Abstract:The nonlinear dynamic behavior of milling process has been accompanied by the entire cutting process, in order to accurately determine and predict chatter stability of machining process, this article studied at both ends of the fixed thin part nonlinear criterion of milling chatter stability with experimental method. The vibration signal of thin part as the study object in the experiment, based on the phase plane method, Poincare method and spectral analyze the vibration signal of different processing parameters, plotted and discussed changes in the relationship between the maximum Lyapunov exponent and the spindle speed and milling depth. Finally, the largest Lyapunov exponent as the criterion, determine the chatter stability domain of milling by contour method, and based on the full discrete method obtains the milling chatter stability domain comparative analysis, the experiments obtained the nonlinear stability criterion of aviation aluminum alloy 7075-T6 thin part.
[1] Gao S. H., Long X. H., Meng G. Noniinear response and nonsmooth bifurcations of an unbalanced machine-tool spindle-bearing system. Nonlinear Dynamics. 2008,54:365-377.
[2] Gradised J., Govekar E., Grabed I.. A chaotic cutting process and determining optimal cutting parameter values using neural networks. Institution Journal Machine Tools and Manufacture. 1996, 36(10):1161-1172.
[3] Gradised J., Govekar E., Grabed I.. Time series analysis in metal cutting: Chatter versus chatter-free cutting. Mechannical Systems and Signal Processing. 1998,12(6)839-854.
[4] David E., Gilsinn D. E.. Estimating critical Hopf bifurcation parameters for a second-order delay differential equation with application to machine tool chatter. Nonlinear Dynamics.2002,30(2):103-154.
[5] Szalai R., Stepan G., Hogan, S.J.. Global dynamics of low immersion high-speed milling. Chaos. 2004, 14(4), 1069–1077.
[6] Stefanski, A., Kapitaniak, T.. Using chaos synchronization to estimate the largest Lyapunov exponent of non-smooth systems. Discrete Dynamics in Nature Sociences. 2000, 4(3):207–215.
[7] Stefanski A., Kapitaniak T., Dabrowski A. The largest Lyapunov exponent of dynamical systems with time delay[C]. Proceedings of IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics, Rome, Italy, 2003.6
[8] Li Z. Q., Liu Q.. Solution and analysis of chatter tability for end milling in the time-domain. Chinese Journal of Aeronautics. 2008, 21(2) :169-178.
[9] 孔繁森,刘鹏,王晓明. 切削振动加速度时间历程演化过程的动力学特征[J]. 振动与冲击. 2011, 30(7):10-15.
KONG Fansen, LIU Peng, WANG Xiaoming. Dynamic characteristics of evolution process of cutting vibration acceleration time history[J]. Journal of Vibration and Shock. 2013, 30(7):10-15.
[10] 刘志兵,王西彬. 微细铣削振动信号非线性特征的试验研究[J]. 兵工学报. 2010, 31(1) :84-87.
LIU Zhibing, WANG Xibin. An expermental study on nonlinear character istic of vibration signal in Micro-end-milling Process[J]. Acta Armamentar. 2010, 31(1):84-87.
[11] 吴石, 刘献礼, 肖飞. 铣削颤振过程中的振动非线性特征试验. 振动测试与诊断. 2012, 32(6): 935-940.
WU Shi, LIU Xianli, XIAO Fei. Experimental study of the nonlinear characteristics of vibration in milling chatter. Journal of Vibrat ion, Measurement and Diagnosis. 2012, 32(6): 935-940.
[12] 王平,陈蜀梅,王知人. 大挠度简支矩形薄板受热力磁耦合作用分岔与混沌. 振动与冲击. 2013, 32(7):129-134.
WANG ping, CHEN Shumei, WANG Zhiren. Bifurcation and chaos of a thin rectangular plate simply upported with large deflection in a coupled environment of heating,force and magnetic field. Journal of Vibration and Shock. 2013, 32(7):129-134.
[13] YEH Yenliang,CHEN Chaokuang,LAI Hsinyi. Chaotic and bifurcation dynamics for a simply supported rectangular plate of themo-mechanical coupling in large deflection. Chaos, Solitons Fractals. 2002, 13(7) :1493-1506.
[14] YEH Yenliang. The effect of thermo-mechanical coupling for a simply supported orthotropic rectangular plate on nonlinear dynamics. Thin-Walled Structures. 2005, 43(8):1277-1295.
[15] 杨智春, 张蕊丽. 基于最大李雅普诺夫指数的壁板热颤振特性分析. 西北工业大学学报, 2009, 27(6):770-776.
YANG Zhichun, ZHANG Ruili. Analysis of panel therm al flutter using max imum Lyapuno v ex ponent. Journal of Northwestern Polytechnical University , 2009, 27( 6) : 770-776.
[16] 闻邦椿,李以农,徐培民等. 工程非线性振动[M].北京:科学出版社,2007.
[17] DING Y., ZHU L. M., ZHANG X. J., et al. A full-discretization method for prediction of milling stability. International Journal of Machine Tools and Manufacture. 2010, 50(5):502–509.