基于三角级数展开的铣削合力频谱推导及刀具偏心估算

基于一元切削力机理模型将立铣刀的切削合力分解为公称力和偏心力，采用周期信号的三角级数展开公称力和偏心力，得到其谐波幅值和相位的表达式。基于以上表达式,推导出偶数齿刀具偏心力的偶数次谐波幅值为0，三齿刀具偏心力的刀齿频率谐波幅值也为0。提出了一种用切削合力的主轴和刀齿频率谐波估算刀具偏心距和偏心角的方法，实验结果表明,采用该方法计算出的偏心值接近实测值。从理论上证明了偶数齿刀具的偏心力不存在偶数次谐波成分，所提出的估算方法只需一套估算式和一次切削实验，且数值计算比较容易。研究结果可用于偶数齿刀具的加工过程偏心和磨损辨识及其偏心量估算。

Spectral Derivation of Resultant Milling Force and Eccentric Estimation of Tool Based on Trigonometric Series Expansion

The  cutting  force  was  discomposed  into  nominal  and  eccentric  component  forces  based  on unary cutting force  model,the trigonometric series of periodic signals  was  applied to expand these two component forces，and then the  amplitude and phase expressions of their harmonics were obtained. Based on these expressions,it  is  deduced  that  the even-harmonics amplitudes of the eccentric force for even-tooth milling  cutter are  zero,the tooth-frequency amplitude of the eccentric force for  3 teeth  milling  cutters is zero too, and a new estimation method of eccentric distance and angle for milling  cutters was presented, which uses  the harmonics of resultant  cutting force in spindle and tooth frequencies, the estimated eccentric values are close to that measured in experiments.It testifies  in theory that there  are no even harmonics in the eccentric component force of even-tooth  milling cutters, the presented method needs only one set of equation and one  cutting test, and its numerical calculation is rather easy for even-tooth milling  cutters. The research  fruits can be used to  identify eccentricity and wear, and estimate  eccentricity in process for even-tooth milling  cutters.