Chaotic behaviour exhibited during contact loss in a clearance joint of a four-bar mechanism

L. D. Seneviratne, S. W.E. Earles

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Abstract

Contact loss at clearance joints of mechanisms gives rise to undesirable impacts when contact is remade. To eliminate contact loss at the design stage an analytical model of the joint is required to predict accurately the clearance joint reaction force. A massless link model, so termed because the extra degree of freedom introduced by the clearance magnitude is modelled as a massless link, is examined. The model has been successfully employed to predict contact loss, although in the past its design usefulness was limited because of the computational demands made by the solution. The present investigation uses a VAX minicomputer and NAG numerical integration software, and demonstrates that with modern digital computers it becomes feasible to solve these equations in a modest design environment. The massless link equations for a four-bar mechanism with a clearance joint are solved in the time and frequency domains, and the clearance joint reaction force and the clearance link angular velocity responses are studied. It is shown that the clearance link response consists of two identifiable regions; a regular region where the response is practically identical to the zero-clearance response and a chaotic region where the response in non-periodic and sensitive to initial conditions. The regular/chaotic boundary is clearly defined and is shown to indicate impending contact loss at the bearing joint. In general, contact will be maintained in regular regions, with contact loss following soon after the joint force chaotic boundary. Thus avoidance of chaotic regions at the design stage should ensure that contact is maintained. Damping of the clearance link appears to have no significant effect on the chaotic characteristics of the massless link model. For the case studied, the massless link model predictions are in good agreement with the zero-clearance criteria proposed earlier.

Original languageBritish English
Pages (from-to)307-321
Number of pages15
JournalMechanism and Machine Theory
Volume27
Issue number3
DOIs
StatePublished - May 1992

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