Nonlinear dynamics and analysis of a four-bar linkage with clearance

Abstract

In this paper, nonlinear dynamic behavior of a four-bar linkage considering clearance is studied. The dynamic model of the linkage with a clearance between coupler and rocker is developed firstly. Then the dynamic equations of this mechanism are solved by a numerical method. According to the calculated response, compliance, force and trajectory of pin in joint bearing are obtained. Effects of clearance magnitude and the relationship between a mechanism with clearance and without clearance are studied. By using Poincare Map, it is proved that strange attractors or chaos exist in the dynamic response. In addition, phenomena of chaos, periodic response and subharmonic response also can be found in the special condition. Bifurcation diagram is used to suggest that bifurcation and fractal phenomena exist in the dynamic response of this mechanism.

Keywords

four-bar linkage / chaos / bifurcation / strange attractors / dynamics

References

[1] Dubowsky S, Freudenstein F. Dynamic of analysis of mechanical system with clearances. Part 1 Formation of dynamic model, Part 2 Dynamic response. ASME Engng Ind, 1971, 93B: 303-309

[2] Dubowsky S, Gardner T N. Dynamic interactions of link elasticity and clearances connections in planar mechanical systems. Journal of Manufacturing Science and Engineering, 1975, 97(2): 652-661

[3] Ravn P. A continuous analysis method for planar multibody systems with joint clearance. Multibody System Dynamics, 1998, 2(1): 1-24

[4] Schwab A L, Meijaard J P, Meijers P. A comparison of revolute joint clearance models in the dynamic analysis of rigid and elastic mechanical systems. Mechanism and Machine Theory, 2002, 37(9): 895-913

[5] Farahanchi F, Shaw S W. Chaotic and periodic dynamics of a slider-crank mechanism with slider clearance. Journal of Sound and Vibration, 1994, 117(3): 307-324

[6] Rhee J, Akay A. Dynamic response of a revolute joint with clearance. Mechanism and Machine Theory, 1996, 31(1): 121-134

[7] Seneviratne L D, Earles S W E. Chaotic behaviour exhibited during contact loss in a clearance joint of a four-bar mechanism. Mechanism and Machine Theory, 1992, 27(3): 307-321

[8] Lin R M, Ewins D J. Chaotic vibration of mechanical system with backlash. Mechanical Systems and Signal Processing, 1993, 7(3): 257-272

[9] Chang Z, Wang Y, Zhang C. Chaotic behavior in four-bar linkage with a clearance. Mechanical Science and Technology, 1998, 17(3): 87-91 (in Chinese)

[10] Feng B. Numerical method for initial problems of general or stiffness ordinary differential equations. Numerical Calculation and Computer Application, 1982, 3 (in Chinese)

[11] Guckenheimer J. Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Field. Springer-Verlag, 1983

[12] Chen Y. Bifurcation and Chaos Theory of Nonlinear Vibration System. Beijing: High Education Press, 1993 (in Chinese)

Acknowledgments

The authors are grateful for the support of the National Natural Science Foundation of China (Grant No. 50605060) and the Science and Technology Foundation for Excellent Middle-age and Young Scientists of the Shandong Province (02BS002).

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg