ZENG Hao-ran, LIU Nian-cong, YANG Jia-rui, CHEN Jian-long, GENG Wei-tao. The Axial Nonlinear Vibration Analysis of Ball-screw about Machine Tool Feeding System[J]. International Journal of Plant Engineering and Management, 2016, 21(3): 181-192

The Axial Nonlinear Vibration Analysis of Ball-screw about Machine Tool Feeding System
ZENG Hao-ran, LIU Nian-cong, YANG Jia-rui, CHEN Jian-long, GENG Wei-tao
College of Nuclear Technology and Automation Engineering, Chengdu University of Technology, Chengdu 610059, P. R. China
The forced state of the ball-screw of machine tool feeding system is analyzed. The ball-screw is simplified as Timoshenko beam and the differential equation of motion for the ball-screw is built. To obtain the axial vibration equation, the differential equation of motion is simplified using the assumed mode method. Axial vibration equation is in form of Duffing equation and has the characteristics of nonlinearity. The numerical simulation of Duffing equation is proceeded by MATLAB/Simulink. The effect of screw length, exciting force and damping coefficient are researched, and the axial vibration phase track diagram and Poincare section are obtained. The stability and period of the axial vibration are analyzed. The limit cycle of phase track diagram is enclosed. Axial vibration has two type-center singularity distributions on both sides of the origin. The singularity attracts vibration to reach a stable state, and Poincare section shows that axial vibration appears chaotic motion and quasi periodic motion or periodic motion. Singularity position changes with the vibration system parameters, while the distribution doesn't change. The period of the vibration is enhanced with increasing frequency and damping coefficient. Test of the feeding system ball-screw axial vibration exists chaos movement. This paper provides a certain theoretical basis for the dynamic characteristic analysis of machine feeding system ball-screw and optimization of structural parameters.
Key words:    ball screw    Timoshenko beam    axial vibration    phase diagram    Poincare section   
Received: 2016-08-17     Revised:
DOI: 10.13434/j.cnki.1007-4546.2016.0305
Corresponding author:     Email:
Author description:
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ZENG Hao-ran
LIU Nian-cong
YANG Jia-rui
CHEN Jian-long
GENG Wei-tao

[1] Huang Z Y. Development and application of precision high-speed ball screw[J]. Manufacturing Technology & Machine Tool, 2002(5):8-11(in Chinese)
[2] Pritschow G. A comparison of linear and conventional electromechanical drives[J]. Annals of the CIRP, 1998,47(2):541-548
[3] Liao B Y,et al. Modern mechanical dynamics and its engineering application[M]. Beijing:China Machine Press, 2003(in Chinese)
[4] Leonard-Cristian Pop. Particularities of modeling ball screw based NC axes as finite degrees of freedom dynamic systems[J]. Buletinul Institutului Polotehnic Din Iasi, 2005, 5:1-6
[5] Leonard-Cristian Pop, Mircea Cretu, Liviu Morar. Methods of evaluation of the mechanical characteristics influences on the NC balls screw drives dynamic behavior[J]. Buletinul Institutului Polotehnic Din Iasi, 2005, 5:13-18
[6] Leonard-Cristian Pop, Liviu Morar. Axial pre-stress of NC machine tools ball screw drives[J]. Buletinul Institutului Polotehnic Din Iasi, 2005, 5:7-12
[7] Yang Z X. Calculation driving rigidity of ballscrew for feed[J]. Manufacturing Technology & Machine Tool, 1999, 7:12-14(in Chinese)
[8] Wu N X, et al. Influence of rigidity of feed system with ball screw in nc lathe on positioning precision[J]. Engineering Sciences,2004,6(9):46-49(in Chinese)
[9] Esmailzaden E, Ohadt A R. Vibration and stability analysis of non-uniform Timoshenko beams under axial and distributed tangential loads[J]. Journal of Sound and Vibration,2000,236(3):443-456
[10] Arboleda-monsalve I G, Zapata-medina D G, Aristizabal-ochoa J D. Stability and natural frequencies of weakened Timoshenko bean-column with generalized end conditions under constant axial load[J]. Journal of Sound and Vibration,2007,307:89-112
[11] Wang L H. Nonlinear dynamic characteristics of NC table[J]. China Mechanical Engineering,2009,20(13):1513-1519(in Chinese)
[12] Wang L H, et al. Chaotic characteristic analysis on dynamic properties of nc table[J]. China Mechanical Engineering,2009,20(14):1656-1659(in Chinese)