Dynamic reliability analysis of linear guides in positioning precision

Abstract 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.

[1]  Guo Yao,et al.  Stochastic forced vibration analysis of a tapered beam with performance deterioration , 2017 .

[2]  Wang Wei,et al.  Effects of wear on dynamic characteristics and stability of linear guides , 2017 .

[3]  Yazhou Jia,et al.  Reliability of a VMC and its improvement , 2001, Reliab. Eng. Syst. Saf..

[4]  Hiroyuki Ohta,et al.  Sound of Linear Guideway Type Recirculating Linear Ball Bearings , 1999 .

[5]  Jae Seok Choi,et al.  Dynamic analysis of a linear motion guide having rolling elements for precision positioning devices , 2008 .

[6]  Shigeo Shimizu,et al.  A New Life Theory for Rolling Bearings—By Linkage between Rolling Contact Fatigue and Structural Fatigue , 2012 .

[7]  Achintya Haldar,et al.  Reliability Assessment Using Stochastic Finite Element Analysis , 2000 .

[8]  T. A. Harris,et al.  Rolling Bearing Analysis , 1967 .

[9]  Jui-Pin Hung,et al.  Effect of preload of linear guides on dynamic characteristics of a vertical column-spindle system , 2010 .

[10]  Hiroyuki Ohta,et al.  A Design of Crowning to Reduce Ball Passage Vibrations of a Linear Guideway Type Recirculating Linear Ball Bearing , 2005 .

[11]  Guo Yao,et al.  Reliability and sensitivity analysis of an axially moving beam , 2016 .

[12]  Sen Hu,et al.  A method to determine kinematic accuracy reliability of gear mechanisms with truncated random variables , 2015 .

[13]  Yaping Zhao,et al.  Reliability design and sensitivity analysis of cylindrical worm pairs , 2014 .

[14]  H. Cramér.  Mathematical Methods of Statistics (PMS-9), Volume 9 , 1946 .

[15]  S. S. Rao,et al.  Probabilistic approach to manipulator kinematics and dynamics , 2001, Reliab. Eng. Syst. Saf..

[16]  Wei Sun,et al.  Statics modeling and analysis of linear rolling guideway considering rolling balls contact , 2015 .

[17]  Hu-Tian Feng,et al.  Model for wear prediction of roller linear guides , 2013 .

[18]  Baolin Wang,et al.  Investigation of the contact stiffness variation of linear rolling guides due to the effects of friction and wear during operation , 2015 .

[19]  Farid Al-Bender,et al.  Characterization of frictional hysteresis in ball-bearing guideways , 2005 .

[20]  Di Zhou,et al.  Dynamic reliability analysis for planetary gear system in shearer mechanisms , 2016 .

[21]  Rong-Shean Lee,et al.  A New Tool-Path Generation Method Using a Cylindrical End Mill for 5-Axis Machining of a Spatial Cam with a Conical Meshing Element , 2001 .

[22]  Jie Gu,et al.  CNC machine tool work offset error compensation method , 2015 .

[23]  Wei Sun,et al.  Dynamic and stability analysis of the linear guide with time-varying, piecewise-nonlinear stiffness by multi-term incremental harmonic balance method , 2015 .

[24]  Wang Wei,et al.  Indexing accuracy reliability sensitivity analysis of power tool tur ret , 2015 .

[25]  Shigeo Shimizu,et al.  Fatigue Limit Concept and Life Prediction Model for Rolling Contact Machine Elements , 2002 .

[26]  Eiji Hayashi,et al.  VIBRATION OF LINEAR GUIDEWAY TYPE RECIRCULATING LINEAR BALL BEARINGS , 2000 .

[27]  Hiroyuki Ohta,et al.  Using Ceramic Balls to Reduce Noise in a Linear Guideway Type Recirculating Linear Ball Bearing , 2003 .

[28]  Bangchun Wen,et al.  Reliability sensitivity of multi-degree-of-freedom uncertain nonlinear systems with independent failure modes , 2007 .

[29]  Wei Zhang,et al.  An experimental method for measuring friction behaviors of linear rolling guides , 2014 .

[30]  Hong-Zhong Huang,et al.  An approach to system reliability analysis with fuzzy random variables , 2012 .

[31]  Liang Wang,et al.  Tests for skewness and kurtosis in the one-way error component model , 2013, J. Multivar. Anal..

[32]  Ching-Yuan Lin,et al.  Modeling the machining stability of a vertical milling machine under the influence of the preloaded linear guide , 2011 .

[33]  J. J. Kalker,et al.  Rolling contact phenomena , 2000 .

[34]  Keisuke Tanaka,et al.  Vertical Stiffnesses of Preloaded Linear Guideway Type Ball Bearings Incorporating the Flexibility of the Carriage and Rail , 2010 .