恒铲背量环面蜗轮滚刀顶后角面设计方法

Design method of top relief surface of the hourglass worm wheel hob with the constant relief-grinding value

环面蜗轮滚刀各个刀齿的齿顶由顶刃带面和顶后角面组成,在实际应用中顶后角面多采用人工手持砂轮加工,此方法得到的顶后角面的结构形状不明确,并难以衡量获得的顶后角的大小。为了更精确地构建顶后角面,针对直槽环面蜗轮滚刀,文中提出由半径不同的环面与相应位置的平面相交获得不同位置的交线,由所有交线构建顶后角面的设计方法。建立了顶后角面的数学方程,求解出完整的顶后角面,并求解得到顶刃带线在顶后角面的法矢量,以该法矢量与顶刃带线在齿顶环面上法矢量的夹角作为顶后角的值,分析了恒铲背量时顶后角的变化规律。算例计算结果表明:当顶铲背量为恒定值3.5 mm时,获得的顶后角在11.27°~11.62°之间;同一位置的顶后角大小与铲背量近似呈线性关系。分析结果可为环面蜗轮滚刀顶后角面铲磨量的选择提供参考。

The tooth top of the hourglass worm wheel hob is composed of the top land surface and the top relief surface. In terms of practical application,the top relief surface is manually processed by a grinding wheel. The structure of the top relief surface obtained by means of this method is not clear,and it’s difficult to measure the size of the top relief angle. In this article,in order to construct the top relief surface more accurately,the design of the top relief surface for the straight groove hourglass worm gear hob is developed. The intersection lines are identified by the intersection of the hourglass surface with different radius and the plane of the corresponding position. All the intersection lines construct the top relief surface. The mathematical equation of the top relief surface is worked out,and the complete top relief surface is solved. The normal vectors of the top land edge on the top relief surface and the top hourglass surface are obtained. Then,the angle between the two normal vectors is taken as the values of the top relief angle. The variation law of the top relief angle with the constant relief-grinding value is explored. These results show that the top relief angle is between 11. 27° and 11. 62° when the top relief-grinding value is 3. 5 mm. Besides,the relationship between the top relief-grinding value and the top relief angle at the same position is approximately linear. The research provides basis for proper selection of the top relief-grinding value of the hourglass worm wheel hob.