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法向直廓(ZN)蜗杆齿面的端截形是否延伸渐开线,对于产品的使用和制造无多大实用意义。但是近年来多次有关的学术会议上有人提出否定意见,《齿轮》1984,4期发表过一次会议的报导,基本上肯定了这一意见.为此,就有人采用定参数ρ(导圆柱半径)、产形直线与端面的夹角δ,论证了 ZN 蜗杆是属于延伸渐开线型蜗杆,同时纠正了[2]及按[2]类同推导的其它一些文献上的齿面形成原理图的错误和方程中的符号。[2]的第二版[3],作者对上述错处作了改正.也有人采用产品图纸直接给定的参数:齿形角α、车刀安装角γ和蜗杆分度圆柱半径r_1等,简明地证实了ZN蜗杆齿面的端截形是延伸或缩短渐开线,但是,方程的推演较简缩,不易引起人们的注意.本文先根据直接给定的参数,按加工方式用矢量及矩阵运算法证明ZN蜗杆是一种延伸渐开线型蜗杆;再变换参数写出蜗杆齿面方程的常见形式.通过理论分析计算,可以确认ZN蜗杆齿面的端截形是延伸渐开线.
Whether the normal straight profile (ZN) worm face of the end truncation extends involute, for the use and manufacture of products of little practical significance. However, in recent years, many people concerned have made negative opinions at the relevant academic conferences and the “Gear” published a conference report in 1984 and April 4, basically confirming this opinion. For this reason, some people use the parameter ρ ), And the angle δ between the straight line and the end face of the progeny. It is demonstrated that the ZN worm belongs to the extended involute worm and the principle diagram of the tooth profile in the other derivations [2] and [2] The error and the symbol in the equation. [2] The second edition of [3], the author made the correction of the above-mentioned mistakes.Some people use the product drawings directly given parameters: tooth angle α, lathe installation angle γ and worm indexing cylinder radius r_1, concise It is confirmed that the end truncation of the ZN worm tooth surface is to extend or shorten the involute, however, the deduction of the equation is relatively shortened, which is not easy to attract people’s attention.This paper first uses vector and matrix operations according to the given parameters, It is proved that the ZN worm is an extended involute worm and the transformation parameter is used to write the common form of the worm tooth surface equation. Through theoretical analysis and calculation, it can be confirmed that the end truncation of the ZN worm gear is an extended involute.