椭圆齿轮传动的非零变位方法探索

Probe on method of non-zero profile shifted modification for elliptical gears

针对椭圆齿轮传动提出了一种非零变位的方法。在传动比函数保持不变的前提下,使传动中心距略微改变(给定一个相对变动量),则会产生变位的效果。变位后的齿轮节曲线仍然是一对共轭的椭圆,其离心率与变位前椭圆节曲线的离心率相同,而大小的相对变动量等于中心距的相对变动量。变位前后节曲线共轭点处的切线、法线的斜率不变,但二者位置发生变化,因此,造成共轭点产生了切向分离和法向分离。切向分离现象是椭圆齿轮传动所特有的,其分离量应作为生成齿条的切向变位量。法向分离现象则类似于圆形齿轮变位时的中心距变动,成为生成齿条的法向变位量。经齿廓曲线图形仿真证实,这种非零变位能够有效地消除根切现象、增大齿厚,从而提高轮齿的强度。

Being directed against elliptical gear drive a kind of non-zero modification method has been advanced.Under the premise of macntaining an invariable function of transmission ratio,while the distance between transamission centers gets a little change(while an amount of relative variation is given)will produce an effect of modification.The pitch curves of gear after modification are still a pair of conjugate ellipse with the same eccentricity as that of elliptical pitch curves before modification,and with the amount of relative variation of their size equals to the amount of relative variation of centre distance.The slopes of tangential lines and normal lines at conjugate points of pitch curves before and after modification are unvarying,but positions of those lines are varied,thus caused the conjugate points to produce tangential departure and normal departure.Phenomenon of tangential departure is peculiar to elliptic gear transmission,its amount of departure should be regarded as the amount of tangential modification for rack generation.Whereas the phenomenon of normal departure is similar to the variation of centre distance in circular gear modification and its amount of departure becomes the amount of normal modification for rack generation.It is verified through graphic simulation of tooth profile curve that this kind of non-zero modification could effectively eliminate the phenomenon of undercut and increase tooth width thus enhanced the strength of gear.