张莹

[摘    要]用于计时仪器及某些精密仪表机构中的传动齿轮的齿形，又称仪表圆弧齿形、修正摆线齿形。在计时仪器中，采用钟表齿形已有很长历史。现代钟表齿形是由摆线齿形演变而来的。内摆线是一滚圆沿另一圆的圆周内面作纯滚动时，滚圆圆周上一点的运动轨迹。滚圆叫做摆线的生成圆，而另一圆叫做摆线的母圆。在摆线啮合中，母圆就是齿轮的分度圆。为了便于制造和改善传动性能，对理论摆线齿形做了一定的修正。最初是用近似理论摆线的圆弧，代替钟表中的轮片和龆轮齿顶部分的外摆线齿形。

[关键词]模数;摆线;齿廓;滚动

[中图分类号]TH132.41 [文献标志码]A [文章编号]2095–6487（2021）03–00–03

[Abstract]It is used for the tooth profile of transmission gears in timing instruments and some precision instruments. It is also called instrument arc tooth profile and modified cycloid tooth profile. It has a long history to use the tooth shape of clocks and watches in timing instruments. The tooth shape of modern clocks and watches is evolved from cycloid tooth shape. Hypocycloid is the motion track of a point on the circle of a rolling circle when a rolling circle rolls along the inner surface of the circle of another circle. A rolling circle is called the generating circle of a cycloid， and another circle is called the parent circle of a cycloid. In cycloid meshing， the mother circle is the indexing circle of the gear. In order to manufacture and improve the transmission performance， the theoretical cycloid profile has been modified. At first， the epicycloid tooth profile of the top part of the wheel and pinion in clocks and watches was replaced by the arc of the approximate theoretical cycloid.

[Keywords]modulus; cycloid; tooth profile; rolling

手表的齒轮传动系，特别是主传动系，广泛采用一种所谓的圆弧齿形。这种齿形是接线齿形演变而来的，因纯摆线齿形加工很难，故用圆弧来代替摆线，也叫修正摆线齿形，能使齿轴的最少齿数为6，从而在轮片齿数不太多的条件下取得大的传动比，这对减小机芯直径、对高频手表极为有利，传动效率高。由于齿形由相啮合的一对齿轮和模数所决定，因此齿数和模数不同，所使用的滚刀和铣刀也不同。修正摆线的齿轮特点是：齿轮的齿顶部分采用近似摆线的圆弧，齿腰部分则是与齿顶圆弧和齿根圆弧圆滑连接的径向线。

滚刀齿形设计的基本原理。根据啮合理论，两个啮合齿形的工作部分，在相对运动时，必须互相迂回。假定把齿轮当作一个基圆滚动，而且不在另一齿轮的节圆上滑动，那么齿轮齿面的各个相继位置便会在与另一齿轮相连的固定单面上形成一组平缓曲线。……