On-machine measurement modification parameter identification method for large-specification involute gear

Abstract

The invention discloses an on-machine measurement modification parameter identification method for a large-specification involute gear. The method specifically comprises the following steps: step 1, determining an optimal fitting order of an error curve by utilizing a moss growth optimization algorithm; 2, fitting on-machine measurement original data with the optimal fitting order to obtain an initial overall curve, and then obtaining an approximate derivative curve of the initial overall curve; 3, according to the approximate derivative curve, judging whether the shape modification type is upper and lower end portion edge modification or drum shape modification; 4, if edge trimming is carried out on the upper end and the lower end, a top edge trimming starting end point and a root edge trimming tail end point are recognized according to the approximate derivative curve, fitting is carried out according to the two end points to form a final error curve, and then the shape trimming amount is obtained according to the final error curve; 5, if drum shape modification is carried out, the bulging height is recognized, then parabola fitting is carried out, and the drum shape quantity is calculated. According to the method, the problem that fitting distortion is easy to occur when polynomial fitting is directly carried out on measured original data in the prior art is solved.

Description

Technical Field

[0001] This invention belongs to the technical field of gear precision measurement methods, and relates to a method for identifying on-machine measurement and modification parameters of large-size involute gears. Background Technology

[0002] Gear transmission is one of the most widely used mechanical transmission methods, characterized by accurate transmission ratios, high efficiency, and compact structure. However, due to unavoidable manufacturing and installation errors, gear transmissions generate vibration and noise. Modification to reduce vibration and noise is a mature and effective technique that can optimize gear meshing, improve transmission performance, and extend service life. Modification parameters mainly include tooth tip trimming, tooth root trimming, and tooth profile bulging, whose values ​​not only affect the load distribution during gear meshing but are also closely related to the gear's fatigue resistance. To ensure machining quality, modified large gears require on-machine measurement during processing. In the measurement of individual gear errors, the evaluation of tooth profile error and helix error, as well as the identification of modification parameters, are crucial for ensuring gear transmission performance.

[0003] In-machine measurement, a crucial component of gear machining and precision control, integrates a measurement system into the machine tool to achieve in-situ precision inspection of the workpiece while it is clamped, thus constructing a closed-loop manufacturing system encompassing machining, measurement, and reshaping. Compared to traditional offline inspection, in-machine measurement avoids secondary clamping errors, improves inspection efficiency, and enables real-time error compensation.

[0004] For large-sized involute gears with a tip circle diameter greater than 500mm, the amount of modification is typically larger than that of ordinary gears, resulting in more complex curvature variations in the tooth surface error curve. When using a trigger-type probe for in-machine measurement of large-sized modified gears, the obtained measurement data has a wide distribution range and limited volume. The geometric characteristics of the modified area differ significantly from other areas, especially the transition region, which is difficult to control. Directly performing polynomial fitting on the raw measurement data can easily lead to fitting distortion and misjudgment of accuracy level. How to fit the actual error curve of large-sized modified gears based on in-machine measurement data and calculate the modification amount to accurately assess machining accuracy is a technical problem that urgently needs to be solved. Summary of the Invention

[0005] The purpose of this invention is to provide a method for identifying the modification parameters of large-size involute gears during in-machine measurement, which solves the problem in the prior art where direct polynomial fitting of the original measurement data easily leads to fitting distortion.

[0006] The technical solution adopted in this invention is a method for identifying on-machine measurement and modification parameters of large-specification involute gears, which is implemented according to the following steps: Step 1: Determine the best fitting order of the error curve using a moss growth optimization algorithm; Step 2: Fit the original in-machine measurement data to obtain the initial overall curve using the best fitting order, and then obtain the approximate derivative curve of the initial overall curve. Step 3: Determine whether the shaping type is edge trimming at the top and bottom or drum-shaped trimming based on the approximate derivative curve; Step 4: If it is edge trimming at the top and bottom ends, identify the starting point of the top edge trimming and the ending point of the root edge trimming according to the approximate derivative curve, fit the two endpoints to form the final error curve, and then obtain the trimming amount according to the final error curve. Step 5: If it is a drum-shaped modification, identify the drum height, then perform parabolic fitting and calculate the drum shape amount.

[0007] Preferably, step 1 specifically includes: Step 1.1, Define the number of optimization parameters for the moss growth algorithm. nvars =1, population size Psize, That is, the number of fitting orders and the dimensionality of the variables. dim =1, penalty factor penaltyFactor Maximum number of iterations MaxGenerations and the order of fitting k The range { k ∈Z| lb ≤ k ≤ ub}, where a population encoded with random integers represents different fitting orders, and Z represents the set of integers. k ∈Z indicates that the fitting order is an integer. lb and ub are the lower and upper limits of the fitting order in the optimization parameters of the moss growth algorithm, respectively. Step 1.2, Construct the individual fitness function The evaluation of an individual's merits and demerits is specifically as follows: (1) in, MSE It is the mean square error of the polynomial fitting, expressed as: (2) in, n The number of raw data points measured on-machine. It is the first i Original data points y The value of direction, Is x i Fitting values ​​of the polynomial, It is the first i Original data points x The direction value, i = 1, 2, 3, ..., n; RungePenalty This is a penalty item for Longge, specifically as follows: (3) In the formula, k and m These are the left and right end Longer detection intervals, respectively. The number of points, The sum of the mean error of the left Runge detection interval This represents the mean error of the right-hand Runge detection interval. In points o Oscillating curves exhibiting Runge phenomenon on the left side Relative Runge detection interval linear interpolation curve The error, In points j Oscillation curve with Runge phenomenon on the right side Relative Runge detection interval linear interpolation curve The error is expressed as: (4); Step 1.3: Calculate the fitness value of all individuals in the current population according to formula (1), execute the hidden generation mechanism to trigger judgment, when the number of historical records reaches the set threshold or the maximum number of iterations is completed, traverse the historical records of each individual, recalculate the fitness of each historical solution, select the best historical solution to replace the current individual, and update the global optimal solution; then enter the wind direction guidance process, screen the population individuals by random arrangement, and update the current optimal solution. BestOrder Threshold filtering is performed to retain individuals that meet the criteria. The wind direction vector is calculated based on the difference between the optimal solution and the mean of the selected individuals, thus guiding the population's movement direction. Finally, the population is updated: individuals first randomly disperse along the wind direction, then initiate dual reproduction with an 80% probability, including a 50% probability of local perturbation near the optimal solution and a 50% probability of randomly selecting either the current solution or the optimal solution. After boundary processing and integerization, a new generation of the population is generated. This process is iterated until the maximum number of iterations is reached to determine the best-fit order. BestOrde.

[0008] Preferably, step 2 specifically includes: Step 2.1, based on the best fit order BestOrder Raw data of in-machine measurement The initial global curve is obtained by fitting. ; Step 2.2, for the initial overall curve discrete point set on , q The total number of discrete points in the set. Represents the initial global curve Upper p discrete points x coordinate, Represents the initial global curve Upperp discrete points y The coordinates, with their 5-point sliding window linearly fitted approximate derivative curve Represented as: (5) in, , , , respectively within the corresponding window and Mean.

[0009] Preferably, in step 3, the approximate derivative curve is used. To determine whether the shaping type is edge trimming at the top and bottom or drum-shaped trimming, the specific steps are as follows: like The curve is consistent with the entire tooth width range x If there are more than 1 intersection points, and the curve in the modified part on the left (i.e., the lower end face) shows a trend of first monotonically increasing to a local maximum and then monotonically decreasing, and the function value in the unmodified part varies within ±3 and the range of the unmodified part does not exceed 6, and the curve in the modified part on the right (i.e., the upper end face) shows a monotonically decreasing trend again, then it is considered to be modified at the upper and lower ends. like The curve is consistent with the entire tooth width range x If there is only one intersection point, it is a drum-shaped modification.

[0010] Preferably, step 4 specifically includes: Step 4.1: If step 3 determines the shaping type to be edge trimming at the top and bottom, then based on the approximate derivative curve... Identify the starting point of the top trimming edge bo1 and the ending point of the root trimming edge bu2; Step 4.2: Taking the top trimming start point bo1 and the root trimming end point bu2 as effective turning points, use polynomial fitting to fit the original on-machine measurement data of the untrimmed area located between the turning points to obtain the error curve. , To indicate the end point bu2 of the root trimming. x coordinate, Indicates the starting point of the top edge, bo1 x Coordinates; and evaluate the gear accuracy grade; Step 4.3, with endpoints and endpoints The derivative at the point is used as a boundary condition to perform piecewise cubic spline fitting on the upper and lower edge trimming parts of the tooth, and then smoothed to form the final error curve; Step 4.4: Calculate the average line of the measured values ​​based on the final error curve to obtain the shaping amount.

[0011] Preferably, in step 4.1, the approximate derivative curve is used. The specific steps for identifying the starting point bo1 of the top trimming edge and the ending point bu2 of the root trimming edge are as follows: Define an index variable denoted as start_idx to store the values ​​of the approximate reciprocal curve, with an initial value of start_idx=1, and define the threshold interval. Starting from start_idx=1, traverse the approximate reciprocal curve. When first encounter At that time, record the index. Continue iterating until the first time you encounter... At that time, record the index. , index and The fitted values ​​at the corresponding locations are denoted as bo1 and bu2.

[0012] Preferably, step 4.1 further includes verifying the effectiveness of the interval detection after obtaining bo1 and bu2, specifically: calculating the points bo1 and bu2 in... x Difference on coordinates , To indicate the end point bu2 of the root trimming. x coordinate, Indicates the starting point of the top edge, bo1 x coordinates, if Greater than 0.7B, where B is the tooth width, and and If all approximate reciprocal curve values ​​between these values ​​fall within the threshold range, then it is confirmed that... and For valid inflection point location index; like If the value is less than or equal to 0.7B, it is considered an invalid inflection point, and thus... Start traversing the approximate reciprocal curve until a new one that meets the conditions is found. and .

[0013] Preferably, step 4.3 specifically includes: For All raw data points within the range h Polynomial fitting yields h The order polynomial fitting curve serves as the error curve. Specifically:

[0014] in, The constant coefficients preceding each term in a polynomial expression are determined based on the degree of the polynomial. The number of coefficients, for an h-order polynomial, is h+1. from , ,……, There are a total of h+1; Then ask At the endpoint derivative at point and derivative at point ; Screening raw measurement data The middle is located in the interval The points outside are divided into top edge data. Data on root repair Piecewise cubic spline fitting was performed on the top edge trimming data and the root edge trimming data respectively to obtain the piecewise cubic spline curves corresponding to the top edge trimming data. , l=1,2,3,...,L , L Indicates the number of segments, and the top edge data is removed from... First and last connections are divided into L Each data segment yields a corresponding cubic spline curve. These represent the start and end points of the corresponding data segment, respectively. ; and the piecewise cubic spline curves corresponding to the root trimming data. , g=1,2,3,...,G , G Indicates the number of segments, and the root trimming data is from First and last connections are divided into G Each data segment yields a corresponding cubic spline curve. These represent the start and end points of the corresponding data segment, respectively. ; for Four coefficients The following conditions must be met: (6) And at the two fixed endpoints of the top edge data. and The boundary conditions for the derivative are: (7) for Four coefficients The following conditions must be met: (8) And at the two fixed endpoints of the root trimming data. and The boundary conditions for the derivative are: (9) If the above conditions are not met, the fitting is repeated until the conditions of formula (6)-formula (9) are met; Then obtain and and error curve The curves are then pieced together to obtain the final error curve.

[0015] Preferably, step 4.4, calculating the average of the measured values ​​based on the final error curve to obtain the shaping amount, specifically involves: On the final error curve, the average line of the measured values ​​of the modified parts at the upper and lower ends of the gear is determined by the least squares method within the measurement range of the edge modification. This gives us the edge modification amount fu at the root of the tooth and the edge modification amount fo at the tip of the tooth.

[0016] The beneficial effects of this invention are: This invention addresses the problem of precision grade evaluation and profile modification parameter identification for large-size involute gears. It utilizes the global search capability of the moss growth optimization algorithm, combined with a fitness penalty mechanism (MSE + Runge phenomenon suppression), to automatically determine the optimal polynomial fitting order without manual trial and error. This also avoids the overfitting problem of traditional methods, ensuring accurate identification of profile modification parameters.

[0017] This invention employs a "multiple segmentation" fitting method. The unmodified region uses polynomial fitting, while the upper and lower edge-modified regions use segmented cubic spline fitting. By constraining the connection points to satisfy the derivative, a smooth transition between the modified and unmodified regions is achieved, filtering out the influence of machine tool errors and fitting errors, ensuring the error curve accurately reflects the tooth surface machining error. During the identification of modification inflection points bo1 and bu2, Savitzky-Golay first-order fitting is used to obtain a 5-point window approximate discrete derivative, avoiding the influence of abrupt changes and noise points in the initial fitting curve. The derivative curve and threshold are used to determine the modification type and locate the modification boundary, achieving accurate identification of modification features. Segmented fitting and smooth connection yield the final error curve, and the modification amounts fu and fo are calculated from the average of the measured values. Attached Figure Description

[0018] Figure 1 This is a flowchart of the method for identifying on-machine measurement and modification parameters of large-size involute gears according to the present invention; Figure 2 In the method for identifying the on-machine measurement and modification parameters of large-size involute gears of this invention, the initial overall curve is obtained by fitting the original on-machine measurement data. Figure 3 In Embodiment 8 of the present invention, the initial overall curve is obtained by fitting the original on-machine measurement data. Figure 4 This is the approximate discrete derivative curve obtained in Embodiment 8 of the present invention through a 5-point window with trimmed upper and lower ends. picture; Figure 5 The error evaluation curves of the upper and lower end trimmed spirals obtained in Embodiment 8 of the present invention are picture; Figure 6 The final error curve obtained by the upper and lower end edge trimming segment fitting smooth connection in Embodiment 8 of the present invention is shown in the figure. Figure 7 This is a high-order polynomial fitting curve of the original data of the drum-shaped shaping measurement in embodiment 9 of the present invention; Figure 8 This is a 5-window discrete approximate derivative curve of the drum-shaped polynomial fitting curve in Embodiment 9 of the present invention. Detailed Implementation

[0019] The following detailed description is provided in conjunction with specific implementation methods.

[0020] Example 1 The present invention provides a method for identifying on-machine measurement and modification parameters of large-size involute gears, the process of which is as follows: Figure 1 As shown, the specific steps are as follows: Step 1: Determine the best fitting order of the error curve using a moss growth optimization algorithm; Step 2: Fit the original in-machine measurement data to obtain the initial overall curve using the best fitting order, and then obtain the approximate derivative curve of the initial overall curve. Step 3: Determine whether the shaping type is edge trimming at the top and bottom or drum-shaped trimming based on the approximate derivative curve; Step 4: If it is edge trimming at the top and bottom ends, identify the starting point of the top edge trimming and the ending point of the root edge trimming according to the approximate derivative curve, fit the two endpoints to form the final error curve, and then obtain the trimming amount according to the final error curve. Step 5: If it is a drum-shaped modification, identify the drum height, then perform parabolic fitting and calculate the drum shape amount.

[0021] Example 2 Based on Example 1, step 1 specifically includes: Step 1.1, Define the number of optimization parameters for the moss growth algorithm. nvars =1, population size Psize, That is, the number of fitting orders and the dimensionality of the variables. dim =1, penalty factor penaltyFactor Maximum number of iterations MaxGenerations and the order of fitting k The range { k ∈Z| lb ≤k ≤ ub}, where a population encoded with random integers represents different fitting orders, and Z represents the set of integers. k ∈Z indicates that the fitting order is an integer. lb and ub are the lower and upper limits of the fitting order in the optimization parameters of the moss growth algorithm, respectively. Step 1.2, Construct the individual fitness function The evaluation of an individual's merits and demerits is specifically as follows: (1) in, MSE It is the mean square error of the polynomial fitting, expressed as: (2) in, n The number of raw data points measured on-machine. It is the first i Original data points y The value of direction, Is x i Fitting values ​​of the polynomial, It is the first i Original data points x The direction value, i = 1, 2, 3, ..., n; After determining the optimal fitting order using the moss growth algorithm, the optimal fitting order was applied to the in-machine measurement points ( x i , y i After polynomial fitting, the fitted polynomial expression is obtained. Substituting this expression into the polynomial expression will yield the final result. x i The fitted value of the polynomial at the given location; RungePenalty This is a penalty item for Longge, specifically as follows: (3) In the formula, k and m These are the left and right end Longer detection intervals, respectively. The number of points, The sum of the mean error of the left Runge detection interval This represents the mean error of the right-hand Runge detection interval. In points o Oscillating curves exhibiting Runge phenomenon on the left side Relative Runge detection interval linear interpolation curve The error, In points j Oscillation curve with Runge phenomenon on the right side Relative Runge detection interval linear interpolation curve The error is expressed as: (4); Step 1.3: Calculate the fitness value of all individuals in the current population according to formula (1), execute the hidden generation mechanism to trigger judgment, when the number of historical records reaches the set threshold or the maximum number of iterations is completed, traverse the historical records of each individual, recalculate the fitness of each historical solution, select the best historical solution to replace the current individual, and update the global optimal solution; then enter the wind direction guidance process, screen the population individuals by random arrangement, and update the current optimal solution. BestOrder Threshold filtering is performed to retain individuals that meet the criteria. The wind direction vector is calculated based on the difference between the optimal solution and the mean of the selected individuals, thus guiding the population's movement direction. Finally, the population is updated: individuals first randomly disperse along the wind direction, then initiate dual reproduction with an 80% probability, including a 50% probability of local perturbation near the optimal solution and a 50% probability of randomly selecting either the current solution or the optimal solution. After boundary processing and integerization, a new generation of the population is generated. This process is iterated until the maximum number of iterations is reached to determine the best-fit order. BestOrde.

[0022] Example 3 Based on Example 2, step 2 specifically includes: Step 2.1, based on the best fit order BestOrder Raw data of in-machine measurement The initial global curve is obtained by fitting. ; Step 2.2, for the initial overall curve discrete point set on q is the total number of discrete points in the set. Represents the initial global curve The p-th discrete point x coordinate, Represents the initial global curve yfit The p-th discrete point y Coordinates, and then Savitzky-Golay is used to initialize the overall curve. A first-order fit was performed to obtain a 5-point window approximate discrete derivative curve. Represented as: (5) in, , , , respectively within the corresponding window and Mean.

[0023] Example 4 Based on Example 3, step 3 is based on the approximate derivative curve. To determine whether the shaping type is edge trimming at the top and bottom or drum-shaped trimming, the specific steps are as follows: like The curve is consistent with the entire tooth width range x If there are more than 1 intersection points, and the curve in the modified part on the left (i.e., the lower end face) shows a trend of first monotonically increasing to a local maximum and then monotonically decreasing, and the function value in the unmodified part varies within ±3 and the range of the unmodified part does not exceed 6, and the curve in the modified part on the right (i.e., the upper end face) shows a monotonically decreasing trend again, then it is considered to be modified at the upper and lower ends. like The curve is consistent with the entire tooth width range x If there is only one intersection point, it is a drum-shaped modification.

[0024] Example 5 Based on Example 4, step 4 specifically includes: Step 4.1, as follows Figure 2 As shown, if step 3 determines the shaping type to be edge trimming at the top and bottom ends, then according to the approximate derivative curve... Identify the starting point bo1 of the top trimming edge and the ending point bu2 of the root trimming edge, specifically as follows: Among them, according to the approximate derivative curve The specific steps for identifying the starting point bo1 of the top trimming edge and the ending point bu2 of the root trimming edge are as follows: Define an index variable denoted as start_idx to store the values ​​of the approximate reciprocal curve, with an initial value of start_idx=1, and define the threshold interval. Starting from start_idx=1, traverse the approximate reciprocal curve. When first encounter At that time, record the index. Continue iterating until the first time you encounter... At that time, record the index. , index and The fitted values ​​at the corresponding positions are denoted as bo1 and bu2; After obtaining bo1 and bu2, verify the effectiveness of the interval detection, specifically by calculating the intervals at points bo1 and bu2. x Difference on coordinates , To indicate the end point bu2 of the root trimming. x coordinate, Indicates the starting point of the top edge, bo1 x coordinates, if Greater than 0.7B, where B is the tooth width, and and If all approximate reciprocal curve values ​​between these values ​​fall within the threshold range, then it is confirmed that... and For valid inflection point location index; like If the value is less than or equal to 0.7B, it is considered an invalid inflection point, and thus... Start traversing the approximate reciprocal curve until a new one that meets the conditions is found. and ; Step 4.2: Taking the top trimming start point bo1 and the root trimming end point bu2 as effective turning points, use polynomial fitting to fit the original on-machine measurement data of the untrimmed area located between the turning points to obtain the error curve. , To indicate the end point bu2 of the root trimming. x coordinate, Indicates the starting point of the top edge, bo1 x Coordinates; and evaluate the gear accuracy grade; Step 4.3, with endpoints and endpoints The derivative at the given point is used as a boundary condition to perform piecewise cubic spline fitting on the upper and lower edge trimming sections of the tooth, and then smoothed to form the final error curve, as follows: For All raw data points within the range h Polynomial fitting yields h The order polynomial fitting curve serves as the error curve. Specifically:

[0025] in, The constant coefficients preceding each term in a polynomial expression are determined based on the degree of the polynomial. The number of coefficients, for an h-order polynomial, is h+1. from , ,……, There are a total of h+1; Then ask At the endpoint derivative at point and derivative at point ; Screening raw measurement data The middle is located in the interval The points outside are divided into top edge data. Data on root repair Piecewise cubic spline fitting was performed on the top edge trimming data and the root edge trimming data respectively to obtain the piecewise cubic spline curves corresponding to the top edge trimming data. ,l=1,2,3,...,L , L Indicates the number of segments, and the top edge data is removed from... First and last connections are divided into L Each data segment yields a corresponding cubic spline curve. These represent the start and end points of the corresponding data segment, respectively. ; and the piecewise cubic spline curves corresponding to the root trimming data. , g=1,2,3,...,G , G Indicates the number of segments, and the root trimming data is from First and last connections are divided into G Each data segment yields a corresponding cubic spline curve. These represent the start and end points of the corresponding data segment, respectively. ; for Four coefficients The following conditions must be met: (6) And at the two fixed endpoints of the top edge data. and The boundary conditions for the derivative are: (7) for Four coefficients The following conditions must be met: (8) And at the two fixed endpoints of the root trimming data. and The boundary conditions for the derivative are: (9) If the above conditions are not met, the fitting is repeated until the conditions of formula (6)-formula (9) are met; Formulas (7) and (9) are derived by applying the cubic polynomial. and Taking the derivative, the resulting quadratic polynomial has endpoints equal to the endpoints. and endpoints The polynomial derivative of the fitted piecewise cubic spline curve and the error curve are obtained by... The connection point is a smooth connection; Then obtain and and error curve The curves are then pieced together to obtain the final error curve.

[0026] Step 4.4: Calculate the average line of the measured values ​​based on the final error curve to obtain the modification amount. Specifically, on the final error curve, determine the average line of the measured values ​​of the modification portion at the upper and lower ends of the gear within the modification measurement range using the least squares method. This will give you the tooth root modification amount fu and the tooth tip modification amount fo.

[0027] Example 6 Based on Example 5, in step 5, after determining that the shaping type is drum-shaped, a regression parabola is fitted to the measurement points within its evaluation range. The intersection of this parabola and the two edges of the evaluation range forms a chord. The distance between the tangent of the regression parabola parallel to this chord and the chord is the drum-shaped depth. Ca The amount of drum-shaped modification can then be calculated. Ca Parabolic fitting directly uses a quadratic polynomial function. y = ax 2 + bx + c (in a , b , c The original measurement points are fitted with polynomial coefficients, the coefficients are determined by the least squares method, and then the drum shape is identified according to the process described above.

[0028] Example 7 Based on Example 5, in step 4.3, the top edge data is used. For example: The top edge data range [ Divide into Z-1 sub-intervals[ ],in Then the fitting function for each sub-interval is:

[0029] Among them, coefficient The following conditions must be met to ensure the continuity of the function values ​​and the continuity of the second derivative:

[0030] Fixed endpoints x 1 and x m The boundary conditions for the derivative are: .

[0031] Example 8 Based on Example 7, the method of the present invention is used to identify the modified gears processed on the five-axis CNC forming gear grinding machine YK73125A using the modified parameter identification algorithm proposed above. The geometric parameters of the modified gears are shown in Table 1.

[0032]

[0033] Taking the on-machine measurement data of tooth #1 on the left tooth surface of 5 sets as an example, the identification is performed, and the number of original points of each on-machine measurement is as follows: n =15, the original data are shown in Tables 2-6.

[0034]

[0035]

[0036]

[0037]

[0038]

[0039] The above 5 sets of in-machine measurement raw data Perform optimal polynomial initial fitting to obtain the fitted curve. ,like Figure 3 As shown, this is the initial overall fitting curve for the first set of data. Image; as shown Figure 4 The figure shows the 5-window discrete approximate derivative curves for the first set of data. Image; as shown Figure 5 The figure shows the error evaluation curves of the upper and lower edge trimmed spiral lines in the first set of data. ,like Figure 6 As shown, the final error curve is obtained by smoothing and fitting the upper and lower edges of the first set of data.

[0040] Table 7 shows the evaluation results of tooth direction error for 5 sets of data.

[0041]

[0042] Table 7 shows the error evaluation results for five groups of gear directions. The evaluation error values ​​for each group are consistent with the measurement results on the measuring instrument (generally, the reports from the gear measuring center or other measuring instruments are used as the standard for comparison). This indicates that the fitting method of "multiple segmentation" can correctly evaluate the accuracy grade of the modified gear and identify the modification amount after determining the modification type. In contrast, the original method of directly performing polynomial fitting on the original on-machine measurement data and then evaluating the accuracy grade cannot correctly identify the accuracy grade of the gear, and will identify high-precision gears as low-precision gears, resulting in misjudgment. Furthermore, the identified modification amount also differs significantly from that of the measuring instrument.

[0043] Example 9 Based on Example 7, and following the method of the present invention, polynomial fitting was performed on the original in-machine measurement data of tooth profile bulging modification in Table 8 to obtain... Figure 7 ,according to Figure 7 The discrete derivative curve is obtained Figure 8 ;according to Figure 8 Once it is determined that the shape is drum-shaped, the amount of shaping can be calculated according to the method of this invention.

[0044]

Claims

1. A method for identifying on-machine measurement and modification parameters of large-specification involute gears, characterized in that, Specifically: Step 1: Determine the best fitting order of the error curve using a moss growth optimization algorithm; Step 2: Fit the original in-machine measurement data to obtain the initial overall curve using the best fitting order, and then obtain the approximate derivative curve of the initial overall curve. Step 3: Determine whether the shaping type is edge trimming at the top and bottom or drum-shaped trimming based on the approximate derivative curve; Step 4: If it is edge trimming at the top and bottom ends, identify the starting point of the top edge trimming and the ending point of the root edge trimming according to the approximate derivative curve, fit the two endpoints to form the final error curve, and then obtain the trimming amount according to the final error curve. Step 5: If it is a drum-shaped modification, identify the drum height, then perform parabolic fitting and calculate the drum shape amount.

2. The method for identifying on-machine measurement and modification parameters of large-size involute gears according to claim 1, characterized in that, Step 1 specifically involves: Step 1.1, Define the number of optimization parameters for the moss growth algorithm. nvars =1, population size Psize, That is, the number of fitting orders and the dimensionality of the variables. dim =1, penalty factor penaltyFactor Maximum number of iterations MaxGenerations and the order of fitting k The range { k ∈Z| lb ≤ k ≤ ub }, where a population encoded with random integers represents different fitting orders, and Z represents the set of integers. k ∈Z indicates that the fitting order is an integer. lb and ub are the lower and upper limits of the fitting order in the optimization parameters of the moss growth algorithm, respectively. Step 1.2, Construct the individual fitness function The evaluation of an individual's merits and demerits is specifically as follows: （1） in, MSE It is the mean square error of the polynomial fitting, expressed as: （2） in, n The number of raw data points measured on-machine. It is the first i Original data points y The value of direction, Is x i Fitting values ​​of the polynomial, It is the first i Original data points x The direction value, i = 1, 2, 3, ..., n; RungePenalty This is a penalty item for Longge, specifically as follows: （3） In the formula, k and m These are the left and right end Longer detection intervals, respectively. The number of points, The sum of the mean error of the left Runge detection interval This represents the mean error of the right-hand Runge detection interval. In points o Oscillating curves exhibiting Runge phenomenon on the left side Relative Runge detection interval linear interpolation curve The error, In points j Oscillation curve with Runge phenomenon on the right side Relative Runge detection interval linear interpolation curve The error is expressed as: （4）； Step 1.3: Calculate the fitness value of all individuals in the current population according to formula (1), execute the hidden generation mechanism to trigger judgment, when the number of historical records reaches the set threshold or the maximum number of iterations is completed, traverse the historical records of each individual, recalculate the fitness of each historical solution, select the best historical solution to replace the current individual, and update the global optimal solution; then enter the wind direction guidance process, screen the population individuals by random arrangement, and update the current optimal solution. BestOrder Threshold filtering is performed to retain individuals that meet the criteria. The wind direction vector is calculated based on the difference between the optimal solution and the mean of the selected individuals, thus guiding the population's movement direction. Finally, the population is updated: individuals first randomly disperse along the wind direction, then initiate dual reproduction with an 80% probability, including a 50% probability of local perturbation near the optimal solution and a 50% probability of randomly selecting either the current solution or the optimal solution. After boundary processing and integerization, a new generation of the population is generated. This process is iterated until the maximum number of iterations is reached to determine the best-fit order. BestOrde .

3. The method for identifying on-machine measurement and modification parameters of large-size involute gears according to claim 1, characterized in that, Step 2 specifically involves: Step 2.1, based on the best fit order BestOrder Raw data of in-machine measurement The initial global curve is obtained by fitting. ; Step 2.2, for the initial overall curve discrete point set on q is the total number of discrete points in the set. Represents the initial global curve The p-th discrete point x coordinate, Represents the initial global curve The p-th discrete point y The coordinates, with their 5-point sliding window linearly fitted approximate derivative curve Represented as: （5） in, , , , respectively within the corresponding window and Mean.

4. The method for identifying on-machine measurement and modification parameters of large-specification involute gears according to claim 3, characterized in that, In step 3, based on the approximate derivative curve To determine whether the shaping type is edge trimming at the top and bottom or drum-shaped trimming, the specific steps are as follows: like The curve is consistent with the entire tooth width range x If there are more than 1 intersection points, and the curve in the modified part on the left (i.e., the lower end face) shows a trend of first monotonically increasing to a local maximum and then monotonically decreasing, and the function value in the unmodified part varies within ±3 and the range of the unmodified part does not exceed 6, and the curve in the modified part on the right (i.e., the upper end face) shows a monotonically decreasing trend again, then it is considered to be modified at the upper and lower ends. like The curve is consistent with the entire tooth width range x If there is only one intersection point, it is a drum-shaped modification.

5. The method for identifying on-machine measurement and modification parameters of large-size involute gears according to claim 4, characterized in that, Step 4 specifically involves: Step 4.1: If step 3 determines the shaping type to be edge trimming at the top and bottom, then based on the approximate derivative curve... Identify the starting point of the top trimming edge bo1 and the ending point of the root trimming edge bu2; Step 4.2: Taking the top trimming start point bo1 and the root trimming end point bu2 as effective turning points, use polynomial fitting to fit the original on-machine measurement data of the untrimmed area located between the turning points to obtain the error curve. , To indicate the end point bu2 of the root trimming. x coordinate, Indicates the starting point of the top edge, bo1 x Coordinates; and evaluate the gear accuracy grade; Step 4.3, with endpoints and endpoints The derivative at the point is used as a boundary condition to perform piecewise cubic spline fitting on the upper and lower edge trimming parts of the tooth, and then smoothed to form the final error curve; Step 4.4: Calculate the average line of the measured values ​​based on the final error curve to obtain the shaping amount.

6. The method for identifying on-machine measurement and modification parameters of large-size involute gears according to claim 5, characterized in that, In step 4.1, based on the approximate derivative curve The specific steps for identifying the starting point bo1 of the top trimming edge and the ending point bu2 of the root trimming edge are as follows: Define an index variable denoted as start_idx to store the values ​​of the approximate reciprocal curve, with an initial value of start_idx=1, and define the threshold interval. Starting from start_idx=1, traverse the approximate reciprocal curve. When first encounter At that time, record the index. Continue iterating until the first time you encounter... At that time, record the index. , index and The fitted values ​​at the corresponding locations are denoted as bo1 and bu2.

7. The method for identifying on-machine measurement and modification parameters of large-size involute gears according to claim 6, characterized in that, Step 4.1 further includes verifying the effectiveness of the interval detection after obtaining bo1 and bu2, specifically: calculating the points bo1 and bu2 in... x Difference on coordinates , To indicate the end point bu2 of the root trimming. x coordinate, Indicates the starting point of the top edge, bo1 x coordinates, if Greater than 0.7B, where B is the tooth width, and and If all approximate reciprocal curve values ​​between these values ​​fall within the threshold range, then it is confirmed that... and For valid inflection point location index; like If the value is less than or equal to 0.7B, it is considered an invalid inflection point, and thus... Start traversing the approximate reciprocal curve until a new one that meets the conditions is found. and .

8. The method for identifying on-machine measurement and modification parameters of large-size involute gears according to claim 7, characterized in that, Step 4.3 specifically involves: For All raw data points within the range h Polynomial fitting yields h The order polynomial fitting curve serves as the error curve. Specifically: in, The constant coefficients preceding each term in a polynomial expression are determined based on the degree of the polynomial. The number of coefficients, for an h-order polynomial, is h+1. from , ,……, There are a total of h+1; Then ask At the endpoint derivative at point and derivative at point ; Screening raw measurement data The middle is located in the interval The points outside are divided into top edge data. Data on root repair Piecewise cubic spline fitting was performed on the top edge trimming data and the root edge trimming data respectively to obtain the piecewise cubic spline curves corresponding to the top edge trimming data. , l=1,2,3,...,L , L Indicates the number of segments, and the top edge data is removed from... First and last connections are divided into L Each data segment yields a corresponding cubic spline curve. These represent the start and end points of the corresponding data segment, respectively. ; and the piecewise cubic spline curves corresponding to the root trimming data. , g=1,2,3,...,G , G Indicates the number of segments, and the root trimming data is from First and last connections are divided into G Each data segment yields a corresponding cubic spline curve. These represent the start and end points of the corresponding data segment, respectively. ; for Four coefficients The following conditions must be met: （6） And at the two fixed endpoints of the top edge data. and The boundary conditions for the derivative are: （7） for Four coefficients The following conditions must be met: （8） And at the two fixed endpoints of the root trimming data. and The boundary conditions for the derivative are: （9） If the above conditions are not met, the fitting is repeated until the conditions of formula (6)-formula (9) are met; Then obtain and and error curve The curves are then pieced together to obtain the final error curve.

9. The method for identifying on-machine measurement and modification parameters of large-size involute gears according to claim 8, characterized in that, Step 4.4, which calculates the average of the measured values ​​based on the final error curve to obtain the shaping amount, specifically involves: On the final error curve, the average line of the measured values ​​of the modified parts at the upper and lower ends of the gear is determined by the least squares method within the measurement range of the edge modification. This gives us the edge modification amount fu at the root of the tooth and the edge modification amount fo at the tip of the tooth.

Images