A method for grouping assembly interface shape errors for three-dimensional selection

Abstract

The application discloses a three-dimensional matching-oriented assembly interface shape error grouping method, and relates to the field of precision assembly, and comprises the following steps: acquiring assembly interface point cloud data and calculating five-dimensional topographic parameters; adopting a greedy allocation K-Means algorithm to cluster and group the five-dimensional topographic parameters; combining principal component analysis to perform three-dimensional visualization on the grouping result; and based on the three-dimensional visualization result, adopting a grouping matching method to match a reference part and a matching part, so as to realize three-dimensional matching-oriented assembly interface shape error grouping. The application solves the problem that the existing size grouping method is two-dimensional size chain model-oriented and is difficult to adapt to three-dimensional matching requirements.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of precision assembly, in particular to a three-dimensional matching-oriented assembly interface shape error grouping method. BACKGROUND

[0002] In the fields of aerospace, precision instruments and high-end equipment manufacturing, the precision assembly quality of parts directly determines the performance of products. The traditional assembly grouping method is mainly based on a two-dimensional dimension chain model, and the error compensation is realized through the grouping strategy of "large assembly, small assembly". However, this method has significant limitations:

[0003] Insufficient three-dimensional matching adaptability: the existing method only uses dimensional error as the grouping basis and does not consider the three-dimensional spatial distribution characteristics of the shape error of the assembly interface. The actual machined surface of the part presents complex three-dimensional characteristics such as peaks, valleys, grooves, etc. Only relying on dimensional grouping cannot accurately represent the surface contact state, resulting in assembly precision fluctuations.

[0004] Theoretical defects of grouping strategy: the grouping method based on the normal distribution assumption (such as genetic algorithm three-stage optimization, equal tolerance band grouping) is prone to produce a large number of remaining parts when the part size is not normally distributed; the non-normal distribution grouping method reduces the remaining amount, but cannot handle complex size chains of multiple parts, and does not establish a quantitative correlation between shape error and assembly function.

[0005] It is difficult to ensure assembly consistency: random selection or traditional grouping methods do not consider the nonlinear effects of three-dimensional topography error, resulting in significant fluctuations in assembly clearance. For example, when the surface topography parameter values of the parts are the same but the distributions are different, the contact state and error accumulation of the assembly body differ significantly. The existing method cannot quantify this difference, making it difficult to ensure the assembly quality consistency of batch products.

[0006] Existing research shows that three-dimensional surface parameters (such as surface arithmetic mean deviation, support index, etc.) can more accurately represent surface functional characteristics, but an effective three-dimensional topography error grouping system has not yet been formed. Therefore, there is an urgent need for a three-dimensional matching-oriented assembly interface shape error grouping method to solve the adaptability problem of traditional two-dimensional dimensional grouping in three-dimensional matching and improve the assembly precision control capability. SUMMARY

[0007] In view of the problem that the existing dimensional grouping method is based on a two-dimensional dimensional chain model and is difficult to adapt to the needs of three-dimensional matching, the present application provides a three-dimensional matching-oriented assembly interface shape error grouping method, which realizes accurate grouping of the assembly interface through multi-dimensional topography parameter representation and improved clustering algorithm, and improves the consistency and precision control capability of batch part assembly.

[0008] To achieve the aforementioned objectives, the present invention employs the following technical solution: a method for grouping assembly interface shape errors for three-dimensional selection, characterized by comprising the following steps:

[0009] S1: Acquire point cloud data from the assembly interface and calculate five-dimensional topographic parameters;

[0010] S2: The five-dimensional morphological parameters are clustered and grouped using the greedy K-Means algorithm.

[0011] S3: Combine principal component analysis to perform three-dimensional visualization of the grouping results;

[0012] S4: Based on the 3D visualization results, the group selection method is used to select the reference parts and matching parts, so as to realize the grouping of assembly interface shape error for 3D selection.

[0013] Furthermore, the five-dimensional topography parameters in S1 include:

[0014] Surface Arithmetic Mean Deviation S a :

[0015]

[0016] Where S represents the sampling area, M represents the number of discrete points sampled in the x-axis direction within S, N represents the number of discrete points sampled in the y-axis direction within S, m represents the number of discrete points collected along the x-axis direction within the sampling area of ​​the assembly interface, n represents the number of discrete points collected along the y-axis direction within the sampling area of ​​the assembly interface, z(·) represents the height of the sampled discrete points on the assembly interface relative to the reference plane, x i This represents the coordinates of the discrete point along the x-axis, y-axis... j This represents the coordinates of the discrete point along the y-axis, used to characterize the microscopic height features of a single sampling point;

[0017] Surface root mean square deviation S q :

[0018]

[0019] Three-dimensional surface support index S bi :

[0020]

[0021] Where, η 0.05 h represents the surface height of 5% of the support area. 0.05 This represents the reciprocal of the surface support index when the support area is 5%.

[0022] Core area liquid retention index S ci :

[0023]

[0024] wherein, V v (h 0.05 ) and V v (h 0.8 ) represent the surface topography volume when the support area is 5% and 80%, respectively, represents the interval between two adjacent sampling discrete points along the x-axis direction (i.e., the sampling step along the x-axis direction), represents the interval between two adjacent sampling discrete points along the y-axis direction (i.e., the sampling step along the y-axis direction);

[0025] the liquid retention index S vi in the valley region:

[0026]

[0027] Further, the S2 includes the following steps:

[0028] S21: standardizing the five-dimensional parameter matrix composed of the five-dimensional topography parameters:

[0029]

[0030] wherein, represents the value obtained after standardizing , V represents the original value of the j-dimensional parameter of the i-th part (sample) in the five-dimensional topography parameter matrix, represents the mean value of the j-th column feature, represents the standard deviation of the j-th column feature;

[0031] S22: randomly selecting K samples as initial cluster center points from the standardized data, and K satisfies N1 mod K = 0, N1 being the number of parts;

[0032] S23: calculating the distance of each sample to each cluster center, and sorting the distance of each sample to all clusters in ascending order to obtain an indexed vector after sorting;

[0033] The distance of each sample to each cluster center is:

[0034]

[0035] wherein, d(·) represents the distance of each sample to each cluster center, represents the standardized data, c k represents the initial centroid of the k-th cluster, k = 1, 2, ···, K, c kjrepresents the value of the initial kth cluster (group) centroid on the jth dimensional feature;

[0036] S24: Fill each cluster to the target capacity N1 / K according to the distance order, for each sample, check the cluster capacity according to the index vector order, if the number of allocated samples of the current candidate cluster is less than the target capacity, allocate the sample to the current candidate cluster, if it is full, check the next candidate cluster, until all samples are successfully allocated, and get the balanced grouping label vector;

[0037] S25: Extract the sample set of each cluster, calculate the mean of all samples of each cluster to update the cluster centroid, and output the grouping result.

[0038] Further, the S3 includes the following steps:

[0039] S31: Perform PCA dimensionality reduction on the normalized five-dimensional parameters, retain the first three principal components, and calculate the coordinates of the samples in the three-dimensional principal component space;

[0040] S32: Color the three-dimensional coordinates after dimensionality reduction according to the grouping label to generate a clustering scatter plot.

[0041] Further, the grouping selection method in S4 includes:

[0042] Strategy one: the first a group of reference parts is paired with the first a group of matching parts;

[0043] Strategy two: the first a group of reference parts is cross-paired with the k+1-a group of matching parts, where k represents the kth cluster;

[0044] Calculate the weighted squared difference gap index of each group pairing, and calculate the mean and variance of the objective function of the grouping selection and random selection;

[0045] The weighted squared difference gap index is:

[0046]

[0047] where f is the weighted squared difference gap index, and are the ath group bth dimensional parameters of the reference parts and the matching parts, respectively, w b is the parameter weight, and A is the number of groups.

[0048] The beneficial effects of the present application are: the present application introduces multi-dimensional parameter representation, quantifies the "peak-valley" morphology and bearing lubrication characteristics by combining amplitude parameters and functional parameters, and is more consistent with the actual assembly contact state than the traditional two-dimensional size grouping. The forced balanced filling strategy ensures that the deviation of the number of samples in each group is less than or equal to 5%, and the distance sorting greedy allocation avoids the local optimal trap of the traditional K-Means, and the grouping uniformity is improved by more than 30%. Experiments show that the mean value of the objective function of the grouping and selection strategies one and two is reduced by 23.63% and 22.51% respectively than the random selection, and the variance is reduced by 35.94%, effectively suppressing the batch assembly precision fluctuation. The PCA dimension reduction visualizes the grouping result, intuitively displays the surface morphology feature difference of different groups, provides a quantitative basis for assembly process planning, and shortens the process planning and debugging cycle. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 The grouping method flow chart of the shape error of the assembly interface for three-dimensional selection provided by the present application.

[0050] Figure 2 The different shape error distribution diagram of two parts with the same shape error value provided by the present application.

[0051] Figure 3 The micro-morphology diagram of the assembly interface 1 provided by the present application.

[0052] Figure 4 The micro-morphology diagram of the assembly interface 2 provided by the present application.

[0053] Figure 5 The micro-morphology diagram of the assembly interface 3 provided by the present application.

[0054] Figure 6 The micro-morphology diagram of the assembly interface 4 provided by the present application.

[0055] Figure 7 The PCA dimension reduction visualization result diagram of the shape error grouping of the assembly interface of part 1 provided by the present application.

[0056] Figure 8 The PCA dimension reduction visualization result diagram of the shape error grouping of the assembly interface of part 2 provided by the present application.

[0057] Figure 9 The target function value comparison column chart of the grouping and selection and the random selection provided by the present application. DETAILED DESCRIPTION

[0058] The present application will be further described below in combination with the drawings and specific embodiments.

[0059] As Figure 1As shown, a three-dimensional selection-oriented assembly interface shape error grouping method, comprising the following steps:

[0060] S1: Obtain assembly interface point cloud data and calculate five-dimensional topographic parameters;

[0061] By sampling, obtain the assembly interface three-dimensional point cloud data with machining error, determine the reference part mating surface (target surface) and the matching part mating surface (to-be-matched surface). Based on the point cloud data, calculate the micro-topographic characterization parameters, and the specific definitions and formulas are as follows:

[0062] Calculate the arithmetic mean of the height of each point in the measurement area and the distance from the reference plane, that is, the surface arithmetic mean deviation S a :

[0063]

[0064] Wherein, S represents the sampling area, M represents the number of discrete points sampled in the S in the x-axis direction, N represents the number of discrete points sampled in the S in the y-axis direction, m represents the number of discrete points collected in the assembly interface sampling area along the x-axis direction, n represents the number of discrete points collected in the assembly interface sampling area along the y-axis direction, z(·) represents the height value of the sampling discrete point on the assembly interface relative to the reference plane, x i represents the coordinate of the discrete point in the x-axis direction, y j represents the coordinate of the discrete point in the y-axis direction, which is used to characterize the micro-height characteristics of a single sampling point;

[0065] Calculate the root mean square value of the height of each point and the distance from the reference plane, that is, the surface root mean square deviation S q :

[0066]

[0067] Calculate the ratio of the surface root mean square deviation to the supporting area ratio curve at 5% height, that is, the three-dimensional surface supporting index S bi :

[0068]

[0069] Wherein, η 0.05 represents the surface height of 5% supporting area, h 0.05 represents the inverse of the surface supporting index when the supporting area is 5%, S bi is mainly used to characterize the supporting and carrying capacity of the test surface, the larger the value, the better the surface supporting and carrying characteristics;

[0070] Calculate the ratio of the core area volume to S q in the supporting area ratio curve, that is, the core area liquid retention index S ci :

[0071]

[0072] Among them, V v (h 0.05 ) and V v (h 0.8 The numbers () represent the surface morphology and volume of the hollow body when the support area is 5% and 80%, respectively. This represents the distance between two adjacent discrete sampling points along the x-axis (i.e., the sampling step size along the x-axis). S represents the distance between two adjacent discrete sampling points along the y-axis (i.e., the sampling step size along the y-axis); ci It can be used to characterize the amount of liquid retained in the core area, thus reflecting the quality of the surface lubrication properties; the larger the value, the more volume the core area occupies and the more liquid is retained.

[0073] The volume of the valley region in the curve for calculating the surface support area ratio is related to S. q The ratio of the two values, i.e., the liquid retention index S in the valley area. vi :

[0074]

[0075] S vi Characterization tests indicate the volume of the valley area, which in turn reflects the amount of fluid retained during lubrication; the larger the value, the more fluid is retained.

[0076] S2: The five-dimensional morphological parameters are clustered and grouped using the greedy K-Means algorithm.

[0077] S2 includes the following sub-steps:

[0078] S21: For the five-dimensional parameter matrix composed of the aforementioned five-dimensional topographic parameters (N1 is the number of parts) is standardized:

[0079]

[0080] in, Indicates to The values ​​obtained after standardization This represents the original value of the j-th dimension parameter of the i-th part (sample) in the five-dimensional topography parameter matrix. This represents the mean of the features in column j. The standard deviation of the j-th column feature;

[0081] S22: Randomly select K samples from the standardized data as the initial cluster centers, which can be represented as {c 1， c 2，···， cK K, and the number of clusters K satisfies N1 mod K = 0, which ensures that the capacity of each group is balanced, and N1 is the number of parts;

[0082] S23: Calculate the distance of each sample to the center of each cluster, and sort the distance of each sample to all clusters in ascending order to obtain an ordered index vector; for example, if the index vector is , it indicates that the nearest cluster of the i-th sample is 3, the second nearest cluster is 1, and the farthest cluster is 2.

[0083] The distance of each sample to the center of each cluster is:

[0084]

[0085] where d(·) represents the distance of each sample to the center of each cluster, , c k represents the initial centroid of the k-th cluster, k = 1, 2,..., K, and c kj represents the value of the initial centroid of the k-th cluster (group) in the j-th feature;

[0086] S24: Fill each cluster to the target capacity according to the distance sorting, and the target capacity is N1 / K. For each sample, check the cluster capacity according to the index vector order. If the number of allocated samples of the current candidate cluster is less than the target capacity, allocate the sample to the current candidate cluster. If it is full, check the next candidate cluster, until all samples are successfully allocated, and obtain the balanced grouping label vector , where ;

[0087] S25: Extract the sample set that satisfies g i = k for each cluster , calculate the mean of all samples in each cluster to update the cluster centroid, and output the grouping result.

[0088] S3: Perform three-dimensional visualization on the grouping result combined with principal component analysis;

[0089] S3 includes the following steps:

[0090] S31: Perform PCA dimensionality reduction on the five-dimensional parameters after standardization, retain the first three principal components, and calculate the coordinates of the samples in the three-dimensional principal component space;

[0091] S32: Color the three-dimensional coordinates after dimensionality reduction according to the grouping label to generate a scatter plot, which intuitively presents the spatial distribution characteristics of each group of samples.

[0092] S4: Based on the three-dimensional visualization result, use the grouping selection method to select the reference part and the matching part, and realize the grouping of the shape error of the assembly interface for three-dimensional selection.

[0093] The grouping matching method in S4 includes:

[0094] Strategy one: the first group of the reference part is matched with the first group of the matching part;

[0095] Strategy two: the first group of the reference part is matched with the k+1-a group of the matching part, wherein k represents the kth cluster;

[0096] The weighted square difference gap index of each group of matching is calculated, the mean and variance of the objective function of the grouping matching and the random matching are counted, and the promotion effect of the grouping on the assembly consistency is verified;

[0097] The weighted square difference gap index, and the objective function expression is:

[0098]

[0099] Wherein, f is the weighted square difference gap index, and are the bth dimensional parameters of the first group of the reference part and the matching part, w b is the parameter weight, and A is the group number.

[0100] In an embodiment of the present application, Figure 2 it is a schematic diagram of different shape error distributions of two parts with the same shape error value provided by the present application, wherein Figure 2 (a) in the figure is the shape error distribution of the assembly interface of part a, Figure 2 (b) in the figure is the shape error distribution of the assembly interface of part b; Figure 3 it is a schematic diagram of the microtopography of the assembly interface 1 provided by the present application, wherein Figure 3 (a) in the figure is a three-dimensional assembly interface diagram, Figure 3 (b) in the figure is a two-dimensional heat map; Figure 4 it is a schematic diagram of the microtopography of the assembly interface 2 provided by the present application, wherein Figure 4 (a) in the figure is a three-dimensional assembly interface diagram, Figure 4 (b) in the figure is a two-dimensional heat map; Figure 5 it is a schematic diagram of the microtopography of the assembly interface 3 provided by the present application, wherein Figure 5 (a) in the figure is a three-dimensional assembly interface diagram, Figure 5 (b) in the figure is a two-dimensional heat map; Figure 6 it is a schematic diagram of the microtopography of the assembly interface 4 provided by the present application, wherein Figure 6 (a) in the figure is a three-dimensional assembly interface diagram, Figure 6 (b) in the figure is a two-dimensional heat map; Figure 7 it is the PCA dimension reduction visualization result of the shape error grouping of the assembly interface of part 1 provided by the present application; Figure 8 it is the PCA dimension reduction visualization result of the shape error grouping of the assembly interface of part 2 provided by the present application; Figure 9A bar chart of target function values of the grouping matching and the random matching is provided.

[0101] As can be seen from Table 1, in the matching result of the two types of parts by the strategy one of the grouping matching method, the average distance of the 11th part in the 50 parts 1 matched with the 22nd part in the parts 2 is the smallest, and is 1.4256e-03 mm; the average distance of the 37th part in the parts 1 matched with the 26th part in the parts 2 is the largest, and is 6.7389e-03 mm.

[0102] Table 1 Matching result of two types of parts by strategy one of grouping matching method

[0103]

[0104] As can be seen from Table 2, in the matching result of the two types of parts by the strategy two of the grouping matching method, the average distance of the 32nd part in the 50 parts 1 matched with the 24th part in the parts 2 is the smallest, and is 1.2602e-03 mm; the average distance of the 47th part in the parts 1 matched with the 17th part in the parts 2 is the largest, and is 5.9204e-03 mm.

[0105] Table 2 Matching result of two types of parts by strategy two of grouping matching method

[0106]

[0107] As can be seen from Table 3, in the matching result of the two types of parts by the random matching method, the average distance of the 37th part in the 50 parts 1 matched with the 17th part in the parts 2 is the smallest, and is 1.0506e-03 mm; the average distance of the 4th part in the parts 1 matched with the 23rd part in the parts 2 is the largest, and is 9.0681e-03 mm.

[0108] Table 3 Matching result of two types of parts by random matching method

[0109]

[0110] As can be seen from Table 4 and Figure 9 It can be seen that, for the grouping matching method, whether it is strategy one or strategy two, the mean and variance are better than the random matching method. The mean of all matching combinations obtained by the two strategies of the grouping matching method is reduced by about 23.63% and 22.51% respectively compared with the random matching, and the variance is smaller than the random matching method.

[0111] Table 4 Comparison of mean and variance of grouping matching method and random matching method

[0112]

[0113] The embodiment proves that the method can accurately realize the assembly interface shape error grouping by complete parameter calculation, algorithm iteration and experimental verification, provides a quantitative basis for three-dimensional selection, and is suitable for batch part grouping in scenes such as aerospace precision parts and high-end machine tool guideways.

[0114] Those skilled in the art will appreciate that the embodiments described herein are presented for the purpose of helping the reader understand the principles of the present application and should be understood as not limiting the scope of protection of the present application to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations according to the technical inspiration disclosed in the present application without departing from the essence of the present application, and these modifications and combinations are still within the scope of protection of the present application.

Claims

1. A method for grouping assembly interface shape errors for three-dimensional fitting, characterized in that, The method comprises the following steps: S1: acquiring assembly interface point cloud data and calculating five-dimensional topography parameters; S2: adopting a greedy distribution K-Means algorithm to cluster and group the five-dimensional topography parameters; The S2 comprises the following steps: S21: performing standardization processing on a five-dimensional parameter matrix composed of the five-dimensional topography parameters; wherein, represents a value obtained after standardization processing is performed on represents the original value of the th parameter of the th part in the five-dimensional topography parameter matrix, represents the mean value of the th column feature, represents the standard deviation of the th column feature;​ S22: randomly select one sample as the initial cluster center point from the standardized data, and S23: calculate the distance between the sample and the initial cluster center point, and S24: if the distance is less than the threshold, add the sample to the cluster, and S25: if the distance is greater than the threshold, add the sample to a new cluster. N: number of parts S23: calculating the distance of each sample to each cluster center, and sorting the distance of each sample to all clusters in ascending order to obtain an index vector after sorting; The distance of each sample to each cluster center is: wherein, denotes the distance of each sample to the cluster centers, denotes the normalized data, denotes the initial first cluster center, , denotes the initial first cluster center on the value of the dimensional feature; S24: filling each cluster to target capacity according to distance ordering, the target capacity being For each sample, checking cluster capacity according to the index vector order, if the number of allocated samples of the current candidate cluster is less than the target capacity, allocating the sample to the current candidate cluster, if it is full, checking the next candidate cluster, until all samples are successfully allocated, obtaining an equalized grouping label vector. S25: extracting a sample set of each cluster, calculating the mean of all samples of each cluster to update the cluster center, and outputting a grouping result; S3: combining principal component analysis to perform three-dimensional visualization on the grouping result; S4: based on the three-dimensional visualization result, adopting a grouping matching method to match the reference part and the matching part, and realizing assembly interface shape error grouping facing three-dimensional matching.

2. The three-dimensional fit-to-order assembly interface shape error grouping method of claim 1, wherein, The five-dimensional topography parameters in the S1 comprise: surface arithmetic mean deviation : in, Indicates the sampling area. Indicates in Inside The number of discrete points sampled along the axial direction. Indicates in Inside The number of discrete points sampled along the axial direction. This indicates that within the sampling area of ​​the assembly interface, along The number of discrete points collected along the axial direction. This indicates that within the sampling area of ​​the assembly interface, along The number of discrete points collected along the axial direction. This represents the height value of the sampled discrete point on the assembly interface relative to the reference plane. This indicates that the discrete point is in Coordinates along the axis, This indicates that the discrete point is in The coordinates along the axis are used to characterize the microscopic height features of a single sampling point; Surface root mean square deviation : Three-dimensional surface support index : wherein, represents the surface height of 5% of the bearing area, represents the inverse of the surface bearing index at 5% of the bearing area; Core-liquid holdup index : wherein, represents the surface morphology volume when the support area is 5% and 80%, respectively, represents the surface morphology volume when the support area is 5% and 80%, respectively, represents the distance between two adjacent sampling discrete points along the represents the distance between two adjacent sampling discrete points along the represents the distance between two adjacent sampling discrete points along the represents the distance between two adjacent sampling discrete points along the Valley region liquid holdup index : 。 3. The three-dimensional fit-to-order assembly interface shape error grouping method of claim 1, wherein, The S3 comprises the following steps: S31: performing PCA dimension reduction on the standardized five-dimensional parameters, retaining the first three principal components, and calculating the coordinates of the samples in the three-dimensional principal component space; S32: coloring the three-dimensional coordinates after dimension reduction according to the grouping labels to generate a clustering scatter plot.

4. The three-dimensional fit-to-order assembly interface shape error grouping method of claim 1, wherein, The grouping matching method in the S4 comprises: Strategy 1: Reference piece first Group with matching piece first Group pairing; Strategy two: the reference member is in the first group and the matching member is in the second group, wherein the first cluster represents the second calculating a weighted squared difference gap index of each group of pairs, and calculating the mean and variance of the objective function of the grouping matching and random matching; The weighted squared difference gap index is: wherein, is a weighted squared difference gap metric, and are the first set of dimensional parameters of the reference and matching parts, respectively, is a parameter weight, is the number of sets.

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