Spur cylindrical gear coordinate system: SG, (OG: XG, YG, ZG) take the center of spur cylindrical gear as the origin og of spur cylindrical gear coordinate system, take the ray starting from the origin og of coordinate system and passing through the position of indexing circle on spur cylindrical gear tooth surface as the positive direction of ZG axis, take the axis of spur cylindrical gear as YG axis, and the positive direction of XG axis of coordinate system is determined by the right-hand rule of Cartesian coordinate system. The coordinate system of spur gear tooth surface model is shown in the figure,
In the figure, plane xgogzg is the end section of spur gear at y = 0 in spur gear coordinate system SG. In plane xgogzg, point C is the point at the indexing circle on the tooth surface of spur gear, and the pressure angle at point C is α 0 Point n is the tangent point between the tooth profile normal and the base circle at point C.
The tooth surface equation of spur gear is also determined by two variables. One of the variables is the pressure angle α ， Represents the pressure angle at any point F on the tooth surface. The tangent point of the tooth profile normal passing through point F on the base circle is point E. Another variable is the axis y of spur gear, which is expressed as the coordinate in YG direction. Thus（ α, y) Any point on the tooth surface of a spur gear can be determined.
Considering that the tooth surface rotates around the YG axis of spur gear, the angle of spur gear can be used φ G represents the angle at which a point on the tooth surface turns around the axis of the spur gear. In the coordinate system SG, the rotation angle of the spur gear around the YG axis is specified when the meshing point of the hob and the spur gear tooth surface coincides at node C φ g=0 。 Thus, a point on the tooth surface of spur gear can be determined by a given set of parameters（ α, y, φ g) To determine.