Advertisement

Tribology Letters

, 66:85 | Cite as

Analysis of the Dynamic Friction of a Gas Face Seal Based on Acoustic Emissions

  • Yuan Yin
  • Weifeng Huang
  • Xiangfeng Liu
  • Ying Liu
  • Zixi Wang
  • Wenjing Fan
  • Songtao Hu
Original Paper

Abstract

Acoustic emission (AE) signals produced by the dynamic friction of a gas face seal are analyzed to uncover their information concerning the status of the seal. Experiments were conducted with a gas face seal test rig. By adjusting different operating parameters, friction occurred in different ways and produced discrepant AE signals. The root-mean-square value of AE signals under different operating conditions has varied fluctuations on a timescale of the rotation period, which distinguishes different dynamic friction patterns and furthermore shows the significant discrepancy of how dynamic friction is affected by different operating parameters. Numerical simulations using a dynamic model for a gas face seal with contact coupled were performed. A combination of the experiments and numerical simulations validates the dynamic friction dependence on waviness, which can be reflected by AE signals. This research demonstrates the approach of revealing the real-time friction status of a seal by analyzing AE signals on a timescale of the rotation period.

Keywords

Mechanical seals Friction test methods Acoustic emission Real-time monitoring 

1 Introduction

Mechanical face seals are a kind of shaft seal offering high performance especially under extreme conditions and are widely used in rotary machines, such as pumps and turbo-machines [1]. When a seal is working properly, the leakage is low and wear is reduced or even eliminated, allowing the seal to serve for a long lifetime as expected. However, it is difficult to acquire detailed real-time information about the status of a seal, which hides deep inside the compact seal structure. Abnormal wear is thus usually undetectable until an unexpected failure happens. Meanwhile, there are various causes that may lead to the poor performance or even failure of a seal, including the misalignment or deformation of seal rings, the vibration of shafting, the malfunctioning of springs or the secondary seal, and the poor quality of the fluid [2, 3]. However, because of a lack of detailed real-time information, the actual cause(s) is usually difficult to uncover, especially when it only appears while the seal is running (e.g., the deformation of seal rings due to heat). Additionally, studies have been conducted on the real-time active control of mechanical face seals [4, 5, 6, 7] for self-curing and self-optimizing, with the performance relying on the information of the real-time status. In summary, the lack of detailed real-time information has reduced the reliability and maintainability of mechanical face seals, and obstructs the development of mechanical face seals.

Various methods have been developed for the real-time monitoring of mechanical face seals [8], mainly including seal face temperature monitoring [6, 9], eddy current proximity monitoring [7, 10], reflected ultrasonic monitoring [11], and acoustic emission (AE) monitoring [12, 13, 14, 15, 16, 17, 18, 19]. Among them, AE monitoring, which aims at measuring AEs generated by the tribo-pair, has outstanding information density [8], friction sensitivity [18], and engineering practicability, and thus great potential application. Attempts at the AE monitoring of mechanical face seals started with Orcutt [12] in 1969, and early success was reported by Miettinen et al. [13] in 1995 and Holenstein et al. [14] in 1996. Recent studies have addressed the abundant information implicated in AE signals. Towsyfyan et al. [16] tried to distinguish different lubrication regimes of a seal from AE signal characteristics, including the RMS value and kurtosis value. Li et al. [17] developed a signal analysis system based on genetic particle filter with autoregression and hypersphere support vector machine, and successfully judged the contact state of the seal using AE signals. In our previous work [18, 19], we analyzed AE signals generated during the starting and stopping of a mechanical face seal, and revealed that the rub impact in a seal produces an AE signal concentrated in particular frequency bands. The above studies proposed various approaches for analyzing AE signals, mainly focusing on the timescale of the acoustic waveform.

As long as sliding occurs between two rings, it becomes the major contributor of AE signals (within particular frequency bands) from a tribo-pair. Therefore, measuring friction severity from AE signals is a reliable approach [19]. However, one detail that has not been carefully considered in the existing research is that when the friction undergoes periodic changes because of rotor excitation, one should infer the seal status from AE signals not at isolated instants but throughout the rotation period. Meanwhile, changes in the AE signal upon shaft rotation directly reveal some common faults, such as the tilts and waviness of seal rings.

The present study analyzed AE signals and uncovered their relation to the dynamic friction of a seal. The operating conditions of the seal rig were adjusted to produce discrepant dynamic friction, the generated AE signals from which were measured. AE signals on a timescale of the shaft rotation period were then examined and compared.

2 Test Rig

The experiment was performed on a test rig as illustrated in Fig. 1. The spiral groove gas face seal, which is employed in this experiment, is a type of mechanical face seal. In a normal and stable seal running process, matching seal rings are separated with a gas film that is both thin enough to slow the leakage and rigid enough to avoid direct solid contact. In this seal rig, there were two stators flexibly mounted on the seats and one rotor with spiral grooves (see Fig. 2) on both faces rigidly mounted on the shaft.

Fig. 1

Illustration of the test rig. A loading mechanism and a PICO sensor are appended to a gas face seal

Fig. 2

The spiral grooves on rotor

A loading mechanism was appended to the outer one of the two stators. When weights were loaded on the mechanism, the outer stator was forced by an additional eccentric force, which tilted the outer stator and pushed it toward the rotor, as shown in Fig. 3. The forces applied on the stator when different masses of weights were loaded are given in Table 1.

Fig. 3

Sketch of three degrees of freedom (axial, tilt around X, and tilt around Y) and the motion of the seal rings when a force is applied

Table 1

Forces applied on the stator when different weights are loaded

Mass of weights loaded (kg)

1

2

3

4

5

Force acting on the stator (N)

29.7

54.6

79.5

104.4

129.3

A miniature sensor, PICO, produced by Physical Acoustics Corporation, was employed in the AE measuring system. The sensor was directly mounted to the back of the outer stator, allowing the clearly monitoring of AE signals from the friction of the outer stator and rotor and greatly concealing AE signals from other parts of the rig. The signals were acquired by AE win software provided by the same company. An AE wave was recorded every 1.3 ms for further processing. Each AE wave contained \(M=1024\) sampling points at a sampling rate of 2000 kHz.

3 Discrepant Dynamic Friction Under Different Operating Conditions

To induce contact, an eccentric force was exerted on the outer stator by the loading mechanism mentioned above. A load heavy enough can break the gas film and thus cause contact between the two rings. The rotor tilt, speed, and pressure affected the seal in different ways. The above parameters were adjusted and the change in dynamic friction was expected to be observed through AE signals.

The adjustment of the four parameters resulted in 18 different operating conditions (nine sets of load, speed, and pressure for each of the two rotor tilt values) in total, as shown in Table 2. AE signals were measured while running the seal stably under each operating condition.

Table 2

Operating conditions

aThe load is represented by the mass of weight loaded

See Fig. 4, the root-mean-square (RMS) value of each wave was calculated from volts \({U}_{i}\) at sampling points as

Fig. 4

Calculating the changes in the RMS of the signal. The wave was recorded every 1.3 ms to give one RMS value

$${\text{RMS}}=\sqrt {\frac{1}{M}} \sum\limits_{{i=1}}^{M} {U_{i}^{2}}.$$
(1)

Then the RMS values of AE waves within a few shaft revolutions were sketched, revealing friction changes, as a greater RMS value generally indicates a more severe friction and vice versa [19]. Taking a speed of 1200 rpm (with the rotation period being 50 ms) as an example, because an AE wave was recorded every 1.3 ms, the average count of RMS values in each period was 50/1.3 ≈ 38.5. This number was sufficient for clearly showing how friction changed upon shaft revolution. The average RMS of the signal in a duration of 5 s was also calculated.

Figure 5a and b, respectively, shows the RMS value measured under varying loads and rotor tilts of 46 and 144 µrad, with the speed fixed at 1200 rpm and the pressure fixed at 4 atm. As expected, the major changes in the RMS value were periodic and exactly in time with the rotation period. A comparison of Fig. 5a and b shows that the difference in tilt hardly affected the shape of RMS curves, and that as long as AE from sliding dominated, the AE RMS value for the larger rotor tilt was greater than that for the smaller rotor tilt as a whole. A vertical comparison of Fig. 5 shows that with an increase in load, the shape of the RMS curves obviously evolved and could be divided into the following stages:

Fig. 5

RMS comparison for varying loads at a fixed speed of 1200 rpm, fixed pressure of 4 atm, and rotor tilts of a 46 µrad, b 144 µrad

  1. 1.

    No friction The AE signals were weak when a load of 1 kg was applied, indicating no friction (or only extremely slight friction).

     
  2. 2.

    Intermittent friction When a load of 2 kg was applied, there were several spires in each rotation period while the valleys of the RMS curves remained low, indicating that friction occurred intermittently. Compared with the 2 kg load condition, when a 3 kg load was applied, the peak value of the RMS was higher and four main spires of different heights and of discrepant time differences in each period were easily distinguished. These spires indicate a complex circumferential nonuniformity, which was probably a result of waviness other than tilt.

     
  3. 3.

    Continuous friction The valley value rose after the load reached 4 kg, indicating that the two rings rubbed continuously throughout each period. In this stage, the peak RMS value no longer increased with the load and a platform form replaced the spires. Compared with the 4 kg load condition, besides the rise of the valley value, new summits rose from the middle of the platforms when a 5 kg load was applied.

     

Figure 6a, b, respectively, shows the RMS curves for varying speeds and rotor tilts of 46 and 144 µrad, while the load was fixed at 3 kg and the pressure was fixed at 4 atm. The difference in speed showed two effects.

Fig. 6

RMS comparison for varying speeds at a fixed load of 3 kg, fixed pressure of 4 atm, and rotor tilts of a 46 µrad, b 144 µrad

  1. 1.

    A higher speed led to greater friction power given a certain contact status, resulting in a greater RMS of the AE signal. This explains why the RMS at a speed of 1500 rpm was greater overall than that at a speed of 1200 rpm.

     
  2. 2.

    A higher speed strengthened the hydrodynamic effect of the spiral groove gas face seal to separate the two rings. This effect dominated the difference between the results obtained for speeds of 900 and 1200 rpm in that the former speed resulted in continuous friction while the latter resulted in intermittent friction.

     

Figure 7a, b, respectively, shows the RMS curves for varying pressures and rotor tilts of 46 and 144 µrad, while the load was fixed at 3 kg and the speed was fixed at 1200 rpm. The difference in pressure affected the friction in two contrary ways. On one hand, the pressure acting on the back of the stator pushed the stator toward the rotor to aggravate the friction; on the other hand, a higher pressure strengthened the hydrostatic effect to separate the rings. In this comparison, the friction was slightest at pressure of 4 atm.

Fig. 7

RMS comparison for varying pressures at a fixed load of 3 kg, fixed speed of 1200 rpm, and rotor tilts of a 46 µrad, b 144 µrad

In summary, the above RMS curves of the diverse shapes show that different dynamic friction patterns can be distinguished from AE signal characteristics on the timescale of the rotation period. Furthermore, the four different operating condition parameters affect the dynamic friction in discrepant ways, and a corresponding discrepancy in AE signals can be observed.

4 Dynamic Contact Dependence on Waviness

As mentioned above, when applying a moderate load, the AE RMS curves indicate that the severity of friction reaches multiple maximums of different heights and discrepant time differences in each period. This can be speculated to be caused by waviness. As an intuitive explanation, one probable status leading to the results observed is shown in Fig. 8, i.e., the potential contact region S1 and S2 on the outer stator contact with R1 and R2 on the outer face of the rotor alternately. The waviness of the two rings results in a unique pattern of the contact strength change.

Fig. 8

A probable status yielding the results of the present experiment. S1, S2 (both on the stator), R1 and R2 (both on the rotor) represent the potential contact regions on the rings. When a pair of them coincides, the friction severity shall reach a local maximum

Owing to the great difficulty of measuring the real-time waviness directly by experiment, a numerical dynamic model for the spiral groove gas face seal with contact coupled is employed to study the effect of waviness on friction.

The dynamic behavior of the gas face seal considering contact is governed by the following equations.

The lubrication equation [20, 21] is
$$\nabla \cdot\left( {\frac{{p{h^3}}}{{12\mu }}\nabla p} \right)=\frac{{\omega \partial \left( {ph} \right)}}{{2\partial \theta }}+\frac{{\partial \left( {ph} \right)}}{{\partial t}}.$$
(2)

Here p is the absolute gas pressure on the seal face, pc is the solid contact pressure, and h is the nominal clearance. Each of the three is a time-varying field defined on the end face \(A=\left\{\left(r,\theta \right)|{r}_{i}\le r\le {r}_{o}\right\}\). \(t\) is time and \(\mu\) is the dynamic viscosity of gas (assumed to be constant).

The contact pressure function [22, 23] is
$${p_c}={p_c}\left( h \right)=\frac{4}{3}EN{R^{\frac{1}{2}}}\int\limits_{h}^{\infty } {{{\left( {Z - h} \right)}^{\frac{3}{2}}}\phi \left( {\frac{{Z - {y_s}}}{{{\sigma _s}}}} \right)} dz.$$
(3)

In the above function, the mated faces are treated as an ideal rigid smooth surface and an equivalent rough surface with the statistics given below: \(E\) is Young’s modulus, \(N\) is the asperity density, \(R\) is the average radius of asperity tips, \({\sigma }_{s}\) is the standard deviation of asperity height, and \({y}_{s}\) is the mean of asperity height relative to the nominal plane. \(\Phi \left( \cdot \right)\) represents the probability density function of the standard normal distribution. Given a certain rotation speed, a greater contact force (which equals to the integral of \({p}_{c}\) on \(A\)) means more severe sliding friction.

The dynamic equation [20, 21] is
$$\left[ {\begin{array}{*{20}{c}} m&{}&{} \\ {}&{{I_X}}&{} \\ {}&{}&{{I_Y}} \end{array}} \right]\ddot {{\varvec{U}}}\varvec{+}\left[ {\begin{array}{*{20}{c}} {{d_{sZ}}}&{}&{} \\ {}&{{d_{syX}}}&{} \\ {}&{}&{{d_{syY}}} \end{array}} \right]\ddot {{\varvec{U}}}\varvec{+}\left[ {\begin{array}{*{20}{c}} {{k_{sZ}}}&{}&{} \\ {}&{{k_{syX}}}&{} \\ {}&{}&{{k_{syY}}} \end{array}} \right]{\varvec{U}}={\varvec{Q}}.$$
(4)
In Fig. 3, \(\varvec{U}={\left[\begin{array}{ccc}Z& {\gamma }_{X}& {\gamma }_{Y}\end{array}\right]}^{\text{T}}\) is the generalized displacement of the stator, consisting of the Z-axis displacement \(Z\), angular displacement around the X axis \({\gamma }_{X},\) and angular displacement around the Y axis \({\gamma }_{Y}\). The generalized force \(\varvec{Q}\) considers the effect of the absolute gas pressure on the face, contact pressure, and the force generated by the loading mechanism
$${\varvec{Q}}=\left[ {\begin{array}{*{20}{c}} {{F_Z}} \\ {{M_X}} \\ {{M_Y}} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} {\int {\int\limits_{A} {\left( {p+{p_c}} \right)dA} } } \\ {\int {\int\limits_{A} {\left( {p+{p_c}} \right)r\sin \theta dA} } } \\ { - \int {\int\limits_{A} {\left( {p+{p_c}} \right)r\cos \theta dA} } } \end{array}} \right]+\left[ {\begin{array}{*{20}{c}} {{F_L}} \\ { - {F_L}{T_L}} \\ 0 \end{array}} \right].$$
(5)

Here \({F}_{L}\) is the force exerted by the loading mechanism and \({r}_{L}\) is the radius at which the force is applied.

The clearance \(h\) can be represented by the generalized displacement as [20, 21]
$$h={h_0}+\left[ {\begin{array}{*{20}{c}} 1&y&{ - x} \end{array}} \right]{\varvec{U}}+{\delta _k}{h_{gr}}.$$
(6)

Here \({h}_{0}\) is the clearance of the land region when \(\varvec{U}=0\). \({h}_{gr}\) is the depth of spiral grooves. \({\delta }_{k}\) takes a value of 1 in grooves and 0 on the land.

The values of parameters are elaborated in the Appendix Table 3.

Three examples are simulated with the above model. The examples marked (a), (b), and (c) are, respectively, about seals with waviness shown in Fig. 9a, b, and c on rings. Example (a) is for an ideal condition where there is no waviness on either ring (but this eliminates the contact so the load and rotor tilt are greater than those in the other two examples to induce contact). In example (b), a two-peak waviness exists on both rings. In example (c), there is the same two-peak waviness on the rotor and an asymmetric waviness mixed of second and third harmonics on the stator.

Fig. 9

Waviness of two seal rings in three examples: a no waviness, b two-peak waviness on both rings, c two-peak waviness on the rotor and second- and third-harmonic mixed waviness on the stator

The contact forces simulated for examples (a), (b), and (c) are, respectively, illustrated in Fig. 10a, b, and c. Figure 9a shows that, in the absence of waviness, except for minor fluctuations caused by the 12 spiral grooves, each rotation period contains one peak and one valley. Figure 10b shows that each rotation period contains two peaks, each resulting from two pairs of waviness crest contacting at the same time (with the height difference resulting from the tilt of the rings). Figure 10c shows that the particular waviness on the two faces produces four contact force maximums, with different magnitude and discrepant time differences, within each period, agreeing with the features of the AE RMS curve observed in the experiment.

Fig. 10

Simulated contact force

Besides the agreement of example (c) and the experiment, a comparison of the three examples shows that the variance of waviness reshapes the contact force curve in terms of the count, relative magnitude, and time differences of the multiple maximums in each period. These results validate that waviness can result in complex fluctuation of the AE RMS value which reflects dynamic friction. Through this, AE monitoring can provide abundant information concerning the waviness on the rings of a running seal. Because waviness on the faces of a running seal, which is difficult to measure, can be different to that of an unassembled seal, this waviness information implied in AE signals is valuable.

5 Conclusions

AE signals generated from the tribo-pair of a gas face seal rig were measured when the seal ran under different operating conditions. The RMS of AE signals, which represents the instant severity of friction, was analyzed. Numerical simulations using a dynamic model for the gas face seal were also performed to support the analysis. The following conclusions are drawn from the results of the study.

  1. 1.

    The AE signal characteristics on the timescale of the rotation period distinguish dynamic friction patterns and show how friction is affected by different operating parameters in discrepant ways as stated below. With other parameters unchanged, the AE RMS value for a larger rotor tilt is greater than that under a smaller tilt as a whole, while the trends remain almost the same. Through an increase in load, the shape of RMS curves evolves, sequentially undergoing an intermittent friction stage and a continuous friction stage. The change in speed has two contrary effects on the dynamic friction, both reflected by the AE signals, as does the change in pressure.

     
  2. 2.

    The results of a simulation of a seal with waviness on rings agree with AE RMS features observed by experiment. Meanwhile, a comparison of examples shows that the waviness variance reshapes the curve in terms of the count, relative magnitude, and time differences of the multiple maximums in each period, indicating the dependence of the dynamic friction on waviness. Information concerning waviness on the faces of a running seal can thus be indicated by AE signals.

     

This study demonstrated a new perspective of analyzing AE signals, i.e., examining AE signals on a timescale of the rotation period to monitor how the tribological interaction (which although only involving friction severity in this article, may include more with further analysis of the AE waves) changes with shaft rotation. Additionally, this approach can be imitated in the monitoring of other rotary machines.

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 51735006 and U1737209) and the National Science and Technology Support Plan Project (Grant No. 2015BAA08B02).

Supplementary material

11249_2018_1037_MOESM1_ESM.rar (802 kb)
Supplementary material 1 (RAR 802 KB)

References

  1. 1.
    Wang, Y., Yang, H., Wang, J., et al.: Theoretical analysis and field applications of gas-film lubricated mechanical face seals with herringbone spiral grooves. Tribol. Trans. 52, 800–806 (2009)CrossRefGoogle Scholar
  2. 2.
    Lebeck, A.O.: Principles and Design of Mechanical Face Seals. Wiley, New York (1991)Google Scholar
  3. 3.
    Nau, B.S.: Rotary mechanical seals in process duties: an assessment of the state of the art. Proc. Inst. Mech. Eng. A. 199, 17–31 (1985)CrossRefGoogle Scholar
  4. 4.
    Heilala, A.J., Kangasniemi, A.: Adjustment and control of a mechanical seal against dry running and severe wear. In: Proceedings of the 11th International Conference on Fluid Seal, pp. 548–575 (1987)Google Scholar
  5. 5.
    Etsion, I., Palmor, Z.J., Harari, N.: Feasibility study of a controlled mechanical seal. Lubr. Eng. 47, 621–625 (1991)Google Scholar
  6. 6.
    Salant, R.F., Navon, S.: Electronically controlled mechanical seal for aerospace applications-part I: design, analysis, and steady state tests. Tribol. Trans. 37, 189–195 (1994)CrossRefGoogle Scholar
  7. 7.
    Zou, M., Green, I.: Clearance control of a mechanical face seal. Tribol. Trans. 42, 535–540 (1999)CrossRefGoogle Scholar
  8. 8.
    Fan, Y., Gu, F., Ball, A.: A review of the condition monitoring of mechanical seals. In: Proceedings of the ASME 7th Biennial Conference on Engineering Systems Design and Analysis, pp. 179–184: (2004)Google Scholar
  9. 9.
    Tournerie, B., Reungent, D., Frene, J.: Temperature measurements by infrared thermography in the Interface of a Radial Face Seal. J. Tribol. 113, 571–576 (1991)CrossRefGoogle Scholar
  10. 10.
    Metcalfe, R.: Dynamic whirl in well-aligned, liquid-lubricated end-face seals with hydrostatic tilt instability. ASLE Trans. 25, 1–6 (1982)CrossRefGoogle Scholar
  11. 11.
    Anderson, W., Jarzynski, J., Salant, R.F.: Condition monitoring of mechanical seals: detection of film collapse using reflected ultrasonic waves. Proc. Inst. Mech. Eng. C 214, 1187–1194 (2000)CrossRefGoogle Scholar
  12. 12.
    Orcutt, F.K.: An investigation of the operation and failure of mechanical face seals. J. Lubr. Tech. 91, 713–725 (1969)CrossRefGoogle Scholar
  13. 13.
    Miettinen, J., Siekkinen, V.: Acoustic emission in monitoring sliding contact behavior. Wear 181–183, 897–900 (1995)CrossRefGoogle Scholar
  14. 14.
    Holenstein, A.P.: Diagnosis of mechanical seals in large pumps. Seal. Technol. 1996, 9–12 (1996)CrossRefGoogle Scholar
  15. 15.
    Mba, D., Roberts, T., Taheri, E., Roddis, A.: Application of acoustic emission technology for detecting the onset and duration of contact in liquid lubricated mechanical seals. Insight 48, 486–487 (2006)CrossRefGoogle Scholar
  16. 16.
    Towsyfyan, H., Wei, N., Gu, F., Ball, A.D.: Identification of lubrication regimes in mechanical seals using acoustic emission for condition monitoring. In: Proceedings of the 54th Annual Conference on British Institute of Non-Destructive Testing, vol. 42, pp. 219–225: (2015)Google Scholar
  17. 17.
    Li, X., Fu, P., Chen, K., Lin, Z., Zhang, E.: The contact state monitoring for seal end faces based on acoustic emission detection. Shock Vib. 2016, 1–8 (2016)Google Scholar
  18. 18.
    Huang, W., Lin, Y., Gao, Z., Fan, W., Suo, S., Wang, Y.: An acoustic emission study on the starting and stopping processes of a dry gas seal for pumps. Tribol. Lett. 49, 379–384 (2013)CrossRefGoogle Scholar
  19. 19.
    Huang, W., Lin, Y., Liu, Y., Liu, X., Gao, Z., Wang, Y.: Face rub-impact monitoring of a dry gas seal using acoustic emission. Tribol. Lett. 52, 253–259 (2013)CrossRefGoogle Scholar
  20. 20.
    Green, I., Barnsby, R.M.: A parametric analysis of the transient forced response of noncontacting coned-face gas seals. J. Tribol. 124, 9–16 (2002)CrossRefGoogle Scholar
  21. 21.
    Hu, S., Huang, W., Liu, X., Wang, Y.: Influence analysis of secondary O-ring seals in dynamic behavior of spiral groove gas face seals. Chin. J. Mech. Eng. 29, 507–514 (2016)CrossRefGoogle Scholar
  22. 22.
    Etsion, I., Front, I.: A model for static sealing performance of end face seals. Tribol. Trans. 37, 111–119 (1994)CrossRefGoogle Scholar
  23. 23.
    Persson, B.N.J.: Contact mechanics for randomly rough surfaces. Surf. Sci. Rep. 61, 201–227 (2006)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of TribologyTsinghua UniversityBeijing 100084China
  2. 2.State Key Laboratory of Mechanical System and VibrationShanghai Jiao Tong UniversityShanghai 200240China

Personalised recommendations