正弦齿条所生成齿轮的根切特性探讨

Investigation on undercutting of gears generated with sinusoidal rack

讨论了基于正弦齿条生成的齿轮的根切特性正弦齿条的几何形状可以认为是由无数个渐开线齿轮的生成齿条所组成.仿照渐开线齿轮的根切特性的讨论方法,推导出正弦齿条所生成齿轮的根切判别依据和无根切最少齿数的计算式.经讨论和仿真证实,正弦齿条所生成的齿轮在一个特定的齿顶高下最容易发生根切,该齿顶高数值只取决于正弦齿轮的设计压力角.相应的无根切最少齿数也仅取决于正弦齿轮的设计压力角,而与齿顶高系数值无关.在相同设计压力角下,正弦齿轮的无根切最少齿数远小于渐开线齿轮的无根切最少齿数.

The undercutting feature of gears generated with sinusoidal rack is discussed. Geometry of the rack can be considered as a constitution of numerous normal racks which generate involute gears. Atter the discussion on the undercutting property of involute gears,the undercutting discriminant and the least teeth number without undercutting of the gears generated with sinusoidal rack are worked out. It is confirmed that the sinusoidal gear can be easily undercut with a specific addendum height value decided only by the design pressure angle of the gear. Accordingly, the least teeth number without undercutting is also decided only by the design pressure angle of the gear,without any relation to the coefficient of addendum height of the gear. Under the same design pressure angle,the least teeth number without undercutting of the sinusoidal gears is much less than that of the involute gears.