滚珠型弧面凸轮分度机构动力学模型建立及模态分析

Dynamic model and modal analysis of globoidal cam indexing mechanism with steel ball

应用拉格朗日方程对一种新型的滚珠型弧面凸轮分度机构进行了动力学建模。忽略滚珠的质量,将滚珠与凸轮之间的接触刚度以及滚珠与分度盘之间的接触刚度近似看作为两个接触刚度的串联,得到等效接触刚度。在建模过程中,利用回转变换张量法对机构中广义坐标几何位移关系进行了分析,建立了考虑扭转弹性模量的滚珠型弧面凸轮分度机构的动力学方程。由动力学方程得到了机构固有频率及其相对应的振型。结果表明,固有频率在分度时期随凸轮转角变化,在停歇时期为恒定值,并且不同阶的固有频率变化趋势也不相同。

The dynamic model of a new type of globoidal cam indexing mechanism with steel ball was established by use of Lagrange equation. In the modeling process, the mass of roller was neglected, and the contact stiffnesses between roller and cam and between roller and indexing plate were regarded as two stiffnesses in serial connection According to the rotary transform tensor theory, the geometric displacement relation between generalized coordinates was analyzed. Dynamic equations of the mechanism considering torsion modulus were built, and the natural frequency and vibration mode of the transmission system were solved. The results show that the natural frequency varies with the variation of cam rotating angle at indexing period and is invariable at dull period, and the varying trends of natural frequencies of different orders are dissimilar.