曲线刀刃双自由度展成曲面的理论和应用

Theory and Application of Surface Generated by Curvilinear Cutter Edge with Two Degrees of Freedom

为研究产形曲线按双自由度运动展成曲面的啮合问题,利用双自由度共轭条件,提出曲线刀刃双自由度展成曲面的理论。将此理论用于直线刀刃双自由度展成环面蜗杆螺旋面的计算,在普通滚齿机上加工出这种蜗杆,用三坐标测量机测量蜗杆螺旋面的结果与理论计算的结果一致,并研究了直线刀刃双自由度展成环面蜗杆副的应用前景。研究表明:利用曲线刀刃双自由度展成曲面理论,可由曲线刀刃和两运动参数变化规律求被展成曲面,或由曲面和曲线刀刃反求出两运动参数变化规律;对两运动参数变化规律作适当限制,可简化曲线刀刃双自由度运动展成曲面的计算;直线刀刃双自由度展成环面蜗杆的'修形'曲线与直廓环面蜗杆的抛物线修形接近,这种蜗杆副不用修形就可避免直廓环面蜗杆副的缺陷,具有良好的应用前景。

In order to study the mesh problem in case that the surface is generated by curvilinear cutter with two degrees of freedom a theory of surface generated by curvilinear cutter edge with two degrees of freedom is put forward by using the conjugate conditions of two degrees of freedom motion. The theory is used to calculate the helical surface of the toroidal worm generated by linear cutter edge whose relative motion has two degrees of freedom. This kind of worm is manufactured on a hob machine and its helical surface of the worm is measured on a CMM. The application prospect of this kind of worm gears is studied. The conclusions are： by using the theory the generate curved surface can be deduced when the curvilinear cutter edge and the varying regularity of the two motion parameters are given or the varying regularity of the two motion parameters can be derived when the generated curved surface and the curvilinear cutter edge are given;the calculation of the curved surface generated by curvilinear cutter edge with two degrees of freedom can be simplified if the varying regularity of the two motion parameters is restricted properly; the ＂modification＂ curve of the worm generated by linear cutter edge with two degrees of freedom is close to that of the hindley worm which is modified in parabolic curve; the defect of the hindley worm gears can be avoided by using this kind of worm gears without needing modification and there is a good application prospect.