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谱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>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。
A Chebyshev spectral method for studying the dynamic characteristics of micro-endmill was presented.Considering the shear deformation and rotary inertia of micro-endmill,the uniform and tapered Timoshenko beam models were used in the dynamic analysis of the segments of endmill. The discrete forms of the dynamic models were gained by Chebyshev spectral method and synthesized by dynamic substructure technique to get the equation of motion of the whole system. A software package for solving the natural frequencies and modal shapes was developed. To validate the method,the impacts of structural parameters on dynamic characteristics were analysed. The simulation results were compared with those obtained by the stepped beam method and finite element method. It is shown that the calculated result converges into a range of 0. 04% when the order of polynomials is larger than 16. The method is of good precision and can be applied to optimize structural parameters of micro-endmill.
出处
《振动与冲击》
EI
CSCD
北大核心
2016年第18期28-33,57,共7页
Journal of Vibration and Shock
基金
国家"973"计划(2013CB733004)
关键词
微细立铣刀
切比雪夫谱方法
动力学特性
动态子结构法
micro-endmill
Chebyshev spectral method
dynamic characteristics
dynamic substructure technique
