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首页> 外文期刊>Mathematical Problems in Engineering >REGULAR AND CHAOTIC MOTION OF A BUSH-SHAFT SYSTEM WITH TRIBOLOGICAL PROCESSES
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REGULAR AND CHAOTIC MOTION OF A BUSH-SHAFT SYSTEM WITH TRIBOLOGICAL PROCESSES

机译：具有摩擦过程的轴-轴系统的规律和混沌运动

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摘要

The methods of both analysis and modeling of contact bush-shaft systems exhibiting heat generation and wear due to friction are presented. From the mathematical point of view, the considered problem is reduced to the analysis of ordinary differential equations governing the change of velocities of the contacting bodies, and to the integral Volterra-type equation governing contact pressure behavior. In the case where tribolog-ical processes are neglected, thresholds of chaos are detected using bifurcation diagrams and Lyapunov exponents identification tools. In addition, analytical Mel'nikov's method is applied to predict chaos. It is shown, among the others, that tribological processes play a stabilizing role. The following theoretical background has been used in the analysis: perturbation methods, Mel'nikov's techniques, Laplace transformations, the theory of integral equations, and various variants of numerical analysis.
机译：介绍了接触衬套轴系统由于摩擦而产生热量和磨损的分析和建模方法。从数学的角度来看，所考虑的问题简化为控制接触体速度变化的常微分方程的分析，以及控制接触压力行为的积分Volterra型方程。在忽略摩擦过程的情况下，可使用分叉图和Lyapunov指数识别工具来检测混沌阈值。另外，将分析梅尔尼科夫方法用于预测混沌。除其他外，表明摩擦过程起稳定作用。分析使用了以下理论背景：摄动方法，梅尔尼科夫技术，拉普拉斯变换，积分方程理论和数值分析的各种变体。

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