Ball gear machining method, device, equipment, medium and machine tool

Abstract

The invention discloses a spherical gear machining method and device, equipment, a medium and a machine tool. The method comprises the steps that a spherical gear shaft section involute profile equation of a target spherical gear is constructed; constructing a grinding wheel shaft section involute profile equation of the grinding wheel according to the spherical gear shaft section involute profile equation; wherein the involute profile of the ball gear shaft section of the target ball gear is the same as the involute profile of the grinding wheel shaft section; planning a machining path of the grinding wheel; according to the tooth surface equation and the machining path of the grinding wheel, initial machining parameters are determined; and machining is conducted according to the initial machining parameters, the intermediate spherical gear is obtained, the tooth surface error between the tooth surface of the intermediate spherical gear and the theoretical tooth surface of the target spherical gear is obtained, error reverse adjustment machining is conducted on the intermediate spherical gear according to the tooth surface error, and the target spherical gear is obtained. Precision machining of the spherical gear can be achieved.

Description

Technical Field

[0001] This application relates to the field of machining technology, and in particular to a method, apparatus, equipment, medium and machine tool for machining ball gears. Background Technology

[0002] The ball gear was developed to meet the need for multi-degree-of-freedom transmission. In emerging fields such as robotics, biomimetic mechanics, and vector propulsion, traditional gears can only rotate around a single axis. To achieve multi-directional motion, academia and industry developed the ball gear. Ball gears significantly simplify joint structures, enabling more complex and dexterous movements with fewer parts and a more compact size. However, ball gears are a relatively new type of gear, and existing CNC machine tools, both domestically and internationally, lack dedicated closed-loop manufacturing modules for them, making precision machining difficult. Summary of the Invention

[0003] This application aims to provide a method, apparatus, equipment, medium, and machine tool for machining ball gears, which can achieve precision machining of ball gears.

[0004] A ball gear machining method according to a first aspect of this application includes: Construct the involute profile equation of the spherical gear shaft section of the target spherical gear; Based on the involute profile equation of the ball gear shaft section, the involute profile equation of the grinding wheel shaft section is constructed; wherein, the involute profile of the target ball gear shaft section is the same as the involute profile of the grinding wheel shaft section. Plan the machining path of the grinding wheel; Based on the tooth surface equation of the grinding wheel and the machining path, determine the initial machining parameters; The intermediate ball gear is processed according to the initial processing parameters. The tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear is obtained. The intermediate ball gear is then processed to adjust the error based on the tooth surface error to obtain the target ball gear.

[0005] A ball gear machining apparatus according to a second aspect embodiment of this application includes: The first construction module is used to construct the involute profile equation of the spherical gear shaft section of the target spherical gear; The second construction module is used to construct the involute profile equation of the grinding wheel shaft section based on the involute profile equation of the ball gear shaft section; wherein, the involute profile of the ball gear shaft section of the target ball gear is the same as the involute profile of the grinding wheel shaft section. The planning module is used to plan the machining path of the grinding wheel; The determination module is used to determine the initial machining parameters based on the tooth surface equation of the grinding wheel and the machining path; The machining module is used to process the intermediate ball gear according to the initial machining parameters, obtain the tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear, and perform error-adjusting machining on the intermediate ball gear according to the tooth surface error to obtain the target ball gear.

[0006] A machine tool according to a third aspect of this application includes a machine tool body and a controller, the controller being configured to perform the ball gear machining method as described in the first aspect of the present application.

[0007] An electronic device according to a fourth aspect of this application includes a processor and a memory, the memory storing a program or instructions executable on the processor, the program or instructions, when executed by the processor, implementing the steps of the ball gear machining method as described in any of the first aspect embodiments above.

[0008] A computer-readable storage medium according to a fifth aspect embodiment of the present application stores computer-executable instructions for performing the ball gear machining method as described in the first aspect embodiment above.

[0009] In this embodiment, based on the tooth profile characteristics of the ball gear, the profile of the grinding wheel is designed and the machining path of the grinding wheel is planned, which can avoid introducing theoretical machining errors and improve the machining accuracy of the ball gear. In addition, the intermediate ball gear obtained by preliminary machining is subjected to error detection to obtain the tooth surface error between its tooth surface and the theoretical tooth surface of the target ball gear. Then, based on the obtained tooth surface error, error back-adjustment correction is performed to achieve precision machining of the target ball gear and realize intelligent manufacturing.

[0010] Other features and advantages of this application will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing this application. Attached Figure Description

[0011] 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: Figure 1 This is a schematic flowchart of an embodiment of the ball gear machining method of this application; Figure 2 This is a schematic diagram of the ball gear structure of an embodiment of the ball gear machining method of this application; Figure 3 This is a schematic diagram of the cross-sectional profile of a ball gear according to an embodiment of the ball gear machining method of this application; Figure 4 This is a schematic diagram of the grinding wheel structure of an embodiment of the ball gear machining method of this application; Figure 5This is a schematic diagram of the ball gear machining process according to an embodiment of the ball gear machining method of this application; Figure 6 This is a schematic diagram of the ball gear machining path according to an embodiment of the ball gear machining method of this application; Figure 7 This is a schematic diagram of tooth surface error in an embodiment of the ball gear machining method of this application; Figure 8 This is a schematic diagram of the machine tool structure of an embodiment of the ball gear machining method of this application; Figure 9 This is a schematic diagram of an embodiment of the ball gear processing apparatus of this application; Figure 10 This is a schematic diagram of the hardware structure of an embodiment of the electronic device of this application. Detailed Implementation

[0012] 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.

[0013] 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.

[0014] 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.

[0015] 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.

[0016] The technical solution of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described below are some embodiments of this application, not all embodiments.

[0017] See below. Figures 1 to 7 The embodiments of this application will be further described below. This application proposes a method for machining ball gears, including the following steps: Step 101: Construct the involute profile equation of the target ball gear shaft section; Step 102: Based on the involute profile equation of the ball gear shaft section, construct the involute profile equation of the grinding wheel shaft section; wherein, the involute profile of the target ball gear shaft section is the same as the involute profile of the grinding wheel shaft section. Step 103: Plan the machining path of the grinding wheel; Step 104: Determine the initial machining parameters based on the tooth surface equation of the grinding wheel and the machining path; Step 105: Machining according to the initial machining parameters to obtain the intermediate ball gear, obtaining the tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear, and performing error-adjusting machining on the intermediate ball gear according to the tooth surface error to obtain the target ball gear.

[0018] In this embodiment, based on the tooth profile characteristics of the ball gear, the profile of the grinding wheel is designed and the machining path of the grinding wheel is planned, which can avoid introducing theoretical machining errors and improve the machining accuracy of the ball gear. In addition, the intermediate ball gear obtained by preliminary machining is subjected to error detection to obtain the tooth surface error between its tooth surface and the theoretical tooth surface of the target ball gear. Then, based on the obtained tooth surface error, error back-adjustment correction is performed to achieve precision machining of the target ball gear and realize intelligent manufacturing.

[0019] The above equation for the involute profile of the spherical gear shaft section can be understood as follows: Figure 2 As shown, a ball gear is a type of gear that can rotate in all directions, breaking through the limitation of traditional gears that can only rotate around a single axis. Figure 3 As shown, the axial section profile of a ball gear is an involute, so the tooth surface of a ball gear can be represented by the equation of the involute profile of the axial section of the ball gear.

[0020] The above-mentioned involute profile equation of the grinding wheel shaft section is constructed based on the involute profile equation of the ball gear shaft section. It can be understood that, in order to ensure that the machined ball gear tooth surface accurately reproduces the target profile, the involute profile of the grinding wheel shaft section, as the tool directly involved in cutting, must strictly match the involute profile of the target ball gear shaft section. Therefore, when designing the grinding wheel, the involute profile equation of the grinding wheel shaft section can be constructed based on the involute profile equation of the ball gear shaft section, such as... Figure 4 As shown. In this way, when the grinding wheel cuts the ball blank according to the planned machining path, its profile can be accurately machined onto the tooth surface of the ball gear, thus avoiding theoretical machining errors caused by the mismatch between the grinding wheel profile and the target tooth profile from the source, laying the foundation for obtaining high-precision tooth surfaces in the future.

[0021] The above-mentioned planning of the grinding wheel's machining path can be understood as a key step in ensuring the machining accuracy and integrity of the ball gear tooth surface. Because ball gears have a complex spatial curved surface structure, their tooth grooves are evenly distributed circumferentially on the spherical surface. Therefore, the grinding wheel's machining path needs to precisely match the tooth groove position and shape of the ball gear.

[0022] Specifically, since the profile of the grinding wheel is consistent with the axial section profile of the ball gear, the machining path of the grinding wheel can be planned during grinding, such as... Figure 5 and Figure 6 As shown, this makes the grinding wheel... y c The shaft is always located in the middle of the tooth groove of the ball gear, and the center of the ball gear is... o s lie in y c On the shaft, the center of the ball gear o s relative to the origin of the grinding wheel o s The distance is always r，r Let be the pitch circle radius of the ball gear. Grinding around the ball gear once will yield one tooth groove, and similarly, other tooth grooves can be obtained by grinding.

[0023] The above-described determination of initial machining parameters based on the grinding wheel's tooth surface equation and machining path illustrates this. The grinding wheel's tooth surface equation determines the spatial shape of its cutting edge, while the machining path defines the relative motion trajectory between the grinding wheel and the ball gear blank. Together, these two elements form the basis for determining the initial machining parameters. In actual machining, given the tooth surface equation and machining path, the initial machining parameters used to input into the machine tool for machining can be solved.

[0024] The above process, based on initial machining parameters, yields an intermediate ball gear. The tooth surface error between the intermediate ball gear's tooth surface and the theoretical tooth surface of the target ball gear is then obtained. Based on this error, the intermediate ball gear is machined in reverse to obtain the target ball gear. It's important to understand that after machining the ball gear blank according to the initial parameters, only the intermediate ball gear can be obtained; the target ball gear cannot be directly obtained. This is because, during actual machining, various factors such as machine tool geometric errors, transmission system clearances, tool wear, workpiece clamping errors, cutting forces, and cutting heat inevitably cause a certain deviation between the actual tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear—this is the tooth surface error. To obtain this tooth surface error, the measured actual tooth surface data is compared with the theoretical tooth surface of the target ball gear, established using the involute profile equation of the ball gear's shaft section. The difference between the actual and theoretical positions at each measurement point is obtained, thus yielding the overall tooth surface error. Figure 7 As shown.

[0025] After obtaining the tooth surface error, error-correction machining is required based on this error. This process is essentially a closed-loop control process for error compensation. By evaluating whether the tooth surface error meets the requirements, if it does, the ball gear machining is completed, and the target ball gear is determined. If it does not meet the requirements, an error-correction optimization model is established, and the initial machining parameters are adjusted to obtain new machining parameters. The intermediate ball gear is then ground again until its tooth surface error meets the requirements, thus determining the target ball gear. This process embodies the core concepts of real-time feedback and dynamic adjustment in intelligent manufacturing, significantly improving the machining accuracy and quality stability of ball gears.

[0026] The above processing can be carried out by milling or grinding.

[0027] In some implementations, the involute profile equation of the spherical gear shaft section of the target spherical gear is constructed.

[0028] In this embodiment, such as Figure 3 As shown, establish the theoretical coordinate system S for the spherical gear. s Then, the points on the involute tooth profile can be represented by the involute profile equation of the spherical gear shaft section. Specifically, the involute profile equation of the spherical gear shaft section is constrained by the following expression: (1) Where, r s The equation representing the involute profile of the spherical gear shaft section is given. r bs Let be the base circle radius of the involute. θ 0s This is the angle parameter at the intersection of the involute and the base circle. θ s For the involute tooth surface parameters, in formula (1) above, the left tooth profile corresponds to the upper symbol "+" in the upper and lower symbols "±", and the right tooth profile corresponds to the lower symbol "-". The angle parameter at the intersection of the involute and the base circle is... θ 0s The tooth width of the involute on the base circle can be determined, and its specific value is related to the number of teeth of the ball gear. For a standard involute, it can be constrained by the following expression: (2) in, N s It is the number of teeth on a ball gear. α It is the pressure angle. invα As an involute function, it can be expressed as: (3) In summary, the involute profile equation of the spherical gear shaft section can be obtained through equations (1) to (3) above.

[0029] In some embodiments, the tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear is obtained, and the intermediate ball gear is subjected to error-correction machining based on the tooth surface error to obtain the target ball gear, including: The intermediate ball gear is measured in-machine to obtain the first tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear; When the first tooth surface error is greater than the first threshold, based on the reverse adjustment optimization model, the machining adjustment parameters are obtained according to the initial machining parameters and the first tooth surface error. The intermediate ball gear is machined according to the machining adjustment parameters, and the process jumps to perform on-machine measurement on the intermediate ball gear to obtain the first tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear. If the first tooth surface error is less than or equal to the first threshold, the intermediate ball gear is determined as the target ball gear.

[0030] In this embodiment, the cyclical process of error measurement, error analysis, machining parameter adjustment, remachining, and remeasurement is continuously repeated until the first tooth surface error is less than or equal to the first threshold. At this point, the tooth surface accuracy of the intermediate ball gear meets the design requirements, and it can be determined as the final target ball gear. This closed-loop feedback control mechanism can effectively and gradually reduce the tooth surface error, ensuring the stability and reliability of machining accuracy, and is especially suitable for ball gear machining scenarios with extremely high precision requirements. In addition, through machine measurement technology, the tooth surface data of the intermediate ball gear can be acquired in real time during the machining process, without the need to remove the workpiece from the machine tool and transfer it to a dedicated measuring device. This significantly shortens the measurement cycle and improves the overall machining efficiency.

[0031] When grinding is used, the tooth surface of ball gears is complex, and a single grinding process is often insufficient to achieve the required tooth surface accuracy. Therefore, error compensation is required. In this embodiment, after each grinding process, the intermediate ball gear is directly measured on-machine to obtain the first tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear. The tooth surface error is evaluated to assess whether it meets the requirements, i.e., whether the error is less than a preset first threshold. If the requirements are met, the grinding process of the ball gear is completed. If the requirements are not met, the grinding parameters need to be adjusted based on the reverse adjustment optimization model, and the ball gear is ground again until the tooth surface error of the ball gear meets the requirements.

[0032] In some embodiments, the tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear is obtained, and the intermediate ball gear is subjected to error-correction machining based on the tooth surface error to obtain the target ball gear, including: A topological measurement is performed on the intermediate ball gear to obtain the second tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear; When the second tooth surface error is greater than the second threshold, based on the reverse adjustment optimization model, the machining adjustment parameters are obtained according to the initial machining parameters and the second tooth surface error. The intermediate ball gear is machined according to the machining adjustment parameters, and the process jumps to the in-machine measurement of the intermediate ball gear to obtain the second tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear. If the second tooth surface error is less than or equal to the second threshold, the intermediate ball gear is determined as the target ball gear.

[0033] In this embodiment, the cyclical process of error measurement, error analysis, machining parameter adjustment, remachining, and remeasurement is continuously repeated until the second tooth surface error is less than or equal to the second threshold. At this point, the tooth surface accuracy of the intermediate ball gear meets the design requirements, and it can be determined as the final target ball gear. This closed-loop feedback control mechanism can effectively and gradually reduce the tooth surface error, ensuring the stability and reliability of machining accuracy, and is especially suitable for ball gear machining scenarios with extremely high precision requirements. In addition, topology measurement technology focuses on accurately characterizing the overall geometry of the intermediate ball gear tooth surface, and can obtain the microscopic morphology and macroscopic contour information of the tooth surface, thereby obtaining a more comprehensive second tooth surface error.

[0034] When milling is used, the tooth surface of ball gears is complex, and a single milling operation is often insufficient to achieve the required tooth surface accuracy. Therefore, error compensation is required. In this embodiment, after each milling operation, the intermediate ball gear is directly measured on-machine to obtain the second tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear. The tooth surface error is evaluated to assess whether it meets the requirements, i.e., whether the error is less than the preset second threshold. If the requirements are met, the milling of the ball gear is completed. If the requirements are not met, the ball gear needs to be milled again based on the reverse adjustment optimization model and the milling parameters are adjusted until the tooth surface error of the ball gear meets the requirements.

[0035] In some implementations, the process of establishing the back-adjustment optimization model used for error back-adjustment processing is as follows.

[0036] Five-axis grinding machine tools such as Figure 8 As shown, it contains 6 motion axes ( A, B, C, X, Y, Z The ball gear is mounted on axis A, and the grinding wheel is mounted on axis C. To facilitate subsequent error compensation, a small variable is introduced into the CNC machine tool's motion axes. The machine tool's linkage motion containing this small variable can then be expressed as: (4) in, X, Y, Z, A, B, C Indicates the initial motion parameters of the CNC machine tool. X、 Y、 Z、 A、 B、 C Represents the minute variable parameters of a CNC machine tool. X ′ 、Y ′ 、Z ′ 、A ′ 、B ′ 、C ′ represents the motion parameters of the CNC machine tool after adjustment.

[0037] Theoretical measurement reference point C for ball gears k Actual measurement reference point C ak By aligning the theoretical and actual measurement reference points, the tooth surface error is evaluated. The tooth surface error can be expressed as: (5) Where, r a Let r be the coordinates of the measured tooth surface points of the spherical gear. s (x) represents the coordinates of the theoretical tooth surface point of the ball gear, n s (x) is the theoretical tooth surface normal vector of the ball gear, x is the CNC machine tool adjustment parameter vector, x=[ X ; Y ; Z ; A ; B ; C ].

[0038] Therefore, the following back-adjustment optimization model is established: (6) in: (7) in, m This represents the number of measurement points on the tooth surface of the ball gear.

[0039] The above-mentioned inverse adjustment optimization model can be solved using a nonlinear least squares algorithm. Specifically, the LM (Levenberg-Marquardt) algorithm or the trust region dogleg algorithm can be used.

[0040] Understandably, initially, the initial machining parameters are substituted into the initial motion parameters of the CNC machine tool in the inverse adjustment optimization model, and then the current tooth surface error is substituted into the inverse adjustment optimization model. The adjusted motion parameters of the CNC machine tool obtained by solving the inverse adjustment optimization model are used as machining adjustment parameters for machining adjustment. After machining adjustment, if the re-detected tooth surface error is still large and exceeds the preset threshold, the previously obtained machining adjustment parameters are substituted into the initial motion parameters of the CNC machine tool in the inverse adjustment optimization model, and then the current tooth surface error is substituted into the inverse adjustment optimization model. The adjusted motion parameters of the CNC machine tool obtained by solving the inverse adjustment optimization model are used as new machining adjustment parameters for machining adjustment again, until the tooth surface error meets the requirements.

[0041] In some implementations, the process of solving the problem using the LM algorithm is as follows.

[0042] Expanding equation (7) using the first-order Taylor series and simplifying it, we get: (8) Where Δx is the iteration step size, J(x) k Let be the Jacobian matrix of the objective function. For each iteration, finding the optimal Δx can be expressed as: (9) in, M (Δx) is a first-order Taylor expansion function. Adding a damping term to the objective function, it can be expressed as: (10) in, μ Here is the damping coefficient, and the damping term is given for excessively large Δ. x The penalty is set so that the derivative of the objective function is zero, resulting in: (11) This can be simplified as follows: (12) Where I is the identity matrix, H k and g k It can be represented as: (13) Define gain rate ρ , can be represented as: (14) in, ρThe numerator can represent the similarity between the first-order Taylor expansion and the true function. A larger numerator indicates a more accurate Taylor approximation, and the damping coefficient should be decreased. Conversely, a smaller numerator indicates a less accurate Taylor approximation, and the damping coefficient should be increased. μ It can be represented as: (15) Given initial value x0, convergence accuracy ε and initial damping coefficient μ By solving the optimization objective, the adjustment parameters of the machine tool motion axes can be obtained. X ′ 、Y ′ 、Z ′ 、A ′ 、B ′ 、C ′.

[0043] In some implementations, the process of solving the problem using the trust region dogleg algorithm is as follows.

[0044] Expanding equation (7) in the second order Taylor series and simplifying it, we get: (16) in, Q k Let F(x) be a second-order Taylor expansion function, d be the iteration step size, and F(x) be a second-order Taylor expansion function. k ) is the optimization model in the th k The value of the next iteration, g k and G k It can be represented as: (17) Wherein, J(x) k ) represents the Jacobian matrix of the objective function.

[0045] The second-order Taylor expansion is a second-order approximation of the original equation. The core idea is to solve for the optimal objective within a certain range using the trust-region algorithm. The trust-region subproblem can be represented as: (18) in, q k (d) is the optimization function for the trust region subproblem, d is the iteration step size, and Δ k The current trust region radius, d The parameters are for iteration; the optimization function needs to adjust the trust region radius in each iteration, and the trust region radius adjustment equation can be expressed as: (19) in, η 1, η 2, γ 1, γ 2 is the control coefficient, Δ up It is the upper limit of the trust region radius and the gain rate. r k It can be represented as: (20) In summary, by using the trust region dogleg algorithm to solve the optimization model, the adjustment parameters of the machine tool motion axes can be obtained. X ′ 、 Y ′ 、Z ′ 、A ′ 、B ′ 、C ′.

[0046] In some implementations, the tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear can be determined using a two-degree-of-freedom ball gear tooth surface error measurement method.

[0047] In some cases, the method for measuring the tooth surface error of a two-degree-of-freedom ball gear involves determining the origin coordinates of the measurement coordinate system based on multiple first coordinate positions, establishing a target plane for the ball gear containing the x-axis and y-axis based on multiple second and third coordinate positions, determining the z-axis of the measurement coordinate system using the right-hand rule based on the origin coordinates of the measurement coordinate system and the target plane, and defining the measurement coordinate system based on the origin coordinates, x-axis, y-axis, and z-axis. By setting multiple measurement points, an accurate measurement coordinate system can be established, laying a good data foundation for subsequent deviation calculations. The method also involves meshing the tooth surface of the two-degree-of-freedom ball gear, setting multiple theoretical measurement points based on the mesh and the theoretical coordinate system, and setting multiple actual measurement points based on the mesh and the measurement coordinate system. The method obtains the first measurement point position for each theoretical measurement point and the second measurement point position for each actual measurement point. Based on the first and second measurement point positions, it calculates the tooth surface deviation, the theoretical tooth thickness and theoretical tooth pitch based on the theoretical coordinate system, and the actual tooth thickness and actual tooth pitch based on the measurement coordinate system. It also calculates the deviation between the theoretical tooth thickness and the actual tooth thickness, and between the theoretical tooth pitch and the actual tooth pitch, thus obtaining the tooth thickness deviation and tooth pitch deviation. By accurately determining the first and second measurement point positions, the method calculates the accurate tooth surface deviation. The method also allows for accurate measurement of the actual tooth thickness and actual tooth pitch using the measurement coordinate system, thereby calculating the accurate tooth thickness deviation and tooth pitch deviation. This improves the accuracy of tooth surface error measurement for two-degree-of-freedom ball gears and provides important support for the machining accuracy of two-degree-of-freedom ball gears.

[0048] In some embodiments, the grinding wheel is a finger grinding wheel, and the involute profile of the spherical gear shaft section is the same as the involute profile of the end shaft section of the finger grinding wheel.

[0049] In this embodiment, a finger-shaped grinding wheel is used, and the involute profile of the spherical gear shaft section is the same as the involute profile of the end shaft section of the finger-shaped grinding wheel. The core advantage is that the end shaft section of the grinding wheel can be dressed to have an involute profile that is completely consistent with the spherical gear shaft section.

[0050] It should be noted that existing technologies often use disc grinding wheels for ball gear machining. When grinding ball gears with disc grinding wheels, there is no theoretical machining error only in the middle position. However, in non-middle positions, the disc grinding wheel will interfere with the tooth surface of the ball gear, introducing theoretical machining error. The error reaches its maximum at both ends of the ball gear. In contrast, when machining ball gears, finger grinding wheels can maintain a non-interference state with the tooth surface regardless of whether it is in the middle or at both ends, without generating theoretical machining error, and can achieve better machining results.

[0051] In some implementations, the involute profile equation of the grinding wheel's axial section is constrained by the following expression: (20) Where, r c The equation represents the involute profile of the grinding wheel's axial section. r bs Let be the base circle radius of the involute. θ 0s The angle parameter is the intersection point of the involute and the base circle. θ s These are the parameters of the involute tooth surface. r Let be the pitch circle radius of the ball gear.

[0052] In this embodiment, the involute profile equation of the grinding wheel shaft section is the key theoretical basis for ensuring that the grinding wheel can accurately machine the spherical gear tooth surface that meets the design requirements. Since the involute profile of the target spherical gear shaft section is the same as the involute profile of the grinding wheel shaft section, the involute profile equation of the grinding wheel shaft section can be obtained by translating the involute profile equation of the spherical gear shaft section, i.e., the above equation (1).

[0053] The above r bs Let be the base circle radius of the involute. θ 0s The angle parameter is the intersection point of the involute and the base circle. θ s These are the parameters of the involute tooth surface. r For the pitch circle radius of the ball gear, please refer to [reference needed]. Figure 3 As shown. In addition, for the above formula (20), the left involute profile corresponds to the upper symbol "+" in the upper and lower symbols "±", and the right involute profile corresponds to the lower symbol "-".

[0054] In some implementations, the machining path of the grinding wheel is constrained by the following expression: ;(twenty one) in, θ Here are the circumferential parameters of the grinding wheel rotating around the ball gear. k This refers to the number of teeth between the tooth groove to be machined and the intermediate tooth groove. z r is the number of teeth on a ball gear. oc Represents the origin of the grinding wheel coordinate system o c Position, r oc Represents the coordinate axes of the grinding wheel y c The location.

[0055] In this embodiment, the profile of the grinding wheel is consistent with the axial section profile of the ball gear. During grinding, if... Figure 5 and Figure 6 As shown, the grinding wheel y c The shaft is always located in the middle of the tooth groove of the ball gear, and the center of the ball gear is... o s lie in y c On the shaft, the center of the ball gear o s relative to the origin of the grinding wheel o s The distance is always r One tooth groove can be obtained by grinding one revolution along the ball gear, and other tooth grooves can be obtained by grinding in the same way. Therefore, by constraining the grinding wheel coordinate system S c The origin o c position r oc and grinding wheel coordinate axis y c position r oc This allows you to determine the machining path of the grinding wheel.

[0056] It is understandable that, for the above formula (21), refer to Figure 5 As shown, the tooth groove on the left side of the middle tooth groove corresponds to the upper symbol "+" in the upper and lower symbols "±", and the tooth groove on the right side of the middle tooth groove corresponds to the lower symbol "-". k A value of 0 indicates an intermediate tooth groove.

[0057] The ball gear machining method provided in this application can be executed by a ball gear machining device 200. This application uses the ball gear machining device 200 executing the ball gear machining method as an example to illustrate the ball gear machining device 200 provided in this application embodiment.

[0058] Please see Figure 9This is a schematic diagram of the structure of a ball gear processing device 200 provided in an embodiment of this application. Figure 9 As shown, the ball gear machining apparatus 200 includes: The first construction module 201 is used to construct the involute profile equation of the spherical gear shaft section of the target spherical gear; The second construction module 202 is used to construct the involute profile equation of the grinding wheel shaft section based on the involute profile equation of the ball gear shaft section; wherein, the involute profile of the target ball gear shaft section is the same as the involute profile of the grinding wheel shaft section. Planning module 203 is used to plan the machining path of the grinding wheel; The determination module 204 is used to determine the initial machining parameters based on the tooth surface equation of the grinding wheel and the machining path; The machining module 205 is used to process the intermediate ball gear according to the initial machining parameters, obtain the tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear, and perform error-adjusting machining on the intermediate ball gear according to the tooth surface error to obtain the target ball gear.

[0059] In some implementations, the processing module 205 can be used for: The intermediate ball gear is measured in-machine to obtain the first tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear; When the first tooth surface error is greater than the first threshold, based on the reverse adjustment optimization model, the machining adjustment parameters are obtained according to the initial machining parameters and the first tooth surface error. The intermediate ball gear is machined according to the machining adjustment parameters, and the process jumps to perform on-machine measurement on the intermediate ball gear to obtain the first tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear. If the first tooth surface error is less than or equal to the first threshold, the intermediate ball gear is determined as the target ball gear.

[0060] In some implementations, the processing module 205 can be used for: A topological measurement is performed on the intermediate ball gear to obtain the second tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear; When the second tooth surface error is greater than the second threshold, based on the reverse adjustment optimization model, the machining adjustment parameters are obtained according to the initial machining parameters and the second tooth surface error. The intermediate ball gear is machined according to the machining adjustment parameters, and the process jumps to the in-machine measurement of the intermediate ball gear to obtain the second tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear. If the second tooth surface error is less than or equal to the second threshold, the intermediate ball gear is determined as the target ball gear.

[0061] In some embodiments, the grinding wheel is a finger grinding wheel, and the involute profile of the spherical gear shaft section is the same as the involute profile of the end shaft section of the finger grinding wheel.

[0062] In some implementations, the involute profile equation of the grinding wheel's axial section is constrained by the following expression: (20) in, r bs Let be the base circle radius of the involute. θ 0s The angle parameter is the intersection point of the involute and the base circle. θ s These are the parameters of the involute tooth surface. r Let be the pitch circle radius of the ball gear.

[0063] In some implementations, the machining path of the grinding wheel is constrained by the following expression: ;(twenty one) in, θ Here are the circumferential parameters of the grinding wheel rotating around the ball gear. k This refers to the number of teeth between the tooth groove to be machined and the intermediate tooth groove. z r is the number of teeth on a ball gear. oc Represents the origin of the grinding wheel coordinate system o c Position, r oc Represents the coordinate axes of the grinding wheel y c The location.

[0064] Since the ball gear processing apparatus 200 adopts all the technical solutions of the ball gear processing method of the above embodiments, it has at least all the beneficial effects brought about by the technical solutions of the above embodiments, and will not be described in detail here.

[0065] This application provides a machine tool including a machine tool body and a controller, the controller being used to execute the ball gear machining method described above.

[0066] In some implementations, the machine tool is a five-axis grinding machine tool, such as... Figure 8 As shown.

[0067] Since the machine tool adopts all the technical solutions of the ball gear machining method of the above embodiments, it has at least all the beneficial effects brought about by the technical solutions of the above embodiments, and will not be described in detail here.

[0068] Figure 10 This is a schematic diagram of the hardware structure of the electronic device provided in the embodiments of this application.

[0069] This electronic device may include a processor 301 and a memory 302 storing computer program instructions.

[0070] Specifically, the processor 301 may include a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0071] Memory 302 may include mass storage for data or instructions. For example, and not limitingly, memory 302 may include a hard disk drive (HDD), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory 302 may include removable or non-removable (or fixed) media. Where appropriate, memory 302 may be internal or external to the integrated gateway disaster recovery device. In a particular embodiment, memory 302 is non-volatile solid-state memory.

[0072] In some embodiments, memory 302 may include read-only memory (ROM), random access memory (RAM), disk storage media device, optical storage media device, flash memory device, electrical, optical, or other physical / tangible memory storage device. Thus, generally, memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described with reference to the method according to one aspect of this disclosure.

[0073] The processor 301 reads and executes computer program instructions stored in the memory 302 to implement any of the ball gear machining methods in the above embodiments.

[0074] In one example, the electronic device may also include a communication interface 303 and a bus 310. For example, Figure 10 As shown, the processor 301, memory 302, and communication interface 303 are connected through bus 310 and complete communication with each other.

[0075] The communication interface 303 is mainly used to realize communication between various modules, devices, units and / or equipment in the embodiments of this application.

[0076] Bus 310 includes hardware, software, or both, that couples components of an online data traffic metering device together. For example, and not limitingly, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), HyperTransport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an Infinite Bandwidth Interconnect, a Low Pin Count (LPC) bus, a memory bus, a Microchannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or other suitable buses, or combinations of two or more of these. Where appropriate, bus 310 may include one or more buses. Although specific buses are described and illustrated in embodiments of this application, any suitable bus or interconnect is contemplated herein.

[0077] This electronic device can perform the ball gear machining method described in the embodiments of this application, thereby achieving a combination. Figure 1 and Figure 9 The method and apparatus for machining ball gears are described.

[0078] Furthermore, in conjunction with the ball gear machining methods described in the above embodiments, this application embodiment can provide a computer storage medium for implementation. This computer storage medium stores computer program instructions; when these computer program instructions are executed by a processor, they implement any of the ball gear machining methods described in the above embodiments.

[0079] It should be clarified that this application is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of this application is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of this application.

[0080] The functional blocks shown in the above-described block diagram can be implemented as hardware, software, firmware, or a combination thereof. When implemented in hardware, they can be electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this application are programs or code segments used to perform the required tasks. Programs or code segments can be stored on a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried on a carrier wave. "Machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, fiber optic media, radio frequency (RF) links, etc. Code segments can be downloaded via computer networks such as the Internet, intranets, etc.

[0081] It should also be noted that the exemplary embodiments mentioned in this application describe methods or systems based on a series of steps or apparatus. However, this application is not limited to the order of the above steps; that is, the steps can be performed in the order mentioned in the embodiments, or in a different order, or several steps can be performed simultaneously.

[0082] The aspects of this disclosure have been described above with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should be understood that each block in the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that these instructions, executable via the processor of the computer or other programmable data processing apparatus, enable the implementation of the functions / actions specified in one or more blocks of the flowchart illustrations and / or block diagrams. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field-programmable logic circuit. It is also understood that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can also be implemented by special-purpose hardware performing the specified functions or actions, or can be implemented by a combination of special-purpose hardware and computer instructions.

[0083] The above description is merely a specific implementation of this application. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, modules, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. It should be understood that the protection scope of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the protection scope of this application.

Claims

1. A method for machining ball gears, characterized in that, include: Construct the involute profile equation of the spherical gear shaft section of the target spherical gear; Based on the involute profile equation of the ball gear shaft section, the involute profile equation of the grinding wheel shaft section is constructed; wherein, the involute profile of the target ball gear shaft section is the same as the involute profile of the grinding wheel shaft section. Plan the machining path of the grinding wheel; Based on the tooth surface equation of the grinding wheel and the machining path, determine the initial machining parameters; The intermediate ball gear is processed according to the initial processing parameters. The tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear is obtained. The intermediate ball gear is then processed to adjust the error based on the tooth surface error to obtain the target ball gear.

2. The ball gear machining method according to claim 1, characterized in that, The step of obtaining the tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear, and performing error-adjusting machining on the intermediate ball gear based on the tooth surface error to obtain the target ball gear, includes: The intermediate ball gear is measured in-machine to obtain the first tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear; When the first tooth surface error is greater than the first threshold, based on the reverse adjustment optimization model, processing adjustment parameters are obtained according to the initial processing parameters and the first tooth surface error. The intermediate ball gear is processed according to the processing adjustment parameters, and the process jumps to the in-machine measurement of the intermediate ball gear to obtain the first tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear. If the first tooth surface error is less than or equal to the first threshold, the intermediate ball gear is determined as the target ball gear.

3. The ball gear machining method according to claim 1, characterized in that, The step of obtaining the tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear, and performing error-adjusting machining on the intermediate ball gear based on the tooth surface error to obtain the target ball gear, includes: A topological measurement is performed on the intermediate ball gear to obtain the second tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear; When the second tooth surface error is greater than the second threshold, based on the reverse adjustment optimization model, processing adjustment parameters are obtained according to the initial processing parameters and the second tooth surface error. The intermediate ball gear is processed according to the processing adjustment parameters, and the process jumps to the in-machine measurement of the intermediate ball gear to obtain the second tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear. If the second tooth surface error is less than or equal to the second threshold, the intermediate ball gear is determined as the target ball gear.

4. The ball gear machining method according to claim 1, characterized in that, The grinding wheel is a finger grinding wheel, and the involute profile of the spherical gear shaft section is the same as the involute profile of the end shaft section of the finger grinding wheel.

5. The ball gear machining method according to claim 1 or 4, characterized in that, The equation for the involute profile of the grinding wheel's axial section is constrained by the following expression: ； Where, r c The equation represents the involute profile of the grinding wheel's axial section. r bs Let be the base circle radius of the involute. θ 0s The angle parameter is the intersection point of the involute and the base circle. θ s These are the parameters of the involute tooth surface. r Let be the pitch circle radius of the ball gear.

6. The ball gear machining method according to claim 1, characterized in that, The machining path of the grinding wheel is constrained by the following expression: ； in, θ Here are the circumferential parameters of the grinding wheel's rotation around the ball gear. k This refers to the number of teeth between the tooth groove to be machined and the intermediate tooth groove. z r is the number of teeth on a ball gear. oc Represents the origin of the grinding wheel coordinate system o c Position, r oc Represents the coordinate axes of the grinding wheel y c The location.

7. A ball gear processing device, characterized in that, include: The first construction module is used to construct the involute profile equation of the spherical gear shaft section of the target spherical gear; The second construction module is used to construct the involute profile equation of the grinding wheel shaft section based on the involute profile equation of the ball gear shaft section; wherein, the involute profile of the ball gear shaft section of the target ball gear is the same as the involute profile of the grinding wheel shaft section. The planning module is used to plan the machining path of the grinding wheel; The determination module is used to determine the initial machining parameters based on the tooth surface equation of the grinding wheel and the machining path; The machining module is used to process the intermediate ball gear according to the initial machining parameters, obtain the tooth surface error between the tooth surface of the intermediate ball gear and the theoretical tooth surface of the target ball gear, and perform error-adjusting machining on the intermediate ball gear according to the tooth surface error to obtain the target ball gear.

8. A machine tool, characterized in that, It includes a machine tool body and a controller, the controller being used to perform the ball gear machining method as described in any one of claims 1 to 6.

9. An electronic device, characterized in that, It includes a processor and a memory, the memory storing a program or instructions that can run on the processor, the program or instructions being executed by the processor to implement the steps of the ball gear machining method as described in any one of claims 1 to 6.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions for causing a computer to perform the ball gear machining method as described in any one of claims 1 to 6.

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