Modeling method of plane secondary envelope torus worm-drive worm gear hob tooth profile

Abstract

The invention relates to a modeling method of a plane secondary envelope torus worm-drive worm gear hob tooth profile. The method comprises the following steps: 1) giving initial design parameters; 2) calculating sum which corresponds to an initiating terminal; 3) obtaining point coordinates on an A tooth face; 4) judging whether the point coordinates are located in the working range of a hob or not, if yes, turning to the step 5, and if not, turning to the step 8; 5) obtaining the point coordinates on the A tooth face; 6) obtaining a coordinate of a middle point; 7) modifying a value, turning to the step 3, and obtaining intersecting lines of a series of intersecting planes and a tooth face of a worm gear hob basic worm; 8) modifying a tail end, and obtaining coordinates of points under the tail end and a middle point; 9) obtaining coordinates of points on a B tooth face and a middle point, wherein the B tooth face is the same with the A tooth face in the tail end; 10) obtaining point coordinates on a tooth root circular arc face; 11) obtaining point coordinates on a main cutting edge; 12) building an axial tooth profile model of a worm gear hob; and 13) building a curved face model of the worm gear hob basic worm. The method is free of building of a solid model, easy to achieve, low in modeling cost, and high in modeling precision.

Description

technical field [0001] The invention relates to a method for modeling the tooth profile of a worm gear hob driven by a plane quadratic enveloping torus. Background technique [0002] At present, the tooth profile model of the planar quadratic enveloping toroidal worm drive worm gear hob needs to be obtained by establishing the basic worm solid model of the planar quadratic enveloping toroidal worm drive worm gear hob, and then obtained by cutting off redundant entities. This method requires prior Establishing the solid model of the basic worm of the worm gear hob requires cumbersome modeling steps and poor model accuracy. At present, there is still a lack of a method that can directly establish the tooth profile model of the planar quadratic enveloping toroidal worm gear hob. [0003] Such as figure 1 It is a plane secondary enveloping toroidal worm driven straight groove worm gear hob, which includes a hob A helicoid surface 10, a hob B helicoid surface 9, a hob addendum ...

AI Technical Summary

Problems solved by technology

However, the solution of this nonlinear equation system is not unique. On the sectional plane, each tooth can find a torus satisfying the radius of point, such as image 3 As shown, it is difficult to solve the root of the common nonlinear equations such as Newton's down-hill method

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