Nonlinear dynamic analysis for machine tool table system mounted on linear guides

In this paper, a three-degree-of-freedom dynamic model of a machine tool table system considering nonlinear contact behaviors is established to obtain vibration characteristics. The relationship between contact deformation and force is derived via Hertz contact theory, and piecewise nonlinear interaction forces are obtained. Then, dynamic differential equations of the three-degree-of-freedom system are constructed. The numerical simulations are solved by Runge–Kutta integration method to investigate the dynamic behaviors of the dynamic system. When the system is under a small excitation force, it exhibits softening nonlinear behavior in the primary resonance region. With excitation amplitude increasing to a larger value, the system exhibits hardening nonlinear behavior. In order to better investigate the effects of excitation amplitude, excitation angle, installation distance and height of work piece on the vibration characteristics, frequency–amplitude curves, 3-D frequency spectrum, time history, frequency domain, phase diagram and Poincare section are employed. Jump discontinuity phenomenon, super-harmonic resonance and varied frequency components are dependent on the key parameters. Some conclusions are drawn to suppress the vibration of machining process and improve the quality of work piece.

[1]  Dongxu Li,et al.  Design and analysis of an intelligent vibration isolation platform for reaction/momentum wheel assemblies , 2012 .

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

[3]  Zhongtao Fu,et al.  Analytical modeling of chatter vibration in orthogonal cutting using a predictive force model , 2014 .

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

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

[6]  James Shih-Shyn Wu,et al.  The effect of contact interface on dynamic characteristics of composite structures , 2007, Math. Comput. Simul..

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

[8]  Shigeo Shimizu,et al.  Life Prediction for Linear Rolling Element Bearings: A New Approach to Reliable Life Assessment , 2002 .

[9]  Binglin Li,et al.  Analytical prediction of cutting forces in orthogonal cutting using unequal division shear-zone model , 2011 .

[10]  Hongyan Zhang,et al.  Effects of axial preload of ball bearing on the nonlinear dynamic characteristics of a rotor-bearing system , 2008 .

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

[12]  Wei Wang,et al.  Dynamic reliability analysis of linear guides in positioning precision , 2017 .

[13]  S. Harsha,et al.  Nonlinear Dynamic Response of a Rotor Bearing System Due to Surface Waviness , 2004 .

[14]  Y. M. Huang,et al.  Predicting dynamic behaviours of a whole machine tool structure based on computer-aided engineering , 2003 .

[15]  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 .

[16]  Jui-Pin Hung,et al.  Load effect on the vibration characteristics of a stage with rolling guides , 2009 .

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

[18]  K. Cavalca,et al.  Formulation of five degrees of freedom ball bearing model accounting for the nonlinear stiffness and damping of elastohydrodynamic point contacts , 2018, Mechanism and Machine Theory.

[19]  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 .

[20]  Fulei Chu,et al.  Nonlinear dynamic model for skidding behavior of angular contact ball bearings , 2015 .

[21]  Hiroyuki Ohta,et al.  Effects of Ball Groupings on Ball Passage Vibrations of a Linear Guideway Type Ball Bearing: Pitching and Yawing Ball Passage Vibrations , 2006 .

[22]  Hirokazu Shimoda,et al.  Study on the Life Distribution and Reliability of Roller-Based Linear Bearing , 2008 .

[23]  Hiroyuki Ohta,et al.  Sound of a ball spline operated at a certain linear velocity , 2009 .

[24]  Homer Rahnejat,et al.  Bearing induced vibration in precision high speed routing spindles , 2000 .

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

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

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

[28]  Shigeo Shimizu,et al.  Tribological Studies of Linear Motion Ball Guide Systems , 1998 .