Time and frequency domain characteristics of a cutting system with time-delay effects
LIU Xianbo1，HE Enyuan2，LONG Xinhua1，MENG Guang1,3
1.State Key Lab of Mechanical Systems and Vibrations, Shanghai Jiao Tong University, Shanghai 200240, China;
2.Shanghai Top CNC Technology Co., Ltd., Shanghai 200125, China;
3.Shanghai Academy of Spaceflight Technology, Shanghai 201109, China
During the machining process, such as turning, milling and drilling, due to the regenerative cutting effect, the equation of motion of the tool-workpiece system suffers time delay effects, which causes changes in dynamic characteristics of the system.The responses of a linear delay differential system with single degree of freedom were studied when subjected to external excitation.Via deriving the transfer function of the system with time delay and delayed stiffness, the frequency response functions were obtained in the parameter space.The results show that the time delay changes the operating mode of the system, and multiple formants appear on the amplitude-frequency response diagram.The delayed stiffness mainly affects the peak value of the formant, while the time delay amount mainly affects the number of formants.Meanwhile, by analyzing the equations of the ridge clusters of formants, the distribution of formants in the parameter space was presented.In addition, the numerical solution yields a distribution of the number of formants.The results show that as the delayed stiffness and the amount of time delay increase, the number of formants increases from 1 to infinity with a continuous interger increment.Finally, modal hammering tests on a turning test platform verify the relevant conclusions of the time-frequency response characteristics in the paper.The research can serve as a basis in machine tool modal analysis and machine dynamic response analysis.
刘显波1， 何恩元2，龙新华1，孟光1,3. 时滞作用下切削系统的时频响应特性研究[J]. 振动与冲击, 2020, 39(6): 8-14.
LIU Xianbo1，HE Enyuan2，LONG Xinhua1，MENG Guang1,3. Time and frequency domain characteristics of a cutting system with time-delay effects. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(6): 8-14.
[1] Tlusty J, Spacek L. Self-excited vibration in machine tools [M]. Prague, 1954.
[2] Tobias S A, Fishwick W. The Chatter of lathe tools under orthogonal cutting conditions. Transactions of the ASME, 1958, 1(80): 1079-1088.
[3] 师汉民. 关于机床自激振动的一个非线性理论模型(第一部分) [J]. 应用力学学报, 1984, 1(1) : 1-14.
Shi H. Nonlinear chatter theory of machine tools (part 1: the stability of machine tool chatter amplitude) [J]. Journal of Applied Mechanics, 1984(1) : 1-14.
[4] 刘习军, 陈予恕. 机床速度型切削颤振的非线性研究[J]. 振动与冲击, 1999, 18(2): 5-10.
Liu X, Chen Y-S. Nonlinear analysis of speed type cutting chatter of machine toools[J]. Journal of Vibration and Shock, 1999, 18(2): 5-10.
[5] Altintas Y, Budak E. Analytical Prediction of Stability Lobes in Milling [J]. CIRP Annals-Manufacturing Technology, 1995, 44(1):357-362
[6] 杨昀, 张卫红, 党建卫, 郑小伟, 万敏. 航空薄壁件铣削加工动力学仿真技术[J]. 航空制造技术, 2018, 61(7): 42-47.
Yang Y, Zhang W, Dang J, Zheng X, Wan M. Dynamic modelling technology on milling process of aerospace thin-walled workpiece. Aeronautical Manufacturing Technology, 2018, 61(7): 42-47.
[7] Altintas Y. Manufacturing automation: metal cutting mechanics, machine tool vibrations, and CNC design[M]. 2012, Cambridge University Press, Cambridge.
[8] Stépán G, Kalmár-Nagy T. Nonlinear Regenerative Machine Tool Vibrations [C]. Proceedings of the 1997 ASME Design Engineering, 1997.
[9] Long X-H, Balachandran B. Stability analysis for milling process[J]. Nonlinear Dynamics, 2007, 49(3): 349-359.
[10] Liu X, Long X, et al. Multiple regenerative effects in cutting process and nonlinear oscillations [J]. International Journal of Dynamics and Control. 2014, 2(1): 86-101.
[11] Liu X, Long X, et al. Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects [J]. Nonlinear Dynamics, 2013, 72(4): 61-77.
[12] Kwiatkowski A W, Al-Samarai H M. Identification of milling machine receptances from random signals during cutting[J]. Annals of the CIRP. 1968. 16(1):110-115
[13] Zaghbani I., Songmene V. Estimation of machine-tool dynamic parameters during machining operation through operational modal analysis[J]. International Journal of Machine Tools and Manufacture, 2009, 49(12-13):947-196.
[14] Bonzanigo F, Tsudi J P. Identification of milling machine structures from the output signal only[C]. Proceedings of Eurisco-83.
[15] Opitz H, Weck M. Determination of the transfer function by means of spectral density measurements and its application to the dynamic investigation of machine tools under machining conditions[C]. Proceeding of the 10th International MTDR Conference. Univ. of Machester, UK, 1969
[16] Cai H, Mao X, Li B, et al. Estimation of FRFs of machine tools in output-only modal analysis[J]. The International Journal of Advanced Manufacturing Technology, 2015, 77(1-4):117-130.
[17] 蔡辉. 基于响应的机床切削自激励与动力学参数识别方法研究[D]. 武汉：华中科技大学，2015.
Cai H. Research on machine tool cutting excitation techniques and dynamic parameters estimation based on responses[D]. Wuhan: Huazhong Univ. of Science and Technology, 2015
[18] 胡海岩, 王在华. 非线性时滞动力系统的研究进展. 力学进展, 1999, 29(4): 501-512
Hu H, Wang Z. Review on nonlinear dynamic systems involving time delays. Advances in Mechanics, 1999, 29(4): 501-512
