考虑刀杆结构非线性的铣削过程颤振稳定性与主共振

PDF(1877 KB)

振动与冲击 ›› 2019, Vol. 38 ›› Issue (23) : 62-69.

论文

任勇生，马伯乐，马静敏

作者信息 +

Flutter stability and main resonance of a milling system considering structural nonlinearity of cutter bar

REN Yongsheng, MA Bole, MA Jingmin

Author information +

文章历史 +

摘要

研究考虑铣刀杆结构非线性和阻尼的颤振稳定性以及主共振。将刀杆简化为平面弯曲悬臂梁结构模型。为了在模型中考虑结构阻尼的影响，假定刀杆由黏弹性材料构成。结合包含再生时滞效应和周期激励的切削力模型，根据Hamilton原理建立非线性运动方程。采用Galerkin法将非线性偏微分运动方程进行化简，导出主坐标表示的非线性常微分运动方程。通过时域数值积分得到铣削系统的稳定性lobes图。采用多尺度法对非线性常微分运动方程进行摄动求解，导出非线性切削系统在周期激励下的主共振响应的近似封闭解。研究刀杆的几何尺寸、结构阻尼、切削力系数、切削深度、齿数和切削力幅值等参数，对铣削过程非线性lobes图以及主共振响应曲线的影响。结果表明，增加刀杆的长度或者降低铣削过程的临界切削深度；切削力系数越大，临界切削深度越小；增加结构阻尼能够明显提高铣削过程的颤振稳定性；主共振响应峰值向右偏斜，由于切削系统存在三次刚度非线性，主共振响应曲线表现出典型的硬弹簧Duffing振子的特性，出现跳跃性和多值区域。

Abstract

Here, flutter stability and main resonance of a milling system considering structural nonlinearity of cutter bar and structural damping were investigated.The cutter bar was simplified as a planar bending cantilevered beam model made of a viscoelastic material with effects of structural damping.Using the cutting force model containing regenerated time delay effect and periodic excitation, the nonlinear dynamic equations for the milling system were built with Hamilton principle.Galerkin method was employed to simplify the partial differential dynamic equations, and derive the ordinary differential ones expressed with principal coordinates.The milling system’s stability lobes figures were obtained through time domain integration.The multi-scale method and the perturbation one were used to solve ordinary differential dynamic equations, and obtain the closed-form approximation solution of the milling system’s main resonance response under periodic excitation.Effects of cutter bar sizes, structural damping, cutting force coefficient, cutting depth and cutting force amplitude, etc.on the system’s lobes figures and main resonance response curves were studied to get several interesting conclusions.

导出引用

任勇生，马伯乐，马静敏. 考虑刀杆结构非线性的铣削过程颤振稳定性与主共振[J]. 振动与冲击, 2019, 38(23): 62-69

REN Yongsheng, MA Bole, MA Jingmin. Flutter stability and main resonance of a milling system considering structural nonlinearity of cutter bar[J]. Journal of Vibration and Shock, 2019, 38(23): 62-69

参考文献

[1]Taylor F. On the art of cutting metals[J]. Trans. ASME,1907, 28:31-350
[2]Tobias S A, Fishnick W. The chatter of lathe tools under orthogonal cutting conditions [J]. Transactions of the American Society of Mechanical Engineers,1958, 80:1079-1086.
[3]Merritt H E. Theory of self-excited machine tool chatter, condition to machine tool chatter research-1[J] Transactions of the American Society of Mechanical Engineers, Journal of Engineering for Industry,1965, 87:447-454.
[4]Kato S, Marui E. On the cause of regenerative chatter due to workpiece defection[J]. Transactions of the American Society of Mechanical Engineers, Journal of Engineering for Industry, 1974,96:179-186.
[5]Wu D W, Li C R. An analytical model of cutting dynamics[J]. Transactions of the American Society of Mechanical Engineers, Journal of Engineering for Industry,1985, 107:107-188.
[6]Altintas Y. Manufacturing automation, metal cutting mechanics, machine tool vibrations, and CNC design[M].Cambridge University Press, 2000,New York
[7]Budak E, Altintas Y. Analytical prediction of chatter stability in milling. Part I: General formulation[J]. Trans. ASME J. Dyn. Syst. Meas. Control,1998, 120: 22-30.
[8]Budak E, Altintas Y. Analytical prediction of chatter stability in milling. Part II: Application of the general formulation to common milling systems[J]. Trans. ASME J. Dyn. Syst. Meas. Control,1998, 120:31-36.
[9]迟玉伦，李郝林. 铣削颤振稳定域叶瓣图确定方法研究[J].振动与冲击,2014,33(4):90-93,148.
CHI Yu-lun，LI Hao-lin. Determination of chatter stability field lobe diagrams for a milling processing[J]. JOURNAL OF VIBRATION AND SHOCK, 2014,33(4):90-93,148.
[10]Hanna N H, Tobias S A. A theory of nonlinear regenerative chatter[J]. Transactions of American Society of Mechanical Engineers, Journal of Engineering For Industry,1974, 96:247-255.
[11]Vela-Martinez L, Jáuregui-Correa J C ,González-Brambila O M, etal. Instability conditions due to structural nonlinearities in regenerative chatter[J].Journal of Nonlinear Dynamics,2009,56:415-427.
[12]Deshpande N, Fofana M S. Nonlinear regenerative chatter in turning[J]. International Journal of Computer Integrated Manufacturing,2001,17:107-112.
[13]Stepan G, Insperger T, Szalai R. Delay, parametric excitation, and the nonlinear dynamics of cutting process[J]. International Journal of Bifurcation and Chaos,2005,15(9):2783-2798.
[14]毛汉颖，刘畅，刘永坚，毛汉领. 混沌特征量识别切削颤振的试验研究[J].振动与冲击，2015,34(16):99-103.
MAO Han-ying，LIU Chang，LIU Yong-jian，MAO Han-ling. Experimental study on the identification of cutting chatter based on its chaotic characteristics[J]. JOURNAL OF VIBRATION AND SHOCK,2015,34(16):99-103.
[15]吴石，边立健，刘献礼，宋盛罡，姜彦翠. 薄板件铣削颤振稳定性的非线性判据实验研究[J].2016,35(17):191-196.
WU Shi，BIAN lijian，LIU Xianli，SONG Shenggang，JIANG Yancui. Tests for milling chatter stability nonlinear criterion of thin parts[J]. JOURNAL OF VIBRATION AND SHOCK, 2016,35(17):191-196.
[16]Pratt J R.Vibration control for chatter suppression[D]. Ph.D. Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA,1997
[17]Moradi H, Movahhedy M R, Vossoughi G. Bifurcation analysis of milling process with tool wear and process damping: regenerative chatter with primary resonance[J]. Nonlinear Dyn, 2012,70(1):481-509
[18]Moradi H, Vossoughi G, Movahhedy MR,etal. Forced vibration analysis of the milling process with structural nonlinearity,internal resonance, tool wear and process damping effects[J].Int J Nonlinear Mech ,2013,54:22-34
[19]Moradi H, Movahhedy M R, Vossoughi G. Dynamics of regenerative chatter and internal resonance in milling process with structural and cutting force nonlinearities[J]. J Sound Vib,2012, 331:3844-3865
[20]Jalili M M, Hesabi J, Abootorabi M M. Simulation of forced vibration in milling process considering gyroscopic moment and rotary inertia[J]. Int J Adv Manuf Technol, 2017,89:2821-2836.
[21]Jung J, Ngo C, Son D, etal. Nonlinear modeling and dynamic simulation using bifurcation and stability analyses of regenerative chatter of ball-end milling process[J]. Mathematical Problems in Engineering Volume 2016, 16 pages.
[22]Altintas Y, Budak E. Analytical prediction of stability lobes in milling[J]. CIRP Annals Manufacturing Technology, 1995, 44(1): 357-362.
[23] 庄润雨. 镗杆动态稳定性与动力学模型的研究[D].石家庄：石家庄铁道大学，2016.
Zhuang runyu. The study of dynamic stability and model of boring bar[D]. Shi JiaZhuang: Shi JiaZhuang Tiedao University,2016.