一种球头铣刀“S”形刃口曲线的数学建模方法  

A Mathematical Modeling Method for the “S” Edge Curves of a Ball End Mill

作　　者：庞思勤[1] 乔小峰[1] 王西彬[1] 彭松[1] 

机构地区：[1]北京理工大学先进加工技术国防重点学科实验室,北京100081

出　　处：《湖南大学学报（自然科学版）》2014年第5期44-49,共6页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(50935001/E050901)

摘　　要：为了简化球头铣刀'S'形刃口的数学模型,推导两个空间平面与球面相交而成的复合型刃口曲线方程,提出并应用了'单球法'和'双球法'两种数学建模方法,并推导了球头铣刀球面部分平面刃口曲线偏转角和螺旋角的数学表达式.结果表明:偏转角和螺旋角两者相等,可以简化球面部分平面刃口曲线的数学模型,既降低了平面刀刃曲线的推导过程的复杂性,同时又为两个或多个空间平面与球头铣刀球面部分相交而成的复合型刃口曲线方程的建模提供了一种有效方法.To simplify the mathematical model for the ＂S＂ edge curves of a ball end mill and derive the composite edge curve equations of the intersection of two space planes and the sphere, this paper proposed and applied the ＂Single Sphere Method＂ and ＂Dual Spheres Method＂ to deduce the mathematical expressions of the deflection angle and helical angle of the flat edge curves on a ball end mill＇s spherical part. The results have shown that the mathematical relationship between the deflection angle and the helical angle is equal, thus simplifying the mathematical model of the plane edge curves on the spherical part with an equal relationship between the two angles. This reduces the complexity of the derivation process of the plane edge curves and provides an effective method for the composite edge curves＇ modeling of the intersections of two or more space planes and the spherical part of the ball end mill.

关 键 词：球头铣刀 “S”形刃口曲线 刀刃曲线 数学模型 

分 类 号：TG714[金属学及工艺—刀具与模具]