Centrifugal compressor assembly error modeling method integrating manufacturing error and assembly deformation

Abstract

The invention discloses a centrifugal compressor assembly error modeling method integrating manufacturing error and assembly deformation, which comprises the following specific steps: S1, measuring an assembly surface by adopting line laser and a three-coordinate measuring machine, assembling surface point clouds of all assembling parts of the centrifugal impeller of the centrifugal compressor are obtained through feature extraction, a surface model of the assembling parts in interference fit with the centrifugal impeller is reconstructed based on an NURBS curved surface modeling method, and deformation calculation of interference fit of the centrifugal impeller is conducted; s2, calculating a matching error of the assembly surface of each assembly part by adopting a point cloud constraint registration method; and S3, based on the assembly constraint relation between the matching surfaces and the improved Jacobian-spinor model, a centrifugal compressor centrifugal impeller assembly chain error transfer model is established. The method has the advantages that the problem that error sources are not comprehensively considered in the actual assembly process is solved, the constraint relation between assembly surface matching errors is considered, and the assembly chain error transmission model is constructed and used for improving the assembly error prediction precision.

Description

Technical Field

[0001] The present invention belongs to the technical field of centrifugal compressor error transfer modeling, and in particular relates to a centrifugal compressor assembly error modeling method that comprehensively considers manufacturing errors and assembly deformations. Background Technique

[0002] A centrifugal compressor is a vane-type rotary machine that compresses gas to do work, and is widely used in compression equipment such as vehicle turbochargers, aero-engines, and gas turbines, playing an important role in fields such as automobiles, aviation, energy power, and petrochemical industry. The assembly quality of the core component, the centrifugal impeller, directly affects the operating performance and life of the equipment. This is because when the centrifugal compressor is working, the internal flow field operates complexly, and the centrifugal impeller is affected by working conditions such as air flow, temperature, and pressure. If the assembly quality of the impeller parts is poor, causing the impeller parts to be assembled obliquely, the internal air flow will oscillate strongly, resulting in the performance of the centrifugal impeller not meeting the working requirements. Therefore, the assembly accuracy of the impeller parts is the key to improving the working performance of the centrifugal compressor.

[0003] To solve the assembly accuracy problem, domestic and foreign scholars have conducted research in assembly technology-related fields such as tolerance modeling, assembly error transfer, assembly accuracy prediction, and digital assembly technology.

[0004] Traditional tolerance modeling methods include vector loop models, screw models, tolerance diagram models, etc. Such errors are mainly based on the analysis of the dimensional, directional, and positional errors of parts. In the analysis of part surface topography errors, Schleich et al. proposed a comprehensive framework for skin model shape simulation, in which the shape deviations generated during the manufacturing process are divided into systematic deviations and random deviations. Homri et al. proposed a method based on modal decomposition to establish part shape errors. QIAO et al. constructed a non-ideal surface error model based on manufacturing error factors and combined with various deviation functions. SHEN et al. proposed a non-Gaussian skin surface model modeling method considering the spatial distribution characteristics of errors to model the cylindrical surface.

[0005] Considering the assembly errors between parts, many commonly used methods for solving the relative position relationship between mating surfaces, such as point cloud registration method, centroid drive method, and differential surface method. In these studies, the mating errors can be effectively calculated, but the deformation generated during the assembly process is not considered. Liu Jianyong et al. proposed an assembly deformation error calculation method for the assembly error problem caused by part deformation. MU et al. constructed an assembly error transfer model that simultaneously considers manufacturing errors and assembly deformations for the assembly accuracy of aero-engine high-pressure rotors.

[0006] In terms of assembly error transfer and precision prediction, Shi Song et al. used the conjugate gradient method to establish a rough surface and established an improved homogeneous transformation matrix assembly error transfer model. JIN et al. considered the main and secondary references of assembled parts and proposed a local parallel Jacobian spinor model to calculate error transfer. Ding Siyi et al. established an overall assembly dimension chain with a multi-feature local parallel relationship based on an improved Jacobian spinor model. LIU et al. proposed an assembly tolerance analysis method based on the Jacobian model and the skin surface model, where the Jacobian model is applicable to error transfer analysis and the skin surface model shape is applicable to tolerance representation. Liu Jianhua et al. analyzed the force on parts using the boundary element method based on the construction of a non-ideal surface model and performed assembly precision analysis on a polyhedron model. SHEN et al. established an assembly error transfer model based on the non-Gaussian skin surface model and the Jacobian spinor model to analyze assembly precision.

[0007] The above research mainly focuses on tolerance modeling or error transfer methods. However, in actual assembly, there are influences such as installation positioning, manufacturing errors, and assembly deformation of the assembled parts themselves. If errors are modeled only through theoretical design, the influences of various error factors under actual installation conditions will be ignored, resulting in a large deviation between the predicted assembly precision and the actual situation. Digital twin technology can truly reflect the surface topography error of parts by constructing a digital model of the part entity. WANG et al. proposed a digital twin model based on general parts, which fuses multi-source data and realizes automatic assembly of parts by mapping assembly information from assembly semantics to geometric elements. Wang Anyang et al. combined the digital twin model with the dimension chain model to analyze assembly deviations.

[0008] At present, although the existing assembly error models consider the influence of surface topography and deformation on assembly errors, the existing surface topography modeling methods mainly rely on statistical data and are mainly oriented towards design and production. They cannot accurately describe the surface topography of a single part, resulting in a large deviation in assembly precision, which urgently needs to be improved. Summary of the Invention

[0009] The technical problem to be solved by the present invention is to provide a centrifugal compressor assembly error modeling method that combines manufacturing errors and assembly deformation, comprehensively considers manufacturing errors and assembly deformation, improves the problem of incomplete consideration of error sources in the actual assembly process, and considers the constraint relationship between the errors of each mating surface to construct an assembly chain error transfer model for improving the prediction accuracy of assembly errors.

[0010] One technical solution adopted by the present invention to solve the above problems is: a centrifugal compressor assembly error modeling method that combines manufacturing errors and assembly deformation, including the following specific steps:

[0011] S1 uses line laser and coordinate measuring machine to measure the assembly surface, obtains the assembly surface point cloud of each assembly part of the centrifugal impeller of the centrifugal compressor through feature extraction, reconstructs the surface model of the interference fit assembly parts of the centrifugal impeller based on the NURBS surface modeling method, and conducts deformation calculation of the interference fit of the centrifugal impeller;

[0012] S2 uses the point cloud constrained registration method to calculate the fit error between the assembly surfaces of each assembly part;

[0013] S3 establishes an error transfer model of the assembly chain of the centrifugal impeller of the centrifugal compressor based on the assembly constraint relationship between the mating surfaces and the improved Jacobian-spin model.

[0014] Compared with the prior art, the advantages of the present invention are that it simultaneously considers the manufacturing error and the assembly deformation of the interference fit of the centrifugal impeller, thereby improving the problem of incomplete consideration of the error sources in the actual assembly process, and considering the fit error between each surface and the assembly constraint relationship existing between the mating surfaces, thereby constructing an error transfer model of the assembly chain of the centrifugal impeller of the centrifugal compressor for accurately calculating the cumulative error variation at the end of the assembly of the centrifugal impeller of the centrifugal compressor and improving the prediction accuracy of the assembly error.

[0015] Preferably, the assembly surfaces of each assembly part of the centrifugal impeller of the centrifugal compressor in step S1 are respectively: the inner end face of the shaft seal sleeve scanned by the line laser, the shaft seal sleeve contact end face, the impeller abutting end face and the cylindrical surface of the first bushing, the impeller contact end face and the end cover pressing end face of the second bushing, the pressing end face and the outer end face of the end cover, the cylindrical surface of the main shaft; the first bushing assembly surface, the second bushing assembly surface and the inner hole surface of the centrifugal impeller measured by the coordinate measuring machine; the inner end face of the shaft seal sleeve and the shaft seal sleeve contact end face of the first bushing are end-face mated, and are denoted as the contact function unit CFE1; the impeller abutting end face of the first bushing and the first bushing assembly surface of the centrifugal impeller are end-face mated, and are denoted as the contact function unit CFE2; the cylindrical surface of the first bushing and the inner hole surface of the centrifugal impeller are interference-fitted, and are denoted as the parallel function unit PFE2; the impeller contact end face of the second bushing and the second bushing assembly surface of the centrifugal impeller are end-face mated, and are denoted as the contact function unit CFE3; the pressing end face of the end cover and the end cover pressing end face of the second bushing are end-face mated, and are denoted as the contact function unit CFE4. Most parts of the centrifugal impeller assembly only require the external feature surface information during assembly. The line laser scanning measurement method can quickly obtain the feature surface; while the inner wall of the centrifugal impeller will block the reflected light and the measurement is incomplete, and the inner hole surface of the centrifugal impeller cannot be measured by the line laser, so the coordinate measuring machine is used to measure the feature surface of the centrifugal impeller.

[0016] Preferably, the deformation calculation of the interference fit of the centrifugal impeller in step S1 is the deformation calculation of the interference fit between the inner hole surface of the centrifugal impeller and the cylindrical surface of the first bushing. The specific steps of the deformation calculation are as follows: Import the surface models of the interference fit assembly parts, that is, the surface model of the centrifugal impeller and the surface model of the first bushing, into the finite element analysis software. According to the material types of the centrifugal impeller and the first bushing, perform mesh division, and under the conditions of contact parameters, contact algorithms, temperature conditions, and fixed constraints applied to the outer contour, calculate the deformation results of the interference fit between the centrifugal impeller and the first bushing at the design temperature, and obtain the deformed point cloud map after heating assembly and cooling.

[0017] Preferably, the centrifugal impeller and the first bushing are made of aluminum alloy; the contact parameters include a normal stiffness factor of 0.3 and a penetration tolerance value of 0.1; the contact algorithm uses the generalized Lagrangian method; the design temperature of the temperature condition is 150 °C.

[0018] Preferably, the error transfer model of the centrifugal impeller assembly chain of the centrifugal compressor includes a series path CFE1 - CFE2 - CFE3 - CFE4 - IFE5 with characteristic end face fits, four parallel paths under the constraint of four main shafts: CFE1 - PFE1, CFE3 - PFE4, CFE4 - PFE5, IFE5 - PFE6, and a group of parallel paths CFE2 - PFE2 - PFE3 under the simultaneous constraint of the interference fit of the shaft hole and the main shaft; where, IFE5 is the internal functional unit, representing the surface topography error between the outer end face of the end cover and the pressing end face; PFE1 is the parallel functional unit, representing the shaft hole fit at the contact end face between the main shaft and the shaft seal sleeve of the first bushing; PFE3 is the parallel functional unit, representing the shaft hole fit at the assembly face between the main shaft and the first bushing of the centrifugal impeller; PFE4 is the parallel functional unit, representing the shaft hole fit at the contact end face between the main shaft and the second bushing impeller; PFE5 is the parallel functional unit, representing the shaft hole fit at the pressing end face between the main shaft and the end cover; PFE6 is the parallel functional unit, representing the shaft hole fit at the outer end face between the main shaft and the end cover. The errors at each mating surface need to be constrained by the main shaft to further calculate the pose at that place. At the same time, for the problem of the compound constraint of two mating errors between parts, the two are solved as a parallel local problem to avoid error accumulation and amplification.

[0019] Preferably, calculate the cumulative error variation of the end face of the centrifugal impeller assembly of the centrifugal compressor according to the error transfer model of the centrifugal impeller assembly chain of the centrifugal compressor.

[0020] Preferably, the cumulative error variation of the end face of the centrifugal impeller assembly of the centrifugal compressor is:

[0021] FR final =FR 5 ∩δ 5 '=(FR' 4+J FE5 ·δ FE5 )∩δ 5 ';

[0022] Among them, FR final is the cumulative error variation of the outer end face of the end cover, FR 5 is the pose of the pressed end face of the end cover, δ 5 ' is the translational component of the main shaft at the pressed end face of the end cover, FR' 4 is the cumulative error variation of the end cover pressing end face of the second bushing, J FE5 is the Jacobian matrix of the outer end face of the end cover, δ FE5 is the influence of the constraint between the end cover and the main shaft on the prediction of the assembly error of the centrifugal impeller of the centrifugal compressor.

[0023] Preferably, the cumulative error variation of the end faces at the ends of the assembly parts of the centrifugal impeller of the centrifugal compressor is:

[0024]

[0025] Among them, FR' i is the cumulative error variation of the end face at the end of the i-th component, FR' i-1 is the cumulative error variation at the end of the (i - 1)-th component, J FEi is the Jacobian matrix of the end face at the end of the i-th component, δ FEi is the influence of the constraint between the i-th component and the main shaft on the prediction of the assembly error of the centrifugal impeller of the centrifugal compressor, δ i ' is the translational component of the main shaft at the inner end face of the i-th component. Description of the Drawings

[0026] Figure 1 This is the assembly model diagram of the centrifugal impeller of the centrifugal compressor of the present invention.

[0027] Figure 2 This is the diagram of the measurement scheme for the characteristics of the main assembly parts of the centrifugal impeller of the centrifugal compressor of the present invention.

[0028] Figure 3 This is the schematic diagram of the NURBS surface modeling process of the two assembly surfaces, inner hole surface of the centrifugal impeller of the centrifugal compressor of the present invention and the first bushing.

[0029] Figure 4 This is the interference fit deformation diagram of the centrifugal impeller of the centrifugal compressor of the present invention and the first bushing.

[0030] Figure 5 This is the assembly schematic diagram of two-stage assembly.

[0031] Figure 6 This is the comparison diagram of the series assembly chain and the constrained assembly chain models of two-stage assembly.

[0032] Figure 7 Schematic diagram of assembly interference for shaft - hole fit and end - face fit

[0033] Figure 8 Schematic diagram of the assembly of the centrifugal impeller of the centrifugal compressor of the present invention without considering the constraint relationship

[0034] Figure 9 Schematic diagram of the assembly of the centrifugal impeller of the centrifugal compressor of the present invention considering the constraint relationship

[0035] Figure 10 Coordinate system diagram of the assembly of the centrifugal impeller of the centrifugal compressor of the present invention

[0036] Figure 11 Error transfer model diagram of the assembly chain of the centrifugal impeller of the centrifugal compressor of the present invention

[0037] Figure 12 Assembly calculation flow chart of the centrifugal impeller of the centrifugal compressor of the present invention Specific embodiments

[0038] The following describes the exemplary embodiments of the present invention with reference to the accompanying drawings. Various details of the embodiments of the present invention are included to facilitate understanding, and they should be considered merely exemplary. Therefore, those of ordinary skill in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the present invention. Similarly, for the sake of clarity and conciseness, the description of well - known functions and structures is omitted below.

[0039] The present invention proposes a method for modeling the assembly error of a centrifugal compressor considering comprehensive manufacturing errors and assembly deformations, including the following specific steps:

[0040] S1 Measure the assembly surface using a line laser and a coordinate measuring machine. Obtain the assembly surface point clouds of each assembly part of the centrifugal impeller of the centrifugal compressor through feature extraction. Reconstruct the surface model of the interference - fit assembly parts of the centrifugal impeller based on the NURBS surface modeling method, and perform deformation calculations for the interference fit of the centrifugal impeller.

[0041] The centrifugal compressor mainly consists of a centrifugal impeller, an air inlet, a diffuser, and a compressor housing. Among them, the centrifugal impeller is the most important part of the centrifugal compressor. The assembly of the centrifugal impeller is composed of the superposition and assembly of multiple - stage parts. The two sides of the centrifugal impeller are supported by two - stage supports. Among them, the second bushing presses the end face of the centrifugal impeller to keep the end face of the centrifugal impeller balanced. The outer cylindrical surface of the first bushing is assembled with the inner hole of the centrifugal impeller to make the axis of the centrifugal impeller in a relatively ideal state, avoiding deviation during the high - speed rotation of the centrifugal impeller. At the same time, the end face cooperates with the second bushing to position the centrifugal impeller. The end caps and shaft seal sleeves on both sides play a role in support and sealing.

[0042] Specifically, asFigure 1 As shown in the figure, the centrifugal impeller assembly consists of a main shaft and a shaft seal sleeve, a first bushing (bushing 1), a centrifugal impeller, a second bushing (bushing 2) and an end cover assembled on the main shaft. The inner end face (end face 1) of the shaft seal sleeve and the shaft seal contact end face (end face 2) of the first bushing are in end face fit. The impeller abutting end face (end face 3) of the first bushing and the first bushing assembly face (end face 4) on one side of the inner hole of the centrifugal impeller are in end face fit. The cylindrical surface (cylindrical surface 1) of the outer circle of the first bushing and the inner hole surface (inner hole 1) of the centrifugal impeller are in interference fit. The second bushing assembly face (end face 5) on the other side of the inner hole of the centrifugal impeller and the impeller contact end face (end face 6) of the second bushing are in end face fit. The end cover pressing end face (end face 7) of the second bushing and the pressing end face (end face 8) of the end cover are in end face fit. Among them, the interference fit is to heat the centrifugal impeller to 150 °C and then install the first bushing into the centrifugal impeller so that the cylindrical surface 1 and the inner hole 1 and the end face 3 and the end face 4 are all closely fitted.

[0043] S1.1 Use line laser and coordinate measuring machine to measure the assembly surface.

[0044] For the structure of the centrifugal impeller assembly, a combination of non-contact line laser scanning and contact probe scanning is adopted. The line laser processes the laser signal reflected by the part surface, which can reflect the tiny manufacturing errors on the surface. The contact probe scanning can continuously scan the surface to form a dense point cloud, which can better reflect the surface topography of the part, and the scanning speed is fast. Compared with the dot contact measurement, the measurement efficiency can be greatly improved. As Figure 2 shown in the figure, for the shaft seal sleeve, the first bushing, the second bushing and the end cover participating in the end face fit, only the external feature surface information is required during assembly. Therefore, the measurement method of line laser scanning can quickly obtain the feature surface. In addition, the cylindrical surface of the main shaft also uses the measurement method of line laser scanning to obtain the feature surface. For the inner end face of the centrifugal impeller, if line laser measurement is used, the inner wall of the centrifugal impeller will block the reflected light and the measurement will be incomplete. The inner hole of the centrifugal impeller cannot be measured by line laser either. Therefore, the feature surfaces of the centrifugal impeller are all obtained by contact probe scanning and measured by a coordinate measuring machine.

[0045] S1.2 Obtain the assembly surface point cloud of each assembly part of the centrifugal compressor centrifugal impeller through feature extraction.

[0046] The purpose of laser scanning is to obtain the point cloud data of the part assembly feature surface. When measuring the point cloud of the part, due to the influence of the environment and manual operation, there are some noise points in the obtained point cloud data. Therefore, the measured point cloud needs to go through various filtering functions to remove the noise points and extract the feature point cloud of the mating surface. Feature segmentation is to extract the point cloud data representing the part assembly features from the original measured point cloud data. The key assembly feature here is the assembly feature surface of each part on the assembly chain in the centrifugal impeller assembly.

[0047] Let the original set of measured point clouds be P cloud ={P 1 , P 2 , P 3 …P n}. Since the position of the feature surface is obvious, by calculating the envelope range x min , x max , y min , y max , z min , z max of the point cloud data packet of the feature surface, the threshold range (x min , x max ) ∪ (y min , y max ), (x min , x max ) ∪ (z min , z max ) and (y min , y max ) ∪ (z min , z max ) of the feature surface is obtained, and the straight-through filter is used to quickly segment the contour of the feature surface to achieve the preliminary segmentation of the feature surface.

[0048] After the preliminary segmentation of the feature surface by the straight-through filter is completed, for the outlier noise of the feature surface, the statistical filtering method is used. Let the coordinates of the point cloud test point be P i =(x i , y i , z i ), and the coordinates of the neighborhood points be P m =(x m , y m , z m ), then the average distance D n of the test point from k neighborhood points is as shown in Equation (1), which is

[0049]

[0050] Assume that the average distance D n follows a Gaussian distribution, then the outlier threshold D max is as shown in Equation (2), which is

[0051] D max = μ ± s·σ (s ∈ N) (2)

[0052] In the formula s is the standard deviation multiple, and N is a natural number.

[0053] By adjusting the number of neighborhood points \(k\) and the standard deviation multiple \(s\) in the statistical filtering algorithm to make the filtering effect reach an ideal state, and then combining with the radius filtering algorithm, substituting the optimal filtering parameter \(k\) for radius filtering. Finally, to further improve the quality of the point cloud data, a bilateral filtering algorithm is used to remove the small-scale noise around the feature surface to obtain the feature surface model.

[0054] S1.3 Reconstruct the surface model of the interference fit assembly parts of the centrifugal impeller based on the NURBS surface modeling method.

[0055] During the high-speed operation of the centrifugal impeller, high stability is required. According to the assembly sequence, the inner hole of the centrifugal impeller and the cylindrical surface of the first bushing need to be interference-fitted first. Since the interference fit will cause large deformation, the pose error caused by its deformation needs to be considered when calculating the assembly error. Based on the surface topography features of the first bushing obtained by line laser scanning in advance, and the inner hole features scanned by the coordinate measuring machine. In order to superimpose the deformation error of the interference fit on the feature surface, first use NURBS surface to reverse model the feature surface point cloud and calculate the deformation error caused by the interference fit.

[0056] Here, the NURBS method is a three-dimensional interpolation model in computer graphics. The most prominent advantage of the NURBS surface is that it can accurately and uniquely represent free surfaces based on a unified mathematical form. The NURBS surface can be regarded as being constructed multiple times by multiple NURBS curves in the \(u\) and \(v\) directions, and its mathematical expression is as shown in Equation (3):

[0057]

[0058] where \(w\) i,j is the weight factor of the control vertex \(P\) i,j , and \(N\) i,p (u) and \(M\) j,p (v) represent the basis functions on the knot vectors \(U\) and \(V\) respectively.

[0059] For the NURBS surface reconstruction of the coordinate measurement point cloud, the interpolation equation of the measurement point \(Q\) k is as shown in Equation (4):

[0060]

[0061] Calculated by the centripetal parameterization method and the knot vector \(U\) is as shown in Equation (5):

[0062]

[0063] The calculation method of the knot vector \(V\) is the same as that of \(U\), and the NURBS surface can be solved by two NURBS curve interpolations, as shown in Equation (6).

[0064] ​​​

[0065] After removing the surface noise points from the point cloud of the surface features of the first bushing and the centrifugal impeller, the feature surface is fitted using NURBS surface, and the feature surface is encapsulated and the CAD model is exported as shown in Figure 3 shown.

[0066] S1.4 Perform the deformation calculation of the interference fit of the centrifugal impeller.

[0067] Then import the interference fit assembly part model into the finite element analysis software Ansys. The materials used for the centrifugal impeller and the first bushing are aluminum alloy 6061. Mesh the assembly of the centrifugal impeller and the first bushing. And set the contact parameters. The normal stiffness factor FKN is 0.3, the penetration tolerance value FTOLN is 0.1, and the maximum contact friction stress TAUMAX is 10 20 , the ratio of the static friction coefficient to the dynamic friction coefficient FACT is 1; the contact algorithm KEYOPT(2) selects the generalized Lagrangian method (also known as the augmented Lagrangian algorithm). The temperature condition is set to the design temperature of 150 °C, and a fixed constraint is applied to the outer contour.

[0068] Through analysis, the deformation result of the interference fit of the impeller assembly at the design temperature of 150 °C is obtained. The deformed point cloud of the deformation result is as shown in Figure 4 shown. At this time, the deformed situation after heating and assembling and cooling is obtained. At this time, the feature surface is the result of considering the manufacturing error and the interference fit deformation. To superimpose the deformation result onto the assembly error transfer model, first export the deformed nodes in coordinate format, and then import the nodes into Cloud Compare to display the deformed point cloud diagram. If the point cloud is directly registered, it is easy to fall into a local optimal solution and reduce the prediction accuracy. Therefore, here, in combination with Figure 2 , the relevant feature end faces are separated, namely end face 2, end face 3, end face 4, end face 5, cylindrical surface 1 and inner hole 1.

[0069] S2 Use the point cloud constraint registration method to calculate the fit error between the assembly surfaces of each assembly part.

[0070] The process of assembling adjacent parts is actually a point cloud registration process of the feature surfaces participating in the contact assembly. Traditional point cloud registration is the process of transforming two point clouds in the same target scene to the same coordinate system through coordinate transformation. However, in the actual assembly process, due to machining errors, the two assembly surfaces cannot completely coincide, and there will be interference on the surfaces. Traditional registration methods cannot be directly used for the registration of feature surfaces. Here, the Iterative Closest Point (ICP) method is adopted, and the method of constrained registration is used to make the two feature surfaces approach each other to the greatest extent to achieve the assembly of parts. Suppose the surface to be positioned is P, and its measurement point set is the original point cloud P = {P 1 , P 2 …P n}, P i is the measurement point scanned by it, the positioning surface is Q, and its measurement point set is the target point cloud Q = {Q 1 , Q 2 …Q n}. To determine the assembly relationship between the source point cloud and the target point cloud, each point in the source point cloud can find the corresponding point in the target point cloud by searching for the nearest Euclidean distance. The constraint condition is that the distance from the point to be registered to the non-ideal surface is greater than 0. By establishing the distance function and the objective function of the constraint, a non-linear constrained optimization problem is formed, as shown in Equation (7):

[0071]

[0072] In the formula, n i represents the unit normal vector of the positioning surface Q, and the sequential quadratic programming algorithm is used to solve the non-linear optimization problem. The optimal translation vector T and the optimal rotation matrix R are obtained, as shown in Equation (8).

[0073]

[0074] In the formula, u, v, and w respectively represent the movements along the x, y, and z axes, and α, β, and γ respectively represent the rotations along the x, y, and z axes.

[0075] Therefore, the fitting error can be represented by the small displacement screw δ = [u, v, w, α, β, γ] T . Here, the fitting errors between the end face and the shaft hole are mainly calculated. Therefore, the small displacement screw of the toroidal surface is δ = [0, 0, w, α, β, 0] T , and the small displacement screw of the cylindrical surface is δ = [u, v, 0, α, β, 0] T .

[0076] S3 Consider the assembly constraint relationship between the mating surfaces, improve the Jacobian-screw model, and establish the error transfer model of the centrifugal compressor assembly chain.

[0077] The Jacobian - screw model consists of a Jacobian matrix and a screw model. The Jacobian matrix can describe the relationship between joint rotational speeds and end - effector Cartesian velocities in a robot. Here, the Jacobian model is used to describe the changes in position and orientation in virtual assembly.

[0078] In error analysis, the Jacobian matrix is used to describe the geometric relationship between functional elements (FE) and functional requirements (FR) in an assembly chain. The FR functional requirement is the cumulative error variation. The small - displacement screw can accurately describe the relative position and orientation changes between parts. Combining with the Jacobian matrix, small errors can be linearized in the screw space, thus facilitating the analysis and calculation of mating errors, as shown in Equation (9).

[0079]

[0080] In the formula, J FEi is the Jacobian matrix of the i - th assembly feature surface, as shown in Equation (10); δ i represents the small - displacement screw in the local coordinate system of the i - th assembly feature surface, and FR i is the error variation of the i - th mating surface.

[0081]

[0082] In the formula, represents the direction change of the local coordinate system i relative to the global coordinate system; [R Pti is the projection matrix; represents the position relationship between coordinate system i and coordinate system 0, as shown in Equation (11).

[0083]

[0084] In the formula,

[0085] Centrifugal compressors usually operate at high rotational speeds. During the assembly process, the assembly errors between components need to be strictly controlled. The traditional Jacobian - screw model assembly features are mainly in series. According to the assembly structure of the centrifugal compressor, there are constraint problems with the assembly features. If only the series method is used for error - transfer calculation, the error will increase. Therefore, it is necessary to consider the existing assembly constraint problems:

[0086] Constraint case 1:

[0087] Taking the mating of two - stage parts as an example, an assembly error - transfer model is established. Figure 5The figure shows a schematic diagram of the two-stage part mating. Here, the center of the lower end face of the first-stage part is set as the global coordinate system (coordinate system 0), the centers of the upper end face of the first-stage part and the lower end face of the second-stage part are local coordinate systems (coordinate systems 1, 2), and the center of the upper end face of the second-stage part is a local coordinate system (coordinate system 3). If only considering the end face mating error, the error sources of this assembly mainly include the mating error between the non-ideal surfaces of the two parts and the surface topography error at the end of the second-stage part. Its assembly chain model is as Figure 6 The left side is the series assembly chain model. First, use the optimized ICP registration method to calculate the screw δ of the end face mating FE1 =[0,0,w 1 ,α 1 ,β 1 ,0] T . The point cloud at the end of the second-stage part is fitted by the least squares method to calculate its small displacement screw δ FE2 =[0,0,w 2 ,α 2 ,β 2 ,0] T . Assume that the heights of the ends of the two-stage parts relative to the global coordinate system are h 1 ,h 2 respectively. Use equations (10) and (11) to calculate the Jacobian matrix, J FE1 is the Jacobian matrix of the mating surface of the two components, and J FE2 is the Jacobian matrix of the end of the second-stage part. According to equation (9), the pose FR final1 of the mating end of the two-stage parts can be expressed as equation (12), which is

[0088]

[0089] If considering the constraint of the spindle on the feature surface, first substitute the screw δ FE1 =[0,0,w 1 ,α 1 ,β 1 ,0] T of the mating surface and the Jacobian matrix J FE1 into equation (9) to calculate the assembly error obtained from the end face mating, which is expressed as equation (13), and is

[0090]

[0091] Then calculate the error amount of the spindle at this mating surface, segment the point cloud of the spindle at this mating surface, calculate the offset of the center of this point cloud relative to the reference coordinate system, and calculate the translational component of the spindle at the first-stage mating as δ' FE1 =[u′ 1 ,v′ 1 ,0] T, since the first - stage mating passes through the Jacobian error - transfer model, the translational components of the lower end - face of the second - stage part are [β 1 ·h 1 , - α 1 ·h 1 , w 1 T . There is an overlapping part with the spindle offset in the x and y directions. If only the two sets of screws are regarded as in series for calculation, the error will increase. Therefore, to eliminate the interference effect caused by the overlapping part, the algebraic operation method is used here to calculate the intersection of the two sets of offsets [β 1 ·h 1 , - α 1 ·h 1 T ∩[u′ 1 , v′ 1 T . At this time, the pose at the first - stage mating surface is FR′ 1 = [β 1 ·h 1 ∩u′ 1 , - α 1 ·h 1 ∩v′ 1 , w 1 , α 1 , β 1 , 0] T . Its assembly - chain model is the series assembly - chain model on the right as Figure 6 . Among them, CFE is the contact - function unit, used to represent the end - face mating; PFE is the parallel - function unit, used to represent the shaft - hole mating; IFE is the internal - function unit, used to represent the surface - topography error of the part.

[0092] When calculating the pose of the end of the second - stage part, substituting the pose FR′ 1 of the first - stage mating surface, δ FE2 and J FE2 into Equation (9), the pose of the upper end - face of the second - stage part can be expressed by Equation (14) as

[0093]

[0094] Then, considering the constraint problem at the end of the second - stage part, the translational component δ' FE2 = [u' 2 , v' 2 , 0] T is calculated through IFE2. Then, the pose FR final2 of the end of the second - stage part can be expressed by Equation (15).

[0095]

[0096] ​​​Constraint condition 2:

[0097] During the assembly process of the centrifugal impeller, when the first bushing is assembled with the centrifugal impeller, there is a combined constraint of both end face fit and shaft hole fit. Let the end face fit error be δ FE1 =[0, 0, w 1 , α 1 , β 1 , 0] T , and the shaft hole interference fit is δ FE2 =[u 2 , v 2 , 0, α 2 , β 2 , 0] T ,

[0098] The translational components of the two are [0, 0, w 1 and [u 2 , v 2 , 0], respectively, and they are independent of each other. The rotational components are [α 1 , β 1 , 0] and [α 2 , β 2 , 0], and there is an overlap between the two in the rotational component. The interference situation is as shown in Figure 7 . If the fit error is directly substituted into equations (9) - (11) for error transfer calculation, the error will be repeatedly accumulated, resulting in a deviation in the prediction result. Therefore, for this type of situation, the error needs to be calculated in parallel to obtain a new fit error, which can be expressed by equation (16) as

[0099]

[0100] where ∏ is ∩ or ∪, depending on whether the components in this direction overlap.

[0101] Therefore, after considering the above constraints, the errors at each mating surface need to be constrained by the main shaft, and further calculate the pose at this place. At the same time, for the problem of the combined constraint of two fit errors between parts, the two are solved as a parallel local problem to avoid the amplification of error accumulation. Figure 9 are the poses of the centrifugal impeller assembly before and after considering the above factors.

[0102] After analyzing the existing assembly constraints, first establish the coordinate system of the centrifugal impeller assembly as Figure 10 . Take the center of the bottom surface of the shaft seal sleeve as the global coordinate system (coordinate system 0), and the remaining local coordinate systems are located at the centers of each assembly surface. To obtain the cumulative error variation at the end of the centrifugal impeller assembly of the centrifugal compressor, it is necessary to establish an assembly chain error transfer model as Figure 11As shown. In this error transfer model diagram of the assembly chain, it first includes a series path: CFE1 - CFE2 - CFE3 - CFE4 - IFE5, which is mainly based on the mating of the feature end faces. In addition, there are four pairs of parallel paths under the spindle constraints: CFE1 - PFE1, CFE3 - PFE4, CFE4 - PFE5, IFE5 - PFE6, and a group of parallel paths under the interference fit of the shaft - hole and the simultaneous constraint of the spindle: CFE2 - PFE2 - PFE3.

[0103] According to the assembly sequence, first calculate the parallel assembly (CFE2 - PFE2) of the interference fit between the first bushing and the centrifugal impeller, obtain the point cloud of the deformed surfaces of the centrifugal impeller and the first bushing, and then use the method of constrained registration for the mating surfaces to calculate the screw δ corresponding to CFE2 and PFE2 FE2-1 and δ FE2-2 , since the two pairs of mating surfaces are locally parallel, algebraic operations need to be performed on the two screws δ FE2 =δ FE2-1 ∩δ FE2-2 . For the end - face mating, the method of constrained registration can be directly used to calculate the screw.

[0104] After obtaining the screws of each mating surface, then consider the parallel connection of each end - face mating and the spindle constraint (CFE1 - PFE1, CFE2 - PFE3, CFE3 - PFE4, CFE4 - PFE5, IFE5 - PFE6). Combining with the three - dimensional point cloud diagram of the spindle, calculate the translational components of the spindle at each mating surface, and then combine with the calculation method of assembly constraint analysis to solve the pose of the end of the end - cover. The specific assembly calculation process is as Figure 12 , and the following table shows the deviation calculation of each mating surface.

[0105] Table of screw, Jacobian matrix and joint pose relationship of each mating surface in the parallel structure of the centrifugal impeller

[0106]

[0107] Taking the centrifugal impeller assembly of the centrifugal compressor as the research object, measure and verify the surface of the end - part of the centrifugal impeller assembly of the centrifugal compressor.

[0108] According to Figure 2 the measurement plan, first scan each component of the impeller assembly with a line laser to obtain the original point - cloud data, then determine the feature surfaces participating in the assembly in combination with the assembly chain, and perform filtering and segmentation processing on the original point cloud to obtain the point - cloud models of the feature surfaces participating in the error transfer in each part of the impeller assembly.

[0109] Then use a scanning coordinate measuring machine to scan the inner hole and inner end - face of the centrifugal impeller. Extract the point - cloud data of end - face 4, end - face 5 and inner hole 1.

[0110] According to the assembly sequence, first, an interference fit assembly is performed on the first bushing and the centrifugal impeller. A surface topography model is established using NURBS surfaces for the surface point clouds of the first bushing and the centrifugal impeller, and an interference fit deformation analysis is carried out on the assembly of the first bushing - centrifugal impeller. The surface deformation nodes are extracted, and the characteristic surface point clouds are segmented.

[0111] Calculate the end face fitting error and the shaft - hole fitting error of the first bushing - centrifugal impeller, and calculate the screw quantity δ of its local parallel connection (CFE2 - PFE2). FE2 = δ FE2-1 ∩δ FE2-2 .

[0112]

[0113] Calculate the screw quantity errors of the end face fittings CFE1, CFE3, CFE4, and CFE5 according to the constraint registration method.

[0114]

[0115] To analyze the influence of local parallel connection and spindle constraint on the prediction of the assembly error of the centrifugal impeller of a centrifugal compressor.

[0116] According to the assembly chain error transmission model, when considering the interference fit deformation, if the assembly chain considering only the assembly in series is CFE1 - CFE2 - PFE2 - CFE3 - CFE4 - IFE5, calculate the end - effector pose FR at this time according to equations (9) - (11). final1 ,

[0117] Considering the interference fit deformation and the local parallel connection of parts, where the local parallel connection included is (CFE2, PFE2), so the assembly chain is CFE1 - (CFE2, PFE2) - CFE3 - CFE4 - IFE5. Calculate the end - effector pose FR at this time according to equations (9) - (11). final2 ,

[0118] The above situations only consider the axial fitting conditions between the centrifugal impeller parts and do not consider the radial constraint of the centrifugal impeller spindle, which will cause a large deviation in the predicted axis, as Figure 8 shown. If we want to consider the interference fit deformation, the local parallel connection, and the parallel situation of the spindle constraint at the same time, according to the Figure 11 assembly chain, and the screw quantities, Jacobian matrices, and joint pose relationship tables of each mating surface in the parallel structure of the centrifugal impeller, calculate the screw quantities of each end - face mating surface. Then, combined with the spindle surface model, calculate the translational components of the spindle at each mating surface according to (IFE1, IFE2, IFE3, IFE4, IFE5) as:

[0119]

[0120] Finally, calculate the pose under the parallel constraints of each mating surface and the pose of the end of the assembly.

[0121] FR final = FR 5 ∩δ′ 5 =(FR' 4 + J FE5 ·δ FE5 )∩δ′ 5 ;

[0122] where, FR' i =(FR' i-1 + J FEi ·δ FEi )∩δ′ i , i < 5; FR' 0 = 0;

[0123]

[0124] Taking the bottom of the shaft seal sleeve as the reference, install according to the marked (phase zero point), and use a coordinate measuring machine to detect the upper surface of the end part of the centrifugal impeller assembly end cover. The detection results are compared with the theoretical calculation as shown in the following table:

[0125] Calculation Results Table of Cumulative Error Variation at the End of the Centrifugal Compressor Centrifugal Impeller Assembly End Cover

[0126]

[0127] As can be seen from the above table, during actual assembly, the offsets of the end of the centrifugal impeller assembly end cover along the x-axis and y-axis are u = 3.42×10 -3 mm and v = -7.93×10 -3 mm respectively, the coaxiality C = 8.64×10 -3 mm, and the rotations along the x-axis and y-axis are α = 3.17×10 -4 rad and β = -5.47×10 -4 rad respectively. When constraints are not considered, the offsets of the end of the centrifugal impeller assembly end cover along the x-axis and y-axis are u = 4.03×10 -3 mm and v = -8.92×10 -3 mm respectively, the coaxiality C = 9.79×10 -3 mm, and the rotations along the x-axis and y-axis are α = 3.96×10 -4 rad and β = -6.23×10 -4rad. At this time, the coaxiality error is 11.75%, and the angular errors along the x-axis and y-axis are 19.95% and 12.20% respectively. When considering the constraints, the offsets of the end of the end cover of the centrifugal impeller assembly along the x-axis and y-axis are u = 3.76×10 -3 mm and v = -8.34×10 -3 mm, the coaxiality C = 9.15×10 -3 mm, and the angles of rotation along the x-axis and y-axis are α = 3.43×10 -4 rad and β = -5.89×10 -4 rad. At this time, the coaxiality error is 5.57%, and the angular errors along the x-axis and y-axis are 7.58% and 7.13% respectively.

[0128] The above specific embodiments do not constitute a limitation on the protection scope of the present invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can occur depending on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A centrifugal compressor assembly error modeling method that integrates manufacturing error and assembly deformation, characterized in that: The specific steps include: S1 uses line laser and three-dimensional coordinate measuring machine to measure the assembly surface, obtains the assembly surface point cloud of each assembly part of the centrifugal impeller of the centrifugal compressor through feature extraction, reconstructs the surface model of the centrifugal impeller interference fit assembly parts based on the NURBS surface modeling method, and performs the deformation calculation of the centrifugal impeller interference fit; S2 uses point cloud constraint registration method to calculate the matching error between the assembly surfaces of each assembly part; S3 establishes an error transmission model for the centrifugal impeller assembly chain of a centrifugal compressor based on the assembly constraint relationship between mating surfaces and the improved Jacobi-screw model.

2. The centrifugal compressor assembly error modeling method based on comprehensive manufacturing error and assembly deformation according to claim 1 is characterized in that: The assembly surfaces of the assembly parts of the centrifugal impeller of the centrifugal compressor described in step S1 are: the inner end face of the shaft seal sleeve, the shaft seal sleeve contact end face of the first bushing, the impeller abutment end face and the cylindrical surface, the impeller contact end face of the second bushing and the pressing end face of the end cover, the pressing end face and the outer end face of the end cover, and the cylindrical surface of the main shaft, which are scanned by line laser; the first bushing assembly surface, the second bushing assembly surface and the inner hole surface of the centrifugal impeller are measured by a three-dimensional coordinate measuring machine; The inner end face of the shaft sealing sleeve is matched with the shaft sealing sleeve contact end face of the first sleeve, and is recorded as a contact functional unit CFE1; the impeller abutment end face of the first sleeve is matched with the first sleeve fitting surface of the centrifugal impeller, and is recorded as a contact functional unit CFE2; the cylindrical surface of the first sleeve is interference fit with the inner hole surface of the centrifugal impeller, and is recorded as a parallel functional unit PFE2; the impeller contact end face of the second sleeve is matched with the second sleeve fitting surface of the centrifugal impeller, and is recorded as a contact functional unit CFE3; the pressing end face of the end cover is matched with the end cover pressing end face of the second sleeve, and is recorded as a contact functional unit CFE4.

3. The centrifugal compressor assembly error modeling method based on comprehensive manufacturing error and assembly deformation according to claim 2 is characterized in that: The deformation calculation of the interference fit of the centrifugal impeller performed in step S1 is the deformation calculation of the interference fit between the inner hole surface of the centrifugal impeller and the cylindrical surface of the first bushing. The specific steps of the deformation calculation are: importing the surface model of the interference fit assembly parts, that is, the surface model of the centrifugal impeller and the surface model of the first bushing into the finite element analysis software, and meshing is performed according to the material type used for the centrifugal impeller and the first bushing. According to the contact parameters, contact algorithm, temperature conditions and fixed constraints imposed on the outer contour, the deformation result of the interference fit between the centrifugal impeller and the first bushing at the design temperature is calculated to obtain the deformation point cloud map after the heated assembly is cooled.

4. The centrifugal compressor assembly error modeling method based on comprehensive manufacturing error and assembly deformation according to claim 3 is characterized in that: The centrifugal impeller and the first bushing are made of aluminum alloy; the contact parameters include a normal stiffness factor of 0.3 and a penetration tolerance value of 0.1; the contact algorithm adopts the generalized Lagrangian method; and the design temperature of the temperature condition is 150°C.

5. The centrifugal compressor assembly error modeling method based on comprehensive manufacturing error and assembly deformation according to claim 2 is characterized in that: The centrifugal impeller assembly chain error transmission model of the centrifugal compressor includes a series path CFE1-CFE2-CFE3-CFE4-IFE5 with characteristic end face fit, four parallel paths under the constraints of the main axis: CFE1-PFE1, CFE3-PFE4, CFE4-PFE5, IFE5-PFE6, and a group of parallel paths CFE2-PFE2-PFE3 under the simultaneous constraints of the shaft hole interference fit and the main axis; Among them, IFE5 is an internal functional unit, which is expressed as the surface morphology error between the outer end face of the end cover and the clamping end face; PFE1 is a parallel functional unit, which represents the shaft hole fit between the main shaft and the first bushing shaft seal sleeve contact end face; PFE3 is a parallel functional unit, which represents the shaft hole fit between the main shaft and the first bushing fitting surface of the centrifugal impeller; PFE4 is a parallel functional unit, which represents the shaft hole fit between the main shaft and the second bushing impeller contact end face; PFE5 is a parallel functional unit, which represents the shaft hole fit between the main shaft and the clamping end face of the end cover; PFE6 is a parallel functional unit, which represents the shaft hole fit between the main shaft and the outer end face of the end cover.

6. The centrifugal compressor assembly error modeling method based on comprehensive manufacturing error and assembly deformation according to claim 5 is characterized in that: The cumulative error variation of the end face of the centrifugal impeller assembly of the centrifugal compressor is calculated based on the error transmission model of the centrifugal impeller assembly chain of the centrifugal compressor.

7. The centrifugal compressor assembly error modeling method based on comprehensive manufacturing error and assembly deformation according to claim 6 is characterized in that: The cumulative error variation of the end face of the centrifugal impeller assembly of the centrifugal compressor is: FR final =FR5∩δ5'=(FR'4+J FE5 ·δ FE5 )∩δ5'; Among them, FR final is the cumulative error variation of the outer end face of the end cover, FR5 is the position of the pressing end face of the end cover, δ5' is the translational component of the main axis at the pressing end face of the end cover, FR'4 is the cumulative error variation of the pressing end face of the end cover of the second bushing, J FE5 is the Jacobian matrix of the outer end surface of the end cap, δ FE5 The influence of end cover and main shaft constraints on the prediction of centrifugal impeller assembly error of centrifugal compressor.

8. The centrifugal compressor assembly error modeling method based on comprehensive manufacturing error and assembly deformation according to claim 7 is characterized in that: The cumulative error variation of the end faces of each assembly part of the centrifugal impeller of the centrifugal compressor is: Among them, FR' i is the cumulative error variation of the end face of the i-th component, FR' i-1 is the cumulative error variation at the end of the i-1th component, J FEi is the Jacobian matrix of the end face of the i-th component, δ FEi is the influence of the i-th component and the main shaft constraint on the assembly error prediction of the centrifugal impeller of the centrifugal compressor, δ i ' is the translational component of the main axis at the end surface of the i-th component.

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