Dynamic reliability analysis of linear guides in positioning precision

With the development of the high-speed machine tools, linear guide has been an important element in machine tools. It is important to analyze the kinematic errors to improve the positioning precision. The failure mode of linear guide in positioning precision is defined as the response errors of the carriage exceeding the walking parallelism tolerance. This paper presents a novel method to estimate the reliability and sensitivity of linear guides with random geometric parameters. The stochastic perturbation method is applied to calculate the statistical moments of the dynamic errors. Additionally, the reliability sensitivity are derived to investigate the parametric significance of random parameters. A SHS-45R linear guide is used as a numerical example to demonstrate the practical applications of the method. According to the dynamic reliability analysis of the linear guide under cycling load, the most dangerous state is determined. A numerical comparison with Monte Carlo simulation is performed to illustrate the accuracy and efficiency of the proposed method. Meanwhile, the effects of the mean and standard deviation of the random geometric parameters on the positioning precision are discussed.