| Mechanical Engineering |
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| Dynamic modeling and vibration response analysis of high speed motorized spindle |
| HUANG Wei di, GAN Chun biao, YANG Shi xi |
| College of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China |
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Abstract A dynamic model of the high speed motorized spindle was built based on the finite element beam theory in order to reduce the vibration of the motorized spindle at high speed. Both the ball bearing contact force by Hertz contact theory and the unbalanced magnet pull using the Maxwell stress tensor method were considered. The bifurcation diagrams of vibration response of the motorized spindle were obtained numerically at different rotation speed, bearing clearance and initial eccentricity distance. Then the dynamic bifurcation phenomena caused by the ball bearing contact force and the unbalanced magnet pull were analyzed. Results show that, period-doubling bifurcation, quasi-period bifurcation and inverse bifurcation will occur in response to the ball bearing contact force and the unbalanced magnet pull, leading to the complicated transition from periodic to quasiperiodic or chaotic vibration of the motorized spindle. Severe vibration can be effectively avoided by adjusting the initial eccentricity distance, the bearing clearance or the rotation speed of the motorized spindle．
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Published: 01 November 2016
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一类高速电主轴的动力学建模及振动响应分析
为了减小电主轴在高转速下的振动,基于有限元梁理论建立电主轴动力学模型,同时分别利用Hertz接触理论与Maxwell应力张量法给出球轴承非光滑接触力与不平衡磁拉力.通过计算不同转速、轴承游隙和初始偏心距下电主轴振动响应的分岔图,分析电主轴受球轴承接触力与不平衡磁拉力作用而产生的动力学现象.结果表明,在轴承接触力与不平衡磁拉力作用下,电主轴振动响应将出现倍周期分岔、拟周期分岔和倒分岔等现象,导致电主轴产生复杂的周期、拟周期与混沌振动之间的转迁.通过合理调整转速、轴承游隙和转子初始偏心距等参数,可以避免电主轴的剧烈振动.
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| ［1］ ABELE E, ALTINTAS Y, BRECHER C. Machine tool spindle units ［J］. CIRP AnnalsManufacturing Technology, 2010, 59(2): 781-802．
［2］ CAO Y, ALTINTAS Y. A general method for the modeling of spindlebearing systems ［J］. Journal of Mechanical Design, 2004, 126(6): 1089-1104.
［3］ GAGNOL V, LE T P, RAY P. Model identification of spindletool unit in highspeed machining［J］. Mechanical Systems and Signal Processing, 2011, 25(7): 2388-2398．
［4］ CAO H R, HOLKUP T, ALTINTAS Y. A comparative study on the dynamics of high speed spindles with respect to different preload mechanisms ［J］. International Journal of Advanced Manufacturing Technoloy, 2011, 57(9): 871-883．
［5］ JONES A. A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions ［J］. Journal of Fluids Engineering, 1960, 82(2): 309-320．
［6］ HARRIS T A. Rolling Bearing Analysis\[M\]. New York:Willey, 1991．
［7］ HARSHA S P. Nonlinear dynamic responses of a balanced rotor supported by rolling element bearings due to radial internal clearance effect ［J］. Mechanism and Machine Theory, 2006, 41(6): 688-706．
［8］ 孟杰,陈小安,合烨. 高速电主轴电动机—主轴系统的机电耦合动力学建模［J］. 机械工程学报,2007, 43(12): 160-165．
MENG Jie, CHEN Xiaoan, HE Ye. Electromechanical coupled dynamical modeling of high speed motorized spindles motorspindle subsystem ［J］. Chinese Journal of Mechanical Engineering, 2007, 43(12): 160-165．
［9］ 杨丹,甘春标,杨世锡,等. 一类初弯曲转子的裂纹碰摩故障响应分析［J］. 浙江大学学报:工学版,2014, 48(8): 1496-1501．
YANG Dan, GAN Chunbiao, YANG Shixi, et al. Analysis on response of a rotor with initial bend deformation under coupling fault of crack and rubimpact ［J］. Journal of Zhejiang University :Engineering Science, 2014, 48(8): 1496-1501．
［10］ 李松生,陈晓阳,张刚,等. 超高速时电主轴轴承的动态支承刚度分析［J］.机械工程学报,2006, 42(11): 60-65．
LI Songsheng, CHEN Xiaoyang, ZHANG Gang, et al. Analyses of dynamic supporting stiffness about spindle bearings at extra highspeed in electric spindles ［J］.Chinese Journal of Mechanical Engineering, 2006, 42(11): 60-65．
［11］ NELSON H D. A finite rotating shaft element using timoshenko beam theory ［J］. ASME Journal of Mechanical Design, 1980, 102(4): 793-803．
［12］ HARSHA S P, KANKAR P K. Stability analysis of a rotor bearing system due to surface waviness and number of balls ［J］.International Journal of Mechanical Sciences. 2004, 46(7): 1057-1081．
［13］ CHENG M, MENG G, WU B Y. Nonlinear dynamics of a rotorball bearing system with Alford force ［J］. Journal of Vibration and Control, 2011, 18(1): 17-27．
［14］ BAI C Q, ZHANG H Y, XU Q Y. Effects of axial preload of ball bearing on the nonlinear dynamic characteristics of a rotorbearing system［J］. Nonlinear Dynamics, 2008, 53(3): 173-190．
［15］ GUO D, CHU F, CHEN D. The unbalanced magnetic pull and its effects on vibration in a threephase generator with eccentric rotor ［J］. Journal of Sound and Vibration, 2002, 254(2): 297312．
［16］ 岳二团,甘春标,杨世锡. 气隙偏心下永磁电机转子系统的振动特性分析［J］.振动与冲击,2014, 33(8): 29-34．
YUE Ertuan, GAN Chunbiao, YANG Shixi. Vibration characteristics analysis of a rotor for a permanent magnet motor with AirGap Eccentricity［J］.Journal of Vibration and Shock, 2014, 33(8): 29-34．
［17］ GAN C B, WANG Y H, YANG S X, et al. Nonparametric modeling and vibration analysis of uncertain Jeffcott rotor with disc offset ［J］. International Journal of Mechanical Sciences, 2014, 78(1):126-134. |
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