Research On Mismatch Mechanism Of Conical Envelope Spiroid Worm Gearing

Different from the previous line-contact meshing between envelope spiroid worm and spiroid worm gear,this paper researches the point-contact between two tooth surfaces,which may be called the mismatch of envelope spiroid worm gearing.Mismatching can reduce the sensitivity to errors,and greatly increase the yield in production.In this paper,the mathematical model which the mismatch of envelope spiroid worm gearing was established,simultaneous equations and simplified to find unknowns.Finally,the influence of parameters on the meshing performance which the mismatch of enveloping spiroid worm gearing is investigated by computer simulation.The main contents of this paper are as follows:(1)The mathematical model of mismatching conical grinding wheel enveloping spiroid worm gear and hob are established,the geometric parameters of the grinding wheel generating flank,the meshing function of the wheel separately enveloping spiroid worm gear and hob as well as the equation of the enveloping surface are deduced,and the meshing characteristic parameters of two tooth surfaces were studied.Then,the calculation principle of the tooth profile in the conical envelope spiroid shaft section is analyzed,and a numerical example is given to verify it.(2)The coordinate system of hob envelope conical spiroid worm gear is established,the meshing function of hob enveloping spiroid worm is deduced and the tooth surface equation of spiroid worm is written out.Then,the meshing characteristic parameters of hob enveloping spiroid worm are analyzed,the selection method of the reference point is given for the meshing of the two tooth surfaces as well as the calculation of the meshing boundary.(3)On the basis of the mathematical model of the mismatched enveloping spiroid worm gearing,find out the equations of the two tooth surface contact point between the spiroid worm and spiroid worm gear,and through simplification,denominator and other methods to find the solution of the equations,then find the contact point of two tooth surfaces,the local comprehensive analysis of the mismatched gearing drive at the instantaneous contact point as well as the kinematic analysis of the mismatched gearing drive.(4)For example,an error free example is provided,the mismatch envelope spiroid worm is comparatively less sensitive to the assembly error through several numerical examples with installation errors,and the tooth number of the two tooth surface meshing is more,the coincidence degree is large,and the meshing performance is good.