一类高速电主轴的动力学建模及振动响应分析

Dynamic modeling and vibration response analysis of high speed motorized spindle

为了减小电主轴在高转速下的振动,基于有限元梁理论建立电主轴动力学模型,同时分别利用Hertz接触理论与Maxwell应力张量法给出球轴承非光滑接触力与不平衡磁拉力.通过计算不同转速、轴承游隙和初始偏心距下电主轴振动响应的分岔图,分析电主轴受球轴承接触力与不平衡磁拉力作用而产生的动力学现象.结果表明,在轴承接触力与不平衡磁拉力作用下,电主轴振动响应将出现倍周期分岔、拟周期分岔和倒分岔等现象,导致电主轴产生复杂的周期、拟周期与混沌振动之间的转迁.通过合理调整转速、轴承游隙和转子初始偏心距等参数,可以避免电主轴的剧烈振动.

A dynamic model of the high speed motorized spindle was built based on the finite element beam theory in order to reduce the vibration of the motorized spindle at high speed. Both the ball bearing contact force by Hertz contact theory and the unbalanced magnet pull using the Maxwell stress tensor method were considered. The bifurcation diagrams of vibration response of the motorized spindle were obtained numerically at different rotation speed, bearing clearance and initial eccentricity distance. Then the dynamic bifurcation phenomena caused by the ball bearing contact force and the unbalanced magnet pull were analyzed. Results show that, period-doubling bifurcation, quasi-period bifurcation and inverse bifurcation will occur in response to the ball bearing contact force and the unbalanced magnet pull, leading to the complicated transition from periodic to quasi-periodic or chaotic vibration of the motorized spindle. Severe vibration can be effectively avoided by adjusting the initial eccentricity distance, the bearing clearance or the rotation speed of the motorized spindle.