CN-121982093-A - Method, system, equipment and medium for measuring tooth surface error of double-degree-of-freedom spherical gear

CN121982093ACN 121982093 ACN121982093 ACN 121982093ACN-121982093-A

Abstract

The application discloses a method, a system, equipment and a medium for measuring tooth surface errors of a spherical gear with double degrees of freedom, wherein a target plane is established; the method comprises the steps of determining a z-axis of a measurement coordinate system according to an origin coordinate of the measurement coordinate system and a target plane through right hand rules, determining the measurement coordinate system, setting a plurality of theoretical measurement points according to a divided grid and the theoretical coordinate system, setting a plurality of actual measurement points according to the divided grid and the measurement coordinate system to obtain a first measurement point position of each theoretical measurement point and a second measurement point position of each actual measurement point, calculating tooth surface deviation based on the first measurement point position and the second measurement point position, calculating theoretical tooth thickness and theoretical tooth pitch based on the theoretical coordinate system, calculating actual tooth thickness and actual tooth pitch based on the measurement coordinate system, and calculating deviation between the theoretical tooth thickness and actual tooth thickness and deviation between the theoretical tooth pitch and the actual tooth pitch to obtain tooth thickness deviation and tooth pitch deviation. The method can improve the accuracy of measuring the tooth surface errors of the double-degree-of-freedom spherical gear.

Inventors

HE HAIYU
ZHOU YUANSHENG
TANG JINYUAN
WANG QIANG

Assignees

中南大学

Dates

Publication Date: 20260505
Application Date: 20260407

Claims (10)

1. The method for measuring the tooth surface error of the spherical gear with two degrees of freedom is characterized by comprising the following steps: Setting a plurality of first measuring points on the top surface of the spherical gear tooth to obtain first coordinate positions of the first measuring points respectively; setting a plurality of second measuring points on the upper tooth surface of the middle tooth of the ball gear to obtain respective second coordinate positions of the second measuring points; setting a plurality of third measuring points on the lower tooth surface of the ball gear intermediate tooth, and obtaining respective third coordinate positions of the third measuring points; Determining origin coordinates of a measurement coordinate system based on a plurality of the first coordinate positions; establishing a target plane containing ball gears of an x-axis and a y-axis based on a plurality of the second coordinate positions and a plurality of the third coordinate positions; determining a z-axis of the measurement coordinate system according to the origin coordinate of the measurement coordinate system and the target plane by a right-hand rule; Determining a measurement coordinate system based on origin coordinates of the measurement coordinate system, the x-axis, the y-axis, and the z-axis; Grid division is carried out on the tooth surface of the spherical gear with double degrees of freedom, a plurality of theoretical measuring points are set according to the divided grid and a theoretical coordinate system, a plurality of actual measuring points are set according to the divided grid and the divided coordinate system, and a first measuring point position of each theoretical measuring point and a second measuring point position of each actual measuring point are obtained; Calculating a tooth surface deviation based on the first measurement point position and the second measurement point position; and calculating the theoretical tooth thickness and the theoretical tooth pitch based on a theoretical coordinate system, calculating the actual tooth thickness and the actual tooth pitch based on the measurement coordinate system, and calculating the deviation between the theoretical tooth thickness and the actual tooth thickness and the deviation between the theoretical tooth pitch and the actual tooth pitch to obtain the tooth thickness deviation and the tooth pitch deviation.
2. The method of measuring a tooth surface error of a spherical gear with two degrees of freedom according to claim 1, wherein the determining origin coordinates of a measurement coordinate system based on a plurality of the first coordinate positions includes: Presetting an origin coordinate of a measurement coordinate system; fitting the origin coordinates and each first coordinate position to construct a space curved surface equation of a plurality of spheres; And constructing an objective function according to the space curved surface equation of the multiple spherical surfaces, and minimizing the objective function to obtain the origin coordinates of the measurement coordinate system.
3. The method of measuring a tooth surface error of a ball gear with two degrees of freedom according to claim 1, wherein the establishing a target plane of the ball gear including an x-axis and a y-axis based on the plurality of the second coordinate positions and the plurality of the third coordinate positions includes: constructing a least squares equation based on the plurality of second coordinate positions and the plurality of third coordinate positions; taking a minimum value from the least square equation to obtain a plane construction coefficient; a target plane containing the ball gears for the x-axis and the y-axis is established by the plane building coefficients.
4. The two-degree-of-freedom spherical gear tooth surface error measurement method according to claim 1, wherein the calculating of the tooth surface deviation based on the first measurement point position and the second measurement point position includes: Obtaining a unit normal vector corresponding to a theoretical measurement point; performing difference calculation on the first measuring point position and the second measuring point position to obtain a difference calculation result; and multiplying the difference value calculation result by the unit normal vector to obtain the tooth surface deviation.
5. The method of measuring a double degree-of-freedom spherical gear tooth surface error according to claim 1, wherein the calculating an actual tooth thickness and an actual tooth pitch based on the measurement coordinate system includes: setting two measurement reference points on each tooth surface of the double-degree-of-freedom ball gear, and obtaining a target distance from each measurement reference point to an origin in the measurement coordinate system and a spatial position of each measurement reference point; and calculating the actual tooth thickness and the actual tooth pitch according to the target distance and the space position.
6. The method of measuring a double degree of freedom spherical gear tooth surface error according to claim 5, wherein the calculating an actual tooth thickness and an actual tooth pitch from the target distance and the spatial position includes: Calculating the actual tooth thickness included angle of the single tooth through an x-axis value and a y-axis value in the spatial position of each tooth surface corresponding to two measurement datum points; and multiplying the actual tooth thickness included angle by the target distance to obtain the actual tooth thickness of the single tooth.
7. The method of measuring a double degree of freedom spherical gear tooth surface error according to claim 5, wherein the calculating an actual tooth thickness and an actual tooth pitch from the target distance and the spatial position includes: Calculating the actual pitch angle of a single tooth through the x-axis value and the y-axis value in the respective spatial positions of the second measuring reference points of the two adjacent tooth surfaces; Multiplying the actual pitch angle of the single tooth by the target distance to obtain the actual pitch of the single tooth; calculating actual pitch angles of the plurality of teeth by the x-axis value and the y-axis value in the respective spatial positions of the second measurement reference point of the last tooth surface and the second measurement reference point of the first tooth surface; and multiplying the actual tooth pitch included angles of the plurality of teeth by the target distance to obtain the actual tooth pitches of the plurality of teeth.
8. A two degree of freedom spherical gear tooth surface error measurement system, the system comprising: The device comprises a data acquisition module, a plurality of second measurement points, a plurality of third measurement points, a data acquisition module and a data acquisition module, wherein the plurality of first measurement points are arranged on the top surface of a spherical gear tooth to obtain respective first coordinate positions of the plurality of first measurement points; the plane determining module is used for determining origin coordinates of a measurement coordinate system based on the plurality of first coordinate positions, and establishing a target plane containing the ball gear of an x axis and a y axis based on the plurality of second coordinate positions and the plurality of third coordinate positions; The z-axis determining module is used for determining the z-axis of the measurement coordinate system according to the original point coordinate of the measurement coordinate system and the target plane by a right-hand rule; A coordinate system determining module for determining a measurement coordinate system based on origin coordinates of the measurement coordinate system, the x-axis, the y-axis, and the z-axis; The position obtaining module is used for carrying out grid division on the tooth surface of the spherical gear with two degrees of freedom, setting a plurality of theoretical measuring points according to the divided grid and a theoretical coordinate system, setting a plurality of actual measuring points according to the divided grid and the divided coordinate system, and obtaining a first measuring point position of each theoretical measuring point and a second measuring point position of each actual measuring point; A first calculation module for calculating a tooth surface deviation based on the first measurement point position and the second measurement point position; And the second calculation module is used for calculating the theoretical tooth thickness and the theoretical tooth pitch based on a theoretical coordinate system, calculating the actual tooth thickness and the actual tooth pitch based on the measurement coordinate system, and calculating the deviation between the theoretical tooth thickness and the actual tooth thickness and the deviation between the theoretical tooth pitch and the actual tooth pitch to obtain the tooth thickness deviation and the tooth pitch deviation.
9. An electronic device comprising at least one control processor and a memory communicatively coupled to the at least one control processor, the memory storing instructions executable by the at least one control processor to enable the at least one control processor to perform the two degree-of-freedom spherical gear tooth surface error measurement method of any one of claims 1 to 7.
10. A computer-readable storage medium storing computer-executable instructions for causing a computer to perform the two-degree-of-freedom spherical gear tooth surface error measurement method according to any one of claims 1 to 7.

Description

Method, system, equipment and medium for measuring tooth surface error of double-degree-of-freedom spherical gear Technical Field The application relates to the technical field of spherical gear tooth surface error measurement, in particular to a method, a system, equipment and a medium for measuring spherical gear tooth surface error with double degrees of freedom. Background The spherical gear technology has subversive significance for improving the core performance of a new generation of robots, particularly high-precision industrial robots and special environment operation robots, and the importance of the spherical gear technology is directly related to the contradiction of flexibility, rigidity and compactness of the robot joints. The unique two-degree-of-freedom space engagement characteristic of the spherical gear enables the spherical gear to realize two-dimensional compound motion around the intersecting axes in a single joint, which brings breakthrough to the design of the robot joint. The ball gear can significantly simplify the joint structure, enabling more complex dexterous movements with fewer parts and more compact dimensions. However, in the prior art, tooth surface errors are measured according to traditional gear mechanisms such as cylindrical gears and bevel gears, and compared with the traditional gear mechanisms, the spherical gears have larger difference, and if the existing domestic and foreign measuring methods or software are adopted to measure the tooth surface errors of the spherical gears with two degrees of freedom, the measuring accuracy is lower. Disclosure of Invention The application aims to provide a method, a system, equipment and a medium for measuring the tooth surface error of a double-degree-of-freedom spherical gear, which can improve the accuracy of measuring the tooth surface error of the double-degree-of-freedom spherical gear. In a first aspect, an embodiment of the present application provides a method for measuring a tooth surface error of a spherical gear with two degrees of freedom, the method including: Setting a plurality of first measuring points on the top surface of the spherical gear tooth to obtain first coordinate positions of the first measuring points respectively; setting a plurality of second measuring points on the upper tooth surface of the middle tooth of the ball gear to obtain respective second coordinate positions of the second measuring points; setting a plurality of third measuring points on the lower tooth surface of the ball gear intermediate tooth, and obtaining respective third coordinate positions of the third measuring points; Determining origin coordinates of a measurement coordinate system based on a plurality of the first coordinate positions; establishing a target plane containing ball gears of an x-axis and a y-axis based on a plurality of the second coordinate positions and a plurality of the third coordinate positions; determining a z-axis of the measurement coordinate system according to the origin coordinate of the measurement coordinate system and the target plane by a right-hand rule; Determining a measurement coordinate system based on origin coordinates of the measurement coordinate system, the x-axis, the y-axis, and the z-axis; Grid division is carried out on the tooth surface of the spherical gear with double degrees of freedom, a plurality of theoretical measuring points are set according to the divided grid and a theoretical coordinate system, a plurality of actual measuring points are set according to the divided grid and the divided coordinate system, and a first measuring point position of each theoretical measuring point and a second measuring point position of each actual measuring point are obtained; Calculating a tooth surface deviation based on the first measurement point position and the second measurement point position; and calculating the theoretical tooth thickness and the theoretical tooth pitch based on a theoretical coordinate system, calculating the actual tooth thickness and the actual tooth pitch based on the measurement coordinate system, and calculating the deviation between the theoretical tooth thickness and the actual tooth thickness and the deviation between the theoretical tooth pitch and the actual tooth pitch to obtain the tooth thickness deviation and the tooth pitch deviation. In some embodiments, the determining origin coordinates of the measurement coordinate system based on the plurality of the first coordinate positions includes: Presetting an origin coordinate of a measurement coordinate system; fitting the origin coordinates and each first coordinate position to construct a space curved surface equation of a plurality of spheres; And constructing an objective function according to the space curved surface equation of the multiple spherical surfaces, and minimizing the objective function to obtain the origin coordinates of the measurement coordinate system. In some embodiments, th