Meshing Theory Research Of Conical Envelope Spiroid Worm Gearing

Spiral surface of the conical envelope spiroid worm is shaped by grinding of the grinding wheel,as a result,the tooth surface accuracy and finish are significantly improved.Besides,conical envelope spiroid worm has a lot of good properties such as,large carrying capacity,good lubrication condition,facilitate adjustment of backlish and so on.In this paper,meshing principle of conical envelope spiroid gearing is discussed,including meshing research on grinding the tooth surface of conical worm with grinding wheel and meshing analysis about the conical envelope spiroid worm gearing.The main contects of the paper are as follows:(1)The equation of grinding wheel profile is obtained and curvature parameters of the instantaneous contact line for the conjugate tooth surfaces are derived.Then,the coordinate system of grinding conical worm "i" and "e" tooth surface is established,based on this,the engagement function and curvature interference boundary function of conical worm could be gained easily.At the same time,in the process of conical envelope spiroid worm gearing,the coordinate system of the conical worm drive is set up,and the engagement function and meshing boundary function of grinding wheel grinding conical worm i"i," and"e" tooth surface could be got separately.In addition,the tooth surface equation of conical envelope spiroid worm and conical worm gear are put forward separetely.(2)The parameters of pitch cone of conical envelope spiroid worm and conical worm gear are calculated by the means of the theory on reference point.However,it is difficult to manufacture the conical worm gear with the tooth top hyperbolic surface,so it is suggested to replace the hyperbolic surface with conical surface thus the wheel blank dimensions of conical worm gear could be obtained expediently.Then the reference conical equation of conical envelope spiroid worm and conical worm gear could be got.(3)It is proposed to a measure of drawing the tooth outline and a method for calculating the tooth angle of conical envelope spiroid worm.It is discovered that the deflection angle of grinding wheel has a great influence on tooth outline and tooth angle.Then the The curvature interference boundary of the conical envelope spiroid worm is studied as well.(4)The distribution of instantaneous contact line on the tooth surface of the conical envelope spiroid worm and conical worm gear in the process of conical worm drive is analyzed by computer simulation,by the way,it is suggested to calculate the induced curvature and slip angle on the point of the instantaneous contact line.Then,the meshing boundary of conical envelope spiroid worm in the process of conical worm drive is studied in detail.