面向动态特性快速求解的铣刀等效建模方法

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The solution of dynamic characteristics for endmills is a part of obtaining dynamic characteristics of the whole ma- chinery by using substructure method. In order to rapidly predict the frequency response function （FRF）, endmills are divided into two parts, tool shank and fluted portion. Three equivalent models based on the principle of equal mass, equal area of cross-section and equal stiffness are proposed as a uniform beam for the fluted portion, and the receptances can be easily ob- tained by using Timoshenko beam element for both tool shank and fluted portion. Endmill/s FRF is shaped by coupling the FRF of individual part. The variation of relative errors from the three equivalent models is analyzed on these four factors： area moment of inertia of the cross-section, helix angle, percent of fluted portion lengh to tool length and ratio of tool length to di- ameter. The results also explain the fact that the equal stiffness method can achieve the best prediction accuracy for endmill A, B, C while the equal mass method is best for endmill D. Compared with three-dimensional harmonic analysis, the equivalent model method of endmills is computationally cheap while has an acceptable accuracy.刀具动态特性的求解是子结构方法获取机床整机动态特性的一个组成环节。为快速获取铣刀的频响特性，将其分成刀杆和刀齿两部分，分别基于等质量、等截面积以及等刚度的原则将刀齿等效为均匀直径梁，并与刀杆一起采用Timoshenko梁单元快速求解出其频率响应分量，最后利用子结构方法将二者进行耦合得到铣刀整体的频响特性。分析了刀齿截面惯性矩、刀齿螺旋角、刀齿长度占总长百分比和铣刀长度与直径比值等4个因素对3种等效方法所引起的相对误差变化规律，并根据此规律解释了铣刀A，B，C采用等刚度法计算精度最高，而铣刀D采用等质量法计算精度最高的原因。与三维谐响应计算相比，铣刀的等效建模对于其频响特性的获取能节约数百倍时间，并具有较好的精度。