Three-degree-of-freedom spherical gear tooth surface error measurement method, system, device and medium

Abstract

The application discloses a three-degree-of-freedom spherical gear tooth surface error measurement method, system, device and medium, the method determines the origin coordinates of the measurement coordinate system based on a plurality of first coordinate positions, establishes the first plane of the spherical gear based on a plurality of second coordinate positions and a plurality of third coordinate positions, establishes the second plane of the spherical gear based on a plurality of fourth coordinate positions and a plurality of fifth coordinate positions; determine the measurement coordinate system based on the origin coordinates of the measurement coordinate system, the first plane and the second plane; calculate the theoretical tooth profile, the theoretical tooth direction, the theoretical tooth thickness and the theoretical tooth spacing based on the theoretical coordinate system, calculate the actual tooth profile, the actual tooth direction, the actual tooth thickness and the actual tooth spacing based on the measurement coordinate system; calculate the deviation between the theoretical tooth profile and the actual tooth profile, the theoretical tooth direction and the actual tooth direction, the theoretical tooth thickness and the actual tooth thickness, and the theoretical tooth spacing and the actual tooth spacing, and obtain the deviation result. The application can improve the accuracy of three-degree-of-freedom spherical gear tooth surface error measurement.

Description

Technical Field

[0001] This application relates to the field of ball gear tooth surface error measurement technology, and in particular to a method, system, device and medium for measuring the tooth surface error of a three-degree-of-freedom ball gear. Background Technology

[0002] Spherical gear technology is revolutionary for enhancing the core performance of next-generation robots, especially high-precision industrial robots and robots operating in special environments. Its importance is directly related to the trade-off between flexibility, rigidity, and compactness in robot joints. The unique two-degree-of-freedom spatial meshing characteristic of spherical gears enables two-dimensional composite motion around intersecting axes within a single joint, bringing a breakthrough to robot joint design. Spherical gears significantly simplify joint structures, achieving more complex and dexterous movements with fewer parts and a more compact size.

[0003] However, existing technologies are mainly used to measure tooth surface errors of traditional gear mechanisms such as cylindrical gears and bevel gears. Ball gears are quite different from traditional gear mechanisms. If existing domestic and foreign measurement methods or software are used to measure the tooth surface error of three-degree-of-freedom ball gears, the measurement accuracy will be relatively low. Summary of the Invention

[0004] This application aims to provide a method, system, device, and medium for measuring the tooth surface error of a three-degree-of-freedom ball gear, which can improve the accuracy of measuring the tooth surface error of a three-degree-of-freedom ball gear.

[0005] In a first aspect, embodiments of this application provide a method for measuring the tooth surface error of a three-degree-of-freedom ball gear, the method comprising:

[0006] Multiple first measurement points are set on the top surface of the ball gear teeth to obtain the first coordinate position of each of the multiple first measurement points; multiple second measurement points are set on the upper tooth surface of the middle tooth of the ball gear to obtain the second coordinate position of each of the multiple second measurement points; multiple third measurement points are set on the lower tooth surface of the middle tooth of the ball gear to obtain the third coordinate position of each of the multiple third measurement points; multiple fourth measurement points are set on the left tooth surface of the middle tooth of the ball gear to obtain the fourth coordinate position of each of the multiple fourth measurement points; and multiple fifth measurement points are set on the right tooth surface of the middle tooth of the ball gear to obtain the fifth coordinate position of each of the multiple fifth measurement points.

[0007] Based on multiple first coordinate positions, the origin coordinates of the measurement coordinate system are determined; based on multiple second coordinate positions and multiple third coordinate positions, a first plane of the ball gear is established; based on multiple fourth coordinate positions and multiple fifth coordinate positions, a second plane of the ball gear is established.

[0008] The measurement coordinate system is determined based on the origin coordinates of the measurement coordinate system, the first plane, and the second plane;

[0009] The theoretical tooth profile, theoretical tooth direction, theoretical tooth thickness, and theoretical tooth pitch are calculated based on the theoretical coordinate system, and the actual tooth profile, actual tooth direction, actual tooth thickness, and actual tooth pitch are calculated based on the measurement coordinate system.

[0010] The deviations between the theoretical tooth profile and the actual tooth profile, the theoretical tooth direction and the actual tooth direction, the theoretical tooth thickness and the actual tooth thickness, and the theoretical tooth pitch and the actual tooth pitch are calculated to obtain the deviation results of the tooth profile, tooth direction, tooth thickness and tooth pitch respectively.

[0011] In some implementations, determining the origin coordinates of the measurement coordinate system based on a plurality of first coordinate positions includes:

[0012] Preset the origin coordinates of the measurement coordinate system;

[0013] By fitting the origin coordinates with each of the first coordinate positions, spatial surface equations for multiple spheres are constructed.

[0014] Based on the spatial surface equations of the multiple spheres, an objective function is constructed, and the objective function is minimized to obtain the origin coordinates of the measurement coordinate system.

[0015] In some embodiments, establishing the first plane of the ball gear based on a plurality of second coordinate positions and a plurality of third coordinate positions includes:

[0016] Based on multiple second coordinate positions and multiple third coordinate positions, a least squares equation is constructed;

[0017] Taking the minimum value of the least squares equation yields the first plane construction coefficients;

[0018] The first plane of the ball gear is established by constructing coefficients using the first plane.

[0019] In some embodiments, determining the measurement coordinate system based on the origin coordinates of the measurement coordinate system, the first plane, and the second plane includes:

[0020] Based on the first plane and the second plane, the x-axis, y-axis and z-axis of the measurement coordinate system are determined;

[0021] A measurement coordinate system is established based on the origin coordinates and the x, y, and z axes of the measurement coordinate system.

[0022] In some embodiments, calculating the actual tooth profile, actual tooth direction, actual tooth thickness, and actual tooth pitch based on the measurement coordinate system includes:

[0023] Based on the theoretical tooth profile and the measurement coordinate system, the actual tooth profile is measured, and based on the theoretical tooth direction and the measurement coordinate system, the actual tooth direction is measured.

[0024] Two measurement reference points are set on each tooth surface of a three-degree-of-freedom ball gear to obtain the target distance from each measurement reference point to the origin of the measurement coordinate system and the spatial position of each measurement reference point.

[0025] Calculate the actual tooth thickness and actual tooth pitch based on the target distance and the spatial position.

[0026] In some implementations, calculating the actual tooth thickness and actual tooth pitch based on the target distance and the spatial position includes:

[0027] The actual tooth thickness angle of a single tooth is calculated by using the x-axis and y-axis values ​​of the spatial positions of each tooth surface corresponding to two measurement reference points;

[0028] Multiply the actual tooth thickness angle by the target distance to obtain the actual tooth thickness of a single tooth.

[0029] In some implementations, calculating the actual tooth thickness and actual tooth pitch based on the target distance and the spatial position includes:

[0030] The actual tooth pitch angle of a single tooth is calculated by using the x-axis and y-axis values ​​of the second measurement reference points of two adjacent tooth surfaces in their respective spatial positions.

[0031] Multiply the actual tooth pitch angle of the single tooth by the target distance to obtain the actual tooth pitch of the single tooth;

[0032] The actual tooth pitch angle of multiple teeth is calculated by using the x-axis and y-axis values ​​of the second measurement reference point on the last tooth surface and the second measurement reference point on the first tooth surface in their respective spatial positions.

[0033] The actual tooth pitch angle of the multiple teeth is multiplied by the target distance to obtain the actual tooth pitch of the multiple teeth.

[0034] Secondly, embodiments of this application also provide a three-degree-of-freedom ball gear tooth surface error measurement system, the system comprising:

[0035] The data acquisition module is used to set multiple first measurement points on the top surface of the ball gear teeth and obtain the first coordinate position of each of the multiple first measurement points; set multiple second measurement points on the upper tooth surface of the middle tooth of the ball gear and obtain the second coordinate position of each of the multiple second measurement points; set multiple third measurement points on the lower tooth surface of the middle tooth of the ball gear and obtain the third coordinate position of each of the multiple third measurement points; set multiple fourth measurement points on the left tooth surface of the middle tooth of the ball gear and obtain the fourth coordinate position of each of the multiple fourth measurement points; and set multiple fifth measurement points on the right tooth surface of the middle tooth of the ball gear and obtain the fifth coordinate position of each of the multiple fifth measurement points.

[0036] A plane establishment module is used to determine the origin coordinates of the measurement coordinate system based on multiple first coordinate positions; establish a first plane of the ball gear based on multiple second coordinate positions and multiple third coordinate positions; and establish a second plane of the ball gear based on multiple fourth coordinate positions and multiple fifth coordinate positions.

[0037] The coordinate system determination module is used to determine the measurement coordinate system based on the origin coordinates of the measurement coordinate system, the first plane, and the second plane;

[0038] The data calculation module is used to calculate the theoretical tooth profile, theoretical tooth direction, theoretical tooth thickness, and theoretical tooth pitch based on the theoretical coordinate system, and to calculate the actual tooth profile, actual tooth direction, actual tooth thickness, and actual tooth pitch based on the measurement coordinate system.

[0039] The deviation calculation module is used to calculate the deviations between the theoretical tooth profile and the actual tooth profile, the theoretical tooth direction and the actual tooth direction, the theoretical tooth thickness and the actual tooth thickness, and the theoretical tooth pitch and the actual tooth pitch, and obtain the deviation results for each of the tooth profile, tooth direction, tooth thickness and tooth pitch.

[0040] Thirdly, embodiments of this application also provide an electronic device, including at least one control processor and a memory for communicatively connecting to the at least one control processor; the memory stores instructions executable by the at least one control processor, which, when executed by the at least one control processor, enable the at least one control processor to perform a three-degree-of-freedom ball gear tooth surface error measurement method as described above.

[0041] Fourthly, embodiments of this application also provide a computer-readable storage medium storing computer-executable instructions for causing a computer to execute a three-degree-of-freedom ball gear tooth surface error measurement method as described above.

[0042] Compared with the prior art, this application has the following beneficial effects:

[0043] This application establishes the origin coordinates of the measurement coordinate system based on multiple first coordinate positions, establishes the first plane of the ball gear based on multiple second and third coordinate positions, and establishes the second plane of the ball gear based on multiple fourth and fifth coordinate positions. The measurement coordinate system is then determined based on the origin coordinates, the first plane, and the second plane. By setting multiple measurement points, an accurate measurement coordinate system can be established, laying a solid data foundation for subsequent deviation calculations. Furthermore, the theoretical tooth profile, theoretical tooth direction, theoretical tooth thickness, and theoretical tooth pitch are calculated based on the theoretical coordinate system. The actual tooth profile, actual tooth direction, actual tooth thickness, and actual tooth pitch are calculated. The deviations between the theoretical tooth profile and the actual tooth profile, theoretical tooth direction and actual tooth direction, theoretical tooth thickness and actual tooth thickness, and theoretical tooth pitch and actual tooth pitch are also calculated. The deviation results of each tooth profile, tooth direction, tooth thickness, and tooth pitch are obtained. By using an accurate measurement coordinate system, the accurate actual tooth profile, actual tooth direction, actual tooth thickness, and actual tooth pitch can be measured, thereby calculating the accurate deviation results of each tooth profile, tooth direction, tooth thickness, and tooth pitch. This improves the accuracy of three-degree-of-freedom ball gear tooth surface error measurement and provides important support for the machining accuracy of three-degree-of-freedom ball gears. Attached Figure Description

[0044] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0045] Figure 1 This is a schematic flowchart of an embodiment of the three-degree-of-freedom ball gear tooth surface error measurement method provided in this application;

[0046] Figure 2 This is a schematic diagram of the theoretical coordinate system of a three-degree-of-freedom ball gear in the preferred embodiment of the three-degree-of-freedom ball gear tooth surface error measurement method provided in this application;

[0047] Figure 3 This is a schematic diagram of the origin of the ball gear measurement coordinate system in the preferred embodiment of the three-degree-of-freedom ball gear tooth surface error measurement method provided in this application;

[0048] Figure 4 This is a schematic diagram of the ball gear measurement coordinate axis in the preferred embodiment of the three-degree-of-freedom ball gear tooth surface error measurement method provided in this application;

[0049] Figure 5 This is a schematic diagram of the ball gear tooth surface measurement reference point in the preferred embodiment of the three-degree-of-freedom ball gear tooth surface error measurement method provided in this application;

[0050] Figure 6 This is a schematic diagram of ball gear profile measurement in the preferred embodiment of the three-degree-of-freedom ball gear tooth surface error measurement method provided in this application;

[0051] Figure 7 This is a schematic diagram of tooth profile error evaluation in the preferred embodiment of the three-degree-of-freedom ball gear tooth surface error measurement method provided in this application;

[0052] Figure 8 This is a schematic diagram of ball gear tooth direction measurement in the preferred embodiment of the three-degree-of-freedom ball gear tooth surface error measurement method provided in this application;

[0053] Figure 9 This is a schematic diagram of tooth direction error evaluation in the preferred embodiment of the three-degree-of-freedom ball gear tooth surface error measurement method provided in this application;

[0054] Figure 10 This is a schematic diagram of the included angle of a single tooth pitch of a ball gear in the preferred embodiment of the three-degree-of-freedom ball gear tooth surface error measurement method provided in this application;

[0055] Figure 11 This is a schematic diagram of an embodiment of the three-degree-of-freedom ball gear tooth surface error measurement system provided in this application;

[0056] Figure 12 This is a schematic diagram of the structure of an embodiment of the electronic device provided in this application. Detailed Implementation

[0057] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0058] In the description of this application, the use of terms such as "first," "second," etc., is for the purpose of distinguishing technical features only and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or the order of the technical features indicated.

[0059] In the description of this application, it should be understood that the orientation descriptions, such as up, down, etc., are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0060] In the description of this application, it should be noted that, unless otherwise explicitly defined, terms such as "setup," "installation," and "connection" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this application in conjunction with the specific content of the technical solution.

[0061] To address the problem of low accuracy in measuring the tooth surface error of three-degree-of-freedom ball gears in related technologies, this application proposes a method, system, equipment, and medium for measuring the tooth surface error of three-degree-of-freedom ball gears.

[0062] Reference Figure 1 This application provides a schematic flowchart of a method for measuring the tooth surface error of a three-degree-of-freedom ball gear. This method is applied to electronic devices, such as servers or mobile terminals. Figure 1 As shown, the method for measuring the tooth surface error of a three-degree-of-freedom ball gear may include the following steps S101 to S105.

[0063] Step S101: Set multiple first measurement points on the top surface of the ball gear teeth and obtain the first coordinate position of each of the multiple first measurement points; set multiple second measurement points on the upper tooth surface of the middle tooth of the ball gear and obtain the second coordinate position of each of the multiple second measurement points; set multiple third measurement points on the lower tooth surface of the middle tooth of the ball gear and obtain the third coordinate position of each of the multiple third measurement points; set multiple fourth measurement points on the left tooth surface of the middle tooth of the ball gear and obtain the fourth coordinate position of each of the multiple fourth measurement points; set multiple fifth measurement points on the right tooth surface of the middle tooth of the ball gear and obtain the fifth coordinate position of each of the multiple fifth measurement points.

[0064] Specifically, the tooth tip of the spherical gear is a spherical surface, and a series of measurement points (i.e., the first measurement point) are planned on the tooth tip of the spherical gear. A measuring rod is used to measure and record the coordinate positions (i.e., the first coordinate positions) of these measurement points. A series of theoretical measurement points are planned on the upper and lower tooth surfaces of the middle tooth of the ball gear. (i.e., the second measurement point) and (i.e., the third measurement point) Using a measuring rod, the coordinate positions of these theoretical measurement points are measured and recorded to obtain the coordinate system position of the actual measurement point. (i.e., the second coordinate position) and (i.e., the third coordinate position). A series of measurement points are planned on the left and right tooth surfaces of the middle tooth of the spherical gear. (i.e., the fourth measurement point) and (i.e., the fifth measurement point) Using a measuring rod, the coordinate positions of these theoretical measurement points are measured and recorded to obtain the coordinate system position of the actual measurement point. (i.e., the fourth coordinate position) and (i.e., the fifth coordinate position).

[0065] Step S102: Determine the origin coordinates of the measurement coordinate system based on multiple first coordinate positions; establish the first plane of the ball gear based on multiple second coordinate positions and multiple third coordinate positions; establish the second plane of the ball gear based on multiple fourth coordinate positions and multiple fifth coordinate positions.

[0066] In this embodiment, the origin coordinates of the preset measurement coordinate system are... The process involves fitting the origin coordinates to each first coordinate position to construct spatial surface equations for multiple spheres. Based on these equations, an objective function is constructed and minimized to obtain the origin coordinates of the measurement coordinate system. Least square equations are then constructed based on multiple second and third coordinate positions. Minimizing these equations yields the first plane construction coefficients, which are used to establish the first plane of the spherical gear. Similarly, least square equations are constructed based on multiple fourth and fifth coordinate positions. Minimizing these equations yields the second plane construction coefficients, which are used to establish the second plane of the spherical gear. By setting multiple measurement points, accurate origin coordinates of the measurement coordinate system can be determined, and accurate first and second planes can be established, laying a solid data foundation for establishing an accurate measurement coordinate system later.

[0067] The above fitting of the origin coordinates and each first coordinate position constructs the spatial surface equations of multiple spheres as follows:

[0068] ;

[0069] in, Indicates the center point of the ball gear coordinates This represents the radius of the actual tip circle of the ball gear.

[0070] Based on the spatial surface equations of multiple spheres, the objective function is constructed as follows:

[0071] ;

[0072] Where n is the number of measurement points, The center point of the ball gear can be found using the least squares method, where the number is real. coordinates .

[0073] The above-mentioned least squares equations are constructed based on multiple second and third coordinate positions; the minimum value of the least squares equations is taken to obtain the first plane construction coefficients; then, the first plane of the ball gear is established through the first plane construction coefficients, specifically including:

[0074] The least squares equation can be constructed as follows:

[0075] ;

[0076] Among them, coefficient , and The unknown is (i.e., the first plane construction coefficient), and m is the number of the second and third measurement points. The x, y, and z axis values ​​represent the second coordinate position. These represent the x, y, and z axis values ​​of the third coordinate position. When the least squares equation takes its minimum value... Then we obtain the well-posed equation, which can be solved to obtain the solution. , and Substituting into the plane equation:

[0077] ;

[0078] The plane is a ball gear. Plane (i.e., the first plane).

[0079] The above process constructs a least squares equation based on multiple fourth and fifth coordinate positions. The minimum value of the least squares equation is taken to obtain the coefficients for constructing the second plane. Then, the second plane of the ball gear is established through the coefficients for constructing the second plane. This process is similar to that of establishing the first plane of the ball gear, and will not be repeated here.

[0080] Step S103: Determine the measurement coordinate system based on the origin coordinates, the first plane, and the second plane.

[0081] In this embodiment, the x-axis, y-axis, and z-axis of the measurement coordinate system are determined based on the first and second planes. The measurement coordinate system is then established according to the coordinates of its origin and the x-axis, y-axis, and z-axis. By setting multiple measurement points, an accurate measurement coordinate system can be established, laying a solid data foundation for subsequent deviation calculations.

[0082] Step S104: Calculate the theoretical tooth profile, theoretical tooth direction, theoretical tooth thickness, and theoretical tooth pitch based on the theoretical coordinate system; and calculate the actual tooth profile, actual tooth direction, actual tooth thickness, and actual tooth pitch based on the measurement coordinate system.

[0083] In this embodiment, the theoretical tooth profile, theoretical tooth direction, theoretical tooth thickness, and theoretical tooth pitch calculated based on the theoretical coordinate system can be obtained using existing techniques known to those skilled in the art, such as the theoretical tooth surface calculation provided in the existing literature "Principle and Motion Analysis of Involute Ring Gear Transmission". This embodiment will not describe this in detail. The actual tooth profile is measured based on the theoretical tooth profile and the measurement coordinate system, and the actual tooth direction is measured based on the theoretical tooth direction and the measurement coordinate system. Two measurement reference points are set on each tooth surface of the three-degree-of-freedom ball gear to obtain the target distance from each measurement reference point to the origin of the measurement coordinate system and the spatial position of each measurement reference point. The actual tooth thickness and actual tooth pitch are calculated based on the target distance and spatial position. Wherein:

[0084] Calculate the actual tooth thickness angle of a single tooth using the x-axis and y-axis values ​​of the spatial positions of the two measurement reference points corresponding to each tooth surface; multiply the actual tooth thickness angle by the target distance to obtain the actual tooth thickness of a single tooth. Calculate the actual tooth pitch angle of a single tooth using the x-axis and y-axis values ​​of the spatial positions of the second measurement reference points of two adjacent tooth surfaces; multiply the actual tooth pitch angle of a single tooth by the target distance to obtain the actual tooth pitch of a single tooth. Calculate the actual tooth pitch angles of multiple teeth using the x-axis and y-axis values ​​of the second measurement reference point of the last tooth surface and the second measurement reference point of the first tooth surface; multiply the actual tooth pitch angles of multiple teeth by the target distance to obtain the actual tooth pitch of multiple teeth.

[0085] In this embodiment, an accurate measurement coordinate system can be used to measure the actual tooth profile, actual tooth direction, actual tooth thickness, and actual tooth pitch, thereby calculating the accurate deviation results of the tooth profile, tooth direction, tooth thickness, and tooth pitch. This improves the accuracy of the tooth surface error measurement of the three-degree-of-freedom ball gear and provides important support for the machining accuracy of the three-degree-of-freedom ball gear.

[0086] The above calculation of the actual tooth thickness angle of a single tooth, based on the x-axis and y-axis values ​​of the spatial positions of each tooth surface corresponding to two measurement reference points, is as follows:

[0087] ;

[0088] in, As a measurement reference point The x and y axis values ​​in the spatial location coordinates, As a measurement reference point The x and y axis values ​​in the spatial location coordinates, This is the actual tooth thickness angle.

[0089] The actual tooth pitch angle of a single tooth is calculated by using the x-axis and y-axis values ​​of the second measurement reference points on two adjacent tooth surfaces, respectively:

[0090] ;

[0091] in, This refers to the actual tooth pitch angle of a single tooth. As a measurement reference point The x and y axis values ​​in the spatial position coordinates.

[0092] The actual tooth pitch angle of multiple teeth is calculated using the x-axis and y-axis values ​​of the second measurement reference point on the last tooth surface and the second measurement reference point on the first tooth surface, respectively.

[0093] ;

[0094] in, As a measurement reference point The x and y axis values ​​in the spatial location coordinates, The cumulative number of teeth for a three-degree-of-freedom gear. The theoretical tooth pitch of a single tooth of a three-degree-of-freedom ball gear is given by r1, where r1 is the measurement reference point. (to the center of the three-degree-of-freedom spherical gear) The target distance.

[0095] Step S105: Calculate the deviations between the theoretical tooth profile and the actual tooth profile, the theoretical tooth direction and the actual tooth direction, the theoretical tooth thickness and the actual tooth thickness, and the theoretical tooth pitch and the actual tooth pitch, and obtain the deviation results of the tooth profile, tooth direction, tooth thickness and tooth pitch respectively.

[0096] Specifically, the theoretical tooth profile of the ball gear is evaluated for error, with the tooth profile deviation being the distance between two designed tooth profile traces obtained by encompassing the actual tooth profile within the theoretical tooth profile. The theoretical tooth direction of the ball gear is also evaluated for error, with the tooth direction deviation being the distance between two designed tooth direction traces obtained by encompassing the actual tooth direction within the theoretical tooth direction. The tooth thickness deviation of the three-degree-of-freedom ball gear is the deviation between the theoretical and actual tooth thickness of a single tooth surface. The single tooth pitch deviation of the three-degree-of-freedom ball gear is the deviation between the theoretical and actual tooth pitch of a single tooth surface. The cumulative tooth pitch deviation of the three-degree-of-freedom ball gear is the deviation between the theoretical and actual tooth pitch of multiple tooth surfaces. By calculating accurate deviations for the tooth profile, tooth direction, tooth thickness, and tooth pitch, the accuracy of the tooth surface error measurement of the three-degree-of-freedom ball gear is improved. The deviation can be the calculated result of the difference between the theoretical and actual values.

[0097] To facilitate understanding by those skilled in the art, a set of preferred embodiments is provided below:

[0098] Existing measurement software, both domestically and internationally, lacks dedicated modules for three-degree-of-freedom ball gears. Current technologies primarily measure tooth surface errors in traditional gear mechanisms such as cylindrical and bevel gears. Ball gears differ significantly from traditional gear mechanisms, leading to low accuracy when using existing measurement methods or software to measure the tooth surface error of three-degree-of-freedom ball gears. Therefore, this embodiment proposes a method for establishing a measurement coordinate system for three-degree-of-freedom ball gears, planning the measurement path, and measuring tooth surface errors. This embodiment iteratively establishes the measurement coordinate system based on the tooth profile characteristics of the three-degree-of-freedom ball gear, plans the measurement path for its tooth surface, and finally evaluates the tooth surface error based on the measurement data. Specifically, it includes:

[0099] 1. Establish the measurement coordinate system through iterative optimization.

[0100] The measurement of the tooth surface of a three-degree-of-freedom ball gear is based on a measurement coordinate system, which needs to coincide with the theoretical coordinate system as much as possible. The theoretical coordinate system of the three-degree-of-freedom ball gear is... ,like Figure 2 As shown.

[0101] First, establish the origin of the three-degree-of-freedom ball gear measurement coordinate system. The tooth tip of a spherical gear is a spherical surface. A series of measurement points (i.e., the first measurement point) are planned on the tooth tip of the spherical gear. The coordinates of these measurement points are measured and recorded using a measuring rod (i.e., the first coordinate position), such as... Figure 3 As shown, the actual measurement point coordinate system position of the ball gear (i.e., the first coordinate position). It can be represented as:

[0102] (1);

[0103] in, Indicates measurement point The x, y, and z axis values ​​are given, and T denotes the transpose. Fitting these measurement points to a sphere, the spatial surface equation of which can be expressed as:

[0104] (2);

[0105] in, Indicates the center point of the ball gear coordinates This represents the radius of the actual tip circle of the ball gear.

[0106] The center point of the spherical gear can be obtained by solving the following objective function. The objective function can be expressed as follows: (The position is given by the objective function.)

[0107] (3);

[0108] Where n is the number of measurement points, The center point of the ball gear can be found using the least squares method, where the number is real. coordinates .

[0109] Next, the coordinate axes of the measurement coordinate system for the ball gear are established. A series of theoretical measurement points are planned on the upper and lower tooth surfaces of the intermediate teeth of the ball gear. (i.e., the second measurement point) and (i.e., the third measurement point), these theoretical measurement points are located from the center of the ball gear. The distances between the theoretical measurement points are all r, where r is the pitch circle radius of the spherical gear. A measuring rod is used to measure and record the coordinate positions of these theoretical measurement points to obtain the coordinate system positions of the actual measurement points. (i.e., the second coordinate position) and (i.e., the third coordinate position) can be represented as:

[0110] (4);

[0111] (5);

[0112] The ball gear is established based on these measurement points. The plane (i.e., the first plane). Constructing the least squares equation, it can be expressed as:

[0113] (6);

[0114] Among them, coefficient , and The unknown is (i.e., the first plane construction coefficient), and m is the number of the second and third measurement points. When the least squares equation takes its minimum value... Then we obtain the well-posed equation, which can be solved to obtain the solution. , and Substituting into the plane equation:

[0115] (7);

[0116] The plane is a ball gear. flat.

[0117] Similarly, a series of measurement points are planned on the left and right tooth surfaces of the middle tooth of the ball gear. (i.e., the fourth measurement point) and (i.e., the fifth measurement point), to obtain the actual coordinate system position of the measurement point. (i.e., the fourth coordinate position) and (i.e., the fifth coordinate position) can be represented as:

[0118] (8);

[0119] (9);

[0120] The ball gear is established based on these measurement points. The plane (i.e., the second plane). Constructing the least squares equation, it can be expressed as:

[0121] (10);

[0122] Among them, coefficient , and The unknown is m, which is the number of measurement points (the fourth and fifth measurement points). When the least squares equation takes its minimum value, Then we obtain the well-posed equation, which can be solved to obtain the solution. , and Substituting into the plane equation:

[0123] (11);

[0124] The plane is a ball gear. flat.

[0125] Based on ball gears plane and A plane can determine the coordinate system of a measurement. axis, shaft and axis.

[0126] Finally, the measurement coordinate system for the ball gear was established, thus completing the measurement coordinate system setup. The establishment, such as Figure 4 As shown.

[0127] 2. Error measurement of the tooth surface of a three-degree-of-freedom ball gear.

[0128] Measurement path planning is performed on the tooth surface of a three-degree-of-freedom spherical gear. The tooth surface error measurement of a three-degree-of-freedom spherical gear mainly includes the detection of errors in tooth profile, tooth direction, tooth thickness, and tooth pitch. The measurement path for the tooth profile of the spherical gear is along the midpoint of the tooth height of a single tooth, while the measurement path for the tooth direction is along the pitch circle positions of multiple teeth.

[0129] To facilitate subsequent evaluation of the tooth surface error of the three-degree-of-freedom ball gear, it is necessary to establish measurement reference points for each tooth surface during path planning, such as... Figure 5 As shown, the measurement reference point ( (to the center of the three-degree-of-freedom spherical gear) The target distance is r1, and the measurement reference point is ( The spatial location of ) can be represented as follows:

[0130] (12);

[0131] (13);

[0132] in, As a measurement reference point Spatial location coordinates, As a measurement reference point Spatial location coordinates, As a measurement reference point The x, y, and z axis values ​​in the spatial location coordinates. As a measurement reference point The x, y, and z axis values ​​in the spatial position coordinates.

[0133] Three-degree-of-freedom ball gear tooth surface error measurement includes deviations in tooth profile, tooth direction, tooth thickness, and tooth pitch. Based on the theoretical tooth profile of the ball gear, the actual tooth profile can be measured, such as... Figure 6 As shown, the error of the theoretical tooth profile of the ball gear is evaluated. The tooth profile deviation is the distance between the two designed tooth profile traces obtained by encompassing the actual tooth profile within the theoretical tooth profile. ,like Figure 7 As shown. Similarly, based on the theoretical tooth direction of a ball gear, the actual tooth direction can be measured, such as... Figure 8 As shown, the theoretical tooth direction of the ball gear is evaluated for error. The tooth direction deviation is the distance between the two designed tooth direction traces obtained by encompassing the actual tooth direction with the theoretical tooth direction. ,like Figure 9 As shown.

[0134] It should be noted that the theoretical tooth profile, theoretical tooth direction, theoretical tooth thickness, and theoretical tooth pitch calculated based on the theoretical coordinate system in this embodiment can be obtained using existing techniques known to those skilled in the art, such as the theoretical tooth surface provided in the existing literature "Principle and Motion Analysis of Involute Ring Gear Transmission", to calculate the theoretical tooth profile, theoretical tooth direction, theoretical tooth thickness, and theoretical tooth pitch. This embodiment will not describe this in detail.

[0135] The tooth thickness deviation of a three-degree-of-freedom ball gear is the deviation between the theoretical tooth thickness and the actual tooth thickness of a single tooth, which can be expressed as:

[0136] (14);

[0137] in, The theoretical tooth thickness of a three-degree-of-freedom ball gear. The actual tooth thickness angle (i.e.) and The angle between them can be expressed as:

[0138] (15);

[0139] The pitch deviation of a single tooth in a three-degree-of-freedom ball gear is the deviation between the theoretical pitch and the actual pitch of a single tooth, which can be expressed as:

[0140] (16);

[0141] in, This represents the theoretical tooth pitch of a single tooth in a three-degree-of-freedom ball gear. For a single actual tooth pitch angle, such as Figure 10 As shown, it can be represented as:

[0142] (17);

[0143] The cumulative pitch deviation of a three-degree-of-freedom ball gear is the deviation between the theoretical pitch and the actual pitch of multiple teeth, which can be expressed as:

[0144] (18);

[0145] in, As a measurement reference point The x and y axis values ​​in the spatial location coordinates, As a measurement reference point The x and y axis values ​​in the spatial location coordinates, The cumulative number of teeth for a three-degree-of-freedom gear.

[0146] This embodiment can realize the measurement of the tooth surface of a three-degree-of-freedom ball gear and the evaluation of the tooth surface error, which improves the accuracy of the tooth surface error measurement of the three-degree-of-freedom ball gear and can provide important support for the machining accuracy of the three-degree-of-freedom ball gear.

[0147] Reference Figure 11 This application also provides a three-degree-of-freedom ball gear tooth surface error measurement system, which includes:

[0148] The data acquisition module 100 is used to set multiple first measurement points on the top surface of the ball gear teeth and obtain the first coordinate positions of each of the multiple first measurement points; set multiple second measurement points on the upper tooth surface of the middle tooth of the ball gear and obtain the second coordinate positions of each of the multiple second measurement points; set multiple third measurement points on the lower tooth surface of the middle tooth of the ball gear and obtain the third coordinate positions of each of the multiple third measurement points; set multiple fourth measurement points on the left tooth surface of the middle tooth of the ball gear and obtain the fourth coordinate positions of each of the multiple fourth measurement points; and set multiple fifth measurement points on the right tooth surface of the middle tooth of the ball gear and obtain the fifth coordinate positions of each of the multiple fifth measurement points.

[0149] The plane establishment module 200 is used to determine the origin coordinates of the measurement coordinate system based on multiple first coordinate positions; to establish the first plane of the ball gear based on multiple second coordinate positions and multiple third coordinate positions; and to establish the second plane of the ball gear based on multiple fourth coordinate positions and multiple fifth coordinate positions.

[0150] The coordinate system determination module 300 is used to determine the measurement coordinate system based on the origin coordinates, the first plane, and the second plane of the measurement coordinate system.

[0151] The data calculation module 400 is used to calculate the theoretical tooth profile, theoretical tooth direction, theoretical tooth thickness and theoretical tooth pitch based on the theoretical coordinate system, and to calculate the actual tooth profile, actual tooth direction, actual tooth thickness and actual tooth pitch based on the measurement coordinate system.

[0152] The deviation calculation module 500 is used to calculate the deviations between the theoretical tooth profile and the actual tooth profile, the theoretical tooth direction and the actual tooth direction, the theoretical tooth thickness and the actual tooth thickness, and the theoretical tooth pitch and the actual tooth pitch, and to obtain the deviation results of the tooth profile, tooth direction, tooth thickness and tooth pitch respectively.

[0153] It should be noted that since the three-degree-of-freedom ball gear tooth surface error measurement system in this embodiment is based on the same inventive concept as the three-degree-of-freedom ball gear tooth surface error measurement method described above, the corresponding content in the method embodiment is also applicable to this system embodiment, and will not be described in detail here.

[0154] Reference Figure 12 This application also provides an electronic device, which includes:

[0155] At least one memory;

[0156] At least one processor;

[0157] At least one program;

[0158] The program is stored in memory, and the processor executes at least one program to implement the three-degree-of-freedom ball gear tooth surface error measurement method described above in this disclosure.

[0159] This electronic device can be any smart terminal, including mobile phones, tablets, personal digital assistants (PDAs), and in-vehicle computers.

[0160] The electronic devices according to embodiments of this application will now be described in detail.

[0161] The processor 1600 can be implemented using a general-purpose central processing unit (CPU), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this disclosure.

[0162] The memory 1700 can be implemented as a read-only memory (ROM), static storage device, dynamic storage device, or random access memory (RAM). The memory 1700 can store the operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 1700 and called by the processor 1600 to execute the three-degree-of-freedom ball gear tooth surface error measurement method of the embodiments of this disclosure.

[0163] The input / output interface 1800 is used to implement information input and output.

[0164] The communication interface 1900 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0165] Bus 2000 transmits information between various components of the device (e.g., processor 1600, memory 1700, input / output interface 1800, and communication interface 1900);

[0166] The processor 1600, memory 1700, input / output interface 1800 and communication interface 1900 are connected to each other within the device via bus 2000.

[0167] This disclosure also provides a storage medium, which is a computer-readable storage medium storing computer-executable instructions for causing a computer to perform the above-described three-degree-of-freedom ball gear tooth surface error measurement method.

[0168] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0169] The embodiments described in this disclosure are for the purpose of more clearly illustrating the technical solutions of this disclosure and do not constitute a limitation on the technical solutions provided by this disclosure. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by this disclosure are also applicable to similar technical problems.

[0170] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this disclosure, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0171] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0172] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0173] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0174] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0175] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0176] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0177] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0178] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks. The embodiments of this application have been described in detail above with reference to the accompanying drawings, but this application is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of this application.

[0179] The embodiments of this application have been described in detail above with reference to the accompanying drawings. However, this application is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of this application.

Claims

1. A method for measuring the tooth surface error of a three-degree-of-freedom ball gear, characterized in that, The method includes: A three-degree-of-freedom spherical gear measurement coordinate system is established. Multiple first measurement points are set on the top surface of the spherical gear teeth, and their respective first coordinate positions are obtained using a probe. Multiple second measurement points are set on the upper tooth surface of the middle tooth of the spherical gear, and their respective second coordinate positions are obtained using a probe. Multiple third measurement points are set on the lower tooth surface of the middle tooth of the spherical gear, and their respective third coordinate positions are obtained using a probe. Multiple fourth measurement points are set on the left tooth surface of the middle tooth of the spherical gear, and their respective fourth coordinate positions are obtained using a probe. Multiple fifth measurement points are set on the right tooth surface of the middle tooth of the spherical gear, and their respective fifth coordinate positions are obtained using a probe. Based on multiple first coordinate positions, the origin coordinates of the measurement coordinate system are determined; based on multiple second coordinate positions and multiple third coordinate positions, a first plane of the ball gear is established; based on multiple fourth coordinate positions and multiple fifth coordinate positions, a second plane of the ball gear is established, including: Preset the origin coordinates of the measurement coordinate system; By fitting the origin coordinates with each of the first coordinate positions, spatial surface equations for multiple spheres are constructed. Based on the spatial surface equations of the multiple spheres, an objective function is constructed, and the objective function is minimized to obtain the origin coordinates of the measurement coordinate system; Based on multiple second coordinate positions and multiple third coordinate positions, a least squares equation is constructed; Taking the minimum value of the least squares equation yields the first plane construction coefficients; The first plane of the ball gear is established by constructing coefficients using the first plane. Determining the measurement coordinate system based on the origin coordinates, the first plane, and the second plane includes: Based on the first plane and the second plane, the x-axis, y-axis and z-axis of the measurement coordinate system are determined; A measurement coordinate system is established based on the origin coordinates and the x-axis, y-axis, and z-axis of the measurement coordinate system. The theoretical tooth profile, theoretical tooth direction, theoretical tooth thickness, and theoretical tooth pitch are calculated based on the theoretical coordinate system. The actual tooth profile, actual tooth direction, actual tooth thickness, and actual tooth pitch are also calculated based on the measurement coordinate system. The measurement path for the spherical gear tooth profile is along the midpoint of the tooth height of a single tooth, and the measurement path for the spherical gear tooth direction is along the pitch circle positions of multiple teeth. Specifically, this includes: Based on the theoretical tooth profile and the measurement coordinate system, the actual tooth profile is measured, and based on the theoretical tooth direction and the measurement coordinate system, the actual tooth direction is measured. Two measurement reference points are set on each tooth surface of a three-degree-of-freedom ball gear to obtain the target distance from each measurement reference point to the origin of the measurement coordinate system and the spatial position of each measurement reference point. Based on the target distance and the spatial position, calculate the actual tooth thickness and actual tooth pitch, including: The actual tooth thickness angle of a single tooth is calculated by using the x-axis and y-axis values ​​of the spatial positions of each tooth surface corresponding to two measurement reference points; Multiply the actual tooth thickness angle by the target distance to obtain the actual tooth thickness of a single tooth; The actual tooth pitch angle of a single tooth is calculated by using the x-axis and y-axis values ​​of the second measurement reference points of two adjacent tooth surfaces in their respective spatial positions. Multiply the actual tooth pitch angle of the single tooth by the target distance to obtain the actual tooth pitch of the single tooth; The actual tooth pitch angle of multiple teeth is calculated by using the x-axis and y-axis values ​​of the second measurement reference point on the last tooth surface and the second measurement reference point on the first tooth surface in their respective spatial positions. Multiply the actual tooth pitch angle of the multiple teeth by the target distance to obtain the actual tooth pitch of the multiple teeth; The deviations between the theoretical tooth profile and the actual tooth profile, the theoretical tooth direction and the actual tooth direction, the theoretical tooth thickness and the actual tooth thickness, and the theoretical tooth pitch and the actual tooth pitch are calculated to obtain the deviation results of the tooth profile, tooth direction, tooth thickness and tooth pitch respectively.

2. A three-degree-of-freedom ball gear tooth surface error measurement system, characterized in that, The system includes: The data acquisition module is used to establish a three-degree-of-freedom ball gear measurement coordinate system. Multiple first measurement points are set on the top surface of the ball gear teeth, and the first coordinate positions of each of the multiple first measurement points are obtained using a probe. Multiple second measurement points are set on the upper tooth surface of the middle tooth of the ball gear, and the second coordinate positions of each of the multiple second measurement points are obtained using a probe. Multiple third measurement points are set on the lower tooth surface of the middle tooth of the ball gear, and the third coordinate positions of each of the multiple third measurement points are obtained using a probe. Multiple fourth measurement points are set on the left tooth surface of the middle tooth of the ball gear, and the fourth coordinate positions of each of the multiple fourth measurement points are obtained using a probe. Multiple fifth measurement points are set on the right tooth surface of the middle tooth of the ball gear, and the fifth coordinate positions of each of the multiple fifth measurement points are obtained using a probe. A plane establishment module is used to determine the origin coordinates of the measurement coordinate system based on multiple first coordinate positions; establish a first plane of the ball gear based on multiple second coordinate positions and multiple third coordinate positions; and establish a second plane of the ball gear based on multiple fourth coordinate positions and multiple fifth coordinate positions, including: Preset the origin coordinates of the measurement coordinate system; By fitting the origin coordinates with each of the first coordinate positions, spatial surface equations for multiple spheres are constructed. Based on the spatial surface equations of the multiple spheres, an objective function is constructed, and the objective function is minimized to obtain the origin coordinates of the measurement coordinate system; Based on multiple second coordinate positions and multiple third coordinate positions, a least squares equation is constructed; Taking the minimum value of the least squares equation yields the first plane construction coefficients; The first plane of the ball gear is established by constructing coefficients using the first plane. The coordinate system determination module is used to determine the measurement coordinate system based on the origin coordinates of the measurement coordinate system, the first plane, and the second plane, including: Based on the first plane and the second plane, the x-axis, y-axis and z-axis of the measurement coordinate system are determined; A measurement coordinate system is established based on the origin coordinates and the x-axis, y-axis, and z-axis of the measurement coordinate system. The data calculation module is used to calculate the theoretical tooth profile, theoretical tooth direction, theoretical tooth thickness, and theoretical tooth pitch based on the theoretical coordinate system, and to calculate the actual tooth profile, actual tooth direction, actual tooth thickness, and actual tooth pitch based on the measurement coordinate system; the measurement path for the spherical gear tooth profile is along the midpoint of the tooth height of a single tooth, and the measurement path for the spherical gear tooth direction is along the pitch circle positions of multiple teeth; specifically including: Based on the theoretical tooth profile and the measurement coordinate system, the actual tooth profile is measured, and based on the theoretical tooth direction and the measurement coordinate system, the actual tooth direction is measured. Two measurement reference points are set on each tooth surface of a three-degree-of-freedom ball gear to obtain the target distance from each measurement reference point to the origin of the measurement coordinate system and the spatial position of each measurement reference point. Based on the target distance and the spatial position, calculate the actual tooth thickness and actual tooth pitch, including: The actual tooth thickness angle of a single tooth is calculated by using the x-axis and y-axis values ​​of the spatial positions of each tooth surface corresponding to two measurement reference points; Multiply the actual tooth thickness angle by the target distance to obtain the actual tooth thickness of a single tooth; The actual tooth pitch angle of a single tooth is calculated by using the x-axis and y-axis values ​​of the second measurement reference points of two adjacent tooth surfaces in their respective spatial positions. Multiply the actual tooth pitch angle of the single tooth by the target distance to obtain the actual tooth pitch of the single tooth; The actual tooth pitch angle of multiple teeth is calculated by using the x-axis and y-axis values ​​of the second measurement reference point on the last tooth surface and the second measurement reference point on the first tooth surface in their respective spatial positions. Multiply the actual tooth pitch angle of the multiple teeth by the target distance to obtain the actual tooth pitch of the multiple teeth; The deviation calculation module is used to calculate the deviations between the theoretical tooth profile and the actual tooth profile, the theoretical tooth direction and the actual tooth direction, the theoretical tooth thickness and the actual tooth thickness, and the theoretical tooth pitch and the actual tooth pitch, and obtain the deviation results for each of the tooth profile, tooth direction, tooth thickness and tooth pitch.

3. An electronic device, characterized in that, It includes at least one control processor and a memory for communicatively connecting to the at least one control processor; the memory stores instructions executable by the at least one control processor, which, when executed by the at least one control processor, enable the at least one control processor to perform the three-degree-of-freedom ball gear tooth surface error measurement method as described in claim 1.

4. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions for causing a computer to perform the three-degree-of-freedom ball gear tooth surface error measurement method as described in claim 1.

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