The parametric modeling of equal height spiral bevel gear with UG / OpenGRIP needs to deduce the corresponding parameter equations, including the spatial rectangular coordinate equations of spherical involute and extended epicycloid and the corresponding basic geometric principle parameter equations. Compared with the standard equal height spiral bevel gear, the equal height spiral bevel gear modeled by UG / OpenGRIP has higher flexibility.
In the modeling process, the selection of input parameters corresponds to the standard gear, that is, the large end modulus, the number of teeth, the tooth width, the pitch cone angle, the midpoint helix angle, the normal pressure angle, the square of the average node radius of the cutterhead, and the number of cutterhead blade groups. In the standard contour gear, the addendum height coefficient and backlash coefficient are standardized and fixed, but they are still used as input parameters in the secondary development of UG / OpenGRIP.
This paper mainly establishes the parameter equation of the spatial curve used in the modeling process of equal height spiral bevel gear, including spherical involute, extended epicycloid and basic geometric principle parameters. The main contents are as follows:
(1) Based on the formation principle and process of spherical involute and the relationship between base circle dimension and pitch cone, the spatial rectangular coordinate equation of spherical involute is established.
(2) Based on the analysis of the formation and properties of the extended epicycloid, the number of teeth of the imaginary plane gear is deduced, the relationship between the cutter position of the milling cutter and the helix angle of the midpoint, and the plane polar coordinate equation of the extended epicycloid are established. Through the transformation, the spatial right angle setting equation of the extended epicycloid and the calculation formula of the helix angle of any point are finally obtained.
(3) Based on the meshing principle of equal height teeth and the relevant knowledge of analytical geometry, and taking the tooth profile profile of equal height teeth as the reference, the calculation method of the radius and cone height of the base circle, pitch circle, tooth tip circle and tooth root circle of equal height spiral bevel gear is established.
(4) The cutter positions of n-type teeth and G-type teeth under different conditions are studied, and the corresponding calculation formula of midpoint helix angle is obtained. According to different conditions, the tooth shape correction methods of two kinds of gears are put forward.