CN-121982094-A - Three-degree-of-freedom spherical gear tooth surface error measurement method, system, equipment and medium

CN121982094ACN 121982094 ACN121982094 ACN 121982094ACN-121982094-A

Abstract

The application discloses a three-degree-of-freedom spherical gear tooth surface error measurement method, a system, equipment and a medium, wherein the method is used for determining an origin coordinate of a measurement coordinate system based on a plurality of first coordinate positions, establishing a first plane of a spherical gear based on a plurality of second coordinate positions and a plurality of third coordinate positions, and establishing a second plane of the spherical gear based on a plurality of fourth coordinate positions and a plurality of fifth coordinate positions; the method comprises the steps of determining a measurement coordinate system based on an origin coordinate of the measurement coordinate system, a first plane and a second plane, calculating a theoretical tooth profile, a theoretical tooth direction, a theoretical tooth thickness and a theoretical tooth pitch based on the theoretical coordinate system, calculating an actual tooth profile, an actual tooth direction, an actual tooth thickness and an actual tooth pitch based on the measurement coordinate system, calculating deviations between the theoretical tooth profile and the actual tooth profile, between the theoretical tooth direction and the actual tooth direction, between the theoretical tooth thickness and the actual tooth thickness and between the theoretical tooth pitch and the actual tooth pitch, and obtaining deviation results. The application can improve the accuracy of measuring the tooth surface error of the three-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 three-degree-of-freedom spherical gear tooth surface error measurement method is characterized by comprising the following steps of: Setting a plurality of first measuring points on the top surface of a spherical gear tooth to obtain respective first coordinate positions of the plurality of first measuring points, setting a plurality of second measuring points on the upper tooth surface of a spherical gear intermediate tooth to obtain respective second coordinate positions of the plurality of second measuring points, setting a plurality of third measuring points on the lower tooth surface of the spherical gear intermediate tooth to obtain respective third coordinate positions of the plurality of third measuring points, setting a plurality of fourth measuring points on the left tooth surface of the spherical gear intermediate tooth to obtain respective fourth coordinate positions of the plurality of fourth measuring points, setting a plurality of fifth measuring points on the right tooth surface of the spherical gear intermediate tooth to obtain respective fifth coordinate positions of the plurality of fifth measuring points; Determining origin coordinates of a measurement coordinate system based on the plurality of first coordinate positions, establishing a first plane of the ball gear based on the plurality of second coordinate positions and the plurality of third coordinate positions; Determining a measurement coordinate system based on origin coordinates of the measurement coordinate system, the first plane and the second plane; Calculating a theoretical tooth profile, a theoretical tooth direction, a theoretical tooth thickness and a theoretical tooth pitch based on a theoretical coordinate system, and calculating an actual tooth profile, an actual tooth direction, an actual tooth thickness and an actual tooth pitch based on the measured coordinate system; And calculating deviations among the theoretical tooth profile, the actual tooth profile, the theoretical tooth direction, the actual tooth direction, the theoretical tooth thickness, the actual tooth thickness and the theoretical tooth pitch and the actual tooth pitch to obtain deviation results of the tooth profile, the tooth direction, the tooth thickness and the tooth pitch.
2. The three degree of freedom spherical gear tooth surface error measurement method 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 three degree of freedom ball gear tooth surface error measurement method of claim 1 wherein the establishing a first plane of the ball gear based on the plurality of second coordinate positions and the plurality of third coordinate positions comprises: 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 first plane construction coefficient; and establishing a first plane of the ball gear through the first plane construction coefficient.
4. The three degree of freedom spherical gear tooth surface error measurement method according to claim 1, wherein the determining a measurement coordinate system based on origin coordinates of the measurement coordinate system, the first plane and the second plane includes: Determining an x-axis, a y-axis, and a z-axis of a measurement coordinate system based on the first plane and the second plane; and establishing a measurement coordinate system according to the origin coordinate of the measurement coordinate system and the x-axis, the y-axis and the z-axis of the measurement coordinate system.
5. The three degree of freedom spherical gear tooth surface error measurement method of claim 1 wherein the calculating of the actual tooth profile, the actual tooth direction, the actual tooth thickness and the actual tooth pitch based on the measurement coordinate system includes: Measuring to obtain an actual tooth profile based on the theoretical tooth profile and the measurement coordinate system, and measuring to obtain an actual tooth direction based on the theoretical tooth direction and the measurement coordinate system; Setting two measurement reference points on each tooth surface of the three-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 three degree of freedom spherical gear tooth surface error measurement method of claim 5 wherein the calculating an actual tooth thickness and an actual tooth pitch from the target distance and the spatial position comprises: 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 three degree of freedom spherical gear tooth surface error measurement method of claim 5 wherein the calculating an actual tooth thickness and an actual tooth pitch from the target distance and the spatial position comprises: 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 three degree of freedom spherical gear tooth surface error measurement system, the system comprising: The data acquisition module is used for setting a plurality of first measuring points on the top surface of the ball gear tooth and acquiring first coordinate positions of the first measuring points; setting a plurality of second measuring points on the upper tooth surface of the ball gear intermediate tooth to obtain respective second coordinate positions of the plurality of second measuring points, setting a plurality of third measuring points on the lower tooth surface of the ball gear intermediate tooth to obtain respective third coordinate positions of the plurality of third measuring points, setting a plurality of fourth measuring points on the left tooth surface of the ball gear intermediate tooth to obtain respective fourth coordinate positions of the plurality of fourth measuring points, setting a plurality of fifth measuring points on the right tooth surface of the ball gear intermediate tooth to obtain respective fifth coordinate positions of the plurality of fifth measuring points; The plane establishing module is used for determining an origin coordinate of a measurement coordinate system based on a plurality of first coordinate positions, establishing a first plane of the ball gear based on a plurality of second coordinate positions and a plurality of third coordinate positions, and establishing a second plane of the ball gear based on a plurality of fourth coordinate positions and a plurality of fifth coordinate positions; A coordinate system determining module for determining a measurement coordinate system based on origin coordinates of the measurement coordinate system, the first plane and the second plane; The data calculation module is used for calculating a theoretical tooth profile, a theoretical tooth direction, a theoretical tooth thickness and a theoretical tooth pitch based on a theoretical coordinate system, and calculating an actual tooth profile, an actual tooth direction, an actual tooth thickness and an actual tooth pitch based on the measurement coordinate system; The deviation calculation module is used for calculating deviations among the theoretical tooth profile, the actual tooth profile, the theoretical tooth direction, the actual tooth direction, the theoretical tooth thickness, the actual tooth thickness and the theoretical tooth pitch, and the actual tooth pitch, and obtaining deviation results of the tooth profile, the tooth direction, the tooth thickness and the tooth pitch.
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 three 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 three-degree-of-freedom spherical gear tooth surface error measurement method according to any one of claims 1 to 7.

Description

Three-degree-of-freedom spherical gear tooth surface error measurement method, system, equipment and medium Technical Field The application relates to the technical field of spherical gear tooth surface error measurement, in particular to a three-degree-of-freedom spherical gear tooth surface error measurement method, system, equipment and medium. 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 three-degree-of-freedom spherical gears, the measuring accuracy is lower. Disclosure of Invention The application aims to provide a three-degree-of-freedom spherical gear tooth surface error measurement method, a system, equipment and a medium, which can improve the accuracy of three-degree-of-freedom spherical gear tooth surface error measurement. In a first aspect, an embodiment of the present application provides a three-degree-of-freedom spherical gear tooth surface error measurement method, where the method includes: Setting a plurality of first measuring points on the top surface of a spherical gear tooth to obtain respective first coordinate positions of the plurality of first measuring points, setting a plurality of second measuring points on the upper tooth surface of a spherical gear intermediate tooth to obtain respective second coordinate positions of the plurality of second measuring points, setting a plurality of third measuring points on the lower tooth surface of the spherical gear intermediate tooth to obtain respective third coordinate positions of the plurality of third measuring points, setting a plurality of fourth measuring points on the left tooth surface of the spherical gear intermediate tooth to obtain respective fourth coordinate positions of the plurality of fourth measuring points, setting a plurality of fifth measuring points on the right tooth surface of the spherical gear intermediate tooth to obtain respective fifth coordinate positions of the plurality of fifth measuring points; Determining origin coordinates of a measurement coordinate system based on the plurality of first coordinate positions, establishing a first plane of the ball gear based on the plurality of second coordinate positions and the plurality of third coordinate positions; Determining a measurement coordinate system based on origin coordinates of the measurement coordinate system, the first plane and the second plane; Calculating a theoretical tooth profile, a theoretical tooth direction, a theoretical tooth thickness and a theoretical tooth pitch based on a theoretical coordinate system, and calculating an actual tooth profile, an actual tooth direction, an actual tooth thickness and an actual tooth pitch based on the measured coordinate system; And calculating deviations among the theoretical tooth profile, the actual tooth profile, the theoretical tooth direction, the actual tooth direction, the theoretical tooth thickness, the actual tooth thickness and the theoretical tooth pitch and the actual tooth pitch to obtain deviation results of the tooth profile, the tooth direction, the tooth thickness and the tooth pitch. 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, the establishing a first plane of the ball gear based on the plurality of the second coordinate positions and the plurality of the third coordinate positions includes: constructing a least squares equati