Friction-induced reverse chatter in rigid-body mechanisms with impacts
Friction-induced reverse chatter in rigid-body mechanisms with impacts
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DOI：
10.1093/imamat/hxq068
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发表时间：
2011-02
影响因子：
1.2
通讯作者：
A. Nordmark;H. Dankowicz;A. Champneys
中科院分区：
文献类型：
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作者：
A. Nordmark;H. Dankowicz;A. Champneys
本文的重点是在存在干摩擦的情况下，具有与刚性约束表面间歇或持续接触的孤立点的平面刚体机械系统的一致和明确的正演模拟模型的可能性。特别是，分析考虑了与持续接触和一个或几个可选的包括自由飞行运动阶段的向前轨迹共存相关的矛盾的模糊性。特别注意所谓的Painleve悖论，在这种悖论中，即使与接触无关的对正常加速度的贡献会导致接触停止，持续接触也是可能的。在这里，通过采用柔顺接触模型的无限刚度极限，解决了持续粘滞条件下的模糊性，有利于持续接触，而解决了持续滑移条件下的模糊性，消除了从开放初始条件集达到这种条件的可能性。对于一个明确的正演模拟模型的目标来说，一个更重要的挑战是，我们发现了一组开放的初始条件和参数值，这些条件和参数值与撞击的左侧积累点或反向抖振的可能性有关——通过一系列无限的撞击过渡到自由飞行，撞击时间从右边的一个极限点开始累积，撞击速度从极限点开始呈指数发散。即使在与接触无关的正常加速度支持持续接触的地方。在这种情况下，柔顺公式的无限刚度极限确定，在一组特定的开放条件下，刚性接触模型中反向颤振的可能性是基于持续滑移阶段端点的正向动力学中不可解决的模糊性。事实上，由于撞击的左侧积累点的存在与可能的向前轨迹的单参数族有关，因此模糊性具有无限多重性。通过一个单刚体力学模型的数值分析，对理论分析的结论进行了说明和验证。
The focus of this paper is on the possibility of formulating a consistent and unambiguous forward simulation model of planar rigid-body mechanical systems with isolated points of intermittent or sustained contact with rigid constraining surfaces in the presence of dry friction. In particular, the analysis considers paradoxical ambiguities associated with the coexistence of sustained contact and one or several alternative forward trajectories that include phases of free-flight motion. Special attention is paid to the so-called Painleve paradoxes where sustained contact is possible even if the contact-independent contribution to the normal acceleration would cause contact to cease. Here, through taking the infinite-stiffness limit of a compliant contact model, the ambiguity in the case of a condition of sustained stick is resolved in favour of sustained contact, whereas the ambiguity in the case of a condition of sustained slip is resolved by eliminating the possibility of reaching such a condition from an open set of initial conditions. A more significant challenge to the goal of an unambiguous forward simulation model is afforded by the discovery of open sets of initial conditions and parameter values associated with the possibility of a left accumulation point of impacts or reverse chatter—a transition to free flight through an infinite sequence of impacts with impact times accumulating from the right on a limit point and with impact velocities diverging exponentially away from the limit point, even where the contact-independent normal acceleration supports sustained contact. In this case, the infinite-stiffness limit of the compliant formulation establishes that, under a specific set of open conditions, the possibility of reverse chatter in the rigid-contact model is an irresolvable ambiguity in the forward dynamics based at the terminal point of a phase of sustained slip. Indeed, as the existence of a left accumulation point of impacts is associated with a one-parameter family of possible forward trajectories, the ambiguity is of infinite multiplicity. The conclusions of the theoretical analysis are illustrated and validated through numerical analysis of an example single-rigid-body mechanical model.