Nonlinear dynamic model for linear guideway with crowning subjected to external load in five directions

•Time-dependent dynamic model of linear guideway with crowning is established.•The idea of coordinate transformation is used to propose the five DOF model.•The possible contact states of each ball are considered due to load distribution.•The ball passage vibration in five directions is predicted. 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.