# Tooth surface curvature of spiral bevel gear

The right-hand wheel and the left-hand production wheel are an aligned hyperboloid gear pair, and the tooth surface of the big wheel is the envelope surface of the production wheel. Knowing the relative motion relationship between them, the tooth surface of the large gear can be determined, and the curvature of the calculated point of the tooth surface of the large wheel can be obtained.

First of all, the relative motion relationship between the production wheel and the wheel is determined. Suppose the angular velocity of the production wheel is ω 02, the angular velocity of the big wheel and the production wheel is ω G2, the velocities of the big wheel and the production wheel at the meshing point of the cutting teeth are vg2 and v02 respectively, the relative velocity is vr2, the relative acceleration is ar2, and the relative angular velocity is ω 02.

The tooth surface of the large wheel profile wheel is a conical surface, which makes t _ 2Powerv _ 2 the two main directions of the tooth surface of the large wheel profile wheel. Among them, the public is in the direction of straight bus, and there is v2=t2Xn2. The normal curvature kngv2,kngt2 and short-range torsion τ ggv2 of the tooth surface of the large gear along the direction of v2PowerT2 are as follows:

In order to determine the induced normal curvature and induced short-range torsion between the large wheel and the production wheel along the direction of T2 and v2, it is necessary to calculate the components of ω R2, vr2 and ar2 along the v2, T2 and N2 directions.

If ω 02 is the direction angle of the contact line between the tooth surface of the big wheel and the tooth surface of the production wheel, that is, the angle between the tangent of the instantaneous contact line and v2, then:

The induced normal curvature Δ kv2, Δ kt2 and induced short-range torsion Δ gv2 along the direction of v2 and T2 are:

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

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