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Crossing and Veering Phenomena in Crank Mechanism Dynamics

机译：曲柄机构动态中的交叉和转向现象

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Modal analysis is widely used both on single components and mechanical complex assemblies and it is recognized to be a fundamental step on the functional design process. From experimental point of view, a change in a system parameter due to the need of describing a different assembly configuration, can require iterative measurements, and can be quite time consuming. On the other hand, by evaluating the dynamic behaviour of the single component instead of the whole system, it is not straightforward to forecast the general dynamics of the entire assembly: inertia and stiffness couplings give rise to curious dynamic phenomena, namely crossing and veering of eigenvalue loci. Many theoretical studies on eigenvalue curve crossing and curve veering, i.e. the coincidence of two eigenfrequencies or the abrupt divergence of natural frequencies trends, have been carried out in recent years, but only few references on detailed test sessions and practical applications are available. The present paper wants to give a better overview on the change of the dynamic properties of a system by comparing global mode shapes to single component mode shapes. The examined structure is a crank mechanism, made of a crankshaft joined to four connecting rods and four pistons. The chosen control parameter that is responsible of a change in the dynamic properties of the system is the crank angle. Numerical models have been used to compute eigenvalues and eigenvectors of the analysed structure, considering both FEM models and multibody approach. Finally, an original graphical interpretation of the transition from component to system dynamics is presented by means of the MAC index.
机译：模态分析在单个组件和机械复杂组件上广泛使用，并且被认为是功能设计过程的基本步骤。从实验的角度来看，由于需要描述不同的组装配置而导致的系统参数的变化可能需要迭代测量，并且可以非常耗时。另一方面，通过评估单个组件的动态行为而不是整个系统，预测整个组件的一般动态并不简单：惯性和刚度联轴器引起好奇的动态现象，即交叉和转向特征值基因座。许多关于特征值曲线交叉和曲线转向的理论研究，即近年来进行了两个特征频率的巧合或自然频率趋势的突然分歧，但只有很少有关于详细测试会和实际应用的参考。本文希望通过将全局模式形状与单个组件模式形状进行比较，更好地概述系统的动态属性的变化。检查的结构是曲柄机构，由连接到四个连杆和四个活塞的曲轴制成。所选择的控制参数负责系统的动态属性的变化是曲柄角。考虑到FEM模型和多体方法，已经用于计算分析结构的特征值和特征向量的数值模型。最后，通过MAC索引提出了从组件到系统动态的转换的原始图形解释。

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