and bearing increased and the effect of both cooling and lubricating declined. It is one of reasons that the friction coefﬁcient of the former higher than one of the latter.
Fig. 8. The vertical deformation of the bearings.
But it should be noted that the friction coefﬁcient is not a material property, but a measured parameter which is highly dependent on the environmental conditions . 4.1.2. Friction coefﬁcient-temperature characteristic test The friction vibration and noise of the bearing is in a certain extent affected by cooling water temperature. Water temperature characteristic test conditions are as follows: p ¼0.212, 0.40 MPa; v ¼0.28 1.845 m/s; T ¼20 °C 40 °C, Q¼13 L/min. The test results of bearing sample B-04 are shown in Fig. 9. In Fig. 9, it can be seen, that under the different water temperature, the changing rule of the friction coefﬁcient-speed characteristic is the same. Under the same speciﬁc pressure and rotary speed conditions, the higher water temperature is, the bigger friction coefﬁcient. For an example, when the pressure, speed are 0.212 MPa and 0.28 m/s respectively, the friction coefﬁcient of water temperature 30 °C is 0.047, and one of water temperature 40 °C is 0.057. The friction coefﬁcient of the latter is increased by 21% than the former. This shows that the rubber material of the bearing lining is more sensitive to water temperature, and easy to produce softening and deformation. Therefore, in the mixed lubrication conditions, both the rupture of local water ﬁlm and the adhesion of contact surface occur, and the viscous force of contact surface is increased, which results in the rise of friction coefﬁcient ﬁnally. For instance of the inﬂuence of speciﬁc pressure on friction coefﬁcient, under water temperature 40 °C and speed 0.28 m/s,
Fig. 7. Finite element models of both bearing and shaft.
H. Wang et al. / Wear 376-377 (2017) 920–930
Fig. 9. Friction coefﬁcient-temperature characteristic curve of bearing B-04.
the friction coefﬁcient of pressure 0.40 MPa is 0.055, and one of pressure of 0.212 MPa is 0.057, the former is only decreased by 3.5% than the latter. The above analysis illustrates that the inﬂuence of water temperature on friction coefﬁcient is more obvious. 4.2. Wear test In the wear test process of the bearings, on the one hand, the variation rule of the friction coefﬁcient is explored, and the surface morphology of the friction pair and its inﬂuence on friction vibration are evaluated; on the other hand, the abrasion resistance of the bearing lining material is assessed to provide with test data for the material selection. 4 kinds of the operating conditions of the bearings wear test were designed, which include speciﬁc pressure, speed, water temperature and test time etc. parameters. The wear tests were sequentially made based on both friction coefﬁcient-speed and friction coefﬁcient-temperature characteristic tests. Test conditions are 1) Test speciﬁc pressure are 0.50, 0.60, 0.75, 0.60 MPa; 2) the rotary speed of the test shaft are 30, 40, 50, 60 r/min; 3) water ﬂow rate is 13 L/min; 4) cooling water temperature are 35 °C and 40 °C; 5) Test time is 500 h (in Table 1). In bearing samples C-03 case, due to the difference parameters of operating conditions (such as speciﬁc pressure, rotary speed, water temperature, etc.), therefore in the 4 kinds of operating condition processes of the test, the friction coefﬁcient of each operating condition has certain variation. As the growth of the wear test time, the wear region between the shaft and bearing is expanded, their contact area is increased and contact pressure is slightly declined, so the friction coefﬁcient in each operating condition is decreased as a whole, but the friction coefﬁcient, wear loss and surface feature of both shaft and bearing are various respectively, as shown in Figs. 10–12 and listed in Table 2. In the wear test, because the wear loss of the test shaft bush is less, so the inﬂuence of the bush wear isn't discussed in detail, and one of the bearing wear is focused on as following. From Figs. 10–12 and Table 1, 4 kinds of the operating conditions of the wear test are proceeded under overpressure and low speed, so the bearing should be in mixed lubrication or boundary lubrication status in the test process, and both shaft and bearing can have a local contact so that wear is taken place. There are few difference on the friction surface morphology of the bearing in two kinds of operating conditions (operating condition 1 and 2), but the friction coefﬁcient in operating condition 2 is higher than one in operating condition 1, and wear loss of the former is slightly lower than one of the latter. Although the speciﬁc pressure (0.75 MPa) in operating condition 3 is slightly lower than one (1.00 MPa) in the operating condition 4, the rotary speed of the former (30, 40 r/min) is lower
Fig. 10. Friction coefﬁcient- test time in wear test. 14 are operating conditions respectively.
Fig. 11. Surface state of test shaft bush after test.
than one of the latter (40, 50, 60 r/min). Therefore, the comprehensive results of the pressure and speed make the lubrication effect of the former is poorer and the friction coefﬁcient is greater, but wear loss is lower than one in operating condition 4. These test results are possibly relative to the test order of operating conditions, speciﬁc pressure, contact area, and lubrication conditions and so on.
5. Inﬂuence of friction and wear on frictional vibration The inﬂuence of both friction and wear on the structure and performance of the bearings has a time-dependence nature. With
H. Wang et al. / Wear 376-377 (2017) 920–930
Fig. 12. Wear state of stern bearing.
the increase of test time, the deformation state of the contact surface between the shaft and bearing will be varied, which makes the contact area of the friction pair, contact pressure, surface temperature and the performance of lining material changed. Finally, adhesive sliding movement appears, and friction resistance is seriously ﬂuctuated and system operation is instable to generate friction vibration and noise, but this kind of state will be relieved and disappeared when the relative sliding speed between the shaft and bearing is higher than the critical speed. The friction vibration test of the bearings was carried out on the testing machine of water lubricated stern bearing. Vibration sensors were installed in the top and side of the bearing test device and the test machine (see Fig. 13), BK analysis software was used to collect and analyze test data. According to the vibration theory of the rotor system, the testing machine may produce some vibration by itself in the test as following: 1) The beat vibration frequency of motor fan blades is commonly the product of the fundamental frequency of rotation axis and the number of fan blades; 2) The axis misalignment of the test machine is easy to produce double rotation frequency amplitude; 3) When both shafting revolving centroid and the theoretical rotation center aren't concentric, the vibration frequency
spectrum feature is that ﬁrst-order transfer frequency amplitude is very big, and is increased with the increase of rotary speed, but not sensitive to the load of shafting [17,18]. In order to identify the friction vibration state of the bearing sample, before the test, the vibration characteristics of the testing machine is detected and analyzed under no-load and different rotation speed in order to determine the vibration frequency of equipment such as motor, supporting bearing and the torque speed meter etc. The vibration spectrum of the testing machine under no-load condition and rotary seed (30, 200 r/min) is shown in Figs. 14 and 15. In Figs. 14 and 15, it can be seen, that the vibration frequencies of motor and torque speed meter distribute near 250 Hz at different rotary speed. Taking bearing sample C-03 as an instance, under speciﬁc pressure 0.35, 0.40, 0.45, 0.50, 0.55, 0.60 MPa, water temperature 30, 35, 40 °C and water ﬂow rate 13 L/min, the friction coefﬁcientspeed characteristic, friction coefﬁcient-temperature characteristic and wear tests are proceeded to detect the critical speed and the corresponding friction coefﬁcient, and the frequency and amplitude of friction vibration, specially to observe relative parameters when bearing singing occurs. Both critical speed and friction coefﬁcient of the bearing is determined according to the singing generation of the bearing in
Table 2 The wear test results of bearing. Operating condition
1 2 3 4
Speciﬁc pressure p / MPa
Rotary speed v/(r/min)
Water ﬂow rate Q/ (L/min)
Water temperature T/°C
0.50 0.60 0.75 1.00
30 30 30, 40 40, 50, 60
13 13 13 13
35 35 40 40
Test time t/h
100 100 150 150
Unit time wear/(μm/h)
0.091 0.085 0.061 0.069
0.004 0.005 0.022 0.014
0.910 0.850 0.407 0.460
0.035 0.046 0.136 0.090
H. Wang et al. / Wear 376-377 (2017) 920–930
Fig. 13. Vibration sensor arrangement. 1- lateral vibration sensor; 2- vertical vibration sensor; 3- vibration sensor of supporting rolling bearing; 4- vibration sensor of motor; 5- vibration sensor of torque speed meter.
Fig. 14. Vibration spectrum of the testing machine (speed 30 r/min).
Fig. 15. Vibration spectrum of the testing machine (speed 200 r/min).
tests. The generation of the singing can be monitored and the severe changes of amplitude viewed. In order to expediently determine the singing generation, the test is carried out from high speed to low speed until singing occurs, then the rotary speed and corresponding friction coefﬁcient at this time are recorded as critical values. Under different speciﬁc pressure, water temperature and frictional wear state, both critical speed and corresponding friction coefﬁcient to generate singing (friction vibration and noise) are listed in Table 3. In Table 3, it is shown that when p ¼0.35 MPa, T ¼30 °C, critical speed and friction coefﬁcient are v ¼21 r/min, f ¼0.072 separately. If rotary speed exceeds the critical speed such as v ¼25 r/min, the singing of the bearing may not be generated, as shown in Fig. 16.
In Fig. 16, the amplitude near 250 Hz frequency is resulted from motor and torque speed meter, both vertical and lateral vibration amplitudes of the bearing sample are smaller and singing don't happen. In friction test (including friction coefﬁcient-speed and friction coefﬁcient-temperature tests), both critical speed and friction coefﬁcient of the bearing sample are lower in wear test when singing occur. It demonstrates that the wear of the bearing changes the feature of the friction surface of the bearing and the ﬁt clearance between the shaft and bearing, and enhances frictional resistance and friction coefﬁcient. Therefore, the wear is easier to result in friction vibration and noise of the bearing than the friction. Taking speciﬁc pressure 0.55 MPa and water temperature 30 °C (in Table 3) for a wear test example, both critical speed and friction
H. Wang et al. / Wear 376-377 (2017) 920–930
Table 3 Inﬂuence of water temperature, operating pressure and wear on friction vibration. Water temperature/°C
Speciﬁc press/MPa 0.35
21 (0.072) 45 (0.073)
26 (0.061) 48 (0.073)
27 (0.073) 55 (0.073)
34 (0.059) 61 (0.074)
35 (0.055) 73 (0.095)
38 (0.048) 118 (0.090)
23 (0.064) 49 (0.118)
24 (0.072) 55 (0.100)
30 (0.064) 68 (0.088)
32 (0.060) 81 (0.099)
33 (0.062) 125 (0.088)
39 (0.055) 140 (0.093)
21 (0.066) 50 (0.096)
23 (0.062) 56 (0.096)
25 (0.065) 71 (0.103)
27 (0.061) 80 (0.109)
30 (0.053) 121 (0.089)
32 (0.059) 141 (0.096)
①Indoor temperature: 27 °C. ②In the Table 3, for example:21(0.0719) means rotary speed is 21 r/min, and friction coefﬁcient is 0.072 under rotary speed 21 r/min.
Fig. 16. Frequency domain (0.35 MPa, 30 °C, 25 r/min).
Fig. 17. Frequency domain (0.55 MPa, 30 °C, 73 r/min).
coefﬁcient of the bearing are 73 r/min and 0.095 respectively, and in friction test, ones are 35 r/min and 0.055 separately, which indicates that the critical speed and friction coefﬁcient of the former are increased by 109% and 73% than the latter respectively; at 35 °C, increased by 282% and 42%; and at 40 °C, increased by 300% and 68%. It shows that inﬂuence of the test conditions of the wear and friction on the friction vibration and noise is very obvious. In wear test, when p¼ 0.55 MPa, n¼73 r/min, T¼ 30 °C, there are multiple peaks with frequency doubling in spectrum of the bearing, maximum accelerations appear at 1.3 kHz, and vertical one is 0.112 m/s2 and horizontal one is 0.360 m/s2 respectively, as shown in Fig. 17. The critical speed of singing generation is increased as the water temperature and pressure are raised. In general test
condition, the inﬂuence of water temperature on water viscosity and density is little, but one on the rubber performance is greater. With the increase of water temperature, the rubber layer hardness and elastic modulus of the bearing are decreased, and the deformation of rubber slat and the contact area between the shaft and bearing are increased so that water wedge is difﬁcult to produce under low speed even at higher speed, and water ﬁlm is still hard to form, which makes the critical speed of the singing generation and the corresponding friction coefﬁcient increased. So in order to restrain the friction vibration and noise, it is necessary for the bearing to keep lower friction coefﬁcient. In Table 3, it shows that in both friction and wear tests, the critical speed of the bearing is increased with the enhancement of
H. Wang et al. / Wear 376-377 (2017) 920–930
Fig. 18. Frequency domain of bearing A-01 (1.0 MPa, 28 °C, 52 r/min, f¼0.060).
speciﬁc pressure, but the variation of the friction coefﬁcient is not yet obvious. At once, the speciﬁc pressure is too high, the water ﬁlm between the shaft and bearing is ruptured easily. At this time, the contact area between the shaft and bearing is increased, the friction resistance is more ﬂuctuated with the change of speed, and stick-slip phenomenon is more serious. In the friction test of bearing A-01, when p¼ 1.0 MPa and T ¼28 °C, the singing generation of the bearing comes forth at rotary speed 52 r/min. At moment, both vertical and lateral amplitudes (acceleration) reach 0.046 m/s2 and 0.117 m/s2 in 4 kHz frequency respectively, which are higher than ones in 7.7 kHz separately, as shown in Fig. 18.
1. The critical speed and friction coefﬁcient of the water lubricated rubber bearing are relative to material composition, speciﬁc pressure, water temperature and frictional wear. The generation of the friction vibration singing of the water lubricated rubber bearing has a certain regularity that the smaller friction coefﬁcient is, the more conducive to restrain the singing. 2. Under the same temperature and speciﬁc pressure, both critical speed and friction coefﬁcient of the bearings in wear test are higher than ones in friction test. In wear test, when speciﬁc pressure is 0.55 MPa and water temperature is 30°C, the critical speed and friction coefﬁcient are 73 r/min and 0.095, and ones in friction test 35 r/min and 0.055 respectively. Both critical speed and friction coefﬁcient of the former are raised by 109% and 73% than the latter separately. The test results indicate that the inﬂuence of wear on both critical speed and friction coefﬁcient of the bearing is very obvious. 3. Under different temperature and uniform speciﬁc pressure, the transformation law of the friction coefﬁcient-speed of the bearings is the same. When keeping both pressure and speed unchanged, the higher the water temperature is, the greater friction coefﬁcient. When speciﬁc pressure is 0.212 MPa and speed is 0.28 m/s, the friction coefﬁcient of bearing B-04 at 30°C, is 0.047, and 0.057 at 40°C,, increased by 21%. This suggests that the rubber material is sensitive to water temperature change, but is not very sensitive to pressure change, such as p ¼0.40 MPa, friction coefﬁcient is 0.055 which only declines by 3.5% than p ¼0.212 MPa.
Acknowledgements This work was ﬁnancially supported by the project of Natural Science Foundation of China (No.51379168), Key Natural Science Foundation of China (No.51139005).
References  N.M. Kinkaid, O.M. O'Reilly, P. Papadopoulos, Automotive disc brake squeal, J. Sound Vib. 267 (2003) 105–166.  Ronald A.L. Rorrer, Vikas Juneja, Friction-induced vibration and noise generation of instrument panel material pairs, Tribol. Int. 35 (2002) 523–531.  M. Nishiwaki, Generalized theory of brake noise, J. Automob. Eng. 207 (3) (1993) 195–202.  Sun Di, Li Guobin, Wei Haijun, Liao Haifeng, Liu Tiny, Study on variation rules of friction in the process of friction and vibration wear, J. Harbin Eng. Univ. 36 (2) (2015) 166–170.  Zhou Jianhui, Liu Zhenglin, Zhu Hanhua, Hai Pengzhou, Experimental study on frictional characteristic of rubber water lubricated stern tube bearings, J. Wuhan. Univ. Technol. (Transp. Sci.) 32 (5) (2008) 842–844.  Zhao Shuhe, The self-excited vibration of ship shafting and tail structure, Ship Sci. Technol. 3 (1992) 11–15.  Su Dan, The Study of Stick-slip Mechanics and Computer Simulation, Lanzhou University of Technology, Lanzhou, 2007.  R.I. Leine, D.H. Van Campen, A. De Kraker, L. Van Den Steen, Stick-slip vibration induced by alternate friction models, Nonlinear Dyn. 16 (1998) 41–54.  Q. Ding, A.Y.T. Leung, J.E. Cooper, Dynamic analysis of a self-excited hysteretic system, J. Sound Vib. 245 (1) (2001) 151–164.  U. Galvanetto, Some discontinuous bifurcations in a two-block stick-slip system[J], J. Sound Vib. 248 (4) (2001) 653–669.  J. Awrjceicz, P. Olejnik, Friction pair modeling by a 2-dof system numerical and experimental investigations, Int. J. Bifurc. Chaos 15 (6) (2005) 1931–1944.  R.A. Ibrahim, Friction-induced vibration, chatter, squeal and chaos, partⅠ: mechanics of contact friction, ASME Appl. Mech. Rev. 47 (7) (1994) 209–226.  Chen Guang-xiong, Zhou Zhong-rong, An experiment investigation on mechanism of generation of friction-induced vibration under reciprocating sliding, Tribology 21 (6) (2001) 425–429.  G.X. Chen, Z.R. Zhou, Experimental observation of the initiation process of friction-induced vibration under reciprocating sliding conditions, Wear 259 (2005) 277–281.  Vladimir P. Sergienko, Sergey N. Bukharov, Noise and Vibration in Friction Systems, Springer International Publishing, Switzerland, 2015.  Pradeep L. Menezes, Sudeep P. IngoleMichael Nosonovsky, Satish V. Kailas, Michael R. Lovell, Tribology for Scientists and Engineers, Springer Science þBusiness Media, New York, 2013.  Jin Yong, Liu Zheng-lin, Experimental research on performance of water-lubricated rubber stern bearing based on vibration analysis, Noise Vib. Control 4 (2011) 64–67.  Tian Yu-zhong, Liu Zheng-lin, Jin Yong, Peng En-gao, Mechanism analysis of squeal of water lubrication stern tube rubber bearing based on experimental study, J. Wuhan. Univ. Technol. 33 (1) (2011) 1–4.