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Modeling and simulation for wear prediction in planar mechanical systems with multiple clearance joints

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Abstract

The main goal of this work is to develop a comprehensive methodology for predicting wear in planar mechanical systems with multiple clearance joints and investigating the interaction between the joint clearance, driving condition, and wear. In the process, an effective contact surface discretization method together with the Lagrangian method are used to establish the dynamic equation of the multibody system. Considering the change of the contact surface, an improved nonlinear contact force model suitable for the complicated contact conditions is utilized to evaluate the intrajoint forces, and the friction effects between the interconnecting bodies are discussed using the LuGre model. Next, the contact forces developed are integrated into the Archard model to compute the wear depth caused by the relative sliding and the geometry of the bearing is updated. Then, a crank slider mechanism with multiple clearance joints is employed to perform numerical simulations in order to demonstrate the efficiency of the dynamic procedures adopted throughout this work. The correctness of the proposed method is verified by comparing with other literature and simulation results. The results show that the wear is sensitive to different initial conditions, and the evolving contact boundary makes the dynamics of mechanical system and the joint wear prediction more complex. This study is helpful for predicting joint wear of mechanical systems with clearance and optimizing the mechanism’s design.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China (Grant No. 51175422) and Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2019JQ-753).

Funding

National Natural Science Foundation of China, 51175422, Min San Wang, Natural Science Basic Research Plan in Shaanxi Province of China, 2019JQ-753, Bo Li.

Author information

Authors and Affiliations

  1. Department of Engineering Product Development, Singapore University of Technology and Design, Singapore, Singapore

    Bo Li & U-Xuan Tan

  2. School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, 710072, China

    Min San Wang

  3. Institute of Steel Structures, School of Civil Engineering, National Technical University of Athens, 9 Heroon Polytechneiou, 15780, Zografou, GR, Greece

    Charis J. Gantes

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  1. Bo Li
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  4. U-Xuan Tan
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Correspondence to Bo Li.

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Appendices

Appendix

Notations

\({\text{e}}\)

Center distance vector

\(\delta\)

Relative penetration (m)

\(\dot{\delta }\)

Relative normal impact velocity in the contact (m/s)

\(\dot{\delta }^{\left( - \right)}\)

Initial impact velocity in the contact (m/s)

\(F_{N}\)

Normal contact force (N)

\(F_{T}\)

Tangential contact force (N)

\(c_{r}\)

Restitution coefficient

\(K_{g}\)

Composite nonlinear stiffness coefficient (N/m2)

\({\text{r}}\)

Global position vector

\({\text{A}}\)

Transformation matrix of coordinate

\({\text{n}}\)

Unit normal vector

\({\mathbf{t}} \)

Unit tangential vector

\(R_{b}\)

Bearing radius (m)

\(R_{j}\)

Journal radius (m)

E

Young’s modulus (N/m2)

\(\nu\)

Poisson’s ratio

\(\mu\)

Instantaneous friction coefficient

\(v_{n}\)

Relative normal velocity (m/s)

\(v_{t}\)

Relative tangential velocity (m/s)

\(\sigma_{0}\)

Bristle stiffness (N/m)

\(\sigma_{1}\)

Microscopic damping (Ns/m)

\(\sigma_{2}\)

Viscous friction coefficient

\(\mu_{k}\)

Kinetic friction coefficient

\(\mu_{s}\)

Static friction coefficient

\(v_{s}\)

Stribeck velocity (m/s)

\(Q_{C}\)

Global contact force (N)

\(T\)

Kinetic energy (J)

\(U\)

Potential energy (J)

\(Q_{j}\)

System generalized force (N)

\(V_{w}\)

Wear amount (m3)

\(s\)

Relative sliding distance (m)

\(k\)

Dimensionless wear coefficient

\(H\)

Hardness of the soft material (Pa)

\(h\)

Wear depth (m)

\(A_{a}\)

Contact stress (m2)

\(P\)

Contact stress (N/m2)

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Li, B., Wang, M.S., Gantes, C.J. et al. Modeling and simulation for wear prediction in planar mechanical systems with multiple clearance joints. Nonlinear Dyn 108, 887–910 (2022). https://doi.org/10.1007/s11071-022-07224-w

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