The motion accuracy of linear guideway is adversely affected by ball passage vibration (BPV) when rolling balls within carriage move in a loop. Reduced vibration amplitude can be realized by a carriage with crowning design by now. However, few dynamic models are availability for the BPV analysis when linear guideway is subjected to actual external load in five directions. In this paper, a nonlinear dynamic model is proposed to investigate the periodic micro fluctuation of linear guideway with crowning subjected to load in five directions. The idea of coordinate transformation is adopted for the easier derivations of time-dependent and piecewise restoring force function. The different contact states of each ball are described in detail due to load distribution. The numerical simulation is employed to deal with equation of motion and discuss the effects of ball grouping, external load, preload and carriage speed. Experiment is also conducted for the verification of proposed model. The analytical model developed here is promising to clarify the mechanism of BPV from a dynamic perspective and serve the walking parallelism accuracy monitoring of linear guideway.

直线导轨的运动精度受到滚珠通道振动 (BPV) 的不利影响，当滚珠在滑架内循环移动时。现在可以通过带有冠状设计的小车来实现降低的振幅。然而，当线性导轨在五个方向上承受实际外部载荷时，很少有动力学模型可用于 BPV 分析。在本文中，提出了一个非线性动力学模型来研究凸度线性导轨在五个方向上承受载荷的周期性微波动。采用坐标变换的思想是为了更容易推导时间相关的分段恢复力函数。由于载荷分布，详细描述了每个球的不同接触状态。采用数值模拟来处理运动方程，并讨论了滚珠分组、外部载荷、预紧力和托架速度的影响。还进行了实验以验证所提出的模型。这里开发的分析模型有望从动态角度阐明 BPV 的机理，并为直线导轨的行走平行度精度监测服务。