Journal of Shanghai Jiao Tong University

Journal of Shanghai Jiaotong University >

2022 , Vol. 56 >Issue 2: 191 - 200

DOI: https://doi.org/10.16183/j.cnki.jsjtu.2020.413

Stability of Orthogonal Cutting System Considering Nonlinear Stiffness

Expand
  • School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China

Received date: 2020-12-07

  Online published: 2022-03-03

Fold

Abstract

In order to accurately predict the stability of orthogonal cutting of cylindrical workpiece, a nonlinear orthogonal cutting system model is established, which includes the nonlinear stiffness caused by the surface wave of work as well as the deformation of the tool and work. The multi-scale method is used to solve the system. The effect of machining parameters and system parameters on the stability of the primary resonance and 1/2 subresonance is analyzed to gain the overall stability cloud map compared with the lobe diagrams of linear approximation system. The results show that the instability of primary resonance, 1/2, 1/3, and 1/4 subresonance occur in the orthogonal cutting system with the quadratic nonlinearity and cubic nonlinearities stiffness, which makes the system have period-doubling, quasi-periodic, and chaotic operation behavior. The comparison indicates that the dynamics model of nonlinear orthogonal cutting can accurately predict the stability of the system.

Key words： chatter; nonlinearity; orthogonal cutting; multi-scale method

Cite this article

SHI Huirong, WANG Haixing, LI Zonggang . Stability of Orthogonal Cutting System Considering Nonlinear Stiffness[J]. Journal of Shanghai Jiaotong University, 2022 , 56(2) : 191 -200 . DOI: 10.16183/j.cnki.jsjtu.2020.413

References

[1] MOLNÁR T G, INSPERGER T, JOHN HOGAN S, et al. Estimation of the bistable zone for machining operations for the case of a distributed cutting-force model[J]. Journal of Computational and Nonlinear Dynamics, 2016, 11(5):051008.
[2] MOLNÁR T G, INSPERGER T, STÉPÁN G. State-dependent distributed-delay model of orthogonal cutting[J]. Nonlinear Dynamics, 2016, 84(3):1147-1156.
[3] WANG A, JIN W Y, WANG G P, et al. Analysis on dynamics of a cutting tool with the thermal distortion in turning process[J]. Nonlinear Dynamics, 2016, 86(2):1183-1191.
[4] NANKALI A, LEE Y S, KALMÁR-NAGY T. Targeted energy transfers for suppressing regenerative machine tool vibrations[J]. Journal of Computational and Nonlinear Dynamics, 2017, 12(1):011010.
[5] CHANDA A, DWIVEDY S K. Nonlinear dynamic analysis of flexible workpiece and tool in turning ope-ration with delay and internal resonance[J]. Journal of Sound and Vibration, 2018, 434:358-378.
[6] TYLER C T, TROUTMAN J R, SCHMITZ T L. A coupled dynamics, multiple degree of freedom process damping model, Part 1: Turning[J]. Precision Engineering, 2016, 46:65-72.
[7] YAN Y, XU J, WIERCIGROCH M. Estimation and improvement of cutting safety[J]. Nonlinear Dyna-mics, 2019, 98(4):2975-2988.
[8] 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.
[8] 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.
[9] 杨毅青, 张斌, 刘强. 铣削建模中多种切削力模型的分析比较[J]. 振动工程学报, 2015, 28(1):82-90.
[9] YANG Yiqing, ZHANG Bin, LIU Qiang. Analysis and comparison of various cutting force models in the milling process simulation[J]. Journal of Vibration Engineering, 2015, 28(1):82-90.
[10] AHMADI K. Analytical investigation of machining chatter by considering the nonlinearity of process damping[J]. Journal of Sound and Vibration, 2017, 393:252-264.
[11] GRAHAM E, MEHRPOUYA M, PARK S S. Robust prediction of chatter stability in milling based on the analytical chatter stability[J]. Journal of Manufacturing Processes, 2013, 15(4):508-517.
[12] ZAKOVOROTNY V L, LAPSHIN V P, BABENKO T S. Assessing the regenerative effect impact on the dynamics of deformation movements of the tool during turning[J]. Procedia Engineering, 2017, 206:68-73.
[13] ZAKOVOROTNY V L, LUKYANOV A D, GUBANOVA A A, et al. Bifurcation of stationary manifolds formed in the neighborhood of the equilibrium in a dynamic system of cutting[J]. Journal of Sound and Vibration, 2016, 368:174-190.
[14] WARMI$\acute{N}$SKI J, LITAK G, CARTMELL M P, et al. Approximate analytical solutions for primary chatter in the non-linear metal cutting model[J]. Journal of Sound and Vibration, 2003, 259(4):917-933.
[15] YU K N, WANG C C, YAU H T, et al. Numerical computation and nonlinear dynamic analysis of ultrasonic cutting system[J]. Computers & Electrical Engineering, 2016, 51:270-283.
[16] DONG X F, QIU Z Z. Stability analysis in milling process based on updated numerical integration method[J]. Mechanical Systems and Signal Processing, 2020, 137:106435.
Options
Outlines

/

〈 〉