Method for determining beta angle changing curve of planar double enveloping worm

Abstract

The invention discloses a method for determining a beta angle changing curve of a planar double enveloping worm. The method includes the steps that a space coordinate system is established according to a beta angle changing planar double enveloping worm forming principle, the beta value is set to be a function of worm gear turn angle phi<2>, and beta angle changing addendum thickness equation delta and tooth surface undercutting discriminant equation r1 are derived on the basis of an envelope method principle; the minimum side addendum thickness value delta<min> meeting the requirement of no sharpening is calculated according to worm parameters; the addendum thickness is made to change regularly and linearly in the worm helical line direction from side teeth to throat teeth; multiple worm gear turn angles phi<2> are obtained according to an equal difference rule to obtain the corresponding thickness values so as to form feature points (phi<2>, delta (beta)); the beta value which each point corresponds to is obtained through the beta angle changing addendum thickness equation, the beta curve is fitted, the fitted beta curve is substituted into the tooth surface undercutting discriminant equation, and an undercutting line is drawn on a worm tooth surface graph; and the undercutting ratio is estimated, if the design requirement is met, the operation is finished, if the design requirement is not met, throat addendum thickness delta<h> is reduced or the addendum thickness change rule is changed to a cosine rule, and the operation returns to the step 3.

Description

technical field [0001] The invention relates to the field of plane-enveloping toroidal worm drive, in particular to a method for determining the β-angle variation curve of a plane-enveloping toroidal worm. Background technique [0002] In the field of planar enveloping toroidal worm transmission, increasing the number of heads and reducing the transmission ratio is an effective way to improve the transmission efficiency of the planar double enveloping toroidal worm transmission pair and increase its load capacity. However, when the number of heads is greater than or equal to 6 and the speed ratio is less than or equal to 10, the performance of the plane enveloping toroidal worm will deteriorate due to serious undercutting of the tooth surface and sharpening of the side tooth tips, resulting in the The number of heads and the speed ratio of the surface worm are limited. The planar enveloping toroidal worm with variable surface inclination angle β is considered to be able to ...

AI Technical Summary

Problems solved by technology

[0003] In the prior art, the β angle change curve can be obtained by making the production plane and the tooth line of the sectional curved surface of the worm constant tangent, and this curve can increase the thickness of the side tooth top of the multi-head small speed ratio plane enveloping toroidal worm, effectively solving the problem of tooth top However, when the undercut condition of the tooth surface does not meet the design requirements, it is impossible to control the performance of the worm only by changing the form of the β curve; it is also possible to specify the β angle that changes according to a certain rule on the basis of the initial β value. curve, but the variable β angle curve obtained by this method cannot guarantee the accuracy, and the selection of the change law and the determination of the coefficient lack scientific basis

It can be seen that the existing method for determining the variable β angle curve of the plane enveloping toroidal worm is not accurate enough, and it is difficult to solve the problem of controlling the influence of undercutting and sharpening. The important reason why the surface worm drive has not been popularized and applied

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