A method for analyzing assembly accuracy based on multi-stage linearized contact

Abstract

The present invention provides an assembly precision analysis method based on multi-stage linearized contact, which solves the problem of how to improve the accuracy of assembly precision analysis. It includes: establishing a micro-convex body model of a part surface considering the morphological error, extracting a part surface group with an assembly relationship; predicting the original posture of the part assembly process in the part surface group under the rigid body assumption, and obtaining the contact point data based on the original posture; dividing the elastic contact process into several stages according to the contact point data, and each stage is subdivided into several linear processes; obtaining the displacement vector of each linear process through the assembly data, and obtaining the final posture of the assembly part surface group based on the displacement vector. The present invention adopts the posture prediction solution of the rigid contact process to obtain a high assembly precision, divides the elastic contact process of the assembly interface into several linear processes, and then converts it into the superposition of several linear processes, realizes the correction of contact stiffness, and improves the reliability of the assembly precision analysis results.

Description

Technical Field

[0001] The invention relates to the field of mechanical manufacturing, and in particular to an assembly accuracy analysis method based on multi-stage linearized contact. Background Art

[0002] In the modern mechanical production process, assembly accuracy directly affects the performance of the product. Assembly accuracy is affected by multiple factors including surface topography error and deformation caused by interaction. The coupling of various factors makes it impossible to directly obtain assembly accuracy. The current assembly accuracy analysis methods are mainly divided into two categories: one is the assembly accuracy analysis method based on the rigid body assumption, and the other is the assembly accuracy analysis method considering deformation.

[0003] In the assembly accuracy analysis method based on the rigid body assumption, the main research is the influence of the manufacturing deviation of the parts themselves and the positioning deviation in the assembly process on the assembly accuracy, without considering the deformation of the parts caused by the assembly load during the assembly process. For example, the document "Chen Qiang. Research and Application of Closed-Loop Quality Deviation Analysis System Based on Dimensional Engineering [D]. Jiangsu University, 2020. DOI: 10.27170 / d.cnki.gjsuu.2020.001111" published online by Wanfang Platform on November 5, 2020, expresses the closed loop as the dependent variable and the component loop as the functional relationship of the independent variable. Through the analysis and processing of the actual measurement data, the verification of product dimensional design and the optimization of structural process are realized, as well as the prediction of product assembly quality and the improvement of the stability of the production process. However, since this method ignores the influence of part deformation on assembly accuracy, the accuracy of its analysis results is limited, and it is difficult to meet the requirements of mechanical products with high precision requirements.

[0004] In the assembly accuracy analysis method considering deformation, in order to solve the problem that the model based on the rigid body assumption cannot accurately describe the surface deformation of parts during the assembly process and further improve the accuracy, it is necessary to establish an assembly accuracy analysis model considering deformation. For example, the literature "Yi Y, Liu X, Liu T, et al. A generic integrated approach of assembly tolerance analysis based on skin model shapes [J]. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2021, 235 (4): 689-704." By combining the skin surface model shape and deviation flow theory, a relative contact positioning method based on different surfaces and progressive contact method is adopted in the deviation transfer model to predict the assembly accuracy in the design stage, thereby guiding the manufacturing and assembly process. However, similar to most assembly accuracy analysis models considering deformation, the accuracy of the analysis results of this method is limited by nonlinear effects. The interface matching problem of precision parts assembly is affected by different deviations such as roughness, positioning / orientation error, and part surface deformation. The mutual coupling between the influencing factors makes the input and output of this problem nonlinear, which seriously affects the accuracy of assembly accuracy analysis. For mechanical products with higher precision requirements, the errors caused by nonlinear effects cannot be ignored, and the accuracy of existing methods still has room for further improvement. Summary of the invention

[0005] The purpose of the present invention is to provide an assembly accuracy analysis method based on multi-stage linearized contact. The assembly accuracy solved by posture prediction of a rigid contact process is high. The translation and rotation of parts in the assembly process are characterized by homogeneous coordinate transformation, so as to realize the prediction of part posture and the determination of contact points under the rigid body assumption. The elastic contact process of the assembly interface is divided into several linear processes, and the elastic deformation of the elastic contact process, a highly nonlinear process, is converted into the superposition of several linear processes, so as to realize the correction of contact stiffness and improve the reliability of the assembly accuracy analysis results.

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

[0007] The present invention provides an assembly accuracy analysis method based on multi-stage linearized contact, comprising:

[0008] Step 1: Establish a part surface micro-convex body model taking into account the morphological error, and extract part surface groups having assembly relationships in the part surface micro-convex body model;

[0009] Step 2: predicting the original posture of the parts assembly process in the part surface group under the rigid body assumption, and obtaining the contact point data of the contacting surfaces in the assembly of the part surface group based on the original posture;

[0010] Step 3: dividing the elastic contact process in the surface assembly of the parts into several stages according to the contact point data, and each stage is subdivided into several linear processes;

[0011] Step 4: obtaining the displacement vector of each linear process through the assembly data in the assembly of the part surface group, and obtaining the final posture of assembling the part surface group based on the displacement vector, wherein the assembly data includes assembly load, rotation angle and displacement of the part;

[0012] Step 5: Analyze the assembly accuracy of parts based on the contact point data, the final posture and the deformation of the micro-convex body during the elastic contact process.

[0013] As a further limitation of the present invention, the step 1 comprises:

[0014] Establishment of micro-convex body model on part surface: linearly superimpose several kernel functions of discrete cosine transform to characterize the morphological errors of different frequencies, and establish the micro-convex body model on part surface between different parts with assembly relationship considering the morphological errors based on the kernel function;

[0015] Part surface group extraction: extracting a part surface group from a plurality of part surface groups having assembly relationships corresponding to a plurality of contacting surfaces of different parts assembled in the part surface micro-convex body model, and simplifying the assembly interface corresponding to the part surface group.

[0016] As a further limitation of the present invention, in the step of establishing the part surface micro-convex body model, establishing the part surface micro-convex body model between different parts having an assembly relationship and taking into account the morphological error based on the kernel function comprises:

[0017] A part surface micro-convex body model considering the morphological error is established based on the ideal plane of the corresponding part and the kernel function; wherein: the kernel function is a function that characterizes the morphological error, and the morphological error is formed by a linear combination of m discrete cosine transform kernel functions, m≥300; the part surface micro-convex body model includes a plurality of rough surface groups that are in contact between different parts having an assembly relationship; specifically, the expression of the morphological error is:

[0018]

[0019] In formula (1), H(x, y) represents the shape error, h represents the basis function, m represents the number of basis functions, a represents the coefficient vector of the basis function, and i represents the index of any basis function;

[0020] The expression of the basis function is:

[0021]

[0022] In formula (2), g(m,n,u,v) represents a kernel function of a discrete cosine transform, m and n represent sampling point numbers, u and v represent frequencies, M represents the number of sampling point rows, N represents the number of sampling point columns, the value of C(u) corresponds to the value of u, and the value of C(v) corresponds to the value of v;

[0023] In the step of extracting the part surface group, extracting a part surface group from a plurality of part surface groups having an assembly relationship corresponding to a plurality of contacting surfaces of different parts assembled in the part surface micro-convex body model comprises:

[0024] During the assembly process, multiple groups of contacting rough surfaces between different parts form multiple rough surface groups, the multiple rough surface groups correspond to multiple part surface groups in the part surface micro-convex body model, and a part surface group is extracted from the multiple part surface groups;

[0025] In the step of extracting the part surface group, simplifying the assembly interface corresponding to the part surface group includes:

[0026] All micro-protrusions in a part surface group are concentrated onto one surface, thereby simplifying the assembly interface of two rough surfaces of the part surface group into an assembly interface in which an equivalent rough surface contacts an ideal rigid surface, wherein each surface in the part surface group includes a number of micro-protrusions corresponding to rough points of the rough surface.

[0027] As a further limitation of the present invention, the step 2 comprises:

[0028] Original pose prediction: original pose of an ideal plane of the part assembly process in the part surface group based on the prediction, wherein the ideal plane is an ideal rigid plane under the rigid body assumption, and the original pose includes position information and direction information of the ideal plane;

[0029] Contact point data acquisition:

[0030] Under the action of the assembly load, the ideal rigid plane gradually approaches the equivalent rough surface until it contacts the highest point of the rough surface, and the highest point is the first contact point;

[0031] A relative coordinate system is established with the first contact point as the origin, and the ideal rigid plane rotates based on the relative coordinate system until it contacts the second contact point on the rough surface;

[0032] Taking the line connecting the first contact point and the second contact point as the axis, the relative coordinate system is subjected to homogeneous coordinate transformation, and the ideal rigid plane is rotated based on the homogeneous coordinate until it contacts the third point on the rough surface;

[0033] It is determined whether the ideal rigid plane is in a stable state. If the ideal rigid plane is unstable, a line connecting the two latest contact points is used as a rotation axis to further rotate based on homogeneous coordinates to obtain a new contact point until the ideal rigid plane reaches a stable state.

[0034] As a further limitation of the present invention, in the contact point data acquisition step:

[0035] The coordinates of the first contact point are (x1, y1, z1);

[0036] The ideal rigid plane and the equivalent rough surface in the part surface group state in the initial state are expressed as formula (3):

[0037]

[0038] In formula (3), D0 represents the ideal rigid plane in the initial state in the global coordinate system, L represents the equivalent rough surface, and the ideal rigid plane and the equivalent rough surface are represented by the coordinate matrices of the point sets on their respective surfaces; x, y, z0 represents the coordinates of the ideal rigid plane, x, y, z represents the coordinates of the equivalent rough surface, and T represents the matrix transpose; where:

[0039] For the first contact point:

[0040] The coordinate matrix of the ideal rigid plane corresponding to the first contact point is expressed as formula (4):

[0041] D1=P z ·D0 Formula (4)

[0042] In formula (4), D1 represents the coordinate matrix corresponding to the first contact point, and D0 represents the coordinate matrix of the ideal rigid plane in the initial state; P z Represents the homogeneous coordinate translation transformation matrix of an ideal rigid plane along the Z axis:

[0043]

[0044] For the second contact point:

[0045] The relative coordinate system O′ is established with the first contact point C1 as the origin, the line connecting the first contact point C1 and the assembly load position is recorded as straight line m0, the straight line passing through the first contact point C1 and perpendicular to the straight line m0 is recorded as straight line m1, the straight line m0 is the X′ axis of the relative coordinate system O′, and the straight line m1 is the Y′ axis of the relative coordinate system O′; the ideal rigid plane is rotated by an angle α based on the X′ axis until it contacts the second contact point C2 on the equivalent rough surface, the coordinates of the second contact point C2 are (x2, y2, z2), and the coordinate matrix expression of the ideal rigid plane in the relative coordinate system is:

[0046] D2′=R Y′ ·D1′ formula (5)

[0047] In formula (5), D1′ represents the coordinate matrix corresponding to the first contact point, D2′ represents the coordinate matrix corresponding to the second contact point C2, and R Y′ Represents the homogeneous coordinate rotation matrix of an ideal rigid plane around the Y′ axis:

[0048]

[0049] For the third contact point:

[0050] With the line m2 connecting the first contact point C1 and the second contact point C2 as the rotation axis, rotate the plane at an angle β along the moment direction of the assembly load on the line m2 until it contacts the third contact point C3 on the rough surface. The coordinates of the third contact point C3 are (x3, y3, z3). The coordinate matrix expression of the ideal rigid plane in the relative coordinate system is:

[0051]

[0052] In formula (6), D2′ represents the coordinate matrix corresponding to the second contact point C2 in the relative coordinate system, and D3′ represents the coordinate matrix corresponding to the third contact point C3 in the relative coordinate system. Represents the homogeneous coordinate rotation matrix of an ideal rigid plane around the line m2:

[0053]

[0054] As a further limitation of the present invention, the original posture information of step 2 is the position information and direction information of the ideal plane in the part surface group; the contact point data of step 2 is the data of a plurality of micro-convex bodies in the part surface group whose rough surface has contacted the ideal plane;

[0055] The step three comprises:

[0056] For a plurality of micro-convex bodies on the rough surface of the part surface group that are not in contact with the ideal plane, a process of elastically contacting the plurality of micro-convex bodies with the ideal plane is divided into a plurality of stages according to a contact sequence between the plurality of micro-convex bodies and the ideal plane;

[0057] For each stage, the displacement between the microconvex body and the ideal plane in the Z direction is equally divided into several linear segments, and each linear segment is a linear process.

[0058] As a further limitation of the present invention, for each stage, the displacement between the convex body and the ideal plane in the Z direction in this stage is equally divided into a number of linear segments, and each linear segment is a linear process, including:

[0059] Divide each stage into several equal parts according to the displacement of the ideal plane in the z direction in this stage. If the next contact point added at the end of the nth stage is M(x′, y′, z′), then:

[0060] Add coordinates as M1(x′,y′,z1′), M2(x′,y′,z′2)...M d (x′,y′,z d ′) of d nodes, where z′ n >z1′>...>z′ d >z′,z′ n is the z coordinate value of the projection point of M on the ideal plane before the start of the nth stage;

[0061] The deformation between the projection point on the ideal plane before the start of the nth stage and the next contact point added at the end of the nth stage is a linear process.

[0062] As a further limitation of the present invention, the coordinate matrix expression of the ideal plane after deformation is:

[0063] D4=T1·D3 Formula (7)

[0064] In formula (7), T1 represents the total homogeneous coordinate transformation matrix during the deformation process, D3 represents the coordinate matrix of the ideal plane after the rigid contact process is stable in the global coordinate system, and D4 represents the coordinate matrix of the ideal plane after the deformation is completed in the global coordinate system; wherein, the total homogeneous coordinate transformation matrix is ​​decomposed into the accumulation of the coordinate transformation matrices of each linear process, and the expression is:

[0065]

[0066] In formula (8), t i represents the coordinate transformation matrix of a linear process, and K represents the total number of linear processes.

[0067] As a further limitation of the present invention, the step of obtaining the displacement vectors of each linear process by assembling the data in step 4 includes:

[0068] The load F during the assembly process is applied step by step, and each linear process corresponds to a step force f k ;

[0069] The pose transformation of each linear process is expressed as: the angle θ of rotation around the X axis xi , the angle of rotation around the Y axis θ yi and the displacement Δz along the Z axis i ;

[0070] Establish about the step force f k and the displacement vector θ around the X axis xk , the displacement vector θ around the Y axis yk , the displacement vector Δz along the Z axis k The displacement vector of each linear process is obtained according to the nonlinear equation group;

[0071] The step of obtaining the final posture of the assembled part surface group based on the displacement vector in step 4 includes:

[0072] Determine a homogeneous coordinate transformation matrix for each linear process according to the displacement vector;

[0073] The sum of the homogeneous coordinate transformation matrices corresponding to several linear processes constitutes the total homogeneous coordinate transformation matrix;

[0074] The final pose coordinate matrix of the assembled part surface group is obtained according to the total homogeneous coordinate transformation matrix.

[0075] As a further limitation of the present invention, obtaining the displacement vector of each linear process according to the nonlinear equation group includes:

[0076] The load F is applied in steps, load F and step force f i The relationship between is formula (9):

[0077]

[0078] In formula (9), F represents the load, K represents the total number of linear processes, and f i represents distributed force;

[0079] The homogeneous coordinate transformation matrix expression corresponding to the posture transformation of any linear process is:

[0080]

[0081] In formula (10), t iRepresents the homogeneous coordinate transformation matrix of the i-th linear process, θ xi represents the angle of rotation of the i-th linear process around the X-axis, θ yi represents the angle of rotation of the i-th linear process around the Y axis, Δz i represents the displacement of the i-th linear process along the Z axis;

[0082] The work done by the assembly load in any linear process is equal to the accumulation of the deformation energy of the asperities involved in contact on the rough surface, expressed as:

[0083]

[0084] In formula (11), f k-1 represents the distributed force of the assembly load of the k-1th linear process, f k represents the step force of the assembly load of the kth linear process. When k=1, f k-1 =0; l k represents the distance that the step force does work in the kth linear process; p represents the number of micro-convex bodies involved in the contact in the linear process;

[0085] The expressions of the contact force of the micro-convex body on the ideal plane, the assembly load position and the coordinate value of the micro-convex body position are:

[0086]

[0087] In formula (12), p represents the number of asperities involved in the contact in the linear process, j represents the jth asperity, and f j (k) represents the contact force of the jth asperity participating in the contact on the ideal plane in the kth linear process, f k The step force representing the assembly load of the kth linear process, x j and j represents the coordinate value of the jth asperity involved in the contact, x z and z The coordinate value representing the position of the assembly load;

[0088] The expression of the ideal plane after the kth linear process is:

[0089] A′x+B′y+C′z+D′=0 Formula (13)

[0090] In formula (13), A′ represents the displacement vector θ rotating around the X axis xk function, B′ represents the displacement vector θ around the Y axis yk function, C′ represents the displacement vector Δz along the Z axis k The function of θ xk represents the displacement vector of the kth linear process rotating around the X axis, θyk represents the displacement vector of the kth linear process rotating around the Y axis, (A, B, C) represents the normal vector of the ideal plane before the start of the kth linear process;

[0091] The expression of the ideal plane after the kth linear process is:

[0092] A′x+B′y+C′z+D′=0 Formula (14)

[0093] In formula (14), A′, B′, and C′ are all about θ xk Function and θ yk Function, (x, y, z) represents the coordinate value of a point on the ideal plane after the kth linear process ends, and D′ is expressed as:

[0094]

[0095] Where (x0′, y0′, z0′) represents the coordinates of any point (x0, y0, z0) on the ideal plane before the start of the kth linear process after the rotation and translation of the kth linear process; θ xk The constant representing the displacement vector of the kth linear process around the X-axis, θ yk The constant representing the displacement vector of the kth linear process around the Y axis, Δz k represents the displacement vector of the kth linear process along the Z axis;

[0096] At the end of the kth linear process, the ideal plane will reach node M. i The location coordinates are (x′, y′, z i ′), node M i The distance to the ideal plane is expressed as:

[0097]

[0098] In formula (14), x′, y′, z i ′ indicates that the ideal plane in the kth linear process is about to reach node M i The coordinates of the location, A′, B′, C′ are calculated by formula (19), and D′ is the xk ,θ yk , Δz k function.

[0099] Compared with the prior art, the present invention has the following beneficial effects:

[0100] 1. The modeling process of the part surface morphology error in the process of generating the part surface micro-convex body model of the present invention has good flexibility and wide applicability. The kernel function of the two-dimensional discrete cosine transform is flexibly combined according to the discrete point coordinate data obtained by measuring the assembly interface of the precision parts to represent different morphology errors, and a model that can describe the surface morphology errors of various parts is generated.

[0101] 2. The present invention concentrates all the micro-convexities in the part surface group into one surface, thereby simplifying it into an equivalent rough surface and an ideal rigid surface. The posture prediction and solution accuracy of the rigid contact process is high. The translation and rotation of the parts in the assembly process are represented by homogeneous coordinate transformation, thereby realizing the part posture prediction and contact point determination under the rigid body assumption.

[0102] 3. The present invention effectively reduces the negative impact of nonlinear effects on the accuracy of assembly precision analysis by adding nodes during the elastic deformation process of parts. By adding nodes, the elastic deformation process of the assembly interface is divided into several linear processes, and the highly nonlinear process of elastic deformation is converted into the superposition of several linear processes. The correction of contact stiffness in the calculation process is realized, and the change curve of contact stiffness is closer to the actual situation, thereby improving the reliability of the assembly precision analysis results. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 A flow chart of an assembly accuracy analysis method based on multi-stage linearized contact provided by the present invention;

[0104] Figure 2 A schematic diagram of a simplified process of roughening a surface provided by the present invention;

[0105] Figure 3 A schematic diagram of the process of translating an ideal plane provided by the present invention until contact is generated;

[0106] Figure 4 A schematic diagram of the first rotation process of the ideal plane provided by the present invention;

[0107] Figure 5 A schematic diagram of the second rotation process of the ideal plane provided by the present invention;

[0108] Figure 6 A rigid contact posture comparison table provided by the present invention;

[0109] Figure 7 A comparison table of rigid contact point positions provided by the present invention;

[0110] Figure 8 A schematic diagram of the change of contact stiffness during the elastic contact process provided by the present invention;

[0111] Fig. 9A schematic diagram of adding nodes in the linear deformation division process provided by the present invention;

[0112] Fig.10 A comparison table of the assembly accuracy analysis method of the present invention and the displacement vector of the simulation analysis;

[0113] Fig.11 It is a schematic diagram of the surface group between the first valve block and the second valve block of the present invention;

[0114] Fig.12 It is a flow chart of the assembly accuracy analysis method of the present invention;

[0115] Fig.13 It is the angle between the normal vectors obtained by the two analysis methods before and after adding the node in the present invention and the normal vector obtained by the finite element analysis. DETAILED DESCRIPTION

[0116] The present invention is described in detail below in conjunction with the various embodiments shown in the accompanying drawings, but it should be noted that these embodiments are not limitations of the present invention, and any equivalent transformations or substitutions in functions, methods, or structures made by ordinary technicians in the field based on these embodiments are all within the scope of protection of the present invention.

[0117] An embodiment of the present invention provides an assembly accuracy analysis method based on multi-stage linearized contact, comprising the following steps:

[0118] Step 1: Establish a part surface micro-asperity model that takes into account the morphological error, and extract part surface groups with assembly relationships in the part surface micro-asperity model.

[0119] Specifically, step one includes: (1) establishing a micro-convex body model on the part surface: linearly superimposing a number of discrete cosine transform kernel functions to characterize the morphological errors of different frequencies, and establishing a micro-convex body model on the part surface between different parts with assembly relationships taking into account the morphological errors based on the kernel function.

[0120] More specifically, in the above-mentioned step of establishing the part surface micro-convex body model, the part surface micro-convex body model between different parts with assembly relationship considering the morphology error is established based on the kernel function, including: establishing the part surface micro-convex body model considering the morphology error based on the ideal plane of the corresponding part and the kernel function; wherein: the kernel function is a function characterizing the morphology error, and the morphology error is formed by a linear combination of the kernel functions of m discrete cosine transforms, m ≥ 300; the part surface micro-convex body model includes a plurality of rough surface groups in contact between different parts with assembly relationship; specifically, the expression of the morphology error is:

[0121]

[0122] In formula (1), H(x, y) represents the shape error, h represents the basis function, m represents the number of basis functions, a represents the coefficient vector of the basis function, and i represents the index of any basis function;

[0123] The expression of the above basis function in the embodiment of the present invention is:

[0124]

[0125] In formula (2), g(m,n,u,v) represents a kernel function of a discrete cosine transform, m and n represent sampling point numbers, u and v represent frequencies, M represents the number of sampling point rows, N represents the number of sampling point columns, the value of C(u) corresponds to the value of u, and the value of C(v) corresponds to the value of v, as follows:

[0126]

[0127] Specifically, step one also includes: (2) part surface group extraction: extracting a part surface group from a plurality of part surface groups with assembly relationships corresponding to a plurality of contacting surfaces of different parts assembled in the part surface micro-convex body model, and simplifying the assembly interface of the corresponding part surface group.

[0128] In the step of extracting the part surface group of the embodiment of the present invention, extracting a part surface group from a plurality of part surface groups having an assembly relationship corresponding to a plurality of contacting surfaces of different parts assembled in the part surface micro-convex body model comprises:

[0129] During the assembly process, multiple groups of contacting rough surfaces between different parts form multiple rough surface groups, the multiple rough surface groups correspond to multiple part surface groups in the part surface micro-convex body model, and one part surface group is extracted from the multiple part surface groups.

[0130] In the step of extracting the part surface group in the embodiment of the present invention, simplifying the assembly interface of the corresponding part surface group includes:

[0131] All the micro-convex bodies in the part surface group are concentrated to one surface, so that the assembly interface of two rough surfaces of the part surface group is simplified into an assembly interface in which an equivalent rough surface contacts an ideal rigid surface, wherein each surface in the part surface group includes a number of micro-convex bodies, and the micro-convex bodies correspond to the rough points of the rough surface.

[0132] Step 2: predict the original pose of the parts assembly process in the part surface group under the rigid body assumption, and obtain the contact point data of the contacting surfaces in the assembly of the part surface group based on the original pose.

[0133] Specifically, step 2 of the embodiment of the present invention includes (1) original pose prediction and (2) contact point data acquisition. Wherein, (1) original pose prediction is specifically: the original pose of the ideal plane of the part assembly process in the predicted part surface group, where the ideal plane is an ideal rigid plane under the rigid body assumption, and the original pose includes the position information and direction information of the ideal plane. Among them, (2) the contact point data acquisition is specifically as follows: (21) under the action of the assembly load, the ideal rigid plane gradually approaches the equivalent rough surface until it contacts the highest point of the rough surface, which is the first contact point; (22) a relative coordinate system is established with the first contact point as the origin, and the ideal rigid plane rotates based on the relative coordinate system until it contacts the second contact point on the rough surface; (23) with the line connecting the first contact point and the second contact point as the axis, the relative coordinate system is transformed into a homogeneous coordinate system, and the ideal rigid plane rotates based on the homogeneous coordinate system until it contacts the third point on the rough surface; (24) it is determined whether the ideal rigid plane is in a stable state. If the ideal rigid plane is unstable, the line connecting the two latest contact points is used as the rotation axis to continue to rotate based on the homogeneous coordinate system to obtain a new contact point until the ideal rigid plane reaches a stable state.

[0134] In the step (2) of acquiring contact point data in the embodiment of the present invention, the coordinates of the first contact point are (x1, y1, z1); the ideal rigid plane and the equivalent rough surface in the part surface group state in the initial state are expressed as formula (3):

[0135]

[0136] In formula (3), D0 represents the coordinate matrix of the ideal rigid plane in the initial state, L represents the equivalent rough surface, and the ideal rigid plane and the equivalent rough surface are represented by the coordinate matrices of the point sets on their respective surfaces; x, y, z0 represents the coordinates of the ideal rigid plane, x, y, z represents the coordinates of the equivalent rough surface, and T represents the matrix transpose; where:

[0137] For the first contact point:

[0138] The coordinate matrix of the ideal rigid plane corresponding to the first contact point is expressed as formula (4):

[0139] D1=P z ·D0 Formula (4)

[0140] In formula (4), D1 represents the coordinate matrix corresponding to the first contact point in the global coordinate system, D0 represents the coordinate matrix of the ideal rigid plane in the initial state in the global coordinate system, and P z Represents the homogeneous coordinate translation transformation matrix of an ideal rigid plane along the Z axis:

[0141]

[0142] For the second contact point:

[0143] The relative coordinate system O′ is established with the first contact point C1 as the origin. The line connecting the first contact point C1 and the assembly load position is recorded as straight line m0. The straight line passing through the first contact point C1 and perpendicular to the straight line m0 is recorded as straight line m1. The straight line m0 is the X′ axis of the relative coordinate system O′, and the straight line m1 is the Y′ axis of the relative coordinate system O′. The ideal rigid plane rotates by an angle α based on the X′ axis until it contacts the second contact point C2 on the equivalent rough surface. The coordinates of the second contact point C2 are (x2, y2, z2). The coordinate matrix expression of the ideal rigid plane in the relative coordinate system is:

[0144] D2′=R Y′ ·D1′ formula (5)

[0145] In formula (5), R Y′ represents the homogeneous coordinate rotation matrix of the ideal rigid plane around the Y′ axis, D1′ represents the coordinate matrix corresponding to the first contact point in the relative coordinate system, and D2′ represents the coordinate matrix corresponding to the second contact point C2 in the relative coordinate system.

[0146]

[0147] For the third contact point:

[0148] Take the line m2 connecting the first contact point C1 and the second contact point C2 as the rotation axis and rotate it by an angle β along the moment direction of the assembly load on the line m2 until it contacts the third contact point C3 on the rough surface. The coordinates of the third contact point C3 are (x3, y3, z3). The coordinate matrix expression of the ideal rigid plane in the relative coordinate system is:

[0149]

[0150] In formula (6), D2′ represents the coordinate matrix corresponding to the second contact point C2 in the relative coordinate system, and D3′ represents the coordinate matrix corresponding to the third contact point C3 in the relative coordinate system. represents the homogeneous coordinate rotation matrix of the ideal rigid plane around the line m2,

[0151]

[0152] It should be pointed out that the original posture information of step 2 of the embodiment of the present invention is the position information and direction information of the ideal plane in the part surface group; the contact point data of step 2 is the data of multiple micro-protrusions in the rough surface of the part surface group that have contacted the ideal plane.

[0153] Step 3: Divide the elastic contact process in the part surface assembly into several stages according to the contact point data, and subdivide each stage into several linear processes.

[0154] Specifically, step three includes: for a number of micro-protrusions on the rough surface of the part surface group that are not in contact with the ideal plane, dividing the process of elastically contacting the micro-protrusions with the ideal plane into a number of stages according to the order in which the micro-protrusions contact the ideal plane;

[0155] For each stage, the displacement between the microconvex body and the ideal plane in the Z direction is equally divided into several linear segments, and each linear segment is a linear process.

[0156] More specifically, in the embodiment of the present invention, for each stage, the displacement between the convex body and the ideal plane in the Z direction in this stage is equally divided into a number of linear segments, and each linear segment is a linear process, including:

[0157] Divide each stage into several equal parts according to the displacement of the ideal plane in the z direction in this stage. If the next contact point added at the end of the nth stage is M(x′, y′, z′), then:

[0158] Add coordinates as M1(x′,y′,z1′), M2(x′,y′,z′2)...M d (x′,y′,z d ′) of d nodes, where z′ n >z1′>...>z′ d >z′,z′ n is the z coordinate value of the projection point of M on the ideal plane before the start of the nth stage;

[0159] The deformation between the projection point on the ideal plane before the start of the nth stage and the next contact point added at the end of the nth stage is a linear process.

[0160] The coordinate matrix expression of the ideal plane after deformation in the embodiment of the present invention is:

[0161] D4=T1·D3 Formula (7)

[0162] In formula (7), T1 represents the total homogeneous coordinate transformation matrix during the deformation process, D3 represents the coordinate matrix of the ideal plane after the rigid contact process is stable in the global coordinate system, and D4 represents the coordinate matrix of the ideal plane after the deformation is completed in the global coordinate system; wherein, the total homogeneous coordinate transformation matrix is ​​decomposed into the accumulation of the coordinate transformation matrices of each linear process, and the expression is:

[0163]

[0164] In formula (8), t irepresents the coordinate transformation matrix of a linear process, and K represents the total number of linear processes.

[0165] Step 4: Obtain the displacement vector of each linear process through the assembly data in the part surface group assembly, and obtain the final posture of the assembled part surface group based on the displacement vector, wherein the assembly data includes the assembly load, the rotation angle and the displacement of the part.

[0166] Specifically, in step 4 of the embodiment of the present invention, obtaining the displacement vectors of each linear process by assembling data includes:

[0167] The load F during the assembly process is applied step by step, and each linear process corresponds to a step force f k ;

[0168] The pose transformation of each linear process is expressed as: the angle θ of rotation around the X axis xi , the angle of rotation around the Y axis θ yi and the displacement Δz along the Z axis i ;

[0169] Establish about the step force f k and the displacement vector θ around the X axis xk , the displacement vector θ around the Y axis yk , the displacement vector Δz along the Z axis k The displacement vector of each linear process is obtained according to the nonlinear equation group.

[0170] More specifically, the embodiment of the present invention obtains the displacement vector of each linear process according to the nonlinear equation group, including:

[0171] The load F is applied in steps, load F and step force f i The relationship between is formula (9):

[0172]

[0173] In formula (9), F represents the load, K represents the total number of linear processes, and f i represents distributed force;

[0174] The homogeneous coordinate transformation matrix expression corresponding to the posture transformation of any linear process is:

[0175]

[0176] In formula (10), t i Represents the homogeneous coordinate transformation matrix of the i-th linear process, θ xi represents the angle of rotation of the i-th linear process around the X-axis, θ yi represents the angle of rotation of the i-th linear process around the Y axis, Δz irepresents the displacement of the i-th linear process along the Z axis;

[0177] The work done by the assembly load in any linear process is equal to the accumulation of the deformation energy of the asperities involved in contact on the rough surface, expressed as:

[0178]

[0179] In formula (11), f k-1 represents the distributed force of the assembly load of the k-1th linear process, f k represents the step force of the assembly load of the kth linear process. When k=1, f k-1 =0; l k represents the distance that the step force does work in the kth linear process; p represents the number of micro-convex bodies involved in the contact in the linear process;

[0180] The expressions of the contact force of the micro-convex body on the ideal plane, the assembly load position and the coordinate value of the micro-convex body position are:

[0181]

[0182] In formula (12), p represents the number of asperities involved in the contact in the linear process, j represents the jth asperity, and f j (k) represents the contact force of the jth asperity participating in the contact on the ideal plane in the kth linear process, f k The step force representing the assembly load of the kth linear process, x j and j represents the coordinate value of the jth asperity involved in the contact, x z and z The coordinate value representing the position of the assembly load;

[0183] The normal vector of the ideal plane before the start of the kth linear process can be obtained from the coordinates of each point, recorded as (A, B, C), then the normal vector of the ideal plane after the end of the kth linear process (A', B', C') is:

[0184]

[0185] Among them, t k for:

[0186]

[0187] Substituting into the above formula we get:

[0188]

[0189] Then the expression of the ideal plane after the kth linear process is:

[0190] A′x+B′y+C′z+D′=0 Formula (14)

[0191] In formula (14), A′ represents the displacement vector θ rotating around the X axis xk function, B′ represents the displacement vector θ around the Y axis yk function, C′ represents the displacement vector Δz along the Z axis k The function of θ xk represents the displacement vector of the kth linear process rotating around the X axis, θ yk represents the displacement vector of the kth linear process rotating around the Y axis; (A, B, C) represents the normal vector of the ideal plane before the start of the kth linear process;

[0192] A′, B′, and C′ are all about θ xk ,θ yk function, then D′ can be expressed as:

[0193] D′=-(A′x+B′y+C′z) formula (a)

[0194] In formula (a), (x, y, z) is the coordinate value of a point on the ideal plane after the kth linear process is completed.

[0195] The coordinates (x0′, y0′, z0′) of any point (x0, y0, z0) on the ideal plane before the start of the k-th sub-step linear process after rotation and translation of the k-th linear process are:

[0196]

[0197] In formula (b), t k Substituting into formula (a) we get:

[0198]

[0199] In formula (c), (A′, B′, C′) and (x0′, y0′, z0′) are substituted into formula (a), and D′ is expressed as xk ,θ yk , Δz k The function is specifically expressed as:

[0200] D′=-(Acosθ yk +Csinθ yk )(x0cosθ yk +z0sinθ yk )

[0201] -(Asinθ xk sinθ yk +Bcosθ xk-Csinθ xk cosθ yk )

[0202] ·(x0sinθ xk sinθ yk +y0cosθ xk -z0sinθ xk cosθ yk )

[0203] -(-Acosθ xk sinθ yk +Bsinθ xk +Ccosθ xk cosθ yk )

[0204] ·(-x0cosθ xk sinθ yk +y0sinθ xk +z0Ccosθ xk cosθ yk -Δz k )

[0205] Where θ xk ,θ yk , Δz k The rest are the constants mentioned above.

[0206] At the end of the kth linear process, the ideal plane will reach node M. i The location of the i ′), that is, the distance between this point and the ideal plane is 0 at the end of the linear process. i The distance to the ideal plane is expressed as:

[0207]

[0208] In formula (15), x′, y′, z i ′ indicates that the ideal plane in the kth linear process is about to reach node M i The coordinates of the location, A′, B′, and C′ are all about θ xk ,θ yk The function of θ is calculated by formula (9), D′ is the xk ,θ yk , Δz k function.

[0209] In step 4, the final pose of the assembly part surface group is obtained based on the displacement vector, including:

[0210] Determine the homogeneous coordinate transformation matrix of each linear process according to the displacement vector;

[0211] The sum of the homogeneous coordinate transformation matrices corresponding to several linear processes constitutes the total homogeneous coordinate transformation matrix;

[0212] The final pose coordinate matrix of the assembly part surface group is obtained according to the total homogeneous coordinate transformation matrix.

[0213] The method of the present invention is to obtain the final pose coordinate matrix of the surface group of the assembled parts according to the total homogeneous coordinate transformation matrix, including: repeatedly obtaining the step force f of each linear process, the angle θ of rotation around the x-axis x , the angle of rotation around the y-axis θ y And the displacement Δz along the z-axis, the final pose coordinate matrix of the part surface group is obtained as D4; among them, the final pose coordinate matrix of the part surface group is consistent with the coordinate matrix expression of the ideal plane after the deformation.

[0214] Step 5: Analyze the assembly accuracy of parts based on the contact point data, final position and deformation of the micro-convex body during elastic contact. Specifically, determine whether the contact between the parts meets the tolerance requirements of the assembly such as parallelism and verticality based on the final position of the parts, and analyze the position accuracy of the parts of the assembly accordingly; determine the surface quality and stability of the parts during contact based on the distribution of contact points between the assembly interfaces and the deformation of the micro-convex body, and realize the assembly accuracy analysis of the parts.

[0215] Taking the assembly accuracy analysis of the first valve block and the second valve block of a multi-way hydraulic valve as an example, an assembly accuracy analysis method based on multi-stage linearized contact according to an embodiment of the present invention is described as follows:

[0216] The embodiment of the present invention is based on an assembly accuracy analysis method for multi-stage linearized contact. A micro-asperity model of a part surface that takes into account morphological errors is established through the linear superposition of discrete cosine transform kernel functions and the assembly interface is simplified. The translation and rotation of the part during the assembly process under the rigid body assumption are predicted based on the homogeneous coordinate transformation, and the description of the elastic contact process is achieved on this basis. The embodiment of the present invention divides the elastic contact process into multiple stages according to the order in which the micro-asperities participate in the contact, and further subdivides it into several linear processes by adding nodes in each stage. The relationship between the assembly load and the deformation is established based on the relevant theories of contact mechanics and the geometric relationship between the assembly interfaces, so as to achieve posture prediction of the part assembly process.

[0217] Taking the assembly accuracy analysis of the first valve block and the second valve block of a multi-way hydraulic valve as an example, the assembly accuracy analysis method based on multi-stage linearized contact in an embodiment of the present invention mainly includes the following steps:

[0218] Step 1. Establish a micro-convex body model of the part surface taking into account the morphological error through the linear superposition of the discrete cosine transform kernel function and simplify the assembly interface. Specifically: the rough surface containing the morphological error can be obtained by combining an ideal plane and a function H that characterizes the morphological error. To characterize the morphological errors of different frequencies, the function H can be expressed as a linear superposition of a set of basis functions h(x, y), as shown in formula (1). The kernel function of the two-dimensional discrete cosine transform is selected as the basis function, and the kernel function g(m, n, u, v) is shown in formula (2). Different u and v values ​​correspond to different basis shapes. By taking different values ​​of the coefficient vector a, the basis shapes of different frequencies can be flexibly combined to achieve the fitting of various curved surfaces. In this embodiment, 400 discrete cosine transform kernel functions are linearly combined to generate two rough surfaces with a flatness tolerance value of 50μm.

[0219] See also Figure 2 The embodiment of the present invention can simplify the contact between two rough surfaces into the contact between an equivalent rough surface and an ideal rigid surface by concentrating the micro-protrusions on the two planes onto one plane. The height z of the micro-protrusions on the equivalent rough surface is equal to the sum of the heights z1 and z2 of the micro-protrusions at the corresponding points on the two rough surfaces, that is: z=z1+z2.

[0220] Step 2: Predict the translation and rotation of parts during assembly under the rigid body assumption based on homogeneous coordinate transformation.

[0221] See also Figure 3 , the ideal rigid plane in the initial state of the embodiment of the present invention gradually approaches the equivalent rough surface under the action of the assembly load until the ideal plane contacts the highest point of the rough surface. This point is the first contact point, denoted as C1, and its coordinates are (x1, y1, z1). For example, the coordinate value of C1 in this embodiment is (-2.666e4, 8.465e3, 41.324). The ideal rigid plane D0 and the equivalent rough surface L in the initial state can be represented by the coordinate matrix of the point set thereon, as shown in formula (3). The coordinate matrix of the ideal rigid plane at the first point contact is shown in formula (5). In formula (5), P z is the homogeneous coordinate translation transformation matrix of the ideal plane along the Z axis, and the expression is as follows:

[0222]

[0223] To describe the rotation of the ideal plane, a relative coordinate system O' is established with C1 as the origin. The line connecting C1 and the assembly load position is recorded as straight line m0, and the straight line passing through C1 and perpendicular to m0 is recorded as m1. m0 and m1 are respectively the X' and Y' axes of the relative coordinate system O'. At this time, the coordinate matrix D1' of the ideal plane in the relative coordinate system O' is expressed as:

[0224] D1′=R z·P xyz D1

[0225] In the above formula, P xyz Represents the homogeneous coordinate transformation matrix for translation along the X, Y, and Z axes, respectively, R z represents the homogeneous coordinate rotation matrix around the Z axis, and D1 represents the coordinate matrix corresponding to the first contact point, where:

[0226]

[0227] In the embodiment of the present invention, θ is the angle between m1 and the Y axis of the global coordinate system.

[0228] See also Figure 4 After the ideal plane rotates, it will rotate by an angle α with m1 as the rotation axis until it contacts the second point on the rough surface. This point is recorded as C2, and its global coordinates are (x2, y2, z2). For example, the coordinate values ​​of C2 in this embodiment are (-1.6416e4, 3.4116e4, 38.661). At this time, the coordinate matrix of the ideal plane in the relative coordinate system is shown in formula (5). Y′ is the homogeneous coordinate rotation matrix of the ideal plane around the Y′ axis, expressed as:

[0229]

[0230] See also Figure 5 In the further rotation of the ideal plane of the embodiment of the present invention, the ideal plane rotates by an angle β along the moment direction of the assembly load on m2 with the line m2 connecting C1 and C2 as the rotation axis until it contacts the third point on the rough surface. This point is denoted as C3, and its global coordinates are (x3, y3, z3). In this embodiment, the coordinate value of the third contact point C3 is (3.7232e4, -3.9898e4, 37.157). At this time, the coordinate matrix of the ideal plane in the relative coordinate system is as shown in formula (6). In formula (6) is the homogeneous coordinate rotation matrix around m2, expressed as:

[0231]

[0232] In the above formula, n x represents the component of the unit direction vector of m2 in the X′ axis direction, n y represents the component of the unit direction vector of m2 in the Y′ axis direction, n z Represents the component of the unit direction vector of m2 in the Z′ axis direction; K = 1-cos(β), λ = n x x′2+n y y′2+n zz′2, x′2, y′2, z′2 are the coordinate values ​​of C2 in the relative coordinate system respectively.

[0233] Under the condition of three actual contact points, the coordinate matrix expression of the ideal plane is:

[0234] D3=T0·D0

[0235] In the formula, D3 represents the coordinate matrix of the ideal plane, T0 is the homogeneous coordinate transformation matrix of the ideal plane from D0 to D3, and D0 represents the coordinate matrix in the initial state;

[0236]

[0237] In the formula, Represents R z The inverse matrix of Indicates P xyz The inverse matrix of represents the homogeneous coordinate rotation matrix of the ideal rigid plane around the line m2, R Y′ represents the homogeneous coordinate rotation matrix of the ideal rigid plane around the Y′ axis, R z Represents the homogeneous coordinate rotation matrix around the Z axis, P xyz represents the homogeneous coordinate transformation matrix for translation along the X, Y, and Z axes, respectively, P z Represents the homogeneous coordinate translation transformation matrix of an ideal rigid plane along the Z axis.

[0238] Determine whether the ideal plane is in a stable state. If the projection of the assembly load in the XOY plane falls within the projection of △C1C2C3 in the XOY plane, the ideal plane is considered to be in a stable state. Otherwise, it is considered to be unstable. If the ideal plane is unstable, it is necessary to further rotate the line connecting the two latest contact points as the axis to obtain a new contact point. The newly added contact point will continue to approach the position of the assembly load, and this cycle will continue until a stable state is reached.

[0239] The embodiment of the present invention uses the above algorithm to predict the rigid contact posture of the parts and uses the finite element method to analyze them. The calculation results of the rigid contact algorithm and the finite element analysis are as follows: Figure 6 and Figure 7 As shown in the figure, the error between the displacement vectors calculated by the rigid contact algorithm and the finite element analysis is within 13%, and the contact points of the rigid contact algorithm basically fall within the contact area calculated by the finite element method.

[0240] Step 3: Divide the elastic deformation process of the assembly interface into several linear processes by adding nodes, and solve the nonlinear equations about the displacement vector to obtain the final position and posture of the part. Specifically:

[0241] As the deformation process proceeds, the number of asperities involved in contact on the rough surface gradually increases. Therefore, the elastic contact process of the assembly interface is divided into several stages according to the order in which the asperities contact the ideal plane. The relationship between the deformation of the asperities and their contact stiffness during the elastic contact process is as follows: Figure 8 As shown by Figure 8 It can be seen that if a stage is regarded as a linear process, taking the contact stiffness value at the beginning of any stage as the contact stiffness of that stage will lead to a large error, so the embodiment of the present invention further subdivides the deformation stage.

[0242] Each stage is divided into several parts according to the displacement of the ideal plane in the z direction in that stage, such as Fig. 9 As shown in the figure, if the next contact point added at the end of the nth stage is M(x′, y′, z′), the added coordinates are M1(x′, y′, z1′), M2(x′, y′, z′2)...M d (x′,y′,z′ d ) nodes, where z′ n >z1′>...>z′ d >z′,z′ n is the z coordinate value of the projection point of M on the ideal plane before the start of the nth stage, and the deformation between the two nodes is regarded as a linear process. The coordinate matrix of the ideal plane at the end of the deformation is shown in formula (7) and formula (8). In this embodiment, the coordinates of the next contact point added at the end of the first stage are (-5.42e3, 1.061e4, 34.35), z′ n The value is 36.49. Four nodes are added, namely M1(-5.42e3,1.061e4,34.78), M2(-5.42e3,1.061e4,35.21), M3(-5.42e3,1.061e4,35.63), and M4(-5.42e3,1.061e4,36.06).

[0243] The load F in the assembly process of the embodiment of the present invention is applied in steps, and each linear process corresponds to a step force f i , load F and step force f i The relationship between is shown in formula (9). The pose transformation of any linear process is determined by the angle θ around the X-axis. xi , the angle of rotation around the Y axis θ yi and the displacement Δz along the Z axis i The homogeneous coordinate transformation matrix of any linear process is shown in formula (10).

[0244] The deformation amount ω of the micro-convex body in contact with the ideal plane in any linear process of this embodiment iIt is related to the relationship between the displacement vectors and the quadrant in which the convex body is located. The specific relationship is as follows:

[0245] When the asperity is located in the first quadrant of the XOY plane: ω 1i =Δz i +ytanθ xi -xtanθ yi ;

[0246] When the asperity is located in the second quadrant of the plane: ω 2i =Δz i +ytanθ xi +xtanθ yi ;

[0247] When the asperity is located in the third quadrant of the plane: ω 3i =Δz i -ytanθ xi +xtanθ yi ;

[0248] When the asperity is located in the fourth quadrant of the plane: ω 4i =Δz i -ytanθ xi -xtanθ yi ;

[0249] In the above formula, x represents the absolute value of the x-axis coordinate value of the micro-convex body in the global coordinate, and y represents the absolute value of the y-axis coordinate value of the micro-convex body in the global coordinate.

[0250] In order to obtain the ideal plane posture after each linear process, the step-by-step force f is established. k and displacement vector θ xk ,θ yk and Δz k The nonlinear equations are used to obtain the displacement vectors of each linear process. The details are as follows:

[0251] According to the principle of conservation of energy, the work done by the assembly load in any linear process is equal to the accumulation of the deformation energy of the micro-convex bodies involved in contact on the rough surface, thus formula (11) can be obtained.

[0252] When k = 1 in formula (11), f k-1 =0; l k is the distance that the step force does work in this linear process, and its calculation method is similar to the deformation of the micro-convex body; p in the kth linear process is k+2; E bj is the strain energy of the jth micro-convex body during deformation in the linear process. The strain energy of a single micro-convex body during deformation is expressed as:

[0253]

[0254] In the above formula, R represents the radius of curvature of the micro-convex body. The deformation of the micro-convex body changes from ω1 to ω2 during the linear process. E is the comprehensive elastic modulus, which is expressed as follows:

[0255] Where E1, E2, ν1, and ν2 are the elastic modulus and Poisson's ratio of the two assembly interfaces, respectively.

[0256] According to the moment balance, the contact force of the micro-convex body on the ideal plane and the resultant moment of the assembly load on the x-axis and y-axis are 0 respectively, thus formula (12) can be obtained.

[0257] The ideal plane in the kth linear process is about to reach node M i The location of the i ′). The normal vector of the ideal plane before the kth linear process starts can be obtained from the coordinates of each point, recorded as (A, B, C). The normal vector of the ideal plane after the kth linear process ends is expressed as:

[0258]

[0259] In the formula, A′, B′, and C′ are respectively xk ,θ yk , Δz k function.

[0260] The equation of the ideal plane after the kth linear process is completed is as shown in formula (13).

[0261] The coordinates (x′0, y′0, z′0) of any point (x0, y0, z0) on the ideal plane before the start of the kth linear process after the rotation and translation of the kth linear process are expressed as:

[0262]

[0263] In the formula, x′0, y′0, z′0 are respectively xk ,θ yk , Δz k function.

[0264] Substituting (x′0, y′0, z′0) into the above formula, D′ is expressed as xk ,θ yk , Δz k function.

[0265] At the end of this linear process, M i The distance to the ideal plane is given by formula (14).

[0266] Solve the step-by-step force f applied in the kth linear process respectively k, the angle of rotation around the x-axis θ xk , the angle of rotation around the y-axis θ yk and the displacement Δz along the z-axis k .

[0267] Repeat the above process to obtain the step-by-step force f and the corresponding θ of each linear process. x ,θ y , Δz, and then the final state of the ideal plane is obtained, that is, D4.

[0268] D4 in this embodiment is a strict ideal plane, so by taking three non-collinear points on it To find the plane equation of the ideal plane.

[0269] Use the above three points to form two vectors in, represents the coordinates of point P1, represents the coordinates of point P2, Represents the coordinates of point P3; and The normal vector of the ideal plane D4 is obtained by cross multiplication

[0270]

[0271] The general form of the ideal plane D4 plane equation is expressed as:

[0272]

[0273] Take any point on the ideal plane D4, such as Substituting into the above formula, we can get

[0274]

[0275] Assume that the least squares fitting plane A of the rough surface L L ,B L ,C L The equation is expressed as:

[0276] A L x+B L y+C L z+D L =0

[0277] To simplify the calculation, let D L =-1, then the above equation can be rewritten as:

[0278] A L x+B L y+C L z-1=0

[0279] Points on the rough surface L The distance to the fitting plane is expressed as:

[0280]

[0281] The error function S is defined as follows:

[0282]

[0283] Where q represents the total number of contact points in the final stable state. Using the genetic algorithm to minimize the error function S as the optimization goal, A is obtained. L , B L , C L The value of .

[0284] The normal vectors on the ideal plane D4 and the fitting plane of the rough surface L are The dot product of two normal vectors is:

[0285]

[0286] The moduli of the two normal vectors are:

[0287]

[0288] Then the cosine of the angle η between the two normal vectors is obtained as:

[0289]

[0290] The specific value of η is obtained according to the inverse trigonometric function.

[0291] In this embodiment, the angle between the two planes is equal to or complementary to the angle between the normal vectors. Obviously, the angle between the ideal plane D4 and the fitting plane of the rough surface L is a very small acute angle. Therefore, the angle λ between the two planes is expressed as:

[0292] λ=min(η,π-η)

[0293] Parallelism is expressed as points on the rough surface L The maximum distance to the ideal plane D4, the parallelism between the rough surface L and the ideal plane D4 is expressed as:

[0294]

[0295] Where M is the number of rows of sampling points on the rough surface L, N is the number of columns of sampling points, and M·N is the total number of sampling points.

[0296] In this embodiment, the angle between the ideal plane D4 and the least square fitting plane of the rough surface L is 0.0064 rad, and the parallelism is 0.0158 mm, which is less than the parallelism error standard of the hydraulic valve sealing surface of 0.03 mm and meets the flatness tolerance requirement of the hydraulic valve mating surface. It is judged that the first valve block and the second valve block have good assembly accuracy.

[0297] See also Fig.10 , Fig.11 and Fig.12 When analyzing the assembly accuracy of the first valve block and the second valve block of the multi-way hydraulic valve, in addition to using the above-mentioned assembly accuracy analysis method to predict the position and posture of the first valve block and the second valve block, the finite element analysis method and the assembly accuracy analysis method without adding nodes are used as controls. The assembly loads are set to 100N, 1000N and 5000N for multiple tests, and the displacement vectors of the valve body during the deformation process are output respectively as follows: Fig.10 As shown. According to the predicted positions of the three methods, the normal vectors of the sealing surface in the final state can be obtained respectively. The angles between the normal vectors obtained by the two analysis methods before and after adding nodes and the normal vector obtained by finite element analysis are shown as follows: Fig.13 The results show that the average errors of the displacement vectors of the two methods are 28.87% and 12.90%, respectively. The average values ​​of the angles between the normal vector of the sealing surface and the normal vector obtained by simulation before and after adding the node are 1.75e-5rad and 1.18e-5rad, respectively. The accuracy of the analysis method is significantly improved after adding the node.

[0298] This embodiment reduces the negative impact of nonlinear effects on the accuracy of assembly precision analysis by dividing the elastic deformation process into several linear processes, significantly improves the accuracy of part posture prediction, and can be used in various assembly precision analysis scenarios in the manufacturing industry, with broad practical application value.

[0299] The series of detailed descriptions listed above are only specific descriptions of feasible implementation methods of the present invention. They are not intended to limit the scope of protection of the present invention. Any equivalent implementation methods or changes that do not deviate from the technical spirit of the present invention should be included in the scope of protection of the present invention.

[0300] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0301] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. An assembly accuracy analysis method based on multi-stage linearized contact, characterized in that: include: Step 1: Establish a part surface micro-convex body model considering the morphological error, and extract a part surface group with an assembly relationship in the part surface micro-convex body model; the part surface group includes a plurality of contacting surfaces of different parts assembled corresponding to a plurality of part surfaces with an assembly relationship; Step 2: predicting the original posture of the parts assembly process in the part surface group under the rigid body assumption condition, and obtaining the contact point data of the contacting surfaces in the assembly of the part surface group based on the original posture; Step 3: dividing the elastic contact process in the assembly of the part surface group into several stages according to the contact point data, and each stage is subdivided into several linear processes; specifically, for several micro-convex bodies on the rough surface of the part surface group that do not contact the ideal plane, the process of elastically contacting the ideal plane of the several micro-convex bodies is divided into several stages according to the contact sequence of the several micro-convex bodies with the ideal plane; for each stage, the displacement of the micro-convex body and the ideal plane in the Z direction in this stage is divided into several linear segments, and each linear segment is a linear process; Step 4: obtaining the displacement vectors of each linear process through the assembly data in the assembly of the part surface group, and obtaining the final posture of assembling the part surface group based on the displacement vectors, wherein the assembly data includes assembly load, rotation angle and displacement of the part; Step 5: Analyze the assembly accuracy of parts based on the contact point data, the final posture and the deformation of the micro-convex body during the elastic contact process.

2. The assembly accuracy analysis method based on multi-stage linearized contact according to claim 1 is characterized in that: The step one comprises: Establishment of micro-convex body model on part surface: linearly superimpose several kernel functions of discrete cosine transform to characterize the morphological errors of different frequencies, and establish the micro-convex body model on part surface between different parts with assembly relationship considering the morphological errors based on the kernel function; Part surface group extraction: extracting a part surface group from a plurality of part surface groups having assembly relationships corresponding to a plurality of contacting surfaces of different parts assembled in the part surface micro-convex body model, and simplifying the assembly interface corresponding to the part surface group.

3. According to the assembly accuracy analysis method based on multi-stage linearized contact in claim 2, in the step of establishing the part surface micro-convex body model, the part surface micro-convex body model between different parts having an assembly relationship and considering the morphological error is established based on the kernel function, comprising: A part surface micro-convex body model considering the morphology error is established based on the ideal plane of the corresponding part and the kernel function; wherein: the kernel function is a function that characterizes the morphology error, and the morphology error is formed by a linear combination of m discrete cosine transform kernel functions, m≥300; the part surface micro-convex body model includes a plurality of rough surface groups that are in contact between different parts having an assembly relationship; specifically, the expression of the morphology error is: In formula (1), H(x, y) represents the shape error, h represents the basis function, m represents the number of basis functions, a represents the coefficient vector of the basis function, and i represents the index of any basis function; The expression of a discrete cosine transform kernel function is: In formula (2), g(m,n,u,v) represents a kernel function of a discrete cosine transform, m and n represent sampling point numbers, u and v represent frequencies, M represents the number of sampling point rows, N represents the number of sampling point columns, the value of C(u) corresponds to the value of u, and the value of C(v) corresponds to the value of v; In the step of extracting the part surface group, extracting a part surface group from a plurality of part surface groups having an assembly relationship corresponding to a plurality of contacting surfaces of different parts assembled in the part surface micro-convex body model comprises: During the assembly process, multiple groups of contacting rough surfaces between different parts form multiple rough surface groups, the multiple rough surface groups correspond to multiple part surface groups in the part surface micro-convex body model, and a part surface group is extracted from the multiple part surface groups; In the step of extracting the part surface group, simplifying the assembly interface corresponding to the part surface group includes: All micro-protrusions in a part surface group are concentrated onto one surface, thereby simplifying the assembly interface of two rough surfaces of the part surface group into an assembly interface in which an equivalent rough surface contacts an ideal rigid surface, wherein each surface in the part surface group includes a number of micro-protrusions corresponding to rough points of the rough surface.

4. The assembly accuracy analysis method based on multi-stage linearized contact according to claim 1 is characterized in that: The second step comprises: Original pose prediction: original pose of an ideal plane of the part assembly process in the part surface group based on the prediction, wherein the ideal plane is an ideal rigid plane under the rigid body assumption, and the original pose includes position information and direction information of the ideal plane; Contact point data acquisition: Under the action of the assembly load, the ideal rigid plane gradually approaches the equivalent rough surface until it contacts the highest point of the rough surface, and the highest point is the first contact point; A relative coordinate system is established with the first contact point as the origin, and the ideal rigid plane rotates based on the relative coordinate system until it contacts the second contact point on the rough surface; Taking the line connecting the first contact point and the second contact point as the axis, the relative coordinate system is subjected to homogeneous coordinate transformation, and the ideal rigid plane is rotated based on the homogeneous coordinate until it contacts the third point on the rough surface; Determine whether the ideal rigid plane is in a stable state. If the ideal rigid plane is unstable, continue to rotate based on the homogeneous coordinates with the line connecting the two latest contact points as the rotation axis to obtain a new contact point until the ideal rigid plane reaches a stable state. Specifically, the projection of the assembly load of the parts assembly process in the XOY plane falls in the projection of △C1C2C3 in the XOY plane, which indicates that it is in the stable state.

5. The assembly accuracy analysis method based on multi-stage linearized contact according to claim 4 is characterized in that: In the contact point data acquisition step: The coordinates of the first contact point are (x1, y1, z1); The ideal rigid plane and the equivalent rough surface in the part surface group state in the initial state are expressed as formula (3): In formula (3), D0 represents the ideal rigid plane in the initial state in the global coordinate system, L represents the equivalent rough surface, and the ideal rigid plane and the equivalent rough surface are represented by the coordinate matrices of the point sets on their respective surfaces; x, y, z0 represents the coordinates of the ideal rigid plane, x, y, z represents the coordinates of the equivalent rough surface, and T represents the matrix transpose; where: For the first contact point: The coordinate matrix of the ideal rigid plane corresponding to the first contact point is expressed as formula (4): D1=P z ·D0 Formula (4) In formula (4), D1 represents the coordinate matrix corresponding to the first contact point in the global coordinate system, P z represents the homogeneous coordinate translation transformation matrix of the ideal rigid plane along the Z axis; D0 represents the coordinate matrix in the initial state in the global coordinate system; For the second contact point: The relative coordinate system O′ is established with the first contact point C1 as the origin, the line connecting the first contact point C1 and the assembly load position is recorded as straight line m0, the straight line passing through the first contact point C1 and perpendicular to the straight line m0 is recorded as straight line m1, straight line m0 is the X′ axis of the relative coordinate system O′, and straight line m1 is the Y′ axis of the relative coordinate system O′; the ideal rigid plane is rotated by an angle α based on the X′ axis until it contacts the second contact point C2 on the equivalent rough surface, the coordinates of the second contact point C2 are (x2, y2, z2), and the coordinate matrix expression of the ideal rigid plane in the relative coordinate system is: D′2=R Y′ ·D′1 Formula (5) In formula (5), R Y′ represents the homogeneous coordinate rotation matrix of the ideal rigid plane around the Y′ axis, D′1 represents the coordinate matrix corresponding to the first contact point in the relative coordinate system, and D′2 represents the coordinate matrix corresponding to the second contact point C2 in the relative coordinate system; For the third contact point: With the line m2 connecting the first contact point C1 and the second contact point C2 as the rotation axis, rotate the plane at an angle β along the moment direction of the assembly load on the line m2 until it contacts the third contact point C3 on the rough surface. The coordinates of the third contact point C3 are (x3, y3, z3). The coordinate matrix expression of the ideal rigid plane in the relative coordinate system is: In formula (6), represents the homogeneous coordinate rotation matrix of the ideal rigid plane around the connecting line m2, D′2 represents the coordinate matrix corresponding to the second contact point C2 in the relative coordinate system, and D′3 represents the coordinate matrix corresponding to the third contact point C3 in the relative coordinate system.

6. The assembly accuracy analysis method based on multi-stage linearized contact according to claim 1 is characterized in that: The original posture information of step 2 is the position information and direction information of the ideal plane in the part surface group; the contact point data of step 2 is the data of multiple micro-convex bodies in the rough surface of the part surface group that have contacted the ideal plane.

7. The assembly accuracy analysis method based on multi-stage linearized contact according to claim 6 is characterized in that: For each stage, the displacement between the convex body and the ideal plane in the Z direction is equally divided into several linear segments, and each linear segment is a linear process, including: Divide each stage into several equal parts according to the displacement of the ideal plane in the z direction in this stage. If the next contact point added at the end of the nth stage is M(x′, y′, z′), then: Add coordinates as M1(x′,y′,z′1), M2(x′,y′,z′2)....M d (x′,y′,z′ d ) of d nodes, where z′ n >z′1>...>z′ d >z′,z′ n is the z coordinate value of the projection point of M on the ideal plane before the start of the nth stage; The deformation between the projection point on the ideal plane before the start of the nth stage and the next contact point added at the end of the nth stage is a linear process.

8. The assembly accuracy analysis method based on multi-stage linearized contact according to claim 7 is characterized in that: The coordinate matrix expression of the ideal plane after deformation is: D4=T1·D3 Formula (7) In formula (7), T1 represents the total homogeneous coordinate transformation matrix during the deformation process, D3 represents the coordinate matrix of the ideal plane after the rigid contact process is stable in the global coordinate system, and D4 represents the coordinate matrix of the ideal plane after the deformation is completed in the global coordinate system; wherein, the total homogeneous coordinate transformation matrix is ​​decomposed into the accumulation of the coordinate transformation matrices of each linear process, and the expression is: In formula (8), t i represents the coordinate transformation matrix of a linear process, and K represents the total number of linear processes.

9. The assembly accuracy analysis method based on multi-stage linearized contact according to claim 1 is characterized in that: The step 4 of obtaining the displacement vectors of each linear process through the assembly data in the part surface group assembly includes: The load F during the assembly process is applied step by step, and each linear process corresponds to a step force f k ; The pose transformation of each linear process is expressed as: the angle θ of rotation around the X axis xi , the angle of rotation around the Y axis θ yi and the displacement Δz along the Z axis i ; Establish about the step force f k and the displacement vector θ around the X axis xk , the displacement vector θ around the Y axis yk , the displacement vector Δz along the Z axis k The displacement vector of each linear process is obtained according to the nonlinear equation group; The step of obtaining the final posture of the assembled part surface group based on the displacement vector in step 4 includes: Determine a homogeneous coordinate transformation matrix for each linear process according to the displacement vector; The sum of the homogeneous coordinate transformation matrices corresponding to several linear processes constitutes the total homogeneous coordinate transformation matrix; The final pose coordinate matrix of the assembled part surface group is obtained according to the total homogeneous coordinate transformation matrix.

10. The assembly accuracy analysis method based on multi-stage linearized contact according to claim 9, characterized in that: The step of obtaining the displacement vector of each linear process according to the nonlinear equation group includes: The load F is applied in steps, load F and step force f i The relationship between is formula (9): In formula (9), F represents the load, K represents the total number of linear processes, and f i represents distributed force; The homogeneous coordinate transformation matrix expression corresponding to the posture transformation of any linear process is: In formula (10), t i Represents the homogeneous coordinate transformation matrix of the i-th linear process, θ xi represents the angle of rotation of the i-th linear process around the X-axis, θ yi represents the angle of rotation of the i-th linear process around the Y axis, Δz i represents the displacement of the i-th linear process along the Z axis; The work done by the assembly load in any linear process is equal to the accumulation of the deformation energy of the asperities involved in contact on the rough surface, expressed as: In formula (11), f k-1 represents the distributed force of the assembly load of the k-1th linear process, f k represents the step force of the assembly load of the kth linear process. When k=1, f k-1 =0; l k represents the distance that the step force does work in the kth linear process; p represents the number of asperities involved in the contact in the linear process, E bj represents the strain energy during the deformation of the jth asperity in the linear process; The expressions of the contact force of the micro-convex body on the ideal plane, the assembly load position and the coordinate value of the micro-convex body position are: In formula (12), p represents the number of asperities involved in the contact in the linear process, j represents the jth asperity, and f j (k) represents the contact force of the jth asperity participating in the contact on the ideal plane in the kth linear process, f k The step force representing the assembly load of the kth linear process, x j and j represents the coordinate value of the jth asperity involved in the contact, x z and z The coordinate value representing the position of the assembly load; The normal vector (A′, B′, C′) of the ideal plane after the kth linear process is: In formula (13), A′ represents the displacement vector θ rotating around the X axis xk function, B′ represents the displacement vector θ around the Y axis yk function, C′ represents the displacement vector Δz along the Z axis k The function of θ xk represents the displacement vector of the kth linear process rotating around the X axis, θ yk represents the displacement vector of the kth linear process rotating around the Y axis; (A, B, C) represents the normal vector of the ideal plane before the start of the kth linear process; The expression of the ideal plane after the kth linear process is: A′x+B′y+C′z+D′=0 Formula (14) In formula (14), A′, B′, and C′ are all about θ xk Function and θ yk Function, (x, y, z) represents the coordinate value of a point on the ideal plane after the kth linear process ends, and D′ is expressed as: Where (x0, y0, z0) represents the coordinates of the point after the rotation and translation of the kth linear process; θ xk The constant representing the displacement vector of the kth linear process around the X-axis, θ yk The constant representing the displacement vector of the kth linear process around the Y axis, Δz k represents the displacement vector of the kth linear process along the Z axis; At the end of the kth linear process, the ideal plane will reach node M. i The location coordinates are (x′, y′, z′ i ), node M i The distance to the ideal plane is expressed as: In formula (15), x′, y′, z′ i Indicates that the ideal plane in the kth linear process is about to reach node M i The coordinates of the location, A′, B′, C′ are calculated by formula (9), and D′ is the coordinate of the location with respect to θ xk ,θ yk , Δz k function.

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