On-machine measurement system credibility evaluation method for shape and position dimensions

Abstract

The invention provides an on-machine measurement system credibility evaluation method for shape and position dimensions, and aims to solve the problems that the measurement repeatability of an on-machine measurement system is unknown, the measurement capability is enough and the measurement result is credible for the shape and position dimensions of specified features. The method comprises the steps of firstly constructing a repeatability model of an on-machine measurement system, including a repeatability covariance matrix of a space error component and a pre-stroke error component, and then constructing a multivariate random variable generator for generating a space error random sample and a pre-stroke error random sample based on the repeatability covariance matrix. A random sample generated by the multivariate random variable generator is utilized to construct a form and position size random sample generator to generate a form and position size random sample, then the standard deviation of the form and position size random sample is predicted based on an adaptive Monte Carlo method, and finally, based on the standard deviation, MSA is utilized to carry out multi-dimensional credibility evaluation on the measurement system.

Description

Technical Field

[0001] The present invention relates to the technical field of in - machine measurement, and particularly relates to a method for evaluating the credibility of an in - machine measurement system for geometric dimensions and tolerances. Background Art

[0002] In the aerospace field, parts with weak rigidity and difficult - to - machine complex features have extremely high requirements for manufacturing technology. Traditional machining methods are difficult to achieve the required high precision, and it is also difficult to ensure the consistency and stability during the machining process. In order to adapt to the rapid development of intelligent manufacturing and meet the more efficient and consistent machining requirements, in - machine measurement technology has been developed and applied more and more widely. As an advanced intelligent automated manufacturing means, in - machine measurement technology can monitor the size, shape, and position of workpieces in real - time during the machining process, thereby reducing manual inspection and rework time and significantly improving machining efficiency.

[0003] In a reliable quality management system, the machining process and the measurement process are separated to achieve high - precision measurement in a strictly controlled environment and accurately judge the machining results of parts. However, in - machine measurement technology combines machining and measurement tasks, bringing new opportunities and also facing new challenges - it is difficult to evaluate the credibility of in - machine measurement systems. The measurement process of in - machine measurement systems belongs to "machining on the same body and measuring on the same body", lacking systematic means to evaluate measurement capabilities. Therefore, the credibility of their measurement results is in doubt, the measurement accuracy is unknown, and the measurement capabilities are difficult to quantify.

[0004] Although some evaluation methods for measurement systems have been proposed in the literature, such as the patent application "Uncertainty Evaluation Method, System, Equipment and Medium for a Large - Size Multilateral Coordinate Measurement System (Application No.: CN202410079102.0)", which evaluates uncertainty by analyzing the measurement uncertainty of an optical multilateral coordinate measurement system; and the patent application "Method for Evaluating the Metrological Performance of an Automated Verification System Based on Measurement System Analysis (Application No.: CN202410616715.3)", which uses the theory of Measurement System Analysis (MSA) to evaluate the metrological performance of an automated verification pipeline with high efficiency and strong usability. However, these methods are difficult to specifically analyze and evaluate the geometric dimensions and tolerances of each feature of each part in production machining. Therefore, there is an urgent need for an evaluation method for in - machine measurement systems targeting the geometric dimensions and tolerances of specified features. Summary of the Invention

[0005] The present invention provides a method for evaluating the credibility of an in - machine measurement system for geometric dimensions and tolerances, aiming to solve the problems that for the geometric dimensions and tolerances of specified features, the measurement repeatability of in - machine measurement systems is unknown, and it is not known whether the measurement capabilities of in - machine measurement systems are sufficient and whether the measurement results are credible.

[0006] The technical solution of the present invention is as follows:

[0007] A method for evaluating the credibility of an in-machine measurement system for geometric dimensions is characterized in that it includes the following steps:

[0008] Step 1: Obtain the set of spatial errors at multiple positions in the stroke of the in-machine measurement system through calibration;

[0009] Step 2: Establish a repeatability model of the in-machine measurement system, including:

[0010] The repeatability covariance matrix Σ of the spatial error components at any position p p , Σ p The main diagonal elements of are the standard deviations of the spatial error δ at any position p in different directions, and the remaining elements are the covariances between the spatial error components in different directions; p The repeatability covariance matrix Σ of the pre-travel error components under the angle combination of the polar angle θ and the azimuth angle

[0011] ;

[0012] Θ , Σ Θ The main diagonal elements of are the standard deviations of the pre-travel errors in different directions, and the remaining elements are the covariances between the pre-travel error components in different directions;

[0012] The set of spatial errors is used to solve the undetermined coefficients in the repeatability covariance matrix Σ p ;

[0013] Step 3: Construct a random sample generator for geometric dimensions;

[0014] Step 3.1: Establish a multivariate random variable generator:

[0015]

[0016] wherein, G p and G Θ are respectively the spatial error random sample at any theoretical point p in the measurement path planning of the in-machine measurement system and the pre-travel error random sample G at the theoretical detection angle combination Θ ; G p and G Θ are both 3×Nums matrices, and each column represents a 3D random vector conforming to the covariance matrix Σ p and Σ Θ ; Z is a 3×Nums matrix, and each column represents a 3D standard normal random vector; L p and L Θ are both lower triangular matrices;

[0017] Step 3.2: Construct a random sample generator for geometric dimensions:

[0018]

[0019] Wherein, R j is the j-th element in the random sample of geometric dimension R = (R1, R2…, R Nums ), j = 1, 2,…, Nums; f is the geometric dimension calculation function; is the random sample of measurement points affected by spatial error and pre-travel error D S (i) represents the i-th column of the theoretical measurement point coordinate matrix D S with a dimension of 3×n S ; and are the random samples of spatial error and pre-travel error of each theoretical measurement point respectively, generated by the multivariate random variable generator established in Step 3.1, i = 1, 2,…, n s ;

[0020] Step 4: Evaluate the credibility of the on-machine measurement system;

[0021] Step 4.1: Predict the standard deviation of the current random sample of the geometric dimension to be measured based on the adaptive Monte Carlo method

[0022] Step 4.2: Use the standard deviation Based on the MSA theory, use the following formula to calculate the credibility evaluation indexes, including the effective resolution NDC, the precision tolerance ratio P / T%, and the repeatability and reproducibility percentage %R&R, and evaluate according to the obtained credibility evaluation indexes.

[0023] Furthermore, in Step 2:

[0024]

[0025] Wherein, is the error component of the spatial error δ p at the p position in the X, Y, and Z directions of the machine tool coordinate system; use the multiple repeated calibration results at the p m position calibrated in Step 1 to estimate the covariance matrix m at the p position, that is, obtain the coefficient of the function representing each element in the covariance matrix Σ p ;

[0026] The calculation formula for the main diagonal elements of

[0027]

[0028] ​ The calculation formulas for the remaining elements are as follows:

[0029]

[0030] In the formula, α X,_ , β X,_ , γ X,_ , α X,Y，_ , α X,Z，_ , α Y,Z，_ , β X,Y,_ , β X,Z,_ , β Y,Z,_ , γ X,Y,_ , γ X,Z,_ , γ Y,Z,_ are undetermined coefficients in the covariance matrix Σ p ; p m,k represents the k-th component of the calibration position p m ; n p represents the number of repeated measurements of the spatial error; is the spatial error of the j-th measurement at the position of p m along the X, Y, and Z directions of the machine tool coordinate system.

[0031] Furthermore, in step 2: The undetermined coefficients in the covariance matrix Σ p are obtained by the least squares estimation method.

[0032] Furthermore, in step 2: The covariance matrix Σ Θ is:

[0033]

[0034] In the formula, σ Θ is the repeatability standard deviation when calibrating the pre-travel error, σ1 is the uncertainty of the standard ball used during calibration, σ2 is the alignment tolerance manually set during calibration, σ3 is the uncertainty of the on-machine probe itself when it leaves the factory; (v x , v y , v z ) are the components of the angle combination converted into the measurement vector in the machine tool coordinate system.

[0035] Furthermore, in step 3.1, L p and L Θ are obtained by using the Cholesky decomposition method for the covariance matrices Σ p and Σ Θ to satisfy the following formula:

[0036] ​

[0037] Further, in step 3.2, the coordinate matrix D of theoretical measurement points S , with a dimension of 2×n S probe angle combination matrix T S , spatial error repeatability covariance matrix Σ p and pre-travel error repeatability covariance matrix Σ Θ are input into the multivariate random variable generator established in step 3.1, and the spatial error random samples of each theoretical measurement point can be obtained and

[0038] Further, the standard deviation obtained in step 4.1 is as follows:

[0039]

[0040] where h is the number of batches of Monte Carlo simulations; is the standard deviation of the first h - 1 batches of form and position dimension random samples; is the mean of the first h - 1 batches of samples, u (h) is the mean of the hth batch of samples.

[0041] Further, in step 4.2:

[0042]

[0043] where σ Act is the empirical value of the standard deviation of the machining error of the current feature form and position dimension;

[0044] If NDC≥5, P / T%≤10%, %R&R≤10%, it indicates that the in - machine measurement system has excellent measurement ability;

[0045] If NDC≥5, 10%≤P / T%≤30%, 10%≤%R&R≤30%, it indicates that the in - machine measurement system has qualified measurement ability;

[0046] If NDC<5, P / T%>30% or %R&R>30%, it indicates that the in - machine measurement system has unqualified measurement ability.

[0047] Advantages of the present invention:

[0048] 1. The present invention proposes a method for evaluating the credibility of an in - machine measurement system. For the form and position dimensions of specific features, through multi - dimensional evaluation indicators, it can analyze and quantify the measurement ability of the in - machine measurement system, effectively judge whether the measurement ability of the in - machine measurement system meets the standard, helps to promote the popularization and application of in - machine measurement technology, and has high engineering application value.

[0049] 2. Before the credibility evaluation of the present invention, it is necessary to predict the standard deviation of the random sample of the geometric dimension to be measured. When predicting the standard deviation of the random sample of the geometric dimension, the adaptive Monte Carlo method is adopted, which improves the prediction efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is the overall process of the credibility evaluation of the on-machine measurement system.

[0051] Figure 2 is the detection angle combination in the spherical coordinate system when the pre-travel error occurs.

[0052] Figure 3 is the credibility evaluation process for geometric dimensions. DETAILED DESCRIPTION OF THE INVENTION

[0053] Due to problems such as mechanical structure errors and assembly clearances of the on-machine measurement system, its measurement results are affected by multiple geometric errors. Therefore, before entering the working state, error calibration devices such as laser interferometers and ballbar testers are usually used to calibrate the errors of the on-machine measurement system. However, there are many error sources in the on-machine measurement system and they are coupled with each other, and systematic errors are usually difficult to completely compensate. On the other hand, the operating conditions of the on-machine measurement system are variable and complex, and the internal errors are dynamically changing. The dynamically changing errors greatly affect the repeatability of the on-machine measurement system. To evaluate the measurement ability of the on-machine measurement system under the influence of the dynamic changes of multi-source errors, the present invention proposes a method for evaluating the credibility of the on-machine measurement system for geometric dimensions.

[0054] The present invention will be further described in detail below with reference to the drawings and embodiments.

[0055] Refer to Figure 1 , the method for evaluating the credibility of the on-machine measurement system for geometric dimensions provided by the embodiment of the present invention includes the following steps:

[0056] Step 1: Calibrate the spatial error of the numerical control machine tool in the on-machine measurement system;

[0057] The on-machine measurement system mainly consists of two parts: the numerical control machine tool body and the on-machine probe. Its systematic errors mainly come from two dimensions: one is the spatial geometric error of the motion axis system of the numerical control machine tool, and the other is the pre-travel error when the on-machine probe is triggered. To accurately evaluate the measurement ability of the system after error compensation, it is necessary to focus on studying the contribution mechanism of the repeatability characteristics of the two types of error sources to the uncertainty of the measurement results.

[0058] From the analysis of the error transfer mechanism, the pre-travel error of the on-machine probe, as an inherent characteristic of contact measurement, its influence quantity can be deterministically calculated through theoretical modeling. In contrast, due to the geometric error coupling involved in multi-axis linkage of the CNC machine tool, the influence of its repeatability characteristics on the measurement results has significant uncertainty. Therefore, it is necessary to accurately obtain the spatial errors at multiple positions in the stroke of the CNC machine tool through experimental calibration methods, so as to provide reliable input parameters for the repeatability covariance matrix of spatial errors.

[0059] The present invention uses the calibration standard device and method disclosed in the patent application "Standard device and calibration method for calibrating multi-source comprehensive errors of on-machine measurement system (Application No.: CN202410071142.0)" to repeatedly calibrate the spatial errors at multiple positions in the stroke of the on-machine measurement system, and a set of spatial errors at multiple positions in the stroke of the on-machine measurement system can be obtained.

[0060]

[0061] Among them, n p represents the number of repeated measurements of spatial errors, N represents the number of measurement positions of spatial errors, represents the spatial error vector of the jth repeated measurement at the calibration position p m in the calibration experiment. To ensure the stability of experimental data and the accuracy of variance estimation, in the present invention, it is required that n p ≥4.

[0062] During the repeated measurement process, in order to consider the influence of environmental temperature and the working conditions of the on-machine measurement system, the repeated measurement times should be distributed at different times of a day and different working periods of the machine tool. It should be noted that the evaluation premise of the present invention is that the on-machine measurement system has been error-calibrated by error calibration devices such as laser interferometers and ballbar testers, that is, the spatial errors have been compensated, and the uncompensated part of the errors is incorporated into the repeatability error of the spatial errors and the repeatability error of the pre-travel error. Therefore, the set of spatial errors measured here is the combined result of the uncompensated part of the errors and the repeatability error.

[0063] Step 2: Establish a repeatability model of the on-machine measurement system, and this repeatability model includes the repeatability covariance matrix Σ p of the spatial error component and the repeatability covariance matrix Σ Θ of the pre-travel error component;

[0064] The entire measurement process of the in-machine measurement system is automated measurement, so accidental human errors will not be introduced, and its random error is only related to the in-machine measurement system. According to the structural composition of the in-machine measurement system, the main sources of its repeatability error are the in-machine probe system and the CNC machine tool motion system. Also, since the in-machine probe system and the CNC machine tool motion system belong to different mechanisms, the repeatability errors caused by the two are independent of each other.

[0065] Step 2.1: Analyze the spatial error distribution of the in-machine measurement system and establish the repeatability covariance matrix Σ of the spatial error components at any position p. p ;

[0066] The spatial error of the in-machine measurement system is a spatial vector, and the spatial error δ measured at any position p within the stroke p can be decomposed into components along the X, Y, and Z directions of the machine tool coordinate system (the coordinate system set by the manufacturer when the CNC machine tool leaves the factory), that is:

[0067]

[0068] To better describe the random characteristics of the spatial error of the in-machine measurement system, based on the central limit theorem, experience, and historical data, it is known that the error often conforms to a normal distribution. Therefore, it is assumed that the spatial error follows a three-variable normal distribution, that is, the random variable is δ p can be expressed as

[0069]

[0070] Since the evaluated in-machine measurement system has been compensated, the distribution of the random variable δ p can be regarded as a three-variable normal distribution with a mean of 0. The influence of the uncompensated part of the error and the repeatability error accumulates together into the covariance matrix Σ p Therefore, Equation (3) is modified to:

[0071]

[0072] Σ p is the repeatability covariance matrix of the three spatial error components at position p, used to describe the relationship between the spatial error components in different directions. Its representation form is:

[0073]

[0074] In the formula, the main diagonal elements are the standard deviations of the random variable δ p at position p, and the off-diagonal elements are the covariances between the spatial error components in different directions.

[0075] The covariance matrix Σ of the spatial error components obtained from the above formula (5) pRepresents the repeatability at position p. This matrix is related to the spatial position. To establish a continuous spatial error repeatability model, the least squares method is used to fit polynomials to determine the covariance matrix Σ p The polynomial functions of the elements in p related to the positions in the X, Y, and Z directions. The main diagonal elements of the covariance matrix Σ

[0076]

[0077] where, represents the three main diagonal elements of the covariance matrix Σ p ; p k represents the k-th component of position p; α U,_ , β U,_ , γ U,_ represent 10 coefficients to be determined, which can be solved based on the set of measured spatial errors (see Equation (1)).

[0078] The off-diagonal elements of the covariance matrix Σ p are represented as the following polynomial functions:

[0079]

[0080] where, represents the off-diagonal elements of the covariance matrix Σ p ; p k represents the k-th component of position p; α V,W,_ , β V,W,_ , γ V,W,_ represent 10 coefficients to be determined, which can be solved based on the set of measured spatial errors (see Equation (1)).

[0081] According to Equation (5), if the coefficients to be determined in the above Equations (6) and (7) can be solved, the covariance matrix Σ p at any position can be obtained through Equations (6) and (7).

[0082] To estimate the coefficients to be determined in Equations (6) and (7), the spatial error values in the multi-position repeated calibration spatial error set calibrated in Step 1 are used (see Equation (1)). The calibrated spatial error values decomposed into the X, Y, and Z directions can be expressed as:

[0083]

[0084] Therefore, combining Equations (6), (7), and (8) gives:

[0085] Calibration position p m The repeatability covariance matrix of the three spatial error components The main diagonal elements can be expressed as the following polynomial functions:

[0086]

[0087] where p m,k represents the k-th coordinate component (i.e., the value of X, Y, or Z) of the calibration position p m (i.e., the three spatial coordinates X, Y, Z).

[0088] At position p m The repeatability covariance matrix of the three spatial error components The non-main diagonal elements can be expressed as the following polynomial functions:

[0089]

[0090] Next, taking the main diagonal element as an example, based on the set of spatial errors at the N positions obtained in step one estimate the 10 coefficients α in the polynomial function of the main diagonal element X,_ , β X,_ , γ X,_ (specifically α X,0 , α X,1 , α X,2 , α X,3 , β X,1 , β X,2 , β X,3 , γ X,1 , γ X,2 , γ X,3 ) values.

[0091] Using the least squares estimation method, first establish the objective function S for minimizing the sum of squared residuals, expressed as follows:

[0092]

[0093] where represents the mean of the components of the spatial error in three directions for n m measurements at position p p . To minimize the objective function S, we take the partial derivatives with respect to each parameter α X,_ , β X,_ , γ X,_ respectively, and set the partial derivatives equal to 0, obtaining a system of equations containing 10 linear equations:

[0094]

[0095] The linear equations in the above formula (12) can be organized into a matrix form, namely:

[0096] Aa=0 (13)

[0097] Among them, A is the coefficient matrix composed of the coefficients of each parameter in the equation system, a=(α X,0 ,α X,1 ,…,γ X,3 ) T is a 10×1 parameter vector. By solving the solution vector of equation (13) through homogeneous transformation, the coefficient estimate can be obtained.

[0098] Similarly, the estimated values ​​of the coefficients in other formulas in equations (9) and (10) can be obtained:

[0099] Finally, the estimated values ​​of the coefficients are substituted into equations (6) and (7), and combined with equation (5), the repeatability covariance matrix Σ of the three spatial error components at any position p within the measurement range can be obtained. p .

[0100] Step 2.2: Analyze the pre-travel error distribution of the on-machine probe in the on-machine measurement system and establish the polar angle θ and azimuth angle Angle combination The repeatability covariance matrix of the pre-travel error component under Θ ;

[0101] Depend on Figure 2 It can be seen that the pre-travel error is a value of δ Θ , the direction is along the detection direction, and δ Θ Deemed to be subject to Θ ~N(E(δ Θ ),D(δ Θ ))One-dimensional normal distribution, where E(δ Θ ) and D(δ Θ ) are their mean and standard deviation respectively. Same as step 2.1, the pre-travel error δ Θ Decomposed into components along the X, Y, and Z directions of the machine tool coordinate system, namely:

[0102]

[0103] Among them, δ Θ is the polar angle θ and the azimuth angle Angle combination The pre-travel error value is measured below. After decomposition, it is expressed as:

[0104]

[0105] Combine the angles and convert them into the components (v x , v y , v z ) of the measurement vector in the machine coordinate system MCS. Then, Equation (15) can be expressed as:

[0106]

[0107] To further describe the randomness of the pre-travel error, similar to Step 2.1, decompose the pre-travel error into a three-dimensional random variable and assume that it follows a three-dimensional normal distribution with a mean of 0:

[0108]

[0109] Σ Θ is the repeatability covariance matrix of the three pre-travel error components for the combination of the polar angle θ and the azimuth angle . Its representation is:

[0110]

[0111] In the formula, the main diagonal elements are the standard deviations of the pre-travel error components in different directions, which can be expressed as:

[0112]

[0113] where: represents the standard deviation of the pre-travel error value at the specified measurement vector (v x , v y , v z ).

[0114] The remaining elements are the covariances between the pre-travel error components in different directions. The covariance is calculated based on the following formula:

[0115]

[0116] where:

[0117] n θ represents the number of repeated measurements, represents the pre-travel error component of the j-th (j ≤ n θ ) measurement, represents the pre-travel error component of the k-th (k ≤ n θ , k ≠ j) measurement.

[0118] Substituting Equation (15) into Equation (20), we get:

[0119]

[0120] Where: represents the value of the pre-travel error obtained from the i-th measurement.

[0121] Since δ Θ follows a distribution of δ Θ ~N(E(δ Θ ), D(δ Θ ))), Equation (21) can be expressed as:

[0122]

[0123] After further simplification, it becomes:

[0124]

[0125] Similarly, it can be calculated that:

[0126]

[0127] Substituting Equations (19), (23), and (24) into Equation (18), the repeatability covariance matrix Σ Θ of the pre-travel error can be expressed as:

[0128]

[0129] When calibrating the pre-travel error, the standard deviation σ Θ of its error repeatability has three sources, namely: the uncertainty σ1 of the standard ball used during calibration; the alignment tolerance σ2 set manually during the calibration process; and the uncertainty σ3 of the on-machine probe itself when it leaves the factory.

[0130] In the method of this embodiment, the calibration equipment used includes a ceramic standard ball and a Renishaw OMP400 type trigger probe. By referring to the calibration certificate of the standard ball, it can be known that its expanded uncertainty is U 95 = 0.5 μm, following a normal distribution. When the confidence level is 95%, the coverage factor is taken as k 95 = 1.96; the alignment tolerance of the ball center set during the calibration process is [0, 2] μm, following a uniform distribution. When the confidence level is 95%, the coverage factor is taken as The nominal repeatability accuracy of the probe is 0.25 μm, following a normal distribution. When the confidence level is 95%, the coverage factor is taken as k 95 = 1.96. Then, the standard deviation of the repeatability introduced by the pre-travel error is calculated as follows:

[0131]

[0132] Therefore, substituting the value calculated by Equation (27) into Equation (25), the angle combinations of the polar angle θ and the azimuth angle are obtained, and the repeatability covariance matrix Σ of the following three pre-travel error components is as follows: Θ That is:

[0133]

[0134] Step 3: Construct a geometric dimension random sample generator;

[0135] Step 3.1: Establish a multivariate random variable generator;

[0136] The main idea of Monte Carlo simulation is to estimate the output quantity Y = f(X) calculated from the sample x according to the input sample X = (x1, x2..., x N ) T and the covariance of the input sample X.

[0137] Before performing Monte Carlo simulation, it is necessary to establish a multivariate random variable generator. Based on this multivariate random variable generator, multivariate random samples that conform to the specified distribution are generated.

[0138] In the multivariate random sample generation model established in the present invention, the input is a theoretical measurement point vector (X m , Y m , Z m ) T in the machine tool coordinate system, the detection angle combination the spatial error repeatability covariance matrix Σ p , and the pre-travel error repeatability covariance matrix Σ Θ . The output is a ternary random sample that satisfies the specified distribution, that is, the theoretical point sample perturbed by the pre-travel error repeatability and the spatial error repeatability, and the number of samples is arbitrary.

[0139] To establish a multivariate random variable generator, first use the Cholesky decomposition method to decompose these two covariance matrices into the product of a lower triangular matrix and the transpose of a lower triangular matrix, which is expressed as:

[0140]

[0141] where L p and L Θ are lower triangular matrices.

[0142] The Cholesky decomposition is to transform the standard normal distribution into a distribution with a target covariance structure through a linear transformation, that is, only by taking a random vector in the multivariate standard normal distribution can it be converted into a random vector conforming to the specified distribution. Since the basis of the adaptive Monte Carlo simulation is to have a large number of random samples, it is necessary to use the linear transformation related to L p and L Θ to obtain a matrix G p and Σ Θ containing Nums covariance random vectors, and the calculation process is expressed as: p and G Θ , where:

[0143]

[0144] Among them, G p and G Θ are 3×Nums matrices, and each column represents a 3D random vector conforming to the covariance matrices Σ p , Σ Θ . Z is also a 3×Nums matrix, and each column represents a 3D standard normal random vector.

[0145] Equation (30) is the multivariate random variable generator established in this step, which can be used to generate random samples of spatial errors G p at any theoretical point p in the measurement path planning of the in-machine measurement system and random samples of pre-travel errors G at the theoretical detection angle combination Θ .

[0146] Step 3.2: Construct a random sample generator for geometric dimension and tolerance;

[0147] The multivariate random variable generator established in Step 3.1 can generate random multivariate samples of spatial errors and pre-travel error repeatability at any theoretical point and theoretical detection angle combination in the in-machine measurement path planning: G p and G Θ . However, in engineering applications, the measurement accuracy of a single measurement point is not actually concerned, but rather the measurement accuracy of the geometric dimension and tolerance of features is given higher priority. Therefore, the evaluation object in this invention is the geometric dimension and tolerance. Further, the characterization result of the geometric dimension and tolerance is related to the distribution, quantity, and calculation method of the measurement points. Therefore, its repeatability analysis is also related to all the above factors. The specific analysis process is as follows:

[0148] Step 3.2.1: Determine the number, coordinate values, and detection angle combinations of the theoretical measurement points required for calculating the geometric dimension and tolerance according to the process plan. Establish a theoretical measurement point coordinate matrix D S and a detection angle combination matrix T S , where DS has a dimension of 3×n S , T S has a dimension of 2×n S , n S represents the number of theoretical measurement points.

[0149] Step 3.2.2: Input the coordinate matrix D of theoretical measurement points S , the detection angle combination matrix T S , the spatial error repeatability covariance matrix Σ p and the pre-travel error repeatability covariance matrix Σ Θ into the multivariate random variable generator established in Step 3.1, and the spatial error random samples of each theoretical measurement point can be obtained The pre-travel error random samples of each detection angle combination The measurement point random samples affected by spatial error and pre-travel error can be expressed as

[0150]

[0151] In the formula: are all matrices of 3×Nums, D S (i) represents the i-th column of D S of.

[0152] Step 3.2.3: According to the form and position dimension fitting and calculation method, the form and position dimension results can be calculated. For different form and position dimensions, their fitting and calculation methods are different, and there are corresponding mature fitting and calculation methods at present. Therefore, the present invention will not introduce them in detail here. Let the form and position dimension calculation function be f, then the form and position dimension random samples calculated from the measurement point random samples obtained in Step 3.2.2 are expressed as R = (R1, R2…, R Nums ), R is a 1×Nums vector, and the j-th element in R is expressed as:

[0153]

[0154] In the formula: represents the j-th column in the matrix.

[0155] Equation (32) is the form and position dimension random sample generator constructed in this step, which can be used to generate form and position dimension random samples at any position.

[0156] Step Four: Evaluate the credibility of the on-machine measurement system for form and position dimensions;

[0157] Step 4.1: Predict the standard deviation of form and position dimension random samples based on the adaptive Monte Carlo method;

[0158] The adaptive Monte Carlo method is an improvement of the traditional Monte Carlo method. It performs Monte Carlo simulations in batches to estimate the distribution (i.e., mean and standard deviation) of the geometric dimension to be measured until the difference between the standard deviations estimated in adjacent batches is less than the numerical tolerance δ, and then outputs the distribution of the geometric dimension to be measured at this time. This method can effectively reduce the computational cost of Monte Carlo and improve the computational efficiency.

[0159] During the adaptive Monte Carlo simulation, the numerical tolerance δ is the threshold for judging whether the simulation converges, and it is expressed as:

[0160]

[0161] where l is the minimum number of significant digits of the evaluation object. For example, if the measured value of the spatial error is 0.021 mm, which is expressed in scientific notation as 2.1×10 -3 mm, then l is -3 and the numerical tolerance is δ = 0.0005 mm.

[0162] First, determine the sample size Nums. To ensure the reliability and stability of the adaptive Monte Carlo simulation, Nums is taken as:

[0163] Nums = max(J, 10 4 ) (34)

[0164] where J is an integer greater than or equal to 100 / (1 - p), and p is the confidence probability, usually taken as 99.5%.

[0165] Next, perform Monte Carlo simulations in batches. The simulation process is as shown in the upper part, and the specific steps are as follows: Figure 3 as follows:

[0166] Step 4.1.1: Let the batch number be 1 (h = 1);

[0167] Step 4.1.2: Based on the geometric dimension random sample generator constructed in Step 3.3, generate the first batch of Nums geometric dimension random samples R (1) , and calculate the mean u (1) of the first batch of samples and the standard deviation s (1) ;

[0168] Step 4.1.3: Increment the batch number by 1 (h = h + 1);

[0169] Step 4.1.4: Based on the geometric dimension random sample generator constructed in Step 3.2, generate the second batch of geometric dimension random samples R (2) , and calculate the mean u (2) of the second batch of samples and the standard deviation s (2) ;

[0170] And so on;

[0171] Step 4.1.5: Based on the geometric dimension random sample generator constructed in Step 3.2, generate the i-th batch of geometric dimension samples R (i) , and calculate the mean u (i) and the standard deviation s (i) (i = 3, 4, …, h);

[0172] Step 4.1.6: Determine the minimum standard deviation s min = min(s (1) , … s (h) ) and the maximum standard deviation s max = max(s (1) , … s (h) );

[0173] Step 4.1.7: Calculate the standard deviation ξ u of the means of each batch and the standard deviation ξ s of the standard deviations of each batch:

[0174]

[0175] Step 4.1.8: Determine whether 2max(s min , s max , ξ u , ξ s ) < δ holds. If it does not hold, the loop condition is satisfied, and Steps 4.1.3 - 4.1.8 are repeated. If it holds, the loop is exited, and the mean and the standard deviation of the current geometric dimension random sample to be measured are calculated. The recursive calculation method is as follows:

[0176]

[0177] where, is the mean of the first h - 1 batches of samples.

[0178]

[0179] where, is the standard deviation of the first h - 1 batches of geometric dimension random samples.

[0180] Step 4.2: Calculate the confidence evaluation index based on the MSA theory;

[0181] The credibility evaluation of the in - machine measurement system refers to measuring its reliability, stability, and the credibility of measurement results by evaluating the measurement ability of the measurement system for the geometric dimensions of specified features. The theory of Measurement System Analysis (MSA) starts from the perspective of products and evaluates the credibility of the measurement system by analyzing product quality and consistency. In step three of the present invention, the prediction of the standard deviation of the specified geometric dimension measurement replaces the product detection process, enhancing the generality of the evaluation while getting rid of the dependence on product parts and greatly reducing the evaluation cost.

[0182] The main indicators for evaluating the measurement ability are the effective resolution NDC, precision - to - tolerance ratio P / T%, and repeatability and reproducibility percentage %R&R defined in MSA. They quantify the performance of the in - machine measurement system from three perspectives respectively:

[0183] (1) The effective resolution NDC is used to quantify the sensitivity of the in - machine measurement system; it mainly evaluates the minimum change that the in - machine measurement system can detect. The in - machine measurement system needs to have sufficient resolution to distinguish measurement errors from part processing errors. Otherwise, it may miss key quality differences and cause misjudgment of products.

[0184] (2) The precision - to - tolerance ratio P / T% is used to quantify the precision of the in - machine measurement system; P / T% compares the precision of the in - machine measurement system with the product tolerance range to ensure that the precision of the in - machine measurement system can meet the process requirements. An excessive P / T% ratio means that the in - machine measurement system is not suitable for the current task and may cause non - conforming products to flow into the downstream process. Therefore, P / T% ensures that the in - machine measurement system can provide sufficient measurement precision and will not cause misjudgment of products due to measurement errors.

[0185] (3) The repeatability and reproducibility percentage %R&R is used to quantify the stability and consistency of the in - machine measurement system; a lower %R&R means that the in - machine measurement system has small errors and consistent measurement results, which is suitable for practical applications.

[0186] The specific calculation methods of these three indicators are as follows:

[0187] Effective resolution NDC:

[0188]

[0189] where σ Act is the empirical value of the standard deviation of the machining error of the geometric dimension of this feature (which can be obtained by cumulative calculation of the machining data of the current machined parts, and the cumulative calculation method is a well - known method), is the predicted value of the standard deviation of the random sample of the geometric dimension obtained in step 4.1.

[0190] For an in - machine measurement system, the higher the value of the effective resolution NDC, the smaller the minimum change that the in - machine measurement system can detect, and the higher the sensitivity of the in - machine measurement system. To ensure the minimum requirement of sufficient fineness for the in - machine measurement system, its effective resolution NDC should be at least 5, that is, the in - machine measurement system can distinguish at least 5 different measurement values.

[0191] Precision tolerance ratio P / T%:

[0192]

[0193] Where TOL is the design tolerance of the geometric dimension.

[0194] For an in - machine measurement system, the smaller the value of the precision tolerance ratio P / T%, the more sufficient the precision of the in - machine measurement system to meet the precision requirements for measuring the geometric dimension. The precision tolerance ratio P / T% should be less than or equal to 10%, that is, the precision error of the in - machine measurement system accounts for less than 10% of the tolerance range. If the precision tolerance ratio P / T% is between 10% - 30%, it means that the in - machine measurement system is still acceptable, but the measurement precision is insufficient and needs to be improved. If the precision tolerance ratio P / T% exceeds 30%, it means that the in - machine measurement system is unqualified and the systematic error is too large.

[0195] Repeatability and reproducibility percentage %R&R:

[0196]

[0197] For an in - machine measurement system, the smaller the value of the repeatability and reproducibility percentage %R&R, the better the stability and consistency of the in - machine measurement system. The repeatability and reproducibility percentage %R&R value should be less than 10%, indicating that the total error of the in - machine measurement system is small and the measurement results are very stable and consistent. If the repeatability and reproducibility percentage %R&R value is between 10% - 30%, it means that the error of the in - machine measurement system is within an acceptable range, but improvement needs to be considered. If the repeatability and reproducibility percentage %R&R value is greater than 30%, it means that the error of the in - machine measurement system is too large and unacceptable, and the equipment needs to be redesigned or replaced.

[0198] In summary, the process for evaluating the credibility of an in - machine measurement system for a specified feature geometric dimension is as Figure 3 shown in the lower part. If any of the three evaluation indicators is unqualified, the credibility of the in - machine measurement system will be unqualified when measuring the specified geometric dimension, and its measurement ability will not be sufficient to meet the measurement requirements.

Claims

1. A method for evaluating the credibility of an on-machine measurement system for shape, position and size, characterized in that: The following steps are involved: Step 1: Obtain the spatial error set at multiple positions in the travel of the on-machine measurement system through calibration; Step 2: Establish a repeatability model for the on-machine measurement system, including: The repeatability covariance matrix Σ of the spatial error component at any position p p ,Σ p The main diagonal elements of are the spatial errors δ at any position p. p The standard deviation of the error components in different directions, and the remaining elements are the covariances between the spatial error components in different directions; Polar angle θ and azimuth angle Angle combination The repeatability covariance matrix of the pre-travel error component under Θ ,Σ Θ The main diagonal elements of are the standard deviations of the pre-travel errors in different directions, and the remaining elements are the covariances between the pre-travel error components in different directions; The spatial error set is used to solve the repeatability covariance matrix Σ p The undetermined coefficients in ; Step 3: Construct a random sample generator of shape, position and size; Step 3.1: Create a multivariate random variable generator: In the formula, G p and G Θ are the random sample of spatial error and the theoretical detection angle combination at any theoretical point p in the measurement path planning of the on-machine measurement system. Random sample of pre-travel error at G Θ ; G p and G Θ Each column is a 3×Nums matrix, and each column represents a covariance matrix Σ p and Σ Θ 3D random vector; Z is a 3×Nums matrix, each column represents a 3D standard normal random vector; L p and L Θ All are lower triangular matrices; Step 3.2: Construct a random sample generator of shape, position and size: In the formula, R j is a random sample of shape and size R = (R1, R2…, R Nums ), j=1,2,…,Nums; f is the shape and position size calculation function; is a random sample of measurement points affected by spatial error and pre-travel error D S (i) indicates that the dimension is 3×n S Theoretical measurement point coordinate matrix D S The i-th column of and are the random samples of spatial error and pre-travel error at each theoretical measurement point, generated by the multivariate random variable generator established in step 3.1, i = 1, 2, …, n s ; Step 4: Evaluate the reliability of the on-machine measurement system; Step 4.1: Predict the standard deviation of the random sample of the current shape and position size to be measured based on the adaptive Monte Carlo method Step 4.2: Using standard deviation Based on the MSA theory, the following formula is used to calculate the reliability evaluation index, including the effective resolution NDC, the precision tolerance ratio P / T%, and the repeatability and reproducibility percentage %R&R, and the evaluation is performed according to the obtained reliability evaluation index.

2. The method for evaluating the credibility of an on-machine measurement system for shape, position and dimension according to claim 1, characterized in that: In step 2: In the formula, is the spatial error δ at position p p Error components in the X, Y, and Z directions of the machine tool coordinate system; Use the p obtained in step 1 m Repeat the calibration results at the position several times to estimate p m Covariance matrix at location The coefficients of the functions representing each element in the equation are obtained, that is, the covariance matrix Σ p The undetermined coefficient values ​​in ; The main diagonal elements of are calculated as: The remaining elements of are calculated as: In the formula, α X,_ ,β X,_ ,γ X,_ , α X,Y，_ ,α X,Z，_ ,α Y,Z，_ ,β X,Y,_ ,β X,Z,_ ,β Y,Z,_ ,γ X,Y,_ ,γ X,Z,_ ,γ Y,Z,_ is the covariance matrix Σ p The unknown coefficient in p m,k Indicates the calibration position p m The kth component of p Indicates the number of repeated measurements of spatial error; For p m Spatial error of the jth measurement at position Components along the X, Y, and Z directions of the machine tool coordinate system.

3. The method for evaluating the credibility of an on-machine measurement system for shape, position and dimension according to claim 2, characterized in that: In step 2: covariance matrix Σ p The unknown coefficients in are obtained by the least squares estimation method.

4. The method for evaluating the credibility of an on-machine measurement system for shape, position and dimension according to claim 3 is characterized in that: In step 2: covariance matrix Σ Θ for: In the formula, σ Θ is the repeatability standard deviation when calibrating the pre-travel error, σ1 is the uncertainty of the standard ball used in calibration, σ2 is the alignment tolerance set manually during calibration, and σ3 is the uncertainty of the probe itself when it leaves the factory; (v x ,v y ,v z ) is the angle combination The components of the measurement vector converted to the machine tool coordinate system.

5. The method for evaluating the credibility of an on-machine measurement system for shape, position and dimension according to any one of claims 1 to 4, characterized in that: In step 3.1, L p and L Θ The covariance matrix Σ is decomposed by Cholesky method. p and Σ Θ Get, satisfying the following formula:

6. The method for evaluating the credibility of an on-machine measurement system for shape, position and dimension according to claim 5, characterized in that: In step 3.2, the theoretical measurement point coordinate matrix D S , dimension is 2×n S Detection angle combination matrix T S , spatial error repeatability covariance matrix Σ p and the pre-travel error repeatability covariance matrix Σ Θ Input into the multivariate random variable generator established in step 3.1, and you can get the random sample of spatial error at each theoretical measurement point. and 7. The method for evaluating the credibility of an on-machine measurement system for shape, position and dimension according to claim 6, characterized in that: The standard deviation obtained in step 4.1 for: Where h is the number of batches of Monte Carlo simulation; is the standard deviation of the random samples of shape and position dimensions of the previous h-1 batches; is the mean of the previous h-1 batches of samples, u (h) is the mean of the hth batch of samples.

8. The method for evaluating the credibility of an on-machine measurement system for shape, position and dimension according to claim 7, characterized in that: In step 4.2: In the formula, σ Act is the empirical value of the standard deviation of the machining error of the current feature shape and size; If NDC ≥ 5, P / T % ≤ 10%, % R&R ≤ 10%, it indicates that the on-machine measurement system has excellent measurement capabilities; If NDC ≥ 5, 10% ≤ P / T% ≤ 30%, 10% ≤ % R&R ≤ 30%, it indicates that the measurement capability of the on-machine measurement system is qualified; If NDC is less than 5, P / T%>30% or %R&R>30%, it indicates that the measurement capability of the on-machine measurement system is unqualified.

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