Method for on-machine measurement and error compensation of spur gear parameters

Abstract

A spur gear parameter on-machine measurement and error compensation method, comprising: 1) obtaining the grid points and measurement path of the spur gear tooth surface measurement based on the trigger probe measurement principle; obtaining the evenly distributed measuring points according to the characteristics of the small curvature of the spur gear tooth surface; obtaining the optimal square spiral type measurement path according to the characteristics of the machine tool X, Y axis movement error; 2) combining the optimal square spiral type measurement path, obtaining the probe delay error, probe measurement error and measurement coordinate error during measurement; obtaining the probe triangle error model based on the measurement principle of the probe, finally integrating the calibration to obtain the total error, so as to obtain the accurate measurement point coordinates after compensation; 3) taking the deviation of the entire face gear tooth surface and the theoretical profile as the tooth surface deviation, calculating the deviation of the actual position and the theoretical normal position direction of the tooth surface measurement point to obtain the error surface of the tooth surface, and performing precision grade evaluation. The present application solves the problems of complex traditional measurement process, low efficiency and high cost.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of face gear measurement, and particularly relates to a straight-tooth face gear parameter on-machine measurement and error compensation method. BACKGROUND

[0002] Most of the measurement technologies in the production process depend on offline measurement, and in industrial production, after the workpiece is processed, offline measurement technology is used for detection. When there are many workpieces to be measured, because each workpiece has to go through clamping, positioning and other processes, the production efficiency is greatly reduced. And because of repeated clamping and errors, the measurement results and the machined surface are difficult to converge. For on-machine measurement of high-precision face gears, the general measurement and evaluation method is low in efficiency and poor in accuracy, and consistency is difficult to guarantee. SUMMARY

[0003] In order to solve the problems of low efficiency and poor accuracy of high-precision straight-tooth face gear machining and measurement in the existing industry, a straight-tooth face gear parameter on-machine measurement and error compensation method is provided. The method introduces the on-machine measurement motion method and data analysis and evaluation method of face gears, which can more conveniently and accurately analyze and evaluate the machining accuracy of face gears, solves the problems of complex traditional measurement process, low efficiency and high cost, integrates machining and measurement, improves the production efficiency of parts, and guarantees the quality of products.

[0004] To achieve the above object, the application adopts the following technical solutions:

[0005] A straight-tooth face gear parameter on-machine measurement and error compensation method comprises the following steps:

[0006] 1) Obtain the grid points and measurement path of the straight-tooth face gear tooth surface based on the measurement principle of the trigger probe; obtain the uniformly distributed measuring points according to the characteristics of the small curvature of the straight-tooth face gear tooth surface; and obtain the optimal square spiral type measurement path according to the characteristics of the X and Y axis motion errors of the machine tool;

[0007] 2) Obtain the probe delay error, probe measurement error and measurement coordinate error during measurement in combination with the optimal square spiral type measurement path in step 1); obtain the probe triangular error model based on the measurement principle of the probe, and finally integrate and calibrate to obtain the total error, so as to obtain the accurate measurement point coordinates after compensation;

[0008] 3) After the measurement is completed, according to the process parameters and detection items of the face gear, based on the face gear gear shaping involute processing principle and non-uniform rational B-spline (NURBS) surface interpolation method, the curved surface of the straight tooth face gear is reconstructed to obtain a smooth tooth surface model, and the model is used for error evaluation; based on the accuracy level of the involute cylindrical gear and the error evaluation algorithm, the error and accuracy evaluation algorithm of the tooth surface deviation of the straight tooth face gear is obtained; the deviation of the entire face gear tooth surface and the theoretical profile is taken as the tooth surface deviation, the error surface of the tooth surface is obtained by calculating the deviation of the actual position and the theoretical normal position direction of the tooth surface measurement point, and the accuracy level evaluation is performed.

[0009] Further improvement of the present application is that the specific implementation method of step 1) is:

[0010] 201) Based on the characteristics of the small curvature of the straight tooth face gear tooth surface, a uniformly distributed point array grid point is set, X, Y and Z three linear shafts are linked to measure, and several measurement stages of "approximation-triggering-backoff" are proposed, each corresponding to a corresponding position;

[0011] 202) Based on the advantages and disadvantages of the three different tooth surface measurement path planning of the spiral type, S type and H type, a square spiral type measurement trajectory is obtained as the optimal measurement trajectory.

[0012] Further improvement of the present application is that in step 2), based on the triggering characteristics of the three contact pairs of the trigger probe, that is, the series electrical circuit composed of three contact pairs separated by 120° in the probe, different stress directions will have different measurement errors, and a probe error triangle model is obtained, that is, the probe will produce different probe errors when measuring different vector directions, and generally presents a triangular shape.

[0013] Further improvement of the present application is that the triangular error model also includes the delay error of the probe data collection, which is related to the hardware equipment and the motion speed, and the sizes of each vector direction are the same.

[0014] Further improvement of the present application is that since the measured data is the result in the workpiece coordinate system, coordinate system transformation is carried out to compensate for the system error caused by different coordinate systems.

[0015] Further improvement of the present application is that in step 3), according to the face gear gear shaping processing principle, the mathematical model of the face gear tooth surface is derived, the involute gear shaping cutter equation is obtained, and the tooth surface equation of the face gear is derived to realize the solution of the theoretical coordinates of the tooth surface measurement elements; first, the coordinate system of the gear shaping cutter and the face gear is established, and the cutter tooth surface equation is obtained through the mathematical model of the involute straight tooth cylindrical gear tooth surface:

[0016]

[0017] The deduced face gear tooth surface equation is:

[0018]

[0019] Wherein, r bs is the base circle radius of the corresponding cutter tooth profile; θ 0s is the angle parameter of the tooth groove symmetry line to the starting point; θ s is the angle corresponding to a point on the cutter involute; u s is the axial coordinate of the current point; m is the module of the gear cutting tool; f is a specific parameter equation combined with the gear meshing principle;

[0020] Finally, the actual data coordinate points are obtained by combining the normal equation.

[0021] Further improvement of the present application is that in step 3), the straight tooth surface gear tooth surface reconstruction is obtained based on non-uniform rational B-spline (NURBS) surface interpolation, the NURBS surface is calculated according to the interpolation method of the theoretical point, the surface reconstruction of the left and right tooth surfaces and the transition surface of the face gear is realized, so as to correspond the actual measurement position to the theoretical position one by one; first, the NURBS surface expression is established as follows:

[0022]

[0023] Wherein, P i,j is a control vertex; w i,j is a weight factor; N i,p (u), N i,q (v) are the basis functions of the node vectors U and V respectively;

[0024] The discrete data points of the face gear tooth surface 15*7 are taken, the cubic NURBS surface reconstruction is carried out according to the above, and the smooth reconstructed surface is obtained.

[0025] Further improvement of the present application is that in step 3), the straight tooth surface gear tooth surface reconstruction is obtained based on the precision level of the involute cylindrical gear and the error evaluation algorithm, and the deviation of the entire face gear tooth surface from the theoretical profile is directly taken as the tooth surface deviation.

[0026] Wherein, the rotation angle of the tooth surface midpoint is φ, the transformed data is obtained by rotating the actual measurement data of the tooth surface by the angle φ, and the calculation is as follows:

[0027]

[0028] Wherein, the shortest distance from the rotated tooth surface measurement data to the theoretical tooth surface is calculated by using the segmentation approximation method, and the tooth surface topological error is established.

[0029] Compared with the prior art, the present application has at least the following beneficial technical effects:

[0030] The application provides a spur gear parameter on-machine measurement and error compensation method, based on NURBS interpolation tooth surface reconstruction principle and trigger type probe measurement principle, proposes a new path form and error source in the measurement process, and proposes an optimal spur gear parameter measurement path and compensation method, improves the on-machine measurement accuracy, avoids the problems of low accuracy and poor efficiency caused by repeated clamping in offline measurement, and improves the production efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 For the measurement process and position map in the embodiment of the application;

[0032] Figure 2 For the involute cylindrical gear section model in the embodiment of the application;

[0033] Figure 3 For the three different measurement path maps of face gear in the embodiment of the application, wherein Figure 3 (a) is a square spiral type, Figure 3 (b) is an S type, Figure 3 (c) is an H type;

[0034] Figure 4 For the square spiral type measurement path map of face gear in the embodiment of the application;

[0035] Figure 5 For the error size model map of different vector directions of the probe in the embodiment of the application;

[0036] Figure 6 For the calibration error size parameter schematic diagram of the probe in the embodiment of the application;

[0037] Figure 7 For the face gear tooth surface detection report schematic diagram in the embodiment of the application;

[0038] Figure 8 For the tooth surface measurement error and measurement center result comparison map in the embodiment of the application, wherein Figure 8 (a) is the left tooth surface error size, Figure 8 (b) is the right tooth surface error size. DETAILED DESCRIPTION

[0039] Exemplary embodiments of the present disclosure will be described in greater detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that the present disclosure can be more thoroughly understood and the scope of the present disclosure can be accurately conveyed to those skilled in the art. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0040] The application provides a spur gear parameter in-situ measurement and error compensation method, which comprises the following steps:

[0041] 1) Based on the trigger probe measurement principle, grid points and measurement paths of the spur gear tooth surface are obtained; according to the small curvature characteristics of the spur gear tooth surface, the measurement points are uniformly distributed; according to the characteristics of the machine tool X and Y axis movement error, the optimal square spiral type measurement path is obtained; the specific implementation method is:

[0042] 201) Based on the small curvature characteristics of the spur gear tooth surface, the uniformly distributed dot matrix grid points are set, X, Y and Z three linear axes are linked to measure, and the "approximation-trigger-back" several measurement stages are proposed, each corresponding to the corresponding position as shown in the accompanying Figure 1 .

[0043] 202) Based on the advantages and disadvantages of the spiral type, S type and H type three different tooth surface measurement path planning for tooth surface measurement, as shown in the accompanying Figure 3 , the square spiral type measurement trajectory is obtained as shown in the accompanying Figure 4 , since the square spiral type measurement trajectory has less X and Y axis movement changes, it has the benefit of reducing the error caused by the X and Y axis movement changes of the machine tool, thereby serving as the optimal measurement trajectory.

[0044] 2) Combined with the optimal square spiral type measurement path in step 1), the probe delay error, probe measurement error and measurement coordinate error during measurement are obtained; based on the measurement principle of the probe, the probe triangular error model is obtained, and finally the total error is integrated and calibrated to obtain the accurate measurement point coordinates after compensation; the specific implementation method is: based on the working principle, measurement principle and system error principle caused by the hardware equipment of the trigger probe, the triangular error model is proposed, which has a relatively comprehensive probe error compensation benefit.

[0045] Among them, based on the trigger characteristics of the three contact pairs of the trigger probe, that is, the series electric circuit composed of three contact pairs separated by 120° in the probe, different stress directions will have different measurement errors, the probe error triangular model is obtained, that is, the probe will produce different probe errors when measuring different vector directions, and the overall shape is triangular, as shown in the accompanying Figure 5 . Figure 6

[0046] In particular, the triangular error model also includes the delay error of the probe data collection, which is related to the hardware equipment and the movement speed, and the sizes of each vector direction are the same; and since the measured data is the result in the workpiece coordinate system, coordinate system transformation is needed to compensate for the system error caused by different coordinate systems.

[0047] ​3) After the measurement is completed, according to the process parameters and detection items of the face gear, based on the face gear gear shaping involute processing principle, non-uniform rational B-spline (NURBS) surface interpolation method, the curved surface reconstruction of the straight tooth face gear is carried out, so as to obtain a smooth tooth surface model, and the model is used for error evaluation; based on the accuracy level of the involute cylindrical gear and the error evaluation algorithm, the error and accuracy evaluation algorithm of the tooth surface deviation of the straight tooth face gear is obtained; the deviation of the entire face gear tooth surface and the theoretical profile is taken as the tooth surface deviation, the error surface of the tooth surface is obtained by calculating the deviation of the actual position and the theoretical normal position direction of the tooth surface measurement point, and the accuracy level evaluation is carried out; the specific implementation method is as follows:

[0048] 301) According to the face gear gear shaping processing principle, the mathematical model of the face gear tooth surface is derived, the gear shaping cutter equation is obtained, and the tooth surface equation of the face gear is derived, so as to realize the solution of the theoretical coordinates of the tooth surface measurement elements. First, the coordinate system of the gear shaping cutter and the face gear is established, and the mathematical model of the involute straight tooth cylindrical gear tooth surface is obtained as shown in the accompanying drawings, so that the cutter tooth surface equation is: Figure 2

[0049]

[0050] The face gear tooth surface equation is derived as follows:

[0051]

[0052] Wherein, r bs is the base circle radius corresponding to the cutter tooth profile; θ 0s is the angle parameter of the starting point to the symmetrical line of the tooth groove; θ s is the angle corresponding to a point on the cutter involute; u s is the axial coordinate of the current point; m is the gear shaping cutter modulus; f is a specific parameter equation combined with the gear meshing principle;

[0053] Finally, the actual data coordinate point can be obtained by combining the normal equation.

[0054] 302) Based on the non-uniform rational B-spline (NURBS) surface interpolation, a straight tooth face gear tooth surface reconstruction method is proposed, the NURBS surface is calculated by using the interpolation method according to the theoretical points, the curved surface reconstruction of the left and right tooth surfaces and the transition curved surface of the face gear is realized, so as to correspond the actual measurement position with the theoretical position. First, the NURBS surface expression is established as follows:

[0055]

[0056] Wherein, P i,j is the control vertex; w i,j is the weight factor; N i,p (u), N i,q ​(v) basis functions of the node vectors U and V, respectively;

[0057] The discrete data points of the face gear tooth surface 15*7 are taken, and the above-mentioned NURBS surface reconstruction is performed three times to obtain a smooth reconstructed surface.

[0058] 303) Based on the accuracy level of the involute cylindrical gear and the error evaluation algorithm, the deviation of the entire face gear tooth surface from the theoretical profile is directly proposed as the tooth surface deviation.

[0059] Wherein, the rotation angle of the tooth surface midpoint is φ, and the transformed data is obtained by rotating the actual tooth surface measurement data by an angle φ, and the calculation is as follows:

[0060]

[0061] Wherein, the shortest distance from the rotated tooth surface measurement data to the theoretical tooth surface is calculated by using the segmentation approximation method, and the tooth surface topological error is established.

[0062] Embodiment

[0063] The present embodiment is a new type of straight tooth surface gear parameter on-machine measurement and error compensation method, and the equipment and materials used are as follows:

[0064] YK7280 numerical control machining grinder, infrared trigger probe, infrared receiver, involute straight tooth cylindrical gear pinion pair, face gear.

[0065] Based on the above on-machine measurement and compensation method, the face gear measurement experiment is carried out.

[0066] 1) According to the face gear parameters, the tooth surface model is established, and the coordinate system transformation is carried out.

[0067] 2) The probe is calibrated, the error model of the probe is obtained, and the trajectory measurement is carried out according to the above method.

[0068] 3) After the measurement data is compensated, the comparison and analysis are carried out.

[0069] The on-machine measurement data and the gear measurement center data of a certain tooth surface are shown in the following table:

[0070] Table 1 On-machine measurement left tooth surface detection data (unit: μm)

[0071]

[0072] Table 2 On-machine measurement right tooth surface detection data (unit: μm)

[0073]

[0074] Table 3 Gear measurement center left tooth surface detection data (unit: μm)

[0075]

[0076] Table 4 Gear measuring center right tooth surface detection data (unit: μm)

[0077]

[0078]

[0079] Extracting the above table data to make error comparison chart as shown in the figure Figure 8 It can be seen that the error of the in-situ measurement and compensation method is within 5.0 μm, and the measurement result has certain reliability.

[0080] Although the present application has been described in detail with general description and specific embodiments, some modifications or improvements can be made on the basis of the present application, which is obvious to those skilled in the art. Therefore, these modifications or improvements made without departing from the spirit of the present application are within the scope of the present application.

Claims

1. A method for on-machine measurement and error compensation of spur gear parameters, characterized in that, Includes the following steps: 1) Based on the measurement principle of the trigger probe, the grid points and measurement path for measuring the tooth surface of the spur gear are obtained; based on the small curvature of the tooth surface of the spur gear, uniformly distributed measurement points are obtained; based on the characteristics of the X and Y axis motion errors of the machine tool, the optimal square spiral measurement path is obtained. 2) Combining the optimal square spiral measurement path from step 1), the probe delay error, probe measurement error, and measurement coordinate error are obtained during measurement; based on the measurement principle of the probe, the probe triangle error model is obtained, and finally the total error is obtained through integration and calibration, thereby obtaining the compensated and accurate measurement point coordinates; 3) After measurement, based on the process parameters and inspection items of the face gear, and using the involute machining principle of face gear shaping and the NURBS surface interpolation method (non-uniform rational B-spline), the surface of the spur face gear was reconstructed to obtain a smooth tooth surface model, which was then used for error evaluation. Based on the accuracy level of the involute cylindrical gear and the error evaluation algorithm, the error and accuracy evaluation algorithm for the tooth surface deviation of the spur face gear was obtained. The deviation between the entire face gear tooth surface and the theoretical profile was taken as the tooth surface deviation. The error surface of the tooth surface was obtained by calculating the deviation between the actual position of the tooth surface measurement point and the theoretical normal position, and the accuracy level was evaluated.

2. The method for on-machine measurement and error compensation of spur gear parameters according to claim 1, characterized in that, The specific implementation method of step 1) is as follows: 201) Based on the small curvature of the tooth surface of spur gears, a uniformly distributed discrete lattice grid is set up, and the X, Y and Z three linear axes are used for linkage measurement. Several measurement stages of "approach-trigger-retreat" are proposed, each corresponding to a specific position. 202) Based on the advantages and disadvantages of three different tooth surface measurement path planning methods (spiral, S-shaped, and H-shaped) for tooth surface measurement, a square spiral measurement trajectory is obtained as the optimal measurement trajectory.

3. The method for on-machine measurement and error compensation of spur gear parameters according to claim 1, characterized in that, In step 2), based on the triggering characteristics of the three contact pairs of the trigger probe, that is, the probe is composed of a series electrical circuit consisting of three contact pairs spaced 120° apart. Different force directions will result in different measurement errors, thus obtaining the probe error triangle model. That is, the probe will produce different probe errors when measuring different vector directions, and the overall error presents a triangular shape.

4. The method for on-machine measurement and error compensation of spur gear parameters according to claim 3, characterized in that, The triangular error model also includes the delay error of the probe's data acquisition, the magnitude of which is related to the hardware and the speed of movement, and all vector directions have the same magnitude.

5. The method for on-machine measurement and error compensation of spur gear parameters according to claim 4, characterized in that, Since the measured data is obtained in the workpiece coordinate system, a coordinate system transformation is required to compensate for the systematic errors caused by the different coordinate systems.

6. The method for on-machine measurement and error compensation of spur gear parameters according to claim 1, characterized in that, In step 3), based on the gear shaping principle, the mathematical model of the gear tooth surface was derived, and the equation of the involute gear shaping tool was obtained, thus deriving the tooth surface equation of the gear and realizing the solution of the theoretical coordinates of the tooth surface measurement elements; firstly, the coordinate system of the gear shaping tool and the gear was established, and through the mathematical model of the involute spur gear tooth surface, the tool tooth surface equation was obtained as follows: The equation for the tooth surface of the gear is derived as follows: Where, r bs θ is the base circle radius corresponding to the tool tooth profile; 0s θ is the angle parameter from the tooth groove symmetry line to the starting point. s The angle corresponding to a point on the involute of the cutting tool; u s is the axial coordinate of the current point; m is the module of the gear shaping tool; f is a specific parametric equation based on the gear meshing principle; Finally, the actual data coordinates are obtained by combining the normal equation.

7. The method for on-machine measurement and error compensation of spur gear parameters according to claim 6, characterized in that, In step 3), the tooth surface reconstruction of the spur gear is obtained based on non-uniform rational B-splines, i.e., NURBS surface interpolation. The NURBS surface is calculated using interpolation based on theoretical points to reconstruct the left and right tooth surfaces and transition surfaces of the gear, thus establishing a one-to-one correspondence between the actual measured positions and the theoretical positions. The NURBS surface expression is first established as follows: Among them, P i,j To control the vertices; w i,j For weighting factors; N i,p (u),N i,q (v) are the basis functions of the node vectors U and V, respectively; Take discrete data points of 15*7 on the tooth surface of the gear, and perform three NURBS surface reconstructions according to the above to obtain a smooth reconstructed surface.

8. The method for on-machine measurement and error compensation of spur gear parameters according to claim 7, characterized in that, In step 3), based on the accuracy level of the involute cylindrical gear and the error evaluation algorithm, the deviation between the entire gear tooth surface and the theoretical profile is directly used as the tooth surface deviation. The rotation angle φ at the midpoint of the tooth surface is calculated. The actual measured data of the tooth surface is rotated by the angle φ to obtain the transformed data, as follows: Among them, the shortest distance from the measured data of the rotated tooth surface to the theoretical tooth surface is calculated by using the segmentation approximation method, and the tooth surface topology error is established.

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