微细立铣刀动力学分析的 Chebyshev 谱方法

黄意新 1, 尹青峰 2,赵 阳 1

振动与冲击 ›› 2016, Vol. 35 ›› Issue (18) : 28-33.

PDF(1475 KB)
PDF(1475 KB)
振动与冲击 ›› 2016, Vol. 35 ›› Issue (18) : 28-33.
论文

微细立铣刀动力学分析的 Chebyshev 谱方法

  • 黄意新 1, 尹青峰 2,赵  阳 1
作者信息 +

Dynamic analysis of micro-endmill by Chebyshev spectral method

  • HUANG Yi-xin 1   Yin Qing-feng 2  Zhao Yang 2
Author information +
文章历史 +

摘要

采用 Chebyshev 谱方法对微细立铣刀动力学特性进行研究。考虑刀具剪切变形与转动惯量效应,建立刀具各段均匀或变截面 Timoshenko 梁动力学模型,利用 Chebyshev 方法对动力学方程进行离散,通过动态子结构法综合得到刀具整体动力学模型,编制了刀具动力学特性分析软件。仿真得到了微细立铣刀固有频率及模态振型并与分段阶梯梁方法及有限元方法进行了比较,验证了方法的可行性。研究了刀柄长度、刀颈半锥角及刀头长径比等刀具结构参数对刀具固有频率的影响,算例的数值计算结果表明:当 Chebyshev 多项式阶数大于16时,前四阶计算结果偏差收敛至 0.04% 内,计算精度较高。该方法可用于微细立铣刀参数优化设计。

Abstract

A Chebyshev spectral method for studying dynamic characteristics of micro-endmill was presented. Considering the shear deformation and rotary inertia of micro-endmill, uniform and tapered Timoshenko beam models were used. The discrete forms of dynamic models were gained by Chebyshev spectral method and synthesized by dynamic substructure technique to get the system equation of motion. A software package for solving the natural frequencies and modal shapes was developed. To validate the method, the impacts of structural parameters to dynamic characteristics were researched. The simulation results were compared to with the ones of stepped beams method and finite element method. It shows that result converges to the range of 0.04% when number of polynomials larger than 16. This method has a good precision and can be applied to optimize structural parameters of micro-endmill.

关键词

微细立铣刀 / Chebyshev 谱方法 / 动力学特性 / 动态子结构法

Key words

micro-endmill / Chebyshev spectral method / dynamic characteristics / dynamic substructure technique

引用本文

导出引用
黄意新 1, 尹青峰 2,赵 阳 1. 微细立铣刀动力学分析的 Chebyshev 谱方法[J]. 振动与冲击, 2016, 35(18): 28-33
HUANG Yi-xin 1 Yin Qing-feng 2 Zhao Yang 2. Dynamic analysis of micro-endmill by Chebyshev spectral method[J]. Journal of Vibration and Shock, 2016, 35(18): 28-33

参考文献

[1]. 肖才伟. 振动微铣削动力学建模及其分析[D]. 哈尔滨工业大学, 2008.
XIAO CaiWei. Dynamic modeling and analysis of vibration assisted micro milling[D]. 哈尔滨: 哈尔滨工业大学, 2008.
[2]. 李迎. 微铣削加工技术研究现状及发展趋势[J]. 电子机械工程, 2008, 24(6):26-32.
LI Ying. Recent adavances in micro milling and its future development trend[J]. Electro-Mechanical Engineering, 2008, 24(6): 26-32.
[3]. 陈明君, 陈妮, 何宁, 等. 微铣削加工机理研究新进展[J]. 机械工程学报, 2014, 50(5):161-172.
CHEN Mingjun, CHEN Ni, HE Ning, et al. The research Progress of Micromilling in Machining Mechanism[J]. Journal of mechanical engineering, 2014, 50(5): 161-172.
[4]. Miao J C, Chen G L, Lai X M, et al. Review of dynamic issues in micro-end-milling[J]. International Journal of Advanced Manufacturing Technology, 2007, 31(9):897-904.
[5]. Shunmugam M S. Machining Challenges: Macro to Micro Cutting[J]. Journal of the Institution of Engineers(India): Series C, 2015, 2(22) :1-19.
[6]. Shi Y, Mahr F, Wagner U V, et al. Chatter frequencies of micromilling processes: Influencing factors and online detection via piezoactuators[J]. International Journal of Machine Tools & Manufacture, 2012, 56(2):10–16.
[7]. 万敏, 张卫红. 铣削过程中误差预测与补偿技术研究进展[J]. 航空学报, 2008, 29(5):1340-1349.
Wan Min, Zhang Weihong. Overviews of Technique Research Progress of Form Error Prediction and Error Compensation in Milling Process[J]. Acta Aeronautica et Astronautica Sinica, 2008, 29(5): 1340-1349.
[8]. 张俊, 黄保华, 赵万华,等. 面向动态特性快速求解的铣刀等效建模方法[J]. 振动工程学报, 2013, 26(3):351-356.
ZHANG Jun, HUANG Bao-hua, ZHAO Wan-hua, et al. Equivalent modeling of endmills for rapid dynamics prediction[J]. Journal of Vibration Engineering, 2013, 26(3): 351-356.
[9]. 方泽平, 王西彬, 刘志兵, 等. 基于Timoshenko梁理论的微细铣刀动力学建模[J]. 振动与冲击, 2014, 33(23): 111-115.
FANG Ze-ping, WANG Xi-bin, LIU Zhi-bing, et al. Dynamic modeling of a micro-endmill based on Timoshenko beam theory[J]. Journal of vibration and shock, 2014, 33(23): 111-115.
[10]. 方泽平. 微细立铣刀的设计基础理论与刃磨技术研究[D]. 北京理工大学, 2014.
XU Hang-shou, JI Zhen-lin, KANG Zhong-xu. Three-dimensional time-domain computational approach for predicting transmission loss of reactive silencers [J]. Journal of vibration and shock, 2010, 29(4): 107-110.
[11]. Rahnama R, Sajjadi M, Park S S. Chatter suppression in micro end milling with process damping[J]. Journal of Materials Processing Technology, 2009, 209(17):5766–5776.
[12]. Yang Y, Wan M, Ma Y C, et al. An improved method for tool point dynamics analysis using a bi-distributed joint interface model[J]. International Journal of Mechanical Sciences, 2015, 105(2016): 239-252.
[13]. Yang Y, Zhang W H, Ma Y C, et al. Generalized method for the analysis of bending, torsional and axial receptances of tool–holder–spindle assembly[J]. International Journal of Machine Tools and Manufacture, 2015, 99(2015): 48-67.
[14]. Mustapha K B, Zhong Z W. A new modeling approach for the dynamics of a micro end mill in high-speed micro-cutting[J]. Journal of Vibration & Control, 2013, 19(6):901-923.
[15]. 李雪慧. 截断Chebyshev多项式的谱方法求解数值微分问题[D]. 兰州大学, 2010.
Li XueHui. Spectral Method for Solving Nmerical Differentiation Problem[D]. Lanzhou University, 2010.
[16]. Yagci B, Filiz S, Romero L L, et al. A spectral-Tchebychev technique for solving linear and nonlinear beam equations[J]. Journal of Sound & Vibration, 2009, 321(1):375–404.
[17]. Lloyd N. Trefethen. Spectral Methods in MATLAB[M]. Philadelphia, Pennsylvania: Society for Industrial & Applied Mathematics , 2001.
[18]. 王健平. 谱方法的基本问题与有限谱法[J]. 空气动力学学报, 2001, 19(2):161-171.
WANG Jian-ping. Fundamental problems in spectral methods and finite spectral method[J]. Acta aerodynamica sinca, 2001, 19(2): 161-171.
[19]. John P. Boyd. Chebyshev and Fourier Spectral Methods, Second Edition[M]. Mineola, New York, 2000.

PDF(1475 KB)

Accesses

Citation

Detail

段落导航
相关文章

/