# Pitch cone parameters of spiral bevel gear pinion machine tool

The pitch distance of the production wheel is R01, the helix angle β 01, and the rolling correction coefficient of the machining gear is 2c. It is known that the R01 and β 01m 2c meet the curvature requirements at the calculation point M of the tooth surface of the small wheel. The curvature of the actual tooth surface of the small wheel machined by the small wheel machine tool at the calculation point M should be equal to the formula, in which the curvature Knv1,Knt1, τ gv1 at the calculation point of the small wheel determined by the curvature of the large wheel, namely:

The following assumption is that the parameters of the pinion wheel are known to deduce the curvature of the calculation point of the pinion. First of all, the relative motion relationship between the production wheel and the small wheel is determined. Let the angular velocity of the pinion wheel be ω 01. If the angular velocity of the small wheel is ω G1, the velocity of the small wheel and the production wheel at the meshing point of the cutting tooth is vg1,v01, the relative velocity is vr1, the relative acceleration is ar1, and the relative angular velocity is ω R1, then:

The tooth surface of the pinion profiling wheel is a conical surface, which makes T1 and v1 the two main directions of the pinion profiling wheel tooth surface. T1 is in the direction of straight bus and has v1=t1Xn1. The hair curvature Kngv1,Kngt1 and short-range torsion τ ggv1 of the tooth surface of the pinion production gear along the direction of v1 and T1 are as follows:

In order to determine the induced normal curvature and induced short-range torsion between the small wheel and the production wheel along the directions T1 and V1, it is necessary to calculate it first ω Components of R1, VR1 and AR1 along V1, T1 and N1:

If ω 01 is the direction angle of the contact line between the tooth surface of the small wheel and the tooth surface of the production wheel, that is, the angle between the tangent of the instantaneous contact line and v1, then:

For the induced normal curvature Δ kv1, Δ kt1 and induced short-range torsion Δ gv1 along the direction of v1 and T1, then:

As a result, the normal curvature and short-range torsion of the tooth surface of the small wheel are calculated.

By using the above formula and solving the system of equations, we can get R01, β 01 and 2c. 