A method for recognizing installation error of a rotary body part based on an elliptical error model

Abstract

The application provides a kind of rotary body part installation error identification method based on elliptical error model, and the analysis result can judge rotary body part geometric eccentricity, phase, end face swing angle, direction simultaneously, to provide conditions for next step accurate detection or processing.The detection principle is to measure the complete contour line of a circle in radial direction of rotary body part by displacement sensor (such as contact scanning probe, non-contact optical probe, etc.) to obtain original relative data set, to obtain contour change data set by wavelet decomposition, to obtain relative data set for optimization by further processing.Due to the influence of rotary body part swing, the measurement section which is theoretically circular will become elliptical, and it is easy to know that the short axis length b of elliptical section is consistent with the actual radius of the measured rotary body part.Using improved Gauss-Newton method to optimize the objective function combined with the data set for optimization, and adjusting the threshold value and increment coefficient of each parameter of increment matrix according to the different iteration convergence speed of optimization parameters.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of installation and positioning of rotary workpieces, and particularly relates to a rotary part installation error identification method based on an elliptical error model. BACKGROUND

[0002] Common rotary parts in engineering mainly include gears, spline shafts, installation centers, etc., and are mostly used for transmission, positioning and clamping. When a rotary part is installed on a rotary table, geometric eccentricity error will be generated due to the gap between the axis of the rotary part and the axis of the rotary table, and parallelism error, i.e. eccentricity error, will be generated due to the inclination angle between the end face of the rotary part and the installation face. The geometric eccentricity error and the eccentricity error are collectively referred to as installation error. In high-precision machining and detection, there is a very high requirement for the accurate installation and positioning of workpieces. For example, high-precision detection of gears is generally performed on a quantity instrument in a constant temperature room and utilizes a center to clamp. At present, high precision of the center is generally relied on to reduce the installation error of the gear, but with the increase of the clamping times, the installation error will gradually increase. More importantly, the gear needs to be installed on different machine tools during different manufacturing processes, and the installation error generated thereby will directly affect the machining precision of the gear surface. Especially for large rotary parts, even a small installation error will be amplified at the end of machining or detection due to the excessively large radius. The causes of the installation error of the rotary part are various, mainly including non-coincidence of the reference in mechanical hoisting and inaccuracy of the detection instrument in manual checking. At present, in the actual production process, a standard ball is mostly used to identify the center parameters of the rotary part by using a small circular arc method or a standard gauge block is mostly used to identify the center parameters of the rotary part by using a standard gauge block method. These methods can only identify one type of geometric error or eccentricity error, and the precision is low. In the actual production process, the current method is to use absolute measurement data to perform elliptical fitting or parameter optimization. For example, some scholars proposed a method of using a high-precision motion axis of a quantity instrument to scan the profile of a measured rotary part to obtain the absolute distance from the points on the profile to the rotary center, so as to perform installation error detection. However, the premise of accurate acquisition of the measurement data by this method is that the center axis of the measured rotary part is error-free, the application scene is limited, and there is a difference between the acquired data and the theoretical requirement. Compared with the absolute measurement data, the profile relative change data of the rotary part during one rotation is easy to acquire, which can be divided into radial profile relative change data of the rotary part and relative distance change data between the radial profile and the sensor, and can be measured by a contact sensor and a non-contact sensor respectively. How to identify the installation error by using the relative measurement data is a problem worth solving. SUMMARY

[0003] The purpose of the present application is to provide a kind of installation error identification method of ellipsoidal part based on elliptical error model, and the analysis result can judge the eccentricity of ellipsoidal part, phase, end face swing angle, direction simultaneously, for guiding installation error correction, to provide conditions for next accurate detection or processing.The detection principle is to measure the complete contour of one circle in radial direction of ellipsoidal part by displacement sensor (such as contact scanning probe, non-contact optical probe, etc.), to obtain original relative data set, to obtain contour change data set by wavelet decomposition, to obtain relative data set for optimization by further processing.Because of the influence of ellipsoidal part swing, the measurement section which is theoretically circular will become elliptical, and it is easy to know that the short axis length b of elliptical section is consistent with the actual radius of the measured ellipsoidal part.An elliptical installation error model is established by elliptical standard equation and coordinate system transformation, a target function with installation error parameters is derived according to the model, the target function is optimized by using improved Gauss-Newton method combined with data set for optimization, and the threshold value and increment coefficient of each parameter of increment matrix are adjusted according to the different iteration convergence speed of optimization parameters.Finally, the installation error parameters obtained by iterative optimization are elliptical center parameters Q (x e ,y e ), long axis direction parameter θ, long axis length parameter a and reference circle radius R.The size and phase of geometric installation error are represented by elliptical center parameters;The swing axis is the short axis of the ellipse, and the size of swing angle can be calculated according to the ratio of short axis to long axis.

[0004] To achieve the above purpose, the present application provides the following technical scheme: a kind of installation error identification method of ellipsoidal part based on elliptical error model, comprising the following steps:

[0005] First step: install the ellipsoidal part on the workbench, check the clamping condition of the fixture of rotary workbench and the measured ellipsoidal part, first ensure the coaxiality of the center axis of the measured ellipsoidal part and the center axis of the rotary workbench and the parallelism of the end face of the measured ellipsoidal part and the end face of the rotary workbench by manual calibration as far as possible;After inspection, install the measuring equipment, place the measuring equipment at any position on the contour to be scanned, and scan the complete contour on the ellipsoidal part by combining rotary interpolation motion of rotary shaft to obtain original relative data set X={x1,x2,x3...x n}, wherein n is the number of elements of original relative data set, x j is original relative data, wherein j=1~n;

[0006] Second step: In order to correctly obtain the profile shape information reflecting the scanned profile of the rotary part, the high frequency components of noise, roughness and waviness in the original relative data set need to be removed, and the low frequency components reflecting the profile are left; therefore, the original relative data set is separated by the method of wavelet decomposition, and the low frequency components are reconstructed to obtain the profile change data set X c = {x c1 ,x c2 ,x c3 ...x cm}, wherein m is the number of elements of the profile change data set, x ci is the profile change data, wherein i = 1 ~ m.

[0007] Third step: The profile change data set X c is divided into 360° equal parts according to the time sequence to determine the angle between the connecting line of each measuring point and the original point and the X axis The calculation formula is:

[0008]

[0009] The profile change data set is processed: the relative value of the measured data is used to determine the length change amount x ci of each measuring point x ci-L , and the calculation formula is:

[0010]

[0011] In formula (2), min(·) is the minimum value function, x cmin is the minimum value in the X c data set; and the relative data set finally applied to the installation error parameter optimization is

[0012] Fourth step: the point (x z , y z ) on the standard ellipse equation in the rectangular coordinate system is obtained by coordinate transformation to obtain the point (x, y) on the elliptical detection model with installation error, and the formula is:

[0013]

[0014] If the measured data is the relative distance change amount between the profile of the rotary part and the axis of the rotary table, the radial profile relative change data, then the part of parameters in formula (3) is further written as:

[0015]

[0016] If the measured data is the relative distance change amount between the profile of the rotary part and the sensor, the relative distance change data between the radial profile and the sensor, then the part of parameters in formula (3) is further written as:

[0017]

[0018] In formula (3), (3-1), (3-2), x e ,y e is the parameter of the center of the ellipse to be optimized, θ is the angle between the major axis of the ellipse to be optimized and the x-axis of the rectangular coordinate system, R is the radius of the reference circle to be optimized, a is the parameter of the major axis of the ellipse to be optimized, b is the radius value of the measured rotary part, and δ is the standard ellipse angle parameter, δ ∈ [0, 2π];

[0019] Step 5: formula (3) is transformed and arranged to obtain

[0020]

[0021] The parameter δ is eliminated, and the least square objective function f target 2 is established, and the following is obtained:

[0022]

[0023] The optimization objective is

[0024]

[0025] Step 6: reasonable initial values of θ, x e ,y e , a, and R are set, and the improved Gauss-Newton method is used to iteratively optimize formula (6), and the specific process is

[0026] 1) define variables A, B, d_A, and d_B as

[0027]

[0028]

[0029]

[0030]

[0031] 2) f target is respectively derived with respect to parameters θ, x e ,y e , a, and R to obtain

[0032]

[0033] 3) the Jacobian gradient matrix is constructed as T is the matrix transpose; wherein The increment matrix can be represented as

[0034]

[0035] In formula (8), f = [f1, f2,..., f m ] T , where f i is the function value obtained by substituting the target function f target ;

[0036] 4) Update the optimization parameter value

[0037]

[0038] In formula (9), p is the iteration number; g i (i = 1 ~ 5) is the increment coefficient, which needs to be reasonably selected according to the change speed of the increment matrix parameter [Δθ; Δx e ; Δy e ; Δa; Δb];

[0039] 5) Iteration end condition: judge whether the variables in the increment matrix are respectively not greater than the set threshold, that is, whether the following conditions are met:

[0040]

[0041] If yes, the optimization solving ends; otherwise, continue to execute from process 3);

[0042] Seventh step: use the optimization parameters θ, x e , y e , a, R obtained by iteration to calculate the installation error

[0043] Geometric eccentricity: Phase angle β = tan -1 (y e / x e ); end face yaw angle Yaw axis phase angle α = (θ ± π / 2);

[0044] Eighth step: adjust the workpiece installation position according to the calculated yaw angle and geometric error to eliminate the installation error.

[0045] Compared with the prior art, the beneficial effects of the present application are as follows:

[0046] The present application adopts relative measurement data for recognizing the installation error of the rotary part, obtains the original relative data set by measuring any complete contour of the rotary part, obtains the contour change data set by using the wavelet decomposition method, and obtains the relative data set for optimization through comparison and difference processing. The absolute distance information of the contour of the rotary part and the axis is not needed, the data acquisition is easier, and the detection method is simple and does not need complex path planning. ​

[0047] The present application is different from the conventional fitting mode, and the installation deviation angle and geometric eccentric error of the rotary part can be simultaneously analyzed and calculated through one-time data processing. The improved target optimization method can avoid fitting error to the greatest extent and obtain accurate actual installation error.

[0048] The present application sets different threshold values for the increment matrix of the optimization parameters of the installation error of the measured rotary part as the iterative recognition stop condition, and introduces an increment coefficient. This processing method can improve the solving efficiency.

[0049] The present application takes the radius value of the measured rotary part as the short axis length of the error ellipse, so that the short axis length does not participate in optimization iteration, and the singularity of the Jacobian matrix is effectively avoided; and an intermediate parameter reference circle radius R is set, and the relative measurement data is converted into absolute measurement data containing unknown radius R for optimization.

[0050] The installation error of the rotary part is directly obtained by solving the parameters of the fitting ellipse, such as the center of the ellipse, the long axis, and the phase angle of the long axis, so that the rounding error of the conventional fitting mode is effectively reduced.

[0051] The installation error detection instrument of the present application can use all sensors that can measure relative displacement information, and the installation error detection method can be applied to all rotary workpieces with complete contour lines and any type of relative measurement data.

[0052] The present application focuses on installation error detection under relative measurement data, but can also be used for installation error detection under absolute measurement data, only R needs to be replaced by an absolute measurement value, and has wide applicability. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 It is a schematic diagram of the physical error model of the present application;

[0054] Figure 2 It is a schematic diagram of each parameter in the elliptical error model of the present application;

[0055] Figure 3 It is a schematic diagram of the conversion of measurement points when the objective function is established, Figure 3 (a) is a schematic diagram of the measurement points before conversion, Figure 3 (b) is a schematic diagram of the measurement points after conversion;

[0056] Figure 4 It is a schematic diagram of the relative data set obtained after processing the measured data of the present application for optimization;

[0057] Figure 5 It is a flowchart of the execution of the method of the present application. DETAILED DESCRIPTION

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] Please see Figures 1-5 This invention provides a technical solution: a method for identifying installation errors of rotating parts based on an elliptic error model, comprising the following steps:

[0060] Step 1: Mount the rotating part on the worktable and check the clamping of the worktable and the rotating part to be tested. First, manually calibrate to ensure the coaxiality of the central axis of the rotating part and the central axis of the worktable, as well as the parallelism of the end face of the rotating part and the end face of the worktable. After checking, install measuring equipment around the rotating part. Figure 1 The diagram shows a rotating part after geometric eccentricity and yaw errors have occurred. L2 is the axis of the rotary table, L1 is the axis of the rotating part to be measured, and the actual height profile measured by the measuring equipment is the measured ellipse shown in the diagram. The actual measured data is the original relative dataset X = {x1, x2, x3...x}. n}, where n is the number of elements in the original relative dataset, x j The original relative data is given, where j = 1 to n. Figure 1 In the figure, OQ represents the geometric eccentricity of the rotating part at the measured position, b represents the measured minor axis radius of the ellipse, and a represents the measured major axis radius of the ellipse. Given the yaw angle, it is easy to see that the minor axis is the yaw axis.

[0061] The second step: To accurately obtain the contour shape information reflecting the scanned profile of the rotating part, it is necessary to remove mid-to-high frequency components such as noise, roughness, and waviness from the original relative dataset, leaving only the low-frequency components reflecting the contour. Therefore, wavelet decomposition is used to separate the frequency components of the original relative dataset and reconstruct the low-frequency components to obtain the contour change dataset X. c ={x c1 ,x c2 ,x c3 ...x cm}, where m is the number of elements in the profile variation dataset, x ci These are the profile variation data, where i = 1 to m;

[0062] Step 3: As Figure 2 As shown, the profile change dataset X c The angle between the line connecting each measuring point to the origin and the X-axis is determined by dividing the time series into 360° equal parts. The calculation formula is:

[0063]

[0064] Processing the profile variation dataset: Determining the x-value of each measurement point based on the relative value of the measurement data. ci The corresponding length change x ci-L ( Figure 2 x shown in ci-L The length change is calculated based on the relative change data of the radial profile of the rotating part. The formula is as follows:

[0065]

[0066] In equation (2), min(·) is the minimum value function, x cmin For X c The minimum value in the dataset. Therefore, the relative dataset ultimately applied to optimize installation error parameters is:

[0067] Step 4: As Figure 3 As shown, the point (x) on the standard ellipse equation in the rectangular coordinate system is... z ,y z The point (x, y) on the elliptical detection model with installation errors is obtained through coordinate system transformation, using the following formula:

[0068]

[0069] If the measured data is the relative distance change between the profile of the rotating part and the axis of the rotary table (relative change data of radial profile, such as when using a contact scanning probe), some parameters in equation (3) can be further written as

[0070]

[0071] If the measured data is the change in the relative distance between the profile of the rotating part and the sensor (data on the change in the relative distance between the radial profile and the sensor, such as when using a non-contact optical probe), some parameters in equation (3) can be further written as

[0072]

[0073] In equation (3), x e ,y e Here, θ represents the center parameter of the ellipse to be optimized, θ is the angle between the major axis of the ellipse to be optimized and the x-axis of the rectangular coordinate system, R is the radius of the reference circle to be optimized, a is the major axis parameter of the ellipse to be optimized, and b is the radius value of the rotating part being measured. The above parameters are illustrated as follows: Figure 2 As shown. δ is the standard ellipse angle parameter, δ∈[0,2π], as... Figure 3As shown in (a).

[0074] Step 5: Transform and rearrange equation (3) to obtain

[0075]

[0076] Eliminate the parameter δ and establish the least squares objective function f. target 2 ,have to:

[0077]

[0078] The optimization goal is

[0079]

[0080] Step 6: Set θ, x e ,y e Reasonable initial values ​​for a and R are obtained, and the improved Gauss-Newton method is used to iteratively optimize equation (6). The specific process is as follows:

[0081] 1) Define variables A, B, d_A, and d_B as...

[0082]

[0083]

[0084]

[0085]

[0086] 2)f target For parameters θ and x respectively e ,y e Differentiating a,R, we get

[0087]

[0088] 3) Construct the Jacobian gradient matrix as follows: T is the matrix transpose; where The increment matrix can then be expressed as

[0089]

[0090] In equation (8), f = [f1, f2, ..., f m ] T , where f i To be Substitute into the objective function f target The obtained function value.

[0091] 4) Update and optimize parameter values

[0092]

[0093] In equation (9), p is the number of iterations; g i (i = 1 to 5) are the increment coefficients, which need to be determined based on the increment matrix parameters [Δθ; Δx]. e ;Δy e Choose the appropriate rate of change for each of the following: Δa and Δb.

[0094] 5) Iteration termination condition: Determine whether all variables in the increment matrix are not greater than the set threshold.

[0095]

[0096] If yes, the optimization process ends; otherwise, continue from process 3).

[0097] Step 7: Based on Figures (1) and (2), use the optimized parameters θ, x obtained through iteration. e ,y e The installation error is calculated as follows:

[0098] Geometric eccentricity: Phase angle: β = tan -1 (y e / x e )

[0099] End face deflection angle: Phase angle of the yaw axis: α=(θ±π / 2)

[0100] Step 8: Adjust the rotary table installation position according to the determined yaw angle and geometric error to eliminate installation errors; during actual measurement, ensure that there is no interference between the sensor probe and the measured object and the measuring equipment, and that the sensor measurement data is valid.

[0101] The following example demonstrates this:

[0102] The measuring sensor uses a scanning Marposs G25 probe with a radius of 3mm. The measured data is the relative change in the radial profile of the measured rotating part. The radius of the measured rotating part is 200mm, therefore, the minor axis radius b of the ellipse in the installation error model is 200mm. To compare and optimize the effect, the preset installation error values ​​are shown in Table 1.

[0103] Table 1 Preset values ​​for installation error of the tested rotating body parts

[0104]

[0105] The original relative dataset is processed to obtain the relative dataset used for optimization. like Figure 4As shown. The increment coefficients are set to g1 = 1000, g2 = g3 = g4 = g5 = 1; the increment matrix thresholds are ε1 = 10^-8, ε2 = ε3 = ε4 = ε5 = 10^-3.

[0106] The initial values ​​for the iteration are shown in Table 2, i.e. The initial values ​​can be set arbitrarily within a reasonable range.

[0107] Table 2 Initial values ​​for optimization iteration

[0108] X-directional geometric eccentricity x e ]] Y-geometric eccentricity y e ]]> Major axis phase angle Θ Reference circle radius R Major axis radius a 0 mm 0 mm 0° 250 mm 240 mm

[0109] The final solution obtained from the experiment, including the optimization parameters, iteration count, and time, is shown in Table 3.

[0110] Table 3 Solution Results

[0111]

[0112] The installation error parameters calculated from Table 3 are as follows:

[0113] Geometric eccentricity:

[0114] Phase angle: β = tan -1 (y e / x e ) = tan -1 (0.05 / 0.009) = 79.796°

[0115] End face deflection angle:

[0116] Phase angle of the yaw axis: α=(θ±π / 2)=(25±90)°

[0117] As shown in Table 3 and the calculation results, the geometric eccentricity and end face sway angle of the present invention are basically consistent with the preset values, and the time taken is 0.42s, which demonstrates extremely high precision and efficiency.

[0118] The detection and calculation method of this invention can achieve high-precision calculation of all parameters of the installation error of rotating parts. Its detection method uses relative measurement data and iteratively applies a target fitting method, effectively solving the installation error detection problem where obtaining absolute measurement data is difficult, but obtaining relative measurement data is relatively easy. This method has a simple detection action and can use any type of displacement sensor, such as a non-contact sensor or a contact scanning probe. It has high solution efficiency and does not reduce overall work efficiency.

[0119] The measurement and evaluation method of this invention can be programmed into the software system as a preparatory step before the inspection or processing of rotating parts, thereby realizing automated and rapid installation error detection and laying an important "high-precision" foundation for subsequent operations.

[0120] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for identifying installation errors of rotating parts based on an elliptic error model, characterized in that, Includes the following steps: Step 1: Mount the rotating part on the worktable and check the clamping of the worktable and the rotating part to be measured. First, manually calibrate to ensure the coaxiality of the central axis of the rotating part and the central axis of the worktable, as well as the parallelism of the end face of the rotating part and the end face of the worktable. After checking, install the measuring equipment and place it at any position on the profile to be scanned. Combine the rotary interpolation motion of the rotary axis to scan the complete contour of the rotating part to obtain the original relative dataset X = {x1, x2, x3... x ... n }, where n is the number of elements in the original relative dataset, x j These are the original relative data, where j = 1 to n; Step 2: To accurately obtain the contour shape information reflecting the scanned profile of the rotating part, it is necessary to remove high-frequency components of noise, roughness, and waviness from the original relative dataset, leaving only the low-frequency components reflecting the contour. Therefore, wavelet decomposition is used to separate the frequency components of the original relative dataset and reconstruct the low-frequency components to obtain the contour change dataset X. c ={x c1 ,x c2 ,x c3 ...x cm }, where m is the number of elements in the profile variation dataset, x ci These are the profile variation data, where i = 1 to m; Step 3: Transfer the silhouette change dataset X c The angle between the line connecting each measuring point to the origin and the X-axis is determined by dividing the time series into 360° equal parts. The calculation formula is: Processing the profile variation dataset: Determine the x-value of each measurement point using the relative value of the measurement data. ci The corresponding length change x ci-L The calculation formula is: In equation (2), min(·) is the minimum value function, x cmin For X c The minimum value in the dataset; then the relative dataset ultimately applied to the optimization of installation error parameters is: Step 4: Find the points (x, y) on the standard ellipse equation in the rectangular coordinate system. z ,y z The point (x, y) on the elliptical detection model with installation error is obtained through coordinate transformation, using the following formula: If the measured data is the relative distance change between the profile of the rotating part and the axis of the rotary table, and the relative change data of the radial profile, then some parameters in equation (3) can be further written as: If the measured data is the change in the relative distance between the profile of the rotating part and the sensor, or the change in the relative distance between the radial profile and the sensor, then some parameters in equation (3) can be further written as: In equations (3), (3-1), and (3-2), x e ,y e Here, θ is the center parameter of the ellipse to be optimized, θ is the angle between the major axis of the ellipse to be optimized and the x-axis of the rectangular coordinate system, R is the radius of the reference circle to be optimized, a is the major axis parameter of the ellipse to be optimized, b is the radius value of the rotating part being measured, and δ is the standard ellipse angle parameter, δ∈[0,2π]. Step 5: Transform and rearrange equation (3) to obtain Eliminate the parameter δ and establish the least squares objective function f. target 2 ,have to: The optimization goal is Step 6: Set θ, x e ,y e Reasonable initial values ​​for a and R are obtained, and the improved Gauss-Newton method is used to iteratively optimize equation (6). The specific process is as follows: 1) Define variables A, B, d_A, and d_B as... 2)f target For parameters θ and x respectively e ,y e Differentiating a,R, we get 3) Construct the Jacobian gradient matrix as follows: T is the matrix transpose; where If i = 1 to m, then the increment matrix can be expressed as: In equation (8), f = [f1, f2, ..., f m ] T , where f i To be Substitute into the objective function f target The obtained function value; 4) Update and optimize parameter values In equation (9), p is the number of iterations; g i (i = 1 to 5) are the increment coefficients, which need to be determined based on the increment matrix parameters [Δθ; Δx]. e ;Δy e Choose the appropriate rate of change for Δa and Δb. 5) Iteration termination condition: Determine whether each variable in the increment matrix is ​​less than or equal to a set threshold. If the conditions are met, the optimization process ends; otherwise, continue from process 3). Step 7: Utilize the optimized parameters θ, x obtained through iteration e ,y e The installation error is calculated as follows: Geometric eccentricity: Phase angle β = tan -1 (y e / x e End face deflection angle The phase angle of the yaw axis is α = (θ ± π / 2); Step 8: Adjust the workpiece installation position based on the calculated yaw angle and geometric error to eliminate installation errors.

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