# Curvature and normal Vector at the Tooth Surface calculation Point of Spiral Bevel Gear

The normal curvature and short-range torsion of the tooth surface of the pinion at the calculated point M are as follows:

The curvature of the tooth surface of the pinion determined by the above formula at the calculation point M is the curvature of the pinion when the tooth surface of the large and small gears is completely co-choked. In order to obtain the local common choke point contact tooth surface, it is also necessary to modify the curvature of the gear tooth surface at the M point, so the following correction formula is adopted.

Where Δ knv and Δ knt are the correction values of normal curvature in the direction of tooth length and tooth profile, and Δ τ gv is the correction value of short-range torsion in the direction of tooth length. F is the ratio of the length of the contact zone to the length of the tooth, which is generally 0.3-0.4. Kp is called tooth height correction coefficient, which is usually taken as Kp=0.63m. B is this width, β 1, β 2 is the midpoint helix angle of the small wheel and the big wheel, Z1 is the number of teeth of the small wheel, and R1 is the pitch circle radius of the small wheel.

In this way, the curvature at the calculated point M of the modified pinion tooth surface is:

In the above formula, the positive and negative sign corresponds to the two tooth faces of the pinion: for the convex surface, the tooth length and the normal curvature correction of the tooth profile direction are positive, and for the concave surface, the tooth length and the normal curvature correction of the tooth profile direction are negative. Only in this way can we ensure the correction to the body of the ferry.

The normal vector at the calculation point of the tooth surface of the small gear is the unit normal vector N2 of the tooth surface of the big wheel at the calculation point.

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