In order to establish the accurate three-dimensional model of cylindrical gear with circular arc tooth profile and study the tooth surface reconstruction and gear structure characteristics, the tooth surface equation coordinate system of circular arc tooth line cylindrical gear machined by rotating cutter head is established, and the tooth surface equation is derived
Where: X, y, z-coordinate of tooth surface, where z-axis is the direction of gear axis; R1, rt-equation of gear tooth surface machined with parallel connecting rod; θ – angle of cutter from middle section of gear blank to end face, clockwise is positive, counter clockwise is negative; φ 1 is gear blank angle, clockwise is positive, counter clockwise is negative; α – tool pressure angle; U-displacement of the point on the tool surface along the generatrix of the conic surface from the reference point.
When B = 0 and θ = 0, they are substituted into the formula, that is, the tooth profile equation of the middle section of the gear is obtained as follows:
When the tooth width b ≠ 0 and θ≠ 0, there are the following relations:
In this case, the tooth profile equation of cylindrical gear with circular arc profile can be expressed as follows: