A firearm assembly precision control method and system supporting large number interchange assembly

Abstract

The application discloses a kind of gun assembly precision control method and system supporting large number interchange assembly, method steps are as follows: first, the position point of geometric element is defined in assembly model, the calculation formula of target size tolerance is derived by the accumulation and decomposition of confidence region, then the optimization of size tolerance is carried out, the theoretical confidence region of target geometric element position coordinate is calculated, the process capability index and the qualified rate of actual size of sampling part are calculated, the actual confidence region of target geometric element position coordinate is calculated, and whether the qualified rate of assembly precision meets the requirement is predicted and monitored by comparing the theoretical confidence region and the actual confidence region;System includes: geometric element position point definition module, size tolerance optimization design module, assembly precision prediction and monitoring module;The application can reduce production cost while improving the interchangeability of gun products, improve the qualified rate of gun assembly precision under large number interchange assembly mode.

Description

Technical Field

[0001] This invention belongs to the field of assembly precision control, and in particular, it is a method and system for controlling the assembly precision of firearms that supports large-scale interchangeable assembly. Background Technology

[0002] Assembly accuracy control refers to ensuring the assembly accuracy of a product during the product design stage and the parts processing and assembly process. Among the methods for ensuring the assembly accuracy of mechanical products, the large number interchangeability method is typically used when the assembly accuracy requirements are high and the number of component links is large. Compared with the complete interchangeability method, under the same assembly accuracy requirements, parts designed using the large number interchangeability method have larger tolerances and are more economical.

[0003] Most existing research on assembly accuracy control technology focuses on tolerance modeling and tolerance analysis optimization techniques in the design phase. When using the large number interchange method for assembly tolerance analysis, allocation, or optimization, it is assumed that the geometric parameters or mathematical transformations of each part follow a certain probability distribution, and that each component (or geometric component) is independent of the others. To achieve large number interchangeability in assembly, the statistical tolerance analysis methods that can be used in assembly accuracy design mainly include: root mean square (RSS) method, Croft method, extended Taylor series approximation method, Hasofer-Lind exponent method, numerical integration or quadrature approximation method, Taguchi method and Monte Carlo simulation method, kernel density estimation method, etc.

[0004] In the process of parts processing and assembly production, the existing quality control methods for assembly accuracy are mainly divided into two categories: (1) assembly accuracy monitoring and prediction methods based on assembly accuracy measurement data; (2) assembly accuracy control methods based on parts processing quality inspection data. The first type of method uses the actual measured assembly accuracy data in the assembly process and establishes a relationship model between assembly characteristic parameters and assembly accuracy targets through machine learning, data mining, state space models and other methods. The second type of method based on parts processing quality inspection data can be applied to interchangeable assembly methods. In production practice, the sampling inspection method is usually adopted. A batch of parts is selected from the finished parts, and the mean and standard deviation of their geometric parameters are statistically analyzed to predict their process capability index (also known as process capability index), or the overall pass rate is predicted based on the probability distribution function. The commonly used process capability index measurement parameters are Cp and Cpk, which are applicable to cases where the mean deviation is not considered and cases where the mean deviation is considered, respectively. When the process capability index is large or the predicted overall pass rate is large, it is considered that the geometric parameters of the processed parts meet the assembly accuracy requirements of the large number interchange method, and thus it is inferred that the assembly accuracy meets the design requirements.

[0005] Firearms are a typical type of mechanical product. The general characteristics of firearm assembly precision design are: high requirements for dimensional tolerances, but a large number of component links. Many firearm components have symmetrical assembly structures about a central plane. Currently, the commonly used assembly precision control methods in firearm production are two-dimensional dimensional chain design, measurement and inspection during assembly, and manual finishing. To ensure the economy of parts processing, the commonly used firearm assembly precision design method usually involves designing the dimensions of a certain part as a finishing link, transforming some geometric tolerance zones into a "loop" in the dimensional chain, and reducing the machining precision requirements of other mating parts. Therefore, a large amount of finishing work is inevitably required during firearm assembly.

[0006] Existing assembly accuracy control methods have the following technical problems:

[0007] (1) The prerequisite for the successful application of the assembly accuracy monitoring and prediction method based on assembly accuracy measurement data is to have a large amount of historical assembly measurement data as training samples. When there are many factors affecting the assembly accuracy (or quality) target (i.e., many input variables of the model) or when the sample size is small, there is a limitation of low prediction accuracy. This prediction and monitoring method based on assembly accuracy measurement data usually requires a lot of measurement work during assembly. It is mainly suitable for repair assembly or adjustment assembly methods in small batch production and is difficult to apply to interchangeable assembly methods.

[0008] (2) For traditional methods based on part machining quality inspection data, when using the large number interchange method for tolerance design, even if a batch of parts passes the random inspection, the assembly accuracy may not meet the requirements after assembly. Furthermore, the part's process capability index cannot be used to determine whether the assembly accuracy meets the requirements. Due to the existence of part machining errors, the probability distribution of the actual geometric parameters of the machined parts often differs from the assumed theoretical distribution. When the actual geometric parameters of the inspected parts fall entirely within the tolerance design range of the large number interchange (probability statistics) method, the assembly accuracy of the parts may still not meet the design requirements. Therefore, if the tolerance design is carried out using the traditional large number interchange (probability statistics) method, the actual assembly accuracy pass rate of the parts often fails to meet the predetermined requirements.

[0009] (3) Existing methods for controlling the accuracy of firearm assembly are not suitable for assembly methods that allow for large-scale interchangeability. In order to achieve the designed assembly accuracy, firearm products are generally assembled using a repair and fitting method. This repair and fitting method is inefficient, requires a lot of manual repair work, is only suitable for small-batch production, is not conducive to automated production, and is also not conducive to the repair and replacement of firearm parts. Therefore, it cannot fully meet the interchangeability requirements of firearm products. Summary of the Invention

[0010] The purpose of this invention is to provide a method and system for controlling the assembly accuracy of firearms that supports large-scale interchangeable assembly. It primarily addresses the problems of existing assembly accuracy control methods being unsuitable for large-scale interchangeable assembly of firearms and having low assembly accuracy pass rates. The system employing this method can control assembly accuracy during the tolerance design and parts manufacturing stages. Compared to existing assembly accuracy design and control methods supporting large-scale interchangeability, this method can improve the assembly accuracy pass rate of firearms while reducing production costs. It also supports large-scale interchangeable assembly modes for medium to large-volume production, facilitating automated assembly.

[0011] The technical solution to achieve the purpose of this invention is as follows:

[0012] A method for controlling the assembly accuracy of firearms that supports large-scale interchangeable assembly includes the following steps:

[0013] Step 1: Define the position points of geometric elements and the origin of the coordinate system in the assembly model, and use an n-variable normal distribution to represent the position coordinates of the geometric elements corresponding to the endpoints of each component ring;

[0014] Step 2: Derive the calculation formula for the target size tolerance by accumulating and decomposing the theoretical confidence region;

[0015] Step 3: Assuming that the distribution of the dimensions of each component ring is normal, the size tolerance of each component ring is obtained by using the optimization design method. The optimization variable is the standard deviation of the component ring size. The optimization objective is to maximize the area or volume of each confidence region. The constraints are the variation range and tolerance requirements of the component ring and closed ring dimensions.

[0016] Step 4: Calculate the theoretical confidence region and the dimensional tolerance of the closed loop for the position coordinates of the target geometric feature;

[0017] Step 5: Calculate the processing capability index and pass rate based on the actual dimensions of the sampled parts; if the pass rate of the actual dimensions of the parts or its processing capability index does not meet the requirements, stop production and adjust the processing of the non-conforming parts; if it meets the requirements, proceed to the next step.

[0018] Step 6: Calculate the actual confidence region of the target geometric element position coordinates based on the actual dimensions of the sampled parts. According to the actual dimensions of the sampled parts, the actual confidence region of the target geometric element position coordinates is calculated using the cumulative method of multivariate normal distribution.

[0019] Step 7: Predict and monitor whether the assembly accuracy pass rate meets the requirements by comparing the theoretical confidence region and the actual confidence region;

[0020] Determine the coordinates of the target geometric element at point a. nIf the actual confidence region is within the theoretical confidence region, and if it exceeds the theoretical confidence region, the error variation range of the actual confidence region in the target direction or position is calculated. The actual confidence region is compared with the tolerance design requirements of the assembly accuracy. Based on the comparison results, the pass rate of the assembly accuracy is predicted and monitored to see if it meets the requirements, and corresponding adjustment suggestions are given.

[0021] A firearm assembly precision control system supporting large-scale interchangeable assembly includes:

[0022] The geometric element location point definition module uses a human-computer interaction method to help users determine the coordinate system origin and the location points of each geometric element in the assembly drawing, and helps users to build a dimension chain diagram, thus establishing the necessary data model for tolerance optimization design and assembly accuracy prediction and monitoring.

[0023] The dimensional tolerance optimization design module performs dimensional tolerance optimization design based on the established geometric element position coordinate model. It can optimize according to the user-provided closed loop tolerance design requirements and the minimum tolerance level design requirements of each component loop using the optimization method in step 3. After searching the standard tolerance database, it converts each tolerance into the closest standard tolerance value, and uses the method in step 4 to check the standardized tolerances, outputting the optimized and standardized dimensional tolerances.

[0024] The assembly accuracy prediction and monitoring module calculates the statistical mean, process capability index, and predicted overall pass rate of each component ring dimension based on the measured data of part dimensions and tolerance design requirements; calculates the actual confidence region of the geometric element position coordinates according to the method in step 6, and generates theoretical and actual confidence region maps; and verifies whether the theoretical confidence region of the target geometric element position coordinates encompasses the actual confidence region based on the tolerance optimization results and the method in step 7, thereby determining whether the actual dimensions of the part meet the assembly accuracy pass rate requirements, and providing early warnings and suggestions for adjustment methods for possible non-conformities.

[0025] The significant features and beneficial effects of this invention are as follows:

[0026] (1) A method for controlling the assembly accuracy of firearm components or parts during the parts processing stage is proposed. Based on the sampling inspection data of the actual size of the parts, the actual assembly accuracy of the components or parts is predicted. Under the premise of ensuring the economic requirements of parts processing, the assembly accuracy qualification rate requirements of the large number interchangeable assembly mode are met. This solves the problem that the existing repair assembly method and the assembly accuracy control based on assembly accuracy measurement data are not applicable to the interchangeable assembly mode. It is also more conducive to the repair and replacement of firearm parts.

[0027] (2) A method for controlling the assembly accuracy of firearms based on statistical correlation coordinates is proposed. This method considers the multivariate probability distribution of the design size and the actual size of the machined parts. By comparing the theoretical confidence region and the actual confidence region of the position coordinates of geometric elements, the assembly accuracy of firearm components or parts is controlled. This solves the problem that the actual assembly accuracy pass rate of existing probabilistic statistical tolerance design methods and part processing quality inspection methods based on process capability index is low. Attached Figure Description

[0028] Figure 1 This is a flowchart illustrating the overall steps of a firearm assembly precision control method that supports a large number of interchangeable assembly methods according to the present invention.

[0029] Figure 2 This is a case study of assembling a locking mechanism model for a light machine gun.

[0030] Figure 3 According to Figure 2 The two-dimensional dimensional chain diagram of the locking mechanism is established from the assembly model.

[0031] Figure 4 This represents the range of error variation in the x-direction within the confidence region of a two-dimensional coordinate system, when the y-coordinate is determined or uncertain.

[0032] Figure 5 The range of error variation is defined as the range of error variation within the confidence region of a two-dimensional coordinate system when the direction of the error variation range is uncertain.

[0033] Figure 6 A schematic diagram illustrating the relationship between the theoretical confidence region and the actual confidence region for the location of a target geometric element.

[0034] (a) indicates that the theoretical confidence region completely encompasses the actual confidence region, (b) indicates that the actual confidence region partially exceeds the theoretical confidence region, and (c) indicates that the actual confidence region completely exceeds the theoretical confidence region.

[0035] Figure 7 A graph showing the relationship between the theoretical confidence region for the location of the target geometric element and the actual confidence region for the first set of samples.

[0036] Figure 8 A graph showing the relationship between the theoretical confidence region for the location of the target geometric element and the actual confidence region for the second set of samples.

[0037] Figure 9 This is a flowchart of the assembly accuracy prediction and monitoring process. Detailed Implementation

[0038] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0039] Combination Figure 1The present invention provides a method for assembly accuracy inspection and control supporting large-scale interchangeable assembly, comprising the following steps:

[0040] Step 1: Define the position points of geometric elements and the origin of the coordinate system in the assembly model, and use an n-variable normal distribution to represent the position coordinates of the geometric elements corresponding to the endpoints of each component ring.

[0041] Step 1.1 To address assembly tolerance design issues, establish a two-dimensional or three-dimensional dimensional chain diagram, including closed loops and component loops.

[0042] Step 1.2 Determine the target geometric features and the origin o of the coordinate system in the assembly model of the parts. The geometric feature corresponding to one endpoint of the closed loop is the target geometric feature; the origin of the coordinate system is selected from the geometric features corresponding to the other endpoint of the closed loop.

[0043] Step 1.3 Assume that the dimension of each part can be represented as a random number following a normal distribution. Assume that the position of any geometric element (point, line, and surface) on the part can be represented by coordinates in an n-dimensional coordinate system. Starting from the origin of the coordinate system, an n-variable normal distribution is used to represent the position coordinates of the geometric elements corresponding to the endpoints of each component ring. Assume that point a on a certain geometric element is used to represent the position of the geometric element, which can be represented as: a ~ N(μ, C), where μ and C are the mean vector and the overall covariance matrix of the multivariate normal distribution, respectively, and N represents the normal distribution.

[0044] During the tolerance design phase, the values ​​of the correlation coefficient ρ in the overall covariance matrix C are discussed in two cases:

[0045] (1) If the two coordinate components of point a (e.g., x and y) belong to different parts, then theoretically there is no correlation, and the correlation coefficient ρ=0 is taken when solving the theoretical analysis.

[0046] (2) If the two coordinate components of point a (e.g., x and y) belong to the same part, the correlation coefficient ρ is taken as 1, -1 or 0 depending on the specific situation: when ρ is 1, it means that the two coordinate components are positively correlated; when ρ is -1, it means that the two coordinate components are negatively correlated; when ρ is 0, it means that the two coordinate components are theoretically uncorrelated.

[0047] Step 2: Derive the calculation formula for the target size tolerance by accumulating and decomposing the theoretical confidence region.

[0048] Step 2.1 Use the cumulative method of multivariate normal distribution to obtain the multivariate normal distribution of the position coordinates of the target geometric feature relative to the origin.

[0049] Step 2.2 According to the target dimensional tolerance design requirements, 'a' represents the position of the target geometric element. nThe confidence region of a point's multivariate normal distribution is decomposed into the range of maximum error variation in a certain direction or location.

[0050] a n The confidence region for a point with a confidence level of 1-α is calculated using the following formula:

[0051]

[0052] The superscript T indicates transpose. The chi-square distribution χ² has n degrees of freedom and a significance level of α. 2 P represents a n The probability (or confidence level) of a point falling within this confidence region is 1-α; C is the population covariance matrix. This indicates that a is a with o as the origin. n For vectors ending at a point, n takes the value of 2 or 3 for two-dimensional or three-dimensional coordinate problems, respectively.

[0053] The formula for calculating the target size tolerance is a. n The formula for calculating the maximum error variation range of a point in a certain direction or position, in a two-dimensional or three-dimensional coordinate system, discusses two cases regarding this error variation range:

[0054] (1) When a n When the direction of the error variation range of a point is known, a n The range of error variation at a point in that direction or at a certain position in that direction is determined by calculating a. n The conditional probability distribution of the multivariate normal distribution of the points is obtained.

[0055] (2) When a n When the direction of the error variation range of a point is uncertain, a n The range of error variation of a point in this direction or at a certain position in this direction is expressed as a. n It is obtained by the side length of the smallest bounding rectangle or cuboid of the confidence region of a point.

[0056] Step 3: Assuming that the distribution of the dimensions of each component ring is normal, the dimensional tolerance of each component ring is obtained by using an optimization design method.

[0057] Assuming the dimensions of each component ring follow a normal distribution with known variance, the dimensional tolerances of each component ring are obtained using an optimization design method at a certain confidence level. The optimization employs the multivariate normal distribution obtained in step 2.1, with the standard deviation of the component ring dimensions as the optimization variable. The optimization objective is to maximize the area or volume of each confidence region. The constraints are the variation range and tolerance requirements of the component and closed ring dimensions, determined based on actual design requirements.

[0058] When the position coordinates of a geometric feature follow a multivariate normal distribution, the larger the area or volume of its confidence region, the better the production economy and the lower the manufacturing cost. Therefore, the objective of tolerance optimization design is:

[0059]

[0060] Where i = 1, 2, ..., k; k is the number of geometric elements participating in the optimization; w i S represents the weight of the i-th geometric element, used to define the importance of a part; i Let be the area or volume of the confidence region for the coordinates of the i-th geometric element on the part.

[0061] Step 4: Calculate the theoretical confidence region and the dimensional tolerance of the closed loop for the position coordinates of the target geometric feature.

[0062] After standardizing the tolerances calculated in step 3, tolerance accumulation analysis is performed using the method in step 2.1 (cumulative method of multivariate normal distribution). Then, the theoretical confidence region of the target geometric element position coordinates is calculated, and the maximum variation range of this theoretical confidence region in the target direction and position is calculated using the method in step 2.2 to verify whether it meets the tolerance design requirements of the closed loop. Only when the tolerance design requirements of the closed loop are met can the next step of calculation be performed.

[0063] Step 5: Calculate the machining capability index and pass rate based on the actual dimensions of the sampled parts.

[0064] During batch processing of parts, the actual dimensions of the component rings on the finished parts are obtained through random sampling, and their average value is calculated. The dimensions of each sampled part are checked to ensure they are within tolerance limits, and the process capability index C is verified. p and C pk The value is used to predict the overall pass rate based on the normal distribution statistical results of the sample; if the pass rate of the actual size of the part or its process capability index does not meet the requirements, production is stopped and the processing of the non-conforming parts is adjusted; if it meets the requirements, the next step is carried out.

[0065] Step 6: Calculate the actual confidence region of the target geometric element position coordinates based on the actual dimensions of the sampled parts.

[0066] Based on the actual dimensions of the sampled parts, the actual confidence region of the target geometric element's position coordinates is calculated using a multivariate normal distribution accumulation method. The method for calculating the actual confidence region is similar to step 2, with the following differences:

[0067] (1) When sampling parts, the overall covariance matrix of the part dimensions is unknown. Therefore, when representing the multivariate normal distribution of the geometric element positions, the sample covariance matrix ∑ is used instead of the overall covariance matrix, and the sample mean is used. Instead of the mean μ of the normal distribution, the standard deviation of the sample is used instead of the standard deviation of the normal distribution;

[0068] (2) The coordinates of the relevant dimensions are calculated based on the actual dimensions of the sampled parts to determine the correlation coefficient between the parts;

[0069] (3) Assume a n A point is used to represent the location of a target geometric feature, a n The confidence region of a multivariate normal distribution of points with a confidence level of 1-α is calculated using the following formula:

[0070]

[0071] in: Where m is the number of samples for sampling inspection, and n is the number of degrees of freedom of the part. α Let P be a T-distribution with a significance level of α, where P represents a n The probability that the point falls within this confidence region is 1-α. For an F-distribution with a significance level of α, This indicates that a is a with o as the origin. n The vector whose endpoint is a. At this point, a n The confidence region for the actual coordinates of a point remains an ellipse (or ellipsoid). The center of the ellipse (or ellipsoid) is point p, and the vector... This represents a vector with origin o and endpoint p. The direction and length of the ellipse (or ellipsoid) axis are determined by the covariance matrix ∑ of the sample.

[0072] Step 7: Predict and monitor whether the assembly accuracy pass rate meets the requirements by comparing the theoretical confidence region and the actual confidence region.

[0073] Determine the position coordinates of the target geometric element a n Whether the actual confidence region of a point lies within the theoretical confidence region. If it exceeds the theoretical confidence region, the error variation range of the actual confidence region in the target direction or position is calculated and compared with the tolerance design requirements of the assembly accuracy. Based on the comparison results, the assembly accuracy pass rate is predicted and monitored to ensure it meets the requirements, and corresponding adjustment suggestions are given. The comparison between the theoretical and actual confidence regions is discussed in three cases:

[0074] (1) When a n When the theoretical confidence region of a point can completely encompass its actual confidence region (e.g.) Figure 6a) If the assembly accuracy pass rate is greater than 1-α, then we accept the assumption that the overall product meets the assembly accuracy requirements. This means that the probability of the overall product meeting the assembly accuracy requirements is greater than 1-α. This indicates that at the confidence level of 1-α, the actual error variation range of the target geometric element position coordinates is within the theoretical error variation range in all directions and positions. The actual assembly accuracy will meet the requirements, so we output a signal to continue production. Figure 6 In case a, any point within the actual confidence ellipse (solid line) lies within the theoretical confidence ellipse (dashed line). No adjustment is required in this case.

[0075] (2) When a n The actual confidence region of a point exceeds the theoretical confidence region (e.g.) Figure 6 (b) Then, to calculate the range of error variation of the actual confidence region in the target direction or position, there are two cases:

[0076] (a) If the error variation range of the actual confidence region in the target direction or position exceeds the tolerance design requirements of the closed loop, it indicates that the actual assembly accuracy will not meet the requirements at confidence level 1-α. Therefore, a signal to stop production is output, and when giving adjustment suggestions, the statistical mean and process capability index C of each part are checked. p and C pk Value: If the C of a certain dimension of the part p A smaller value indicates a larger random error; if C p The value meets the requirements, but C pk If the overall pass rate of the value or prediction is small, it indicates that the statistical mean of the dimension is significantly off from the center of the tolerance zone. In this case, the dimension is the cause of the systematic error. The relative position between the tool and the machined part should be adjusted so that the statistical mean of the actual dimension is closer to the center of the tolerance zone, that is, closer to the mean of the theoretical normal distribution.

[0077] (b) If the actual confidence area is within the tolerance design requirements of the closed loop in a certain direction or position, it means that the actual assembly accuracy will meet the tolerance design requirements of the closed loop in that direction or position. However, the position of the target geometric element may exceed the theoretical design range in other directions or positions. Therefore, production can continue, but a warning signal is output, suggesting that the size with the larger system error be increased or decreased to make it closer to the center of the tolerance zone.

[0078] Based on the above-mentioned method for controlling the assembly accuracy of firearms that supports a large number of interchangeable assembly methods, this invention also provides a firearms assembly accuracy control system that supports a large number of interchangeable assembly methods. This system is used to control the assembly accuracy of firearms during the tolerance design stage and the parts processing stage. The system includes three functional modules: a geometric element location point definition module, a dimensional tolerance optimization design module, and an assembly accuracy prediction and monitoring module.

[0079] The main function of the geometric element location point definition module is to assist users in determining the location points of each geometric element in the assembly drawing through human-computer interaction, and to assist users in building dimension chain diagrams, thereby establishing necessary data models for tolerance optimization design and assembly accuracy prediction and monitoring. Its specific implementation is as follows: First, the user establishes an assembly accuracy analysis project and imports the corresponding assembly drawing model. Then, the user is assisted in building a dimension chain diagram and determining the closed loop through human-computer interaction. Next, the user specifies the origin of the coordinate system, the location points of the target geometric element, and the location points of associated geometric elements.

[0080] The main function of the dimensional tolerance optimization design module is to optimize dimensional tolerances based on the established geometric element position coordinate model. It can optimize the closed-loop tolerance design requirements and the minimum tolerance grade design requirements for each component ring according to the user-provided requirements. Using the optimization method in step 3, it converts each tolerance to the closest standard tolerance value after searching the standard tolerance database. Then, it verifies the standardized tolerances using the method in step 4 and outputs the optimized and standardized dimensional tolerances. The specific implementation is as follows: First, the user inputs the nominal dimension value of each component ring, the nominal value of the angle and the error variation range, the maximum allowable tolerance value and dimensional variation range of the closed loop, specifies the dimensions to be designed and their minimum tolerance grade requirements, and inputs the pass rate requirements for the closed-loop assembly accuracy. Then, it uses the optimization method in step 3 to optimize the tolerances. The system converts the optimized tolerance values ​​to the closest standard tolerance values ​​by searching the standard tolerance database. Finally, the system verifies the standardized tolerances using the method in step 4 and outputs the optimized and standardized dimensional tolerances.

[0081] The main functions of the assembly accuracy prediction and monitoring module are as follows: Based on the measured data of part dimensions and tolerance design requirements, calculate the statistical mean of each component ring dimension, the process capability index, and the predicted overall pass rate; calculate the actual confidence region of the geometric element position coordinates according to the method in step 6, generating theoretical and actual confidence region maps; verify whether the theoretical confidence region of the target geometric element position coordinates encompasses the actual confidence region based on the tolerance optimization results and the method in step 7, thereby determining whether the actual dimensions of the part meet the assembly accuracy pass rate requirements, and providing early warnings and adjustment suggestions for possible non-conformities. The flowchart of the assembly accuracy prediction and monitoring method used in the assembly accuracy prediction and monitoring module is as follows: Figure 9The specific implementation of this module is as follows: In the opened assembly accuracy analysis project, the system first reads or imports the measured data table of the ring dimensions on m sampled parts. Then, the system uses the method in step 5 to verify and outputs the statistical mean, process capability index, and predicted overall pass rate of each ring dimension. Assuming that the actual dimensions conform to a normal distribution, if each ring dimension meets the predicted overall pass rate and the specified process capability index requirements, then the method in step 6 is used to calculate the actual confidence region of the geometric element position coordinates, generating theoretical and actual confidence region maps. Finally, the system uses the method in step 7 to judge whether the theoretical confidence region of the target geometric element position coordinates encompasses the actual confidence region. If the theoretical confidence region encompasses the actual confidence region, it means that at a specific confidence level, the actual error variation range of the target geometric element position coordinates is within the theoretical error variation range in all directions and positions, and the actual assembly accuracy will meet the requirements. Therefore, the system outputs the following: If the theoretical confidence region cannot encompass the actual confidence region, the error variation range of the actual confidence region in the target direction or position is calculated. If the error variation range of the actual confidence region in the target direction or position exceeds the tolerance design requirements of the closed loop, it indicates that the actual assembly accuracy will not meet the requirements at this confidence level. Therefore, a signal to stop production is output, along with the dimensions with larger system errors, suggesting increasing or decreasing these dimensions. If the theoretical confidence region cannot completely encompass the actual confidence region, but the error variation range of the actual confidence region in the specified direction or position is within the tolerance design requirements of the closed loop, it indicates that the actual assembly accuracy will meet the tolerance design requirements of the closed loop in that direction or position. However, the position of the target geometric element may exceed the theoretical design range in other directions or positions. Therefore, production can continue, but a warning signal is output, providing a suggested adjustment method, namely, increasing or decreasing the dimensions with larger system errors to bring them closer to the center of the tolerance zone.

[0082] Example 1

[0083] Combination Figures 1-9 The assembly accuracy inspection and control method for supporting large-scale interchangeable assembly of the present invention includes the following steps:

[0084] Step 1: Define the location points of geometric elements in the assembly model.

[0085] Step 1.1 To address assembly tolerance design issues, establish a two-dimensional or three-dimensional dimensional chain diagram, including closed loops and component loops.

[0086] An example of the implementation method is as follows: The main components of the locking mechanism of a light machine gun are as follows: Figure 2 As shown. Figure 2The gap X formed after assembly is a closed loop. Dimension X is the horizontal (x-axis) distance formed by end face A on the sleeve and end face B on the barrel, and X is the target dimension that needs to be controlled. According to traditional precision design methods, it can be drawn as follows... Figure 3 The diagram shows a two-dimensional dimension chain.

[0087] Step 1.2 Determine the target geometric features and the origin of the coordinate system in the assembly model of the parts. The geometric feature corresponding to one endpoint of the closed loop is the target geometric feature; the origin of the coordinate system is selected from the geometric features corresponding to the other endpoint of the closed loop.

[0088] An example of the implementation method is as follows: In Figure 3 In the end face A corresponding to the left endpoint of the closed loop X, select the origin o of the coordinate system, as follows: Figure 3 As shown, the end face B corresponding to the right endpoint of the closed loop X is set as the target geometric element, and point d on end face B is taken as the position point of end face B, with the y-coordinate of point d being the same as that of point o. Therefore, the tolerance analysis problem is to solve for the range of variation of the distance between od and o.

[0089] Step 1.3 Assume that the dimension of each part can be represented as a random number following a normal distribution. Assume that the position of any geometric element (point, line, and surface) on the part can be represented by coordinates in an n-dimensional coordinate system. Starting from the origin of the coordinate system, an n-variable normal distribution is used to represent the position coordinates of the geometric elements corresponding to the endpoints of each component ring. Assume that point a on a certain geometric element is used to represent the position of the geometric element, which can be represented as: a ~ N(μ, C), where μ and C are the mean vector and the overall covariance matrix of the multivariate normal distribution, respectively, and N represents the normal distribution.

[0090] For example, assuming that point 'a' on a certain geometric element is represented by two-dimensional coordinates [x, y], then the random probability distribution of point 'a' in the x-axis and y-axis directions can be represented by the following bivariate normal distribution:

[0091] a~N(μ,C) ~ (1)

[0092] in Let be the mean of the bivariate normal distribution along the x-axis. Let be the mean of a bivariate normal distribution along the y-axis. The correlation coefficients are in the x-axis and y-axis directions. Let x be the standard deviation of the bivariate normal distribution along the x-axis. y is the standard deviation of the bivariate normal distribution along the y-axis.

[0093] During the tolerance design phase, the values ​​of the correlation coefficient ρ in the overall covariance matrix C are discussed in two cases:

[0094] (1) If the two coordinate components of point a (e.g., x and y) belong to different parts, then theoretically there is no correlation, and the correlation coefficient ρ=0 is taken when solving the theoretical analysis.

[0095] (2) If the two coordinate components of point a (e.g., x and y) belong to the same part, the correlation coefficient ρ is taken as 1, -1 or 0 depending on the specific situation: when ρ is 1, it means that the two coordinate components are positively correlated; when ρ is -1, it means that the two coordinate components are negatively correlated; when ρ is 0, it means that the two coordinate components are theoretically uncorrelated.

[0096] For example Figure 2 Both the medium-sized D1 and D2 belong to the cartridge case. When D1 increases, D2 decreases proportionally. It can be proven that the correlation coefficient ρ between D1 and D2 / 2 is -1.

[0097] Step 2: Derive the calculation formula for the target size tolerance by accumulating and decomposing the theoretical confidence region.

[0098] Step 2.1 Use the cumulative method of multivariate normal distribution to obtain the multivariate normal distribution of the position coordinates of the target geometric feature relative to the origin.

[0099] The following is an example of the implementation method: (Combined with...) Figure 2 For the assembly model, the multivariate normal distribution of point 'a' on the bolt or cartridge case relative to the origin 'o' is represented as:

[0100] (2)

[0101] Assuming that each size follows a normal distribution, in equation (2) Let T be the mean of a normal distribution. Let G be the mean of a normal distribution. The mean of the normal distribution of size H1, Let T be the standard deviation of the normal distribution of size T. Let G be the standard deviation of the normal distribution of the size G. Let H1 be the standard deviation of the normal distribution.

[0102] The multivariate normal distribution of point b on the cartridge case relative to point a is represented as:

[0103] (3)

[0104] in Let D1 be the mean of a normal distribution. Let D2 be the mean of a normal distribution. Let D1 be the standard deviation of the normal distribution. Let be the standard deviation of the normal distribution of size D2.

[0105] The multivariate normal distribution of point c relative to point b is represented as follows:

[0106] (4)

[0107] in The mean of the normal distribution of size D3, Rotation matrix:

[0108] The multivariate normal distribution of point d relative to point c is expressed as:

[0109] (5)

[0110] in Let H2 be the mean of a normal distribution. The mean of the normal distribution of size H3, Let H2 be the standard deviation of the normal distribution. Let H3 be the standard deviation of the normal distribution.

[0111] The multivariate normal distribution of point d relative to the origin o is the sum of the multivariate normal distributions in equations (2) to (5).

[0112] Step 2.2 According to the target dimensional tolerance design requirements, 'a' represents the position of the target geometric element. n The confidence region of a point's multivariate normal distribution is decomposed into the range of maximum error variation in a certain direction or location.

[0113] a n The confidence region for a point with a confidence level of 1-α is calculated using the following formula:

[0114]

[0115] The superscript T indicates transpose. The chi-square distribution χ² has n degrees of freedom and a significance level of α. 2 P represents a n The probability (or confidence level) of a point falling within this confidence region is 1-α; C is the population covariance matrix. This indicates that a is a with o as the origin. n For vectors ending at a point, n takes the value of 2 or 3 for two-dimensional or three-dimensional coordinate problems, respectively.

[0116] The formula for calculating the target size tolerance is a. n The formula for calculating the maximum error variation range of a point in a certain direction or position, in a two-dimensional or three-dimensional coordinate system, discusses two cases regarding this error variation range:

[0117] (1) When a n When the direction of the error variation range of a point is known, an The range of error variation at a point in that direction or at a certain position in that direction is determined by calculating a. n The conditional probability distribution of the multivariate normal distribution of the points is obtained.

[0118] (2) When a n When the direction of the error variation range of a point is uncertain, use a. n The calculation is based on the side length of the smallest bounding rectangle or cuboid of the confidence region of a point.

[0119] The implementation method example is as follows: Assume Figure 2 The position coordinates of point d on the target geometric element relative to the origin o can be represented by a bivariate normal distribution, with its confidence region being an ellipse. The equation of this ellipse is:

[0120] (7)

[0121] in The inverse matrix of the covariance matrix of point d with respect to point o. The element in the i-th row and j-th column (i=1,2,……;j=1,2,……).

[0122] Combination Figure 2 , Figure 4 and Figure 5 The confidence region at point d is an ellipse, and we will discuss two cases:

[0123] (1) Combination Figure 2 and Figure 4 Given that the error variation range of point d is in the x-direction, if the position of point d in the y-direction is known, i.e., the y-coordinate is a fixed value, such as y=y1, then the maximum error variation range of the x-coordinate is the length of the intercept l1 between the line parallel to the x-axis and the confidence ellipse. Since... Figure 2 The distance between point d and point o represents the distance between two parallel planes. The y-coordinate of point d is uncertain; therefore, the range of error for point d in the x-direction is the length l of the maximum intercept parallel to the x-axis and passing through the center of the ellipse. max(x) .

[0124] When y=y1, the formula for calculating the target size tolerance, i.e., the maximum error range of the x-coordinate, is:

[0125] (8)

[0126] Where s 12 s 11 and s 22 Depend on Obtain, μ y The y-coordinate of the center of the confidence ellipse.

[0127] (2) Combination Figure 2 and Figure 5 If the direction of the error variation range at point d is uncertain, then construct the minimum bounding rectangle of the confidence ellipse. The width L of this rectangle in the x-axis direction (or y-axis direction) is... x or L y That is, the maximum range of variation of point d in the x-axis direction (or y-axis direction), such as Figure 5 As shown.

[0128] Figure 5 In the formula for calculating the target dimensional tolerance, the error variation ranges in the x and y directions are as follows:

[0129] (9)

[0130] (10)

[0131] in, Let s be a chi-square distribution with n degrees of freedom and a significance level of α. 12 s 11 and s 22 Depend on get.

[0132] Step 3: Assuming that the distribution of the dimensions of each component ring is normal, the dimensional tolerance of each component ring is obtained by using the optimization design method.

[0133] Assuming the dimensions of each component ring follow a normal distribution with known variance, an optimization design method is used to obtain the dimensional tolerance of each component ring at a certain confidence level. The optimization employs the multivariate normal distribution obtained in step 2.1, with the standard deviation of the component ring dimensions as the optimization variable. The optimization objective is to maximize the area or volume of each confidence region, and the constraints are the variation range and tolerance requirements of the component and closed ring dimensions.

[0134] When the position coordinates of a geometric feature follow a multivariate normal distribution, the larger the area or volume of its confidence region, the better the production economy and the lower the manufacturing cost. Therefore, the objective of tolerance optimization design is:

[0135] (11)

[0136] Where i = 1, 2, ..., k; w i S is the weight used to define the importance of a part; i Let k be the area or volume of the confidence region for the coordinates of a certain geometric element on the part, and k is the number of geometric elements involved in the optimization.

[0137] The implementation method example is as follows: (Combined with...) Figure 2The assembly model assumes that the design requirement is that the closed loop X satisfies 0.1 mm ≤ X ≤ 0.9 mm, and the tolerance T of X is... X) ≤0.7 mm. When optimizing the tolerance, it is assumed that the weights of each coordinate point are the same, and the optimization objective is the area S of the multivariate normal distribution information region at coordinate points a, b, c, and d. i The sum is maximized, that is: The optimization variable is the standard deviation of the dimensions of each component ring that needs to be designed. Since the tolerances of the cartridge case dimensions (D1, D2, and D3) are already determined in this problem, no design is required. Therefore, the optimization variable is: σ T σ G , σ H2 σ H3 .

[0138] The constraint is: when the value of y is constant, the maximum range of error variation at point d in the x-direction is: Furthermore, the tolerance zone should be within the bounding rectangle:

[0139] (12)

[0140] (13)

[0141] Where μ d(x) Let d be the x-coordinate of point d.

[0142] Simultaneously, based on the tolerance requirements of the lowest precision grade for each dimension, constraints on the standard deviation of each dimension are established:

[0143] (14)

[0144] Where σ i For each of the above optimization variables, T i These represent the maximum standard tolerances for each dimension. The optimized dimensional tolerances for each component ring are: .

[0145] Step 4: Calculate the theoretical confidence region and the dimensional tolerance of the closed loop for the position coordinates of the target geometric feature.

[0146] After standardizing the tolerances calculated in step 3, tolerance accumulation analysis is performed using the method in step 2.1 to calculate the theoretical confidence region of the target geometric element position coordinates. Then, the maximum variation range of this theoretical confidence region in the target direction and position is calculated using the method in step 2.2, which is the dimensional tolerance of the closed loop.

[0147] The implementation method is illustrated below: After converting the calculated dimensional tolerances of each component ring into the closest standardized tolerance, the calculations are performed according to steps 2.1 and 2.2, yielding the following results: Within a specified confidence level of 99.7%, when the y-value is constant, the maximum error variation range of point d in the X-axis direction is: l d(x) =0.5508 mm, which is less than the tolerance required by the clearance X design; when the y value is uncertain, the maximum error variation range of point d in the x-axis direction is: 0.1934≤x d(min) <x d(max) ≤0.7864, which is within the range of variation required by the clearance X design.

[0148] Step 5: Calculate the process capability index and pass rate of the sampled parts based on their actual dimensions.

[0149] During batch processing of parts, the actual dimensions of the component rings on the finished parts are obtained through random sampling, and their average value is calculated. The dimensions of each sampled part are checked to ensure they are within tolerance limits, and the process capability index C is verified. p and C pk The value is used to predict the overall pass rate based on the normal distribution statistical results of the sample; if the pass rate of the actual size of the part or its process capability index does not meet the requirements, production is stopped and the processing of the non-conforming parts is adjusted.

[0150] The implementation method example is as follows: (Combined with...) Figure 2 For the assembly model, the actual dimensions of the completed parts are measured and statistically analyzed during the production quality inspection process. 32 parts of each type are sampled for inspection, and the actual dimensions of the sampled parts are all within the tolerance zone. Assuming the population follows a normal distribution, the inspection statistics of the first group of sampled parts are shown in Table 1.

[0151] Table 1 Statistical results of the first group of sampled parts

[0152]

[0153] Similarly, 32 parts of each type were sampled for inspection, and the inspection statistics of the second group of sampled parts are shown in Table 2.

[0154] Table 2 Statistical results of the second group of sampled parts

[0155]

[0156] Assume that the pass rate and process capability index of each dimension of both sets of parts meet the process requirements.

[0157] Step 6: Calculate the actual confidence region of the target geometric element position coordinates based on the actual dimensions of the sampled parts.

[0158] Based on the actual dimensions of the sampled parts, the actual confidence region of the target geometric element's position coordinates is calculated using a multivariate normal distribution accumulation method. The method for calculating the actual confidence region is similar to step 2, with the following differences:

[0159] (1) When sampling parts, the overall covariance matrix of the part dimensions is unknown. Therefore, when representing the multivariate normal distribution of the geometric element positions, the sample covariance matrix ∑ is used instead of the overall covariance matrix, and the sample mean is used. Instead of the mean μ of the normal population, the standard deviation of the sample is used instead of the standard deviation of the normal population;

[0160] (2) The correlation coefficient of the coordinates of the relevant dimensions is calculated based on the actual dimensions of the sampled parts;

[0161] (3) Assume a n A point is used to represent the location of a target geometric feature, a n The confidence region of the multivariate normal distribution of point coordinates with a confidence level of 1-α is calculated using formula (15):

[0162] (15)

[0163] in: Where m is the number of samples in the sampling inspection, and n is the number of degrees of freedom. α Let P be a T-distribution with a significance level of α, where P represents a n The probability that the point falls within this confidence region is 1-α. For an F-distribution with a significance level of α, This indicates that a is a with o as the origin. n The vector whose endpoint is a. At this point, a n The confidence region for the actual coordinates of a point remains an ellipse (or ellipsoid). The center of the ellipse (or ellipsoid) is point p, and the vector... This represents a vector with origin o and endpoint p. The direction and length of the ellipse (or ellipsoid) axis are determined by the covariance matrix ∑ of the sample.

[0164] The implementation method example is as follows: (Combined with...) Figure 2 For the assembly model, based on the statistical results of the first group of sampled parts (see Table 1), a multivariate normal distribution is constructed using the statistical mean, statistical standard deviation, and correlation coefficient of the actual dimensions. Considering the correlation between dimensions T and H1 / 2, the multivariate normal distribution covariance of point a relative to the origin is expressed as:

[0165] (16)

[0166] The covariance matrix of point b relative to point a (considering the correlation between dimensions D1 and D2 / 2):

[0167] (17)

[0168] Covariance matrix of point c relative to point b:

[0169] (15)

[0170] The covariance matrix of point d relative to point c:

[0171] (18)

[0172] Therefore, the covariance matrix of point d relative to the origin is the sum of the above covariance matrices:

[0173] (19)

[0174] Step 7: Predict and monitor whether the assembly accuracy pass rate meets the requirements by comparing the theoretical confidence region and the actual confidence region.

[0175] Determine the position coordinates of the target geometric element a n Whether the actual confidence region of a point lies within the theoretical confidence region. If it exceeds the theoretical confidence region, the error variation range of the actual confidence region in the target direction or position is calculated and compared with the tolerance design requirements of the assembly accuracy. Based on the comparison results, the assembly accuracy pass rate is predicted and monitored to ensure it meets the requirements, and corresponding adjustment suggestions are given. The comparison between the theoretical and actual confidence regions is discussed in three cases:

[0176] (1) When a n When the theoretical confidence region of a point can completely encompass its actual confidence region (e.g.) Figure 6 a) If the assembly accuracy pass rate is greater than 1-α, then we accept the assumption that the overall product meets the assembly accuracy requirements. This means that the probability of the overall product meeting the assembly accuracy requirements is greater than 1-α. This indicates that at the confidence level of 1-α, the actual error variation range of the target geometric element position coordinates is within the theoretical error variation range in all directions and positions. The actual assembly accuracy will meet the requirements, so we output a signal to continue production. Figure 6 In equation a, any point in the actual confidence ellipse (solid line) lies within the range of the theoretical confidence ellipse (dashed line).

[0177] (2) When a n The actual confidence region of a point exceeds the theoretical confidence region (e.g.) Figure 6 b or Figure 6c) Calculate the error variation range of the actual confidence region in the target direction or position. If the error variation range of the actual confidence region in the target direction or position exceeds the tolerance design requirements of the closed loop, it indicates that the actual assembly accuracy will not meet the requirements at confidence level 1-α. Therefore, output a signal to stop production. When giving adjustment suggestions, check the statistical mean and process capability index C of each part. p and C pk Value: If the C of a certain dimension of the part p A smaller value indicates a larger random error; if C p The value meets the requirements, but C pk If the overall pass rate of the value or prediction is small, it indicates that the statistical mean of the dimension is significantly off from the center of the tolerance zone. In this case, the dimension is the cause of the systematic error. The relative position between the tool and the machined part should be adjusted so that the statistical mean of the actual dimension is closer to the center of the tolerance zone, that is, closer to the mean of the theoretical normal distribution.

[0178] (3) When a n When the actual confidence region of a point exceeds the theoretical confidence region (e.g.) Figure 6 (b) However, if the error variation range of the actual confidence area in the specified direction or position is within the tolerance design requirement range of the closed loop, it means that the actual assembly accuracy will meet the tolerance design requirement of the closed loop in that direction or position. However, the position of the target geometric element in other directions or positions may exceed the theoretical design range. Therefore, production can continue, but an alarm signal is output, and it is recommended to increase or decrease the size with larger system error in accordance with the method of (2).

[0179] The implementation method example is as follows: (Combined with...) Figure 2 The assembly model assumes that the design requirement is that the closed loop X satisfies 0.1 mm ≤ X ≤ 0.9 mm, and the tolerance T of X is... X) ≤0.7 mm. Based on the statistical results of the first group of sampled parts (see Table 1), the cumulative method of the multivariate normal distribution was used to obtain the multivariate normal distribution of the target geometric element coordinate point d relative to the origin. At a confidence level of 1-α=99.73%, when the direction of error variation is determined, the maximum error variation range of point d in the X-axis direction is the intercept through the center of the confidence ellipse, i.e.: T d(x) =0.4187 mm. When the direction of error variation is uncertain, the error variation range of point d in the x-axis direction is: 0.3623 ≤ x d(min) <x d(max) ≤0.8014. Although the range of assembly clearance error predicted by the sampling inspection results meets the design requirements, it has exceeded the theoretical confidence ellipse range (e.g., Figure 7 If the area has entered the warning zone, the cause should be identified and adjustments made promptly.

[0180] As shown in Table 1, compared with the tolerance zone center, the statistical mean of the increasing ring D1 is larger, and the statistical mean of the decreasing ring H2 is smaller. This results in the mean point at d being positioned too large, causing the actual confidence region to exceed the theoretical confidence region. The improvement method is to adjust the mean values ​​of D1 and H2 to reduce the constant systematic error, which can be achieved by adjusting the relative positions of the tool and the part.

[0181] Based on the statistical results of the second group of sampled parts (see Table 2), the cumulative method of the multivariate normal distribution was used to obtain the multivariate normal distribution of the target geometric element coordinate point d relative to the origin. At a confidence level of 1-α = 99.73%, when the direction of error variation is determined, the maximum error variation range of point d in the X-axis direction is the intercept through the center of the confidence ellipse, i.e., T. d(x) =0.508 mm. When the direction of error variation is uncertain, the error variation range of point d in the x-axis direction is: 0.2053 ≤ x d(min) <x d(max) ≤0.7454. The actual dimensions of the sampled parts were all within the tolerance zone, although the predicted overall pass rates for dimensions H2 and H3 were both less than 99.97% and C pk The values ​​are all less than 1, but the actual confidence ellipse at point d is within the range of the theoretical confidence ellipse (e.g., ...). Figure 8 The reason for this is that the statistical mean values ​​of the decreasing ring H2 and the increasing ring H3 are both relatively small, but the dimensional deviations of these rings cancel each other out on the effect of the closed ring, so the fitting accuracy still meets the requirements.

[0182] Based on the above-mentioned method for controlling the assembly accuracy of firearms that supports a large number of interchangeable assembly methods, this invention also provides a firearms assembly accuracy control system that supports a large number of interchangeable assembly methods. This system is used to control the assembly accuracy of firearms during the tolerance design stage and the parts processing stage. The system includes three functional modules: a geometric element location point definition module, a dimensional tolerance optimization design module, and an assembly accuracy prediction and monitoring module.

[0183] The geometric element location point definition module uses a human-computer interaction method to assist users in determining the location points of each geometric element in the assembly drawing, and helps users build a dimension chain diagram, thus establishing the necessary data model for tolerance optimization design and assembly accuracy prediction and monitoring. The specific implementation of the geometric element location point definition module is as follows: First, the user creates an assembly accuracy analysis project and imports the corresponding assembly drawing model. Then, a human-computer interaction method assists the user in building a dimension chain diagram and determining the closed loop. Next, the user specifies the origin of the coordinate system, the location points of the target geometric element, and the location points of associated geometric elements.

[0184] The dimensional tolerance optimization design module can perform dimensional tolerance optimization design based on the established geometric element position coordinate model, and output optimized and standardized dimensional tolerances according to the tolerance design requirements given by the user. The specific implementation of the dimensional tolerance optimization design module is as follows: First, the user inputs the nominal dimension value of each component ring, the nominal value and error variation range of the angle, the maximum allowable tolerance value and dimensional variation range of the closed ring, specifies the dimension to be designed and the minimum tolerance grade requirement for that dimension, and inputs the pass rate requirement for the assembly accuracy of the closed ring. Then, the optimization method in step 3 is used for optimization. The system converts the optimized tolerance value into the closest standard tolerance value by searching the standard tolerance database. Next, the system uses the method in step 4 to check the standardized tolerance and outputs the optimized and standardized dimensional tolerances.

[0185] The assembly accuracy prediction and monitoring module can predict and monitor assembly accuracy based on measured data of part dimensions and tolerance optimization results. It determines whether the actual dimensions of the parts meet the assembly accuracy pass rate requirements and provides early warnings and adjustment suggestions for potential non-conformities. The flowchart of the assembly accuracy prediction and monitoring method used in the module is as follows: Figure 9The specific implementation of this module is as follows: In the opened assembly accuracy analysis project, the system first reads or imports the measured data table of the ring dimensions on m sampled parts. Then, the system uses the method in step 5 to verify and outputs the statistical mean, process capability index, and predicted overall pass rate of each ring dimension. Assuming that the actual dimensions conform to a normal distribution, if each ring dimension meets the predicted overall pass rate and the specified process capability index requirements, then the method in step 6 is used to calculate the actual confidence region of the geometric element position coordinates, generating theoretical and actual confidence region maps. Finally, the system uses the method in step 7 to judge whether the theoretical confidence region of the target geometric element position coordinates encompasses the actual confidence region. If the theoretical confidence region encompasses the actual confidence region, it means that at a specific confidence level, the actual error variation range of the target geometric element position coordinates is within the theoretical error variation range in all directions and positions, and the actual assembly accuracy will meet the requirements. Therefore, the system outputs the following: If the theoretical confidence region cannot encompass the actual confidence region, the error variation range of the actual confidence region in the target direction or position is calculated. If the error variation range of the actual confidence region in the target direction or position exceeds the tolerance design requirements of the closed loop, it indicates that the actual assembly accuracy will not meet the requirements at this confidence level. Therefore, a signal to stop production is output, along with the dimensions with larger system errors, suggesting increasing or decreasing these dimensions. If the theoretical confidence region cannot completely encompass the actual confidence region, but the error variation range of the actual confidence region in the specified direction or position is within the tolerance design requirements of the closed loop, it indicates that the actual assembly accuracy will meet the tolerance design requirements of the closed loop in that direction or position. However, the position of the target geometric element may exceed the theoretical design range in other directions or positions. Therefore, production can continue, but a warning signal is output, providing a suggested adjustment method, namely, increasing or decreasing the dimensions with larger system errors to bring them closer to the center of the tolerance zone.

Claims

1. A method for controlling the assembly accuracy of firearms that supports large-scale interchangeable assembly, characterized in that, Includes the following steps: Step 1: Define the position points of geometric elements and the origin of the coordinate system in the assembly model, and use an n-variable normal distribution to represent the position coordinates of the geometric elements corresponding to the endpoints of each component ring; Step 2: Derive the calculation formula for the target size tolerance by accumulating and decomposing the theoretical confidence region; Step 3: Assume that the distribution of the dimensions of each component ring is normal. Use the optimization design method to obtain the dimensional tolerance of each component ring. The optimization variable is the standard deviation of the component ring dimensions. The optimization objective is to maximize the area or volume of each confidence region. The constraints are the variation range and tolerance requirements of the dimensions of the component rings and the closed ring. Step 4: Calculate the theoretical confidence region and the dimensional tolerance of the closed loop for the position coordinates of the target geometric feature; Step 5: Calculate the processing capability index and pass rate based on the actual dimensions of the sampled parts; if the pass rate of the actual dimensions of the parts or its processing capability index does not meet the requirements, stop production and adjust the processing of the non-conforming parts; if it meets the requirements, proceed to the next step. Step 6: Calculate the actual confidence region of the target geometric element's position coordinates based on the actual dimensions of the sampled parts. The actual confidence region of the target geometric element's position coordinates is calculated using a multivariate normal distribution accumulation method based on the actual dimensions of the sampled parts. This specifically includes the following steps: Based on the actual dimensions of the sampled parts, the actual confidence region of the target geometric element's position coordinates is calculated using a multivariate normal distribution accumulation method. The method for calculating the actual confidence region is as follows: (1) When sampling parts, the overall covariance matrix of the part dimensions is unknown. When representing the multivariate normal distribution of the geometric element positions, the sample covariance matrix ∑ is used to replace the overall covariance matrix, and the sample mean is used. Instead of the mean μ of the normal distribution, the standard deviation of the sample is used instead of the standard deviation of the normal distribution; (2) The coordinates of the relevant dimensions are calculated based on the actual dimensions of the sampled parts to determine the correlation coefficient between the parts; (3) Let a n A point is used to represent the location of a target geometric feature, a n The confidence region of a multivariate normal distribution of points with a confidence level of 1-α is calculated using the following formula: Where T α For a T-distribution with a significance level of α, m is the number of samples for sampling inspection, n is the number of degrees of freedom of the part, and P represents a. n The probability that the point falls within this confidence region is 1-α. For an F-distribution with a significance level of α, This indicates that the origin is o and a n The vector that ends at the destination, the vector Let a represent a vector with origin o and endpoint p. n The confidence region of the actual coordinates of the point is still an ellipse centered at point p, and the direction and length of the ellipse axis are determined by the covariance matrix ∑ of the sample. Step 7: Predict and monitor whether the assembly accuracy pass rate meets the requirements by comparing the theoretical confidence region and the actual confidence region; Determine the coordinates of the target geometric element at point a. n If the actual confidence region is within the theoretical confidence region, and if it exceeds the theoretical confidence region, the error variation range of the actual confidence region in the target direction or position is calculated. The actual confidence region is compared with the tolerance design requirements of the assembly accuracy. Based on the comparison results, the pass rate of the assembly accuracy is predicted and monitored to see if it meets the requirements, and corresponding adjustment suggestions are given.

2. The firearm assembly precision control method supporting large-scale interchangeable assembly according to claim 1, characterized in that, Step 1 specifically includes the following steps: Step 1.1 Create a two-dimensional or three-dimensional dimensional chain diagram, including closing loops and component loops; Step 1.2 Determine the target geometric features and the origin of the coordinate system in the assembly model of the parts; the geometric feature corresponding to one endpoint of the closed loop is the target geometric feature; the origin of the coordinate system is selected from the geometric features corresponding to the other endpoint of the closed loop; Step 1.3 Assume that the dimension value of each part is represented as a random number that follows a normal distribution. Assume that the position of any geometric element on the part is represented by coordinates in an n-dimensional coordinate system. Starting from the origin of the coordinate system, an n-variable normal distribution is used to represent the position coordinates of the geometric elements corresponding to the endpoints of each component ring.

3. The method for controlling the assembly accuracy of firearms supporting large-scale interchangeable assembly according to claim 1, characterized in that, Step 2 specifically includes the following steps: Step 2.1 Use the cumulative method of multivariate normal distribution to obtain the multivariate normal distribution of the position coordinates of the target geometric feature relative to the origin; Step 2.2 According to the target dimensional tolerance design requirements, mark the coordinates of point a representing the position of the target geometric element. n The confidence region of a multivariate normal distribution is decomposed into the range of maximum error variation in a certain direction or location; a n The confidence region for a point with a confidence level of 1-α is calculated using the following formula: Where T represents transpose. The chi-square distribution χ² has n degrees of freedom and a significance level of α. 2 P represents a n The probability that a point falls within this confidence region is 1-α; C is the population covariance matrix. This indicates that the origin is o and a n The vector with endpoint is n, which takes the value of 2 or 3 for two-dimensional or three-dimensional coordinate problems, respectively; μ is the mean vector of a multivariate normal distribution. The formula for calculating the target size tolerance is a. n The formula for calculating the maximum error variation range of a point in a certain direction or position, when a n When the direction of the error variation range of a point is known, a n The range of error variation at a point in that direction or at a certain position in that direction is determined by calculating a. n The conditional probability distribution of a point's multivariate normal distribution is obtained when a n When the direction of the error variation range of a point is uncertain, a n The range of error variation of a point in this direction or at a certain position in this direction is expressed as a. n It is obtained by the side length of the smallest bounding rectangle or cuboid of the confidence region of a point.

4. The method for controlling the assembly accuracy of firearms supporting large-scale interchangeable assembly according to claim 1, characterized in that, In step 7, when comparing the theoretical confidence region and the actual confidence region, there are two cases: (1) When a n If the theoretical confidence region of a point can completely encompass its actual confidence region, then the assumption that the assembly accuracy pass rate is >1-α is accepted, and a signal to continue production is output, where α is the significance level. (2) When a n If the actual confidence region of a point exceeds the theoretical confidence region, then the error variation range of the actual confidence region in the target direction or position is calculated, including the following two cases: (a) If the error variation range of the actual confidence region in the target direction or position exceeds the tolerance design requirements of the closed loop, it indicates that the actual assembly accuracy will not meet the requirements at confidence level 1-α. Therefore, a signal to stop production is output, and when giving adjustment suggestions, the statistical mean and process capability index C of each part are checked. p and C pk Value: If the C of a certain dimension of the part p A smaller value indicates a larger random error; if C p The value meets the requirements, but C pk If the overall pass rate of the value or prediction is small, it indicates that the statistical mean of the dimension is offset from the center of the tolerance zone. In this case, the dimension is the cause of the systematic error. The relative position between the tool and the machined part should be adjusted so that the statistical mean of the actual dimension is closer to the center of the tolerance zone, that is, closer to the mean of the theoretical normal distribution. (b) If the actual confidence area is within the tolerance design requirements of the closed loop in a certain direction or position, it means that the actual assembly accuracy will meet the tolerance design requirements of the closed loop in that direction or position. However, the position of the target geometric element may exceed the theoretical design range in other directions or positions. Therefore, production can continue, but a warning signal is output, suggesting that the size with the larger system error be increased or decreased to be closer to the center of the tolerance zone.

5. The control system designed according to the method for controlling the accuracy of firearm assembly supporting large-scale interchangeable assembly as described in claim 1, characterized in that, include: The geometric element location point definition module uses a human-computer interaction method to help users determine the coordinate system origin and the location points of each geometric element in the assembly drawing, and helps users to build a dimension chain diagram, thus establishing the necessary data model for tolerance optimization design and assembly accuracy prediction and monitoring. The dimensional tolerance optimization design module performs dimensional tolerance optimization design based on the established geometric element position coordinate model. It can optimize according to the user-provided closed loop tolerance design requirements and the minimum tolerance level design requirements of each component loop using the optimization method in step 3. After searching the standard tolerance database, it converts each tolerance into the closest standard tolerance value, and uses the method in step 4 to check the standardized tolerances, outputting the optimized and standardized dimensional tolerances. The assembly accuracy prediction and monitoring module calculates the statistical mean of the dimensions of each component ring, the process capability index, and the predicted overall pass rate based on the measured data of the part dimensions and the tolerance design requirements. Calculate the actual confidence region of the geometric element position coordinates according to the method in step 6, and generate theoretical and actual confidence region maps; verify whether the theoretical confidence region of the target geometric element position coordinates encompasses the actual confidence region based on the tolerance optimization results and the method in step 7, thereby determining whether the actual dimensions of the part meet the requirements of the assembly accuracy pass rate, and providing early warnings and suggestions for adjustment methods for possible non-conformities.

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