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A comprehensive model for 3D revolute joints with clearances in mechanical systems

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Abstract

A mechanical system with clearance joints is well known as a nonlinear dynamic system that may exhibit chaotic responses under certain conditions. In the previous literature, the model for clearance joint is extensively investigated since it plays a significant role in prediction of kinematic and dynamic behavior of the system. A large volume of the literature only focuses on radial clearances, whereas, due to manufacturing and assembling errors, axial clearances also exist in joints, which have been scarcely considered. In this study, a comprehensive model for 3D revolute joints with radial and axial clearances is proposed. An experiment of the 3D revolute joint with clearances is firstly conducted to reveal the characteristics of the relative motion between the journal and bearing. According to the kinematic features, a model for 3D revolute joints with radial and axial clearances is proposed. This model presents a comprehensive description of the contact modes in which a group of contact force models are employed to reflect different contact–impact phenomena. Thus, the axial movement of the journal relative to the bearing and misalignment between the two elements could be characterized by this model. Moreover, a numerical simulation of the experiment is performed to validate the model presented in this study. Finally, a four-bar mechanism is taken as an example to illustrate its application and investigate the nonlinear dynamics of this system.

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Abbreviations

\(O-{\varvec{i}}_1 {\varvec{i}}_2 {\varvec{i}}_{3}\) :

Global coordinate system

\(O-{\varvec{e}}_1 {\varvec{e}}_2 {\varvec{e}}_3\) :

Local coordinate system

\(R\) :

Radius (m)

\(\delta \) :

Penetration depth (m)

\(F\) :

Magnitude of a force (N)

\(M\) :

Magnitude of a moment \((\hbox {N}\,\hbox {m})\)

\(K\) :

Generalized stiffness \((\hbox {N}/\hbox {m}^{1.5})\)

\(D\) :

Damping coefficient \((\hbox {N}\,\hbox {s/m})\)

\(\upsilon \) :

Poisson’s ratio of each sphere \((i=1,2)\)

\(E\) :

Young’s modulus of each sphere \((i=1,2)\), GPa

\(\dot{\delta }\) :

Penetration velocity \((\hbox {m/s})\)

\(\dot{\delta }^{-}\) :

Initial impact velocity \((\hbox {m/s})\)

\(s\) :

Half-length of contact area width (m)

\(l\) :

Length of the contact area (m)

\(p\) :

Pressure \((\hbox {m}\,\hbox {Pa})\)

\(V\) :

Relative tangential velocity (m/s)

\(V_\mathrm{s}\) :

Stick-slip switch velocity (m/s)

\(V_\mathrm{d}\) :

Static-sliding friction switch velocity (m/s)

\(\mu _\mathrm{s}\) :

Static friction coefficient

\(\mu _\mathrm{d}\) :

Sliding friction coefficient

\(\omega \) :

Angular velocity (rad/s)

\(c\) :

Radial clearance (mm)

\(N/T\) :

Normal/ tangential direction

front/back:

Front/back base of the bearing

r/a:

Radial/axial direction

\(k\) :

Relative to the bearing

\(l\) :

Relative to the journal

\(k\hbox {o}\) :

Relative to the outer surface of the bearing

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Acknowledgments

This work was supported by National Science Foundation of China under Contract No. 11272171, Education Ministry Doctoral Fund of China under Contract No. 20120002110070 and the Beijing Natural Science Foundation under Contract No. 3132030.

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Authors and Affiliations

  1. State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, People’s Republic of China

    Shaoze Yan, Wuweikai Xiang & Lin Zhang

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  1. Shaoze Yan
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Correspondence to Shaoze Yan.

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Yan, S., Xiang, W. & Zhang, L. A comprehensive model for 3D revolute joints with clearances in mechanical systems. Nonlinear Dyn 80, 309–328 (2015). https://doi.org/10.1007/s11071-014-1870-7

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