CN-121211616-B - Face gear pair local line contact shaping method and electronic equipment

CN121211616BCN 121211616 BCN121211616 BCN 121211616BCN-121211616-B

Abstract

The application belongs to the technical field of gear design, and provides a partial line contact shaping method of a face gear pair and electronic equipment, wherein the method comprises the steps of carrying out digital discrete treatment on a contact surface of the face gear pair to obtain a tooth surface contact line of the face gear pair; dividing the area where the tooth surface contact line is positioned into a non-contact shape-modifying area and a contact shape-modifying area based on a preset contact track; and superposing the tooth surface contact line of the contact modification area with a preset sectional modification function, and superposing the tooth surface contact line of the non-contact modification area with a preset secondary modification function so as to modify the tooth surface contact line towards one side far away from the contact edge of the face gear pair. According to the technical scheme, the edge contact of the face gear pair can be reduced while the stress dispersion is ensured.

Inventors

HE KUN
LI RONGHAO
LI GUOLONG

Assignees

重庆工商大学

Dates

Publication Date: 20260512
Application Date: 20250923

Claims (8)

1. A method for partial line contact shaping of a face gear pair, the method comprising: performing digital discrete treatment on the contact surface of the face gear pair to obtain a tooth surface contact line of the face gear pair; Dividing the area where the tooth surface contact line is positioned into a non-contact shape-modifying area and a contact shape-modifying area based on a preset contact track; Setting a start point coordinate and an end point coordinate of the contact track to construct a parabolic function corresponding to the contact track based on the start point coordinate, the end point coordinate and the midpoint coordinate, and determining a preset contact track according to the parabolic function; Superposing a tooth surface contact line of the contact modification area and a preset sectional modification function, and superposing a tooth surface contact line of the non-contact modification area and a preset secondary modification function, so that the tooth surface contact line is modified towards one side far away from the contact edge of the face gear pair; The piecewise shaping function uses the following expression: In the formula, Representing the dependent variable of the modification function, , The coefficient of the shape-modifying is represented, 、 And Representing the dependent variable of the modification function, And Respectively representing the endpoint axis coordinates of the tooth surface contact line in the inner diameter direction and the outer diameter direction of the gear, Then the axis coordinate of a moving point on the tooth surface contact line where the contact point is located is represented; The secondary shaping function adopts the following expression: In the formula, Representing the dependent variable of the modification function, , The coefficient of the shape-modifying is represented, 、 And Representing the argument of the modification function, And The preset contact track starting points respectively representing the tooth top and tooth bottom directions, Representing a moving point moving along the original contact trajectory outside the preset contact trajectory start point.
2. The method of partial line contact modification of a face gear set according to claim 1, wherein the digitally discretizing the contact surface of the face gear set to obtain a tooth surface contact line of the face gear set comprises: acquiring a tooth surface equation and a meshing equation of the face gear pair; inputting preset face gear parameters into an equation set formed by combining the tooth surface equation and the meshing equation, and calculating to obtain a discrete tooth surface formed based on the tooth surface contact line; And determining the tooth surface contact line of the face gear pair according to the discrete tooth surfaces.
3. The partial line contact modification method of a face gear pair according to claim 2, wherein the dividing the area where the tooth surface contact line is located into a non-contact modification area and a contact modification area based on a preset contact locus includes: determining a tooth surface contact line in the central area of the contact surface of the face gear pair, and acquiring the midpoint coordinate of the tooth surface contact line; Setting a starting point coordinate and an ending point coordinate of the contact track, constructing a parabolic function corresponding to the contact track based on the starting point coordinate, the ending point coordinate and the midpoint coordinate, and determining a preset contact track according to the parabolic function.
4. The partial line contact modification method of a face gear pair according to claim 1, wherein, when the contact surface of the face gear pair is digitally discretized, the tooth surface of the face gear adopts the following expression: In the formula, Representing the tooth surface function of the face gear, A transformation matrix representing the face gear coordinates, Representing the tool tooth surface function of the generated face gear, Representing the axis coordinates in the tooth width direction, The parameters of the involute angle are represented by, Representing the rotation angle of the small wheel, f is the engagement equation for the following Represented as Is a function of (2).
5. The face gear pair partial line contact shaping method according to claim 1, wherein when constructing a parabolic function corresponding to the contact track, the parabolic function adopts the following expression: where r represents a parabolic function, Representing the midpoint of the contact trajectory, d representing the apex height, Representing the vectors of directions perpendicular to each other, =( - )/| - |, = ∙( - ), 、 And t is the length coefficient of the contact line for the contact path starting point.
6. The face gear pair partial line contact shaping method according to claim 1, wherein the tooth surface contact line is shaped toward a side away from a contact edge of the face gear pair, using the following expression: In the formula, Representing the tooth surface function of the face gear, Representing the tool tooth surface function of the generated face gear, Representing the Y-axis coordinate in the tooth width direction, As the parameter of the angle of the involute, The segment-wise shaping function is represented as, The second order shape-modifying function is represented, Is a normal vector of tooth surface points.
7. A computer program product comprising a computer program which, when executed by a processor, implements the steps of the face gear pair partial line contact modification method of any one of claims 1 to 6.
8. An electronic device, the electronic device comprising: at least one processor, and A memory communicatively coupled to the at least one processor, wherein the memory stores a computer program executable by the at least one processor to enable the at least one processor to perform the face gear pair partial line contact modification method of any one of claims 1 to 6.

Description

Face gear pair local line contact shaping method and electronic equipment Technical Field The invention relates to the technical field of gear design, in particular to a partial line contact shaping method of a face gear pair and electronic equipment. Background The face gear transmission is widely applied to key fields of helicopter main speed reducers and the like due to the advantages of high contact ratio, small axial force and the like. However, the actual meshing state of the face gear pair is affected by machining errors, mounting errors and the like, and edge contact is liable to occur to cause stress concentration, so that meshing performance is lowered. Therefore, in the design process of the face gear pair, a number of face gear pair shaping designs are required to solve the above problems. Regarding the shaping design of the pinion gear pair, LITVIN et al in the prior art documents propose a shaping method with optimized tooth number, which achieves point contact by designing the pinion tooth number to be 1-3 teeth less than the pinion cutter. TSAY et al propose a free-form surface modification method, which realizes topology modification by superposing a modification function on a tooth surface point, thereby improving the contact performance of face gear transmission. However, in the face gear pair shaping design in the prior art, the point contact mode of the face gear pair causes the problem of stress concentration, and the edge contact of the face gear pair is easy to cause. Disclosure of Invention The application aims to at least solve the technical problems in the prior art and provides a partial line contact shape modification method of a face gear pair and electronic equipment. According to one aspect of the embodiment of the application, the application provides a partial line contact shaping method of a face gear pair and electronic equipment, wherein the method comprises the steps of carrying out digital discrete treatment on a contact surface of the face gear pair to obtain a tooth surface contact line of the face gear pair; dividing the area where the tooth surface contact line is positioned into a non-contact shape-modifying area and a contact shape-modifying area based on a preset contact track; and superposing the tooth surface contact line of the contact modification area with a preset sectional modification function, and superposing the tooth surface contact line of the non-contact modification area with a preset secondary modification function so as to modify the tooth surface contact line towards one side far away from the contact edge of the face gear pair. In one embodiment of the application, based on the technical scheme, the method for carrying out digital discrete processing on the contact surface of the face gear pair to obtain the tooth surface contact line of the face gear pair comprises the steps of obtaining a tooth surface equation and a meshing equation of the face gear pair, inputting preset face gear parameters into an equation set formed by combining the tooth surface equation and the meshing equation, calculating to obtain a discrete tooth surface formed based on the tooth surface contact line, and determining the tooth surface contact line of the face gear pair according to the discrete tooth surface. In one embodiment of the application, based on the above technical scheme, the area where the tooth surface contact line is located is divided into a non-contact modified area and a contact modified area, which comprises determining a tooth surface contact line in a central area of a contact surface of the face gear pair and obtaining a midpoint coordinate of the tooth surface contact line, setting a start point coordinate and an end point coordinate of the contact track, constructing a parabolic function corresponding to the contact track based on the start point coordinate, the end point coordinate and the midpoint coordinate, and determining the preset contact track according to the parabolic function. In one embodiment of the present application, based on the above technical solution, when the contact surface of the face gear pair is digitally and discretely processed, the tooth surface of the face gear adopts the following expression: In the formula, Representing the tooth surface function of the face gear,A transformation matrix representing the face gear coordinates,Representing the tool tooth surface function of the generated face gear,Representing the axis coordinates in the tooth width direction,The parameters of the involute angle are represented by,Representing the rotation angle of the small wheel, f is the engagement equation for the followingRepresented asIs a function of (2). In one embodiment of the present application, based on the above technical solution, when constructing the parabolic function corresponding to the contact track, the parabolic function uses the following expression: where r represents a parabolic function, Representing the