铰链具有间隙的曲柄滑块机构运动稳定性研究  

Stability of Motion of Slider-Crank Mechanism with Clearances in Joints Considered

作　　者：张劲夫[1] 许庆余[1] 

机构地区：[1]西安交通大学工程力学系,陕西西安710049

出　　处：《西北工业大学学报》2001年第4期533-536,共4页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金 (5 9875 0 6 8)

摘　　要：以铰链具有间隙的曲柄滑块机构的运动微分方程为数学模型 ,联合应用里雅普诺夫首次方法和 Floquet理论 ,分析了这种机构的周期运动的稳定性 ,并通过一个算例讨论了阻尼对周期运动稳定性的影响。结果表明增大阻尼可以有效地改善机构周期运动的稳定性。This paper is a progress report of a project supported by NNSFC (National Natural Science Foundation of China) still in progress. In actual mechanisms, clearances in joints are unavoidable. In the open literature such clearances, to our best knowledge, are neglected; we suspected that such neglection may be due to the fact that consideration of such clearances cause the nonlinearity of the differential equation of motion to be greater. We used Lyapunov first approximation method to linearize nonlinear dynamic eq.(1) for slider-crank mechanism with clearances in joints and obtained first approximation eq.(12) for the mechanism; according to Lyapunov theory, the stability of periodical solution of eq.(1) was transformed into the stability of zero solution of eq.(12). Considering that eq.(12) is a linear differential equation with periodical coefficients, we analyzed the stability of zero solution of eq.(12) using the Floquet theory. In section 2, we give a numerical example. The results of analog computation show preliminarily that increasing damping tends to make periodical motion of the slider-crank mechanism more stable.

关 键 词：曲柄滑块机构 铰链 间隙 稳定性 周期运动 

分 类 号：TH133.5[机械工程—机械制造及自动化] TH113.25