A reliability evaluation method for on-machine measurement systems oriented towards geometric dimensions

Abstract

This invention provides a reliability assessment method for in-machine measurement systems focusing on geometric dimensions, aiming to address the problems of unknown measurement repeatability, sufficiency of measurement capability, and reliability of measurement results for specific geometric dimensions. The invention first constructs a repeatability model of the in-machine measurement system, including the repeatability covariance matrix of spatial error components and pre-travel error components. Then, based on the repeatability covariance matrix, a multivariate random variable generator is constructed to generate random samples of spatial error and pre-travel error. Next, a random sample generator for geometric dimensions is constructed using the random samples generated by the multivariate random variable generator to generate random samples of geometric dimensions. Then, the standard deviation of the random samples of geometric dimensions is predicted using the adaptive Monte Carlo method. Finally, based on this standard deviation, MSA (Mean Satisfaction Analysis) is used to perform a multi-dimensional reliability assessment of the measurement system.

Description

Technical Field

[0001] This invention relates to the field of in-machine measurement technology, and more specifically to a reliability assessment method for in-machine measurement systems oriented towards geometric dimensions. Background Technology

[0002] In the aerospace field, complex, weakly rigid, and difficult-to-machine parts place extremely stringent demands on manufacturing technology. Traditional machining methods struggle to achieve the required high precision and ensure consistency and stability throughout the process. To keep pace with the rapid development of intelligent manufacturing and meet the demands for more efficient and consistent machining, in-machine measurement technology has seen increasingly widespread development and application. As an advanced intelligent automated manufacturing method, in-machine measurement technology can monitor the size, shape, and position of workpieces in real time during machining, thereby reducing manual inspection and rework time and significantly improving machining efficiency.

[0003] In a reliable quality management system, the machining and measurement processes are separated to achieve high-precision measurement under strict control and accurately judge the machining results of parts. However, in-machine measurement technology combines machining and measurement tasks, bringing new opportunities but also new challenges—the reliability of in-machine measurement systems is difficult to assess. The measurement process of in-machine measurement systems is "body machining and body measurement," lacking systematic means to evaluate measurement capabilities. Therefore, the reliability of its measurement results is questionable, the measurement accuracy is unknown, and the measurement capability is difficult to quantify.

[0004] While some evaluation methods for measurement systems have been proposed in the literature, such as patent application "An Uncertainty Evaluation Method, System, Equipment and Medium for a Large-Size Polygonal Coordinate Measurement System (Application No.: CN202410079102.0)," which evaluates uncertainty by analyzing the measurement uncertainty of an optical polygonal coordinate measurement system; and patent application "A Metrological Performance Evaluation Method for Automated Verification Systems Based on Measurement System Analysis (Application No.: CN202410616715.3)," which uses measurement system analysis (MSA) theory to evaluate the metrological performance of automated verification lines, offering high efficiency and usability, these methods are difficult to implement for specific analysis and evaluation of the geometric dimensions of each feature of every part in production and processing. Therefore, there is an urgent need for an evaluation method for on-machine measurement systems that focuses on the geometric dimensions of specified features. Summary of the Invention

[0005] This invention provides a reliability evaluation method for in-machine measurement systems oriented towards geometric dimensions, aiming to solve the problems of unknown measurement repeatability of in-machine measurement systems for specified geometric dimensions, whether the measurement capability of in-machine measurement systems is sufficient, and whether the measurement results are reliable.

[0006] The technical solution of this invention is:

[0007] A reliability evaluation method for an in-machine measurement system oriented towards geometric dimensions, characterized by the following steps:

[0008] Step 1: Obtain the set of spatial errors at multiple locations during the travel of the on-machine measurement system through calibration;

[0009] Step 2: Establish a repeatability model for 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 element is the spatial error 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;

[0011] Polar angle θ and azimuth angle Angle Combination The repeatability covariance matrix Σ of the pre-travel error components Θ , Σ Θ The main diagonal elements 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 spatial error set is used to solve the repeatability covariance matrix Σ. p The undetermined coefficients in;

[0013] Step 3: Construct a random sample generator for shape, position, and size;

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

[0015]

[0016] In the formula, G p and G Θ These represent random spatial error samples and theoretical detection angle combinations at any theoretical point p in the measurement path planning of the on-board measurement system. Random sample G of the pre-travel error at the location 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 Z is a 3-dimensional random vector; Z is a 3×Nums matrix, where each column represents a 3-dimensional standard normal random vector; L p and L Θ All are lower triangular matrices;

[0017] Step 3.2: Construct a random sample generator for shape, position, and size:

[0018]

[0019] In the formula, R j For a random sample of shape and size, R = (R1, R2, ..., R...) Nums The j-th element in the expression, where j = 1, 2, ..., Nums; f is the function for calculating geometric dimensions; Random samples of measurement points affected by spatial errors and pre-travel errors D S (i) indicates a dimension of 3×n S The theoretical measurement point coordinate matrix D S The i-th column; and These are random samples of spatial error and random samples of pre-trip error for each theoretical measurement point, generated by the multivariate random variable generator established in step 3.1, i = 1, 2, ..., n. s ;

[0020] Step 4: Evaluate the reliability of the in-machine measurement system;

[0021] Step 4.1: Predict the standard deviation of random samples of the current form and position dimensions to be measured based on the adaptive Monte Carlo method.

[0022] Step 4.2: Using standard deviation Based on MSA theory, the reliability assessment index is calculated using the following formula, including effective resolution (NDC), accuracy tolerance ratio (P / T%), and repeatability and reproducibility percentage (R&R). The reliability assessment is then performed based on the obtained reliability assessment index.

[0023] Furthermore, in step 2:

[0024]

[0025] In the formula, The spatial error δ at position p p Error components in the X, Y, and Z directions of the machine tool coordinate system; using p obtained from the calibration in step 1. m Repeated calibration results at the location are used to estimate p. m Covariance matrix at location The coefficients of the functions represented by each element are used to obtain the covariance matrix Σ. p The undetermined coefficient values ​​in;

[0026] The formula for calculating the main diagonal elements is:

[0027]

[0028] The formulas for calculating the remaining elements are:

[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,_ The covariance matrix Σ p The undetermined coefficients in p; m,k Indicates the calibration position p m The k-th component; n p Indicates the number of repeated measurements for spatial error; For p m Spatial error of the j-th measurement at location The components along the X, Y, and Z directions of the machine tool coordinate system.

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

[0032] Furthermore, in step 2: the covariance matrix Σ Θ for:

[0033]

[0034] In the formula, σ Θ To calibrate the repeatability standard deviation when determining the pre-stroke error, σ1 is the uncertainty of the standard sphere used during calibration, σ2 is the manually set correction tolerance during calibration, and σ3 is the inherent uncertainty of the probe at the time of manufacture; (v x ,v y ,v z ( ) is an angle combination Convert the components of the measurement vector into the machine tool coordinate system.

[0035] Furthermore, in step 3.1, L p and L Θ The Cholesky decomposition method is used to analyze the covariance matrix Σ. p and Σ Θ We obtain the following equation:

[0036]

[0037] Furthermore, in step 3.2, the theoretical measurement point coordinate matrix D... S The dimension is 2×n S Detection angle combination matrix T S Spatial error repeatability covariance matrix Σ p and the repeatability covariance matrix Σ of the pre-travel error Θ By inputting the multivariate random variable generator established in step 3.1, random samples of spatial errors for each theoretical measurement point can be obtained. and

[0038] Furthermore, the standard deviation obtained in step 4.1 for:

[0039]

[0040] In the formula, h represents the number of batches simulated in the Monte Carlo simulation; The standard deviation of the first h-1 batch of random samples of shape and dimension; The mean of the first h-1 batches of samples, u (h) is the mean of the h-th batch of samples.

[0041] Furthermore, in step 4.2:

[0042]

[0043] In the formula, σ Act This is the empirical value of the standard deviation of the current feature shape and dimension machining error;

[0044] If NDC≥5, P / T%≤10%, and %R&R≤10%, it indicates that the on-machine measurement system has excellent measurement capabilities.

[0045] If NDC≥5, 10%≤P / T%≤30%, and 10%≤%R&R≤30%, it indicates that the measurement capability of the on-machine measurement system is qualified.

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

[0047] The beneficial effects of this invention are:

[0048] 1. This invention proposes a reliability evaluation method for in-machine measurement systems. For specific features of shape and position dimensions, it can analyze and quantify the measurement capability of the in-machine measurement system through multi-dimensional evaluation indicators. It can effectively determine whether the measurement capability of the in-machine measurement system meets the standards, which helps to promote the popularization and application of in-machine measurement technology and has high engineering application value.

[0049] 2. Before the credibility assessment, this invention needs to predict the standard deviation of random samples of the shape and size to be tested. The adaptive Monte Carlo method is used to predict the standard deviation of random samples of shape and size, which improves the prediction efficiency. Attached Figure Description

[0050] Figure 1 This is the overall process for evaluating the reliability of in-machine measurement systems.

[0051] Figure 2 It is a combination of detection angles in spherical coordinates. Pre-travel error at that time.

[0052] Figure 3 It is a reliability assessment process oriented towards geometric dimensions. Detailed Implementation

[0053] Due to mechanical structural errors and assembly clearances, the measurement results of in-machine measurement systems are affected by multiple geometric errors. Therefore, before entering the working state, error calibration devices such as laser interferometers and ballbars are typically used to calibrate the errors of the in-machine measurement system. However, in-machine measurement systems have numerous and coupled error sources, making it difficult to completely compensate for system errors. On the other hand, the operating conditions of in-machine measurement systems are varied and complex, and their internal errors are dynamically changing, which greatly affects the repeatability of the in-machine measurement system. To evaluate the measurement capability of in-machine measurement systems under the influence of dynamic changes in multi-source errors, this invention proposes a reliability evaluation method for in-machine measurement systems focusing on geometric dimensions.

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

[0055] Reference Figure 1 The reliability evaluation method for an in-machine measurement system oriented towards geometric dimensions provided in this embodiment of the invention includes the following steps:

[0056] Step 1: Spatial error calibration of CNC machine tools in the machine measurement system;

[0057] The in-machine measurement system mainly consists of two parts: the CNC machine tool body and the in-machine probe. Its system error primarily originates from two dimensions: the spatial geometric error of the CNC machine tool's motion axes and the pre-stroke error when the in-machine probe is triggered. To accurately assess the system's measurement capability after error compensation, it is necessary to focus on studying the contribution mechanism of the repeatability characteristics of these two error sources to the measurement result uncertainty.

[0058] From the perspective of error propagation mechanism analysis, the pre-stroke error of the machine probe, as an inherent characteristic of contact measurement, can be deterministically calculated through theoretical modeling. In contrast, the spatial error of CNC machine tools, due to the geometric error coupling involved in multi-axis linkage, exhibits significant uncertainty in its repeatability characteristics and impact on measurement results. Therefore, it is necessary to accurately obtain the spatial error at multiple positions during the CNC machine tool's stroke through experimental calibration methods, thereby providing reliable input parameters for the spatial error repeatability covariance matrix.

[0059] This invention employs the calibration standard and method disclosed in patent application "Standard for Calibration of Multi-Source Integrated Error of In-Machine Measurement System and Calibration Method (Application No.: CN202410071142.0)" to repeatedly calibrate the spatial errors at multiple locations during the travel of the in-machine measurement system, thereby obtaining the set of spatial errors at multiple locations during the travel of the in-machine measurement system.

[0060]

[0061] Where, n p This represents the number of repeated measurements of spatial error, where N represents the number of spatial error measurement locations. Indicates the calibration position p in the calibration experiment. m The spatial error vector of the j-th repeated measurement. To ensure the stability of the experimental data and the accuracy of the variance estimation, this invention requires n... p ≥4.

[0062] During repeated measurements, to account for the influence of ambient temperature and the operating conditions of the on-machine measurement system, the number of repeated measurements should be distributed across different times of the day and different working periods of the machine tool. It is worth noting that the evaluation premise of this invention is that the on-machine measurement system has already undergone error calibration using error calibration devices such as laser interferometers and ballbars; that is, the spatial error has been compensated. Any incompletely compensated errors are incorporated into the repeatability error of the spatial error and the repeatability error of the pre-travel error. Therefore, the set of spatial errors obtained here... This is the result of the combined effects of incompletely compensated partial errors and repeatability errors.

[0063] Step 2: Establish a repeatability model for the on-machine measurement system. This repeatability model includes the repeatability covariance matrix Σ of the spatial error components. p The repeatability covariance matrix Σ of the pre-travel error components Θ ;

[0064] The entire measurement process of the on-machine measurement system is automated, thus eliminating the introduction of human error; its random errors are solely related to the on-machine measurement system. Based on the structure of the on-machine measurement system, its repeatability errors primarily originate from the on-machine probe system and the CNC machine tool motion system. Since the on-machine probe system and the CNC machine tool motion system belong to different mechanisms, the repeatability errors caused by them are independent of each other.

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

[0066] The spatial error of an in-flight measurement system is a spatial vector, and the spatial error δ measured at any position p within the travel range is... p It 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), namely:

[0067]

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

[0069]

[0070] Since the on-machine measurement system being evaluated has been compensated, the random variable is δ. p The distribution can be considered as a ternary normal distribution with a mean of 0. The effects of incompletely compensated errors and repeatability errors accumulate in the covariance matrix Σ. p Therefore, equation (3) is modified as follows:

[0071]

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

[0073]

[0074] In the formula, the main diagonal element is the random variable δ at position p. p The standard deviation is given, and the off-diagonal elements are the covariance between spatial error components in different directions.

[0075] The covariance matrix Σ of the spatial error components obtained by equation (5) above pThe covariance matrix Σ represents the repeatability at position p and is spatially related. To establish a continuous spatial error repeatability model, the least squares method is used to fit a polynomial to determine the covariance matrix Σ. p The polynomial functions relating each element to its position in the X, Y, and Z directions will be used to construct the covariance matrix Σ. p The main diagonal elements represent the following polynomial function:

[0076]

[0077] in, Represents the covariance matrix Σ p The three main diagonal elements; p k α represents the k-th component at position p; U,_ ,β U,_ ,γ U,_ This represents 10 coefficients to be determined, which can be based on the measured set of spatial errors. (See equation (1)) Solve.

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

[0079]

[0080] in, Represents the covariance matrix Σ p off-diagonal elements, p k α represents the k-th component at position p; V,W,_ ,β V,W,_ ,γ V,W,_ This represents 10 coefficients to be determined, which can be based on the measured set of spatial errors. (See equation (1)) Solve.

[0081] According to equation (5), if the undetermined coefficients in equations (6) and (7) can be obtained, the covariance matrix Σ at any position in equations (6) and (7) can be obtained. p .

[0082] To estimate the undetermined coefficients in equations (6) and (7), the set of repeated calibration spatial errors at multiple locations obtained in step one is used. Spatial error value (See equation (1)), the spatial error value obtained from the calibration Decomposed into the three directions of X, Y, and Z, it can be represented as:

[0083]

[0084] Therefore, combining equations (6), (7), and (8), we can obtain:

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

[0086]

[0087] Where, p m,k Indicates the calibration position p m (i.e., the kth coordinate component of the three spatial coordinates X, Y, Z) (i.e., the value of X, Y or Z).

[0088] In p m Repeatability covariance matrix of the three spatial error components at the calibration location The non-main diagonal elements can be represented as the following polynomial function:

[0089]

[0090] Next, we'll focus on the main diagonal elements. For example, based on the spatial error set at N locations obtained in step one... Estimate the main diagonal elements The 10 coefficients α in the polynomial function (i.e., the first formula in equation (9)) 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 The value of ).

[0091] Using the least squares estimation method, we first establish the objective function S that minimizes the sum of squared residuals, as follows:

[0092]

[0093] in, p m Location n p The mean of the spatial error of the measurement in three directions. To minimize the objective function S, we consider each parameter α... X,_ ,β X,_ ,γ X,_ Taking the partial derivatives and setting them to zero, we obtain a system of 10 linear equations:

[0094]

[0095] The linear equations in equation (12) above can be rearranged into matrix form, i.e.:

[0096] Aa=0 (13)

[0097] Where A is the coefficient matrix composed of the coefficients of each parameter in the system of equations, a = (α X,0 ,α X,1 ,…,γ X,3 ) T Given a 10×1 parameter vector, the coefficient estimates can be obtained by solving equation (13) using a homogeneous transformation to find the solution vector.

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

[0099] Finally, substituting the estimated values ​​of each coefficient obtained from the solution into equations (6) and (7), and combining them with equation (5), we can obtain the repeatability covariance matrix Σ of the three spatial error components at any position p within the measurement range. p .

[0100] Step 2.2: Analyze the pre-stroke 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 Σ of the pre-travel error components Θ ;

[0101] Depend on Figure 2 It can be seen that the pre-travel error is a factor of δ. Θ The vector along the direction of detection will have δ Θ Considered to obey δ Θ ~N(E(δ) Θ ),D(δ Θ A one-dimensional normal distribution, where E(δ) Θ ) and D(δ Θ These are its mean and standard deviation, respectively. Similar to step 2.1, the pre-travel error δ can be... Θ It can be decomposed into components along the X, Y, and Z directions of the machine tool coordinate system, which are:

[0102]

[0103] Where, δ Θ Polar angle θ and azimuth angle Angle Combination The pre-travel error value obtained from the measurement is decomposed as follows:

[0104]

[0105] Combine angles Components of the measurement vector converted to the machine tool coordinate system (MCS) x ,v y ,v z After that, equation (15) can be expressed as:

[0106]

[0107] To further describe the randomness of the pre-travel error, similar to step 2.1, the pre-travel error is... Decompose it into ternary random variables, and assume that they follow a ternary normal distribution with a mean of 0:

[0108]

[0109] Σ Θ Polar angle θ and azimuth angle combination The repeatability covariance matrix of the next three pre-trip error components is expressed as follows:

[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] In the formula: Indicates the measurement vector (v) x ,v y ,v z The standard deviation of the pre-travel error value at ().

[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] In the formula:

[0117] n θ Indicates the number of times the measurement was repeated. It represents the j-th (j≤n) θ The pre-stroke error component of the measurement. It represents the kth (k≤n) θ The pre-travel error component of (k≠j) measurements.

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

[0119]

[0120] In the formula: This represents the magnitude of the pre-travel error obtained from the i-th measurement.

[0121] Due to δ Θ Obeying δ Θ ~N(E(δ) Θ ),D(δ Θ If the distribution is such that equation (21) can be expressed as:

[0122]

[0123] Further simplification yields:

[0124]

[0125] Similarly, we can calculate:

[0126]

[0127] Substituting equations (19), (23), and (24) into equation (18) yields the repeatability covariance matrix Σ of the pre-trip error. Θ Represented as:

[0128]

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

[0130] In the method of this embodiment, the calibration device used includes The ceramic standard sphere is used with a Renishaw OMP400 trigger probe. By consulting the calibration certificate of the standard sphere, its expanded uncertainty is found to be U. 95 =0.5μm, follows a normal distribution, and takes a coverage factor of k at a confidence level of 95%. 95 =1.96; The allowable error for sphere center alignment during calibration is set to [0,2] μm, which follows a uniform distribution. At a confidence level of 95%, the coverage factor is taken as... The probe has a nominal repeatability accuracy of 0.25 μm, which follows a normal distribution. At a confidence level of 95%, the coverage factor is taken as k. 95 =1.96, then the repeatability standard deviation introduced by the pre-travel error is calculated as follows:

[0131]

[0132] Therefore, the result obtained from equation (27) Substituting the values ​​into equation (25), we obtain the polar angle θ and the azimuth angle. Angle Combination Repeatability covariance matrix Σ of the next three pre-stroke error components Θ for:

[0133]

[0134] Step 3: Construct a random sample generator for shape, position, and size;

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

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

[0137] Before conducting Monte Carlo simulations, a multivariate random variable generator needs to be established. Based on this multivariate random variable generator, multivariate random samples that conform to a specified distribution are generated.

[0138] The multivariate random sample generation model established in this invention takes as input a theoretical measurement point vector (X) in the machine tool coordinate system. m ,Y m Z m ) T Detection angle combination Spatial error repeatability covariance matrix Σ p Pre-travel error repeatability covariance matrix Σ Θ The output is a ternary random sample that satisfies the specified distribution, which is a sample of theoretical points after being disturbed by the repeatability of pre-trip error and the repeatability of spatial error, and the number of samples is arbitrary.

[0139] To build a multivariate random variable generator, the Cholesky decomposition method is first used to decompose the two covariance matrices into the product of a lower triangular matrix and the transpose of the lower triangular matrix, as follows:

[0140]

[0141] Among them, L p and L Θ It is a lower triangular matrix.

[0142] Cholesky decomposition aims to transform a standard normal distribution into a distribution with a target covariance structure through linear transformation. In other words, it only requires taking random vectors from the multivariate standard normal distribution to convert it into random vectors conforming to a specified distribution. Since adaptive Monte Carlo simulation relies on a large number of random samples, it is necessary to utilize methods similar to L... p and L Θ The relevant linear transformation yields a number of Nums that conform to Σ p and Σ Θ The matrix G of the covariance random vector p and G Θ The calculation process is expressed as follows:

[0143]

[0144] Among them, G p and G Θ It is a 3×Nums matrix, where each column represents a covariance matrix Σ. p , Σ Θ Z is a 3-dimensional random vector, and Z is also a 3×Nums matrix, with each column representing a 3-dimensional standard normal random vector.

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

[0146] Step 3.2: Construct a random sample generator for shape, position, and size;

[0147] The multivariate random variable generator established in step 3.1 can generate repeatable random multivariate samples of spatial error and pre-travel error for any combination of theoretical points and theoretical detection angles in in-machine measurement path planning: G p and G Θ However, in engineering applications, the accuracy of measurement at a single point is not the primary concern; rather, the accuracy of measuring the shape and position dimensions of features is given priority. Therefore, the evaluation object in this invention is shape and position dimensions. Furthermore, the characterization results of shape and position dimensions are related to the distribution and number of measurement points, as well as the calculation method. Therefore, its repeatability analysis is also related to all of the above factors. The specific analysis process is as follows:

[0148] Step 3.2.1: Based on the process plan, determine the number, coordinate values, and detection angle combinations of the theoretical measurement points required for the geometric dimensions calculation. Establish the theoretical measurement point coordinate matrix D. S And the detection angle combination matrix T S DS The dimension is 3×n S T S The dimension is 2×n S n S This indicates the number of theoretical measurement points.

[0149] Step 3.2.2: Convert the theoretical measurement point coordinate matrix D S Detection angle combination matrix T S Spatial error repeatability covariance matrix Σ p and the repeatability covariance matrix Σ of the pre-travel error Θ By inputting the multivariate random variable generator established in step 3.1, random samples of spatial error for each theoretical measurement point can be obtained. Random sample of pre-travel error for each detection angle combination Random samples of measurement points affected by spatial errors and pre-travel errors can be represented as follows:

[0150]

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

[0152] Step 3.2.3: The form and position dimensions can be calculated using the fitting and calculation methods. Different form and position dimensions require different fitting and calculation methods, and there are currently mature methods available; therefore, this invention will not elaborate on them here. Let the form and position dimension calculation function be f, then the random sample of measurement points obtained in step 3.2.2... The calculated random sample of geometric dimensions is represented as R = (R1, R2, ..., R...). Nums R is a 1×Nums vector, and the j-th element in R is represented as:

[0153]

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

[0155] Equation (32) is the random sample generator for shape and size constructed in this step, which can be used to generate random samples of shape and size at any location.

[0156] Step 4: Assess the reliability of the on-machine measurement system for geometric and dimensional evaluation;

[0157] Step 4.1: Predict the standard deviation of random samples of geometric dimensions based on the adaptive Monte Carlo method;

[0158] The adaptive Monte Carlo method is an improvement on the traditional Monte Carlo method. It employs batch Monte Carlo simulations to estimate the distribution (mean and standard deviation) of the dimensions to be measured, until the difference in standard deviation between adjacent batch estimates is less than the numerical tolerance δ, at which point the distribution of the dimensions to be measured is output. This method can effectively reduce the computational cost of Monte Carlo simulations and improve computational efficiency.

[0159] In adaptive Monte Carlo simulation, the numerical tolerance δ is the threshold for determining whether the simulation has converged, and it is expressed as:

[0160]

[0161] Where l represents the minimum number of significant figures for the evaluated object. For example, a spatial error measurement of 0.021 mm is expressed in scientific notation as 2.1 × 10⁻⁶. -3 If 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 set as follows:

[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, Monte Carlo simulations will be conducted in batches, with the simulation process as follows: Figure 3 The specific steps are as shown in the upper part:

[0166] Step 4.1.1: Set the batch number to 1 (h = 1);

[0167] Step 4.1.2: Based on the random sample generator for shapes and dimensions constructed in Step 3.3, generate the first batch of Nums random samples R of shapes and dimensions. (1) Calculate the mean u of the first batch of samples. (1) with 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 random sample generator for shapes and dimensions constructed in Step 3.2, generate the second batch of random samples for shapes and dimensions, R. (2) Calculate the mean u of the second batch of samples. (2) with standard deviation s (2) ;

[0170] And so on;

[0171] Step 4.1.5: Based on the random sample generator for shapes and dimensions constructed in Step 3.2, generate the i-th batch of shape and dimension samples R. (i) Calculate the mean u of the i-th batch of samples. (i) with 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 maximum standard deviation s max =max(s (1) ,…s (h) );

[0173] Step 4.1.7: Calculate the standard deviation ξ of the mean for each batch. u and the standard deviation ξ of each batch standard deviation s :

[0174]

[0175] Step 4.1.8: Determine 2max(s) min ,s max ,ξ u ,ξ s If δ < 0, then the loop condition is met, and steps 4.1.3-4.1.8 are repeated. If δ < 0, then the loop is exited, and the mean of the random sample of the current measured shape and position dimensions is calculated. and standard deviation The recursive calculation method is as follows:

[0176]

[0177] in, This is the mean of the first h-1 batch of samples.

[0178]

[0179] in, is the standard deviation of the first h-1 batch of random samples of shape, position, and size.

[0180] Step 4.2: Calculate the credibility assessment index based on MSA theory;

[0181] In-machine measurement system reliability assessment refers to evaluating the reliability, stability, and credibility of measurement results by assessing the measurement system's ability to measure the geometric dimensions of specified features. Measurement System Analysis (MSA) theory takes a product-centric approach, evaluating the reliability of the measurement system by analyzing product quality and consistency. In step three of this invention, the prediction of the standard deviation of the specified geometric dimensions replaces the product inspection process, enhancing the versatility of the assessment while eliminating reliance on product parts and significantly reducing assessment costs.

[0182] The main metrics for evaluating measurement capability are the effective resolution (NDC), accuracy tolerance ratio (P / T%), and repeatability and reproducibility percentage (R&R), as defined in the MSA. These metrics quantify the performance of an on-machine measurement system from three perspectives:

[0183] (1) Effective resolution (NDC) is used to quantify the sensitivity of an in-machine measurement system; it mainly evaluates the smallest change that an in-machine measurement system can detect. An in-machine measurement system needs sufficient resolution to distinguish between measurement errors and part machining errors; otherwise, it may miss critical quality differences and cause misjudgment of the product.

[0184] (2) The accuracy tolerance ratio (P / T%) is used to quantify the accuracy of the in-machine measurement system. P / T% compares the accuracy of the in-machine measurement system with the product tolerance range to ensure that the accuracy of the in-machine measurement system meets process requirements. An excessively high P / T% ratio indicates that the in-machine measurement system is unsuitable for the current task, which may lead to non-conforming products flowing into downstream processes. Therefore, P / T% ensures that the in-machine measurement system provides sufficient measurement accuracy and prevents misjudgment of products due to measurement errors.

[0185] (3) 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, making it suitable for practical applications.

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

[0187] Effective resolution NDC:

[0188]

[0189] Where, σ Act This is the empirical value of the standard deviation of the machining error of this feature's shape and position dimensions (which can be calculated cumulatively from the machining data of the currently machined part; the cumulative calculation method is a known method). The standard deviation prediction value of the random sample of shape and position dimensions obtained in step 4.1.

[0190] For in-machine measurement systems, a higher effective resolution (NDC) means a smaller minimum change that the system can detect, and thus higher sensitivity. To ensure sufficient precision, the in-machine measurement system should have an effective resolution (NDC) of at least 5, meaning it can distinguish at least 5 different measurements.

[0191] Precision tolerance ratio P / T%:

[0192]

[0193] In the formula, TOL represents the design tolerance of the geometric dimension.

[0194] For in-machine measurement systems, the smaller the accuracy tolerance ratio (P / T%), the more sufficient the system's accuracy is to meet the requirements of the dimensional and positional measurement. The accuracy tolerance ratio (P / T%) should be less than or equal to 10%, meaning the accuracy error of the in-machine measurement system is less than 10% of the tolerance range. If the accuracy tolerance ratio (P / T%) is between 10% and 30%, the in-machine measurement system is still acceptable, but the measurement accuracy is insufficient and needs improvement. If the accuracy tolerance ratio (P / T%) exceeds 30%, the in-machine measurement system is unqualified, and the system error is too large.

[0195] Repeatability and Reproducibility Percentage (R&R):

[0196]

[0197] For in-machine measurement systems, a lower repeatability and reproducibility percentage (%R&R) indicates better stability and consistency. A %R&R value less than 10% indicates a small total error and highly stable, consistent measurement results. A %R&R value between 10% and 30% suggests acceptable error, but improvements are needed. A %R&R value greater than 30% indicates unacceptable error, requiring redesign or equipment replacement.

[0198] In summary, the process for evaluating the reliability of an on-machine measurement system for specified feature shapes and dimensions is as follows: Figure 3 As shown in the lower part, if any of the three evaluation indicators fails to meet the requirements, the reliability of the on-machine measurement system will be unqualified when measuring the specified geometric dimensions, and the measurement capability will be insufficient to meet the measurement requirements.

Claims

1. A reliability evaluation method for an in-machine measurement system oriented towards geometric dimensions, characterized in that, Includes the following steps: Step 1: Obtain the set of spatial errors at multiple locations during the travel of the on-machine measurement system through calibration; Step 2: Establish a repeatability model for the in-machine measurement system, including: The repeatability covariance matrix Σ of the spatial error components at any position p p , Σ p The main diagonal element is the spatial error 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 Σ of the pre-travel error components Θ , Σ Θ The main diagonal elements 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 for shape, position, and size; Step 3.1: Establish a multivariate random variable generator: In the formula, G p and G Θ These represent random spatial error samples and theoretical detection angle combinations at any theoretical point p in the measurement path planning of the on-board measurement system. Random sample G of the pre-travel error at the location 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 Z is a 3-dimensional random vector; Z is a 3×Nums matrix, where each column represents a 3-dimensional standard normal random vector; L p and L Θ All are lower triangular matrices; Step 3.2: Construct a random sample generator for shape, position, and size: In the formula, R j For a random sample of shape and size, R = (R1, R2, ..., R...) Nums The j-th element in the expression, where j = 1, 2, ..., Nums; f is the function for calculating geometric dimensions; Random samples of measurement points affected by spatial errors and pre-travel errors D S (i) indicates a dimension of 3×n S The theoretical measurement point coordinate matrix D S The i-th column; and These are random samples of spatial error and random samples of pre-trip error for 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 in-machine measurement system; Step 4.1: Predict the standard deviation of random samples of the current form and position dimensions to be measured based on the adaptive Monte Carlo method. Step 4.2: Using standard deviation Based on MSA theory, the reliability assessment index is calculated using the following formula, including effective resolution (NDC), accuracy tolerance ratio (P / T%), and repeatability and reproducibility percentage (R&R). The reliability assessment is then performed based on the obtained reliability assessment index.

2. The reliability evaluation method for an on-machine measurement system oriented towards geometric dimensions according to claim 1, characterized in that, In step 2: In the formula, The spatial error δ at position p p Error components in the X, Y, and Z directions of the machine tool coordinate system; p obtained from the calibration in step 1 m Repeated calibration results at the location are used to estimate p. m Covariance matrix at location The coefficients of the functions represented by each element are used to obtain the covariance matrix Σ. p The undetermined coefficient values ​​in; The formula for calculating the main diagonal elements is: The formulas for calculating the remaining elements are: 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,_ The covariance matrix Σ p The undetermined coefficients in p; m,k Indicates the calibration position p m The k-th component; n p Indicates the number of repeated measurements for spatial error; For p m Spatial error of the j-th measurement at location The components along the X, Y, and Z directions of the machine tool coordinate system.

3. The reliability evaluation method for an on-machine measurement system oriented towards geometric dimensions according to claim 2, characterized in that, In step 2: covariance matrix Σ p The undetermined coefficients in the equation are obtained using the least squares estimation method.

4. The reliability evaluation method for an on-machine measurement system oriented towards geometric dimensions according to claim 3, characterized in that, In step 2: covariance matrix Σ Θ for: In the formula, σ Θ To calibrate the repeatability standard deviation when determining the pre-stroke error, σ1 is the uncertainty of the standard sphere used during calibration, σ2 is the manually set correction tolerance during calibration, and σ3 is the inherent uncertainty of the probe at the time of manufacture; (v x ,v y ,v z ( ) is an angle combination Convert the components of the measurement vector into the machine tool coordinate system.

5. The reliability evaluation method for an in-machine measurement system oriented towards geometric dimensions according to any one of claims 1-4, characterized in that, In step 3.1, L p and L Θ The Cholesky decomposition method is used to analyze the covariance matrix Σ. p and Σ Θ We obtain the following equation:

6. The reliability evaluation method for an on-machine measurement system oriented towards geometric dimensions according to claim 5, characterized in that, In step 3.2, the theoretical measurement point coordinate matrix D is... S The dimension is 2×n S Detection angle combination matrix T S Spatial error repeatability covariance matrix Σ p and the repeatability covariance matrix Σ of the pre-travel error Θ By inputting the multivariate random variable generator established in step 3.1, random samples of spatial errors for each theoretical measurement point can be obtained. and 7. The reliability evaluation method for an in-machine measurement system oriented towards geometric dimensions according to claim 6, characterized in that, The standard deviation obtained in step 4.1 for: In the formula, h represents the number of batches simulated in the Monte Carlo simulation; The standard deviation of the first h-1 batch of random samples of shape and dimension; The mean of the first h-1 batches of samples. u (h) is the mean of the h-th batch of samples.

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

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