Aircraft large component coordinated assembly method considering pre-manufacturing cumulative errors

Abstract

The application relates to an aircraft large component coordinated assembly method considering previous manufacturing cumulative errors, comprising the following steps: constructing an error mapping relationship based on a small rotation error model, establishing an assembly deviation mapping model under a single station; constructing an error transmission relationship under multiple stations based on a state space model, establishing an assembly deviation cumulative transmission model; generating a large amount of deviation source data randomly by adopting a Monte Carlo simulation algorithm, obtaining a plurality of simulation sample data of component fitting element deviation; collecting actual measurement sample data of the component fitting element deviation, fusing the simulation sample data, and obtaining a deviation statistical distribution mean value by adopting a maximum likelihood estimation algorithm; taking the component fitting element with the deviation statistical distribution mean value as a reference, and solving a component optimal pose transformation by adopting a singular value decomposition algorithm. Compared with a traditional strategy of positioning an aircraft component by taking feature points given by a digital design model as a reference, the application can greatly improve the coordination accuracy of multiple components in a fitting area.

Description

Technical Field

[0001] This invention relates to the field of aircraft digital assembly technology, and in particular to a coordinated assembly method for large aircraft components that takes into account accumulated errors in previous manufacturing processes. Background Technology

[0002] The accuracy of aircraft component orientation in space is crucial for ensuring coordination between multiple components and is a key factor influencing assembly quality. Since the introduction of spatial point measurement equipment such as laser trackers into the aerospace manufacturing field in the 1980s, digital assembly technology for aircraft, which uses the three-dimensional coordinate information of computer virtual models as the positioning reference, has matured considerably and has largely replaced the traditional manufacturing method that uses the shape and size information of templates as the coordination reference. In the traditional assembly process of large components such as wings and fuselage sections, the orientation of the component is characterized by the detection coordinates of multiple feature points on it. The orientation of the assembled component is optimized and adjusted based on the coordinate data given in the digital design model, treating the component as a rigid body consistent with the digital model and ignoring its previous manufacturing errors and flexible deformations. The mating areas of new-generation aircraft components are long and wide, and the traditional assembly strategy based on the feature points of the components cannot guarantee the coordination between multiple components.

[0003] With the goal of achieving precise fit between components, domestic and international scholars, based on component rigid pose transformation estimation algorithms, have proposed numerous component pose adjustment and optimization strategies by comprehensively considering aircraft product characteristic constraints such as coaxiality of intersection holes, multi-point symmetry, coplanarity, and collinearity, and integrating precision-influencing factors such as component self-weight deformation and thermal deformation. These strategies have effectively improved assembly accuracy. However, there is still no pose correction method that considers the transmission law of manufacturing errors in the preceding processing and assembly process. The cumulative error of a single large component in the preceding component assembly stage has a significant impact on the key geometric elements of its mating area. Therefore, it is necessary to explore the mapping mechanism of multi-source errors in the preceding manufacturing process on component mating elements, reveal the variation law of mating element deviations, and use the mating elements with deviations as a benchmark to calculate the optimal positioning attitude of the component, thereby improving the coordination accuracy of fit between multiple components. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a coordinated assembly method for large aircraft components that considers cumulative errors in preceding manufacturing processes. This method solves the problems of traditional methods that ignore preceding manufacturing errors and flexible deformation, cannot guarantee the coordination between multiple components, and do not consider the orientation correction of components based on the transmission law of manufacturing errors during preceding processing and assembly.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a coordinated assembly method for large aircraft components considering cumulative errors in previous manufacturing processes, comprising the following steps:

[0006] S1. Based on the small rotation error model, establish the mapping relationship between the positioning pin hole axis pose error of the tooling fixture under a single station, the part pose error of the positioned reference part, the hole machining error of the reference part connected to the non-reference part, and the connection hole error of the non-reference part connected to the part of the next station, and establish the assembly deviation mapping model under a single station.

[0007] S2. Based on the assembly deviation mapping model established in step S1 under a single workstation, the connection hole position error transmission relationship of the assembly parts connection under multiple workstations is constructed based on the state space model. Then, the positional orientation error of the positioning pin hole axis of the tooling fixture and the hole position machining error of the part connection under each workstation are obtained to the positional deviation transmission relationship of the intersection holes and mating surfaces of the large aircraft components. The assembly deviation cumulative transmission model of the fuselage section in the previous processing and assembly process is established. The positional orientation deviation of the intersection hole includes position offset and axial deviation, and the positional orientation deviation of the mating surface includes normal deviation.

[0008] S3. Within the tolerance zone of tooling pin hole positioning and part connection hole machining at each workstation, a large amount of deviation source data is randomly generated using the Monte Carlo simulation algorithm. Using the assembly deviation cumulative transmission model established in step S2, several simulation sample data of the positional deviation of the component intersection hole and mating surface are obtained.

[0009] S4. Use digital measurement equipment to collect the coordinates of multiple points in the docking area of ​​multiple batches of aircraft components. Calculate the pose deviation data of the component intersection holes and mating surfaces through the point coordinates. Then, fuse the measured sample data obtained by the calculation with the simulation sample data obtained in step 3. Use the maximum likelihood estimation algorithm to obtain the statistical distribution mean of the pose deviation of the component intersection holes and mating surfaces.

[0010] S5. Using the statistical distribution mean of the pose deviations of the component intersection holes and mating surfaces obtained in step 4, and taking the axis of the intersection hole with the deviation statistical distribution mean, the center of the end face, and the normal vector of the mating surface as the reference, the singular value decomposition algorithm is used to solve the transformation relationship of the component from the initial pose to the optimal pose, thereby improving the coordination between the components.

[0011] Furthermore, in step S1, the specific process includes the following steps:

[0012] S11. Based on the small rotation error model, define the mapping relationship between the pose error of a single positioning pin hole axis and the pose error of the positioning reference part:

[0013]

[0014] Where Δp and Δn represent the position error of the center of the mating end face of the positioning pin hole and the direction vector error of the hole axis, respectively; u, v, w are the coordinates representing the position error of the positioned part; α, β, γ are the Euler angles representing the spatial attitude error of the positioned part; and J is the Jacobian matrix representing the mapping relationship between the part pose error ξ of the positioning reference part and the pose error Δζ of the positioning pin hole axis.

[0015] S12. Based on the mapping relationship obtained in S11, the mapping relationship between the pose errors of multiple positioning pin hole axes and the pose errors of the reference part being positioned is derived:

[0016]

[0017] In the formula J i J is the Jacobian matrix corresponding to the i-th locating pin hole. A It is J i The augmented Jacobian matrix represents the pose error Δζ of the axes of all m locating pin holes. A The mapping relationship between the part pose error ξ of the positioned reference part;

[0018] S13. Based on the least squares optimization objective, by augmenting the Jacobian matrix J... A The generalized inverse form further represents the pose error Δζ of the m locating pin hole axes. A Mapping relationship between the part pose error and the positioning reference part:

[0019]

[0020] S14. Based on the positional error of the locating pin hole axis, further integrate the machining error of the holes connecting the reference part and the non-reference part. Let p be a certain connecting hole position on the reference part. i p caused by machining error of connecting hole i The initial position offset of the theoretical point in the relative numerical model is δ. i The initial axial deviation of the connecting hole is v i The positional error Δζ of the reference part along the axis of the m locating pin holes is then calculated. A Under the influence of the non-reference part, the connection hole position error E between the non-reference part and the part at the next station is reduced. i Represented as:

[0021]

[0022] The above formula is the assembly deviation mapping model under a single workstation, where e pi e represents the position vector deviation of the connecting hole position on a non-reference part. ni This indicates the normal deviation of the connection hole position.

[0023] Furthermore, in step S2, the specific process includes the following steps:

[0024] S21. Suppose that the assembly part at the j-th station in a certain series branch takes the assembly part at the (j-1)-th station as the positioning reference, and they are connected through n connecting holes. The positional error of these connecting holes is denoted as E. 1j E 2j ,…E nj The positional error E of the i-th connecting hole of the (j+1)-th assembly on the j-th assembly is... i,j+1 for:

[0025]

[0026] In the formula δ i,j+1 and v i,j+1 These are the positional offset and axial deviation of the i-th connection hole position relative to assembly j+1 caused by machining errors in the connection hole positions of assembly j; J i,j+1 J is the Jacobian matrix representing the mapping relationship between the part pose error of assembly j and the position error of the i-th connecting hole; A,j+1 It is the augmented Jacobian matrix composed of the positional errors of the n connecting holes of assembly j-1 and j to the positional errors of the parts of assembly j;

[0027] S22. For an assembly connection of p components connected in series from the inside out, the transmission relationship of the initial hole machining error and the axial orientation error of the locating pin hole of the tooling fixture to the orientation deviation of the i-th wing-body intersection hole on the aircraft component is as follows:

[0028]

[0029] In the formula E i,p+1 It is the position and orientation deviation vector of the i-th intersection hole on the large aircraft component after p+1 assembly processes, δ i,p+1 and v i,p+1 These are the positional offset and axial deviation of the i-th intersection hole caused by the machining forming error of the last part participating in the assembly in the p+1th process, respectively. The normal deviation of the mating surface of the large aircraft component is obtained by averaging the axial deviations of all intersection holes on it, thus completing the establishment of the assembly deviation accumulation and transmission model of the large aircraft component in the preceding machining and assembly process.

[0030] Further, in step S4, the process of calculating the pose deviation data of the component intersection hole and mating surface using point coordinates specifically includes the following steps:

[0031] S41. Based on the coordinates of three points on the end face circle of a certain intersection hole, construct analytical expressions for the hole axis direction vector and the end face circle center coordinates of the intersection hole with respect to these three point coordinates, and then calculate the hole axis direction deviation and end face circle center deviation of the intersection hole, that is, the axial deviation and position offset of the intersection hole.

[0032] S42. Based on the coordinates of the three points on the mating surface, construct an analytical expression for the normal vector of the mating surface with respect to the coordinates of these three points, and then calculate the normal deviation of the mating surface. The calculation method is the same as that used in step S41 to calculate the direction vector of the hole axis.

[0033] Further, in step S41, the analytical expressions for the hole axis direction vector and the end face center coordinates of the intersection hole with respect to these three point coordinates are constructed respectively. The specific process includes the following steps:

[0034] S411. Suppose the coordinates of three points collected on the end face of a hole at a certain intersection are p1(x1,y1,z1), p2(x2,y2,z2), and p3(x3,y3,z3). Then the direction vector of the hole axis is s(s x ,s y ,s z The analytical expression for the coordinates of these three points on the circle is:

[0035]

[0036] The expression for parameter C in the formula with respect to the coordinates of the three points is:

[0037]

[0038] S412, coordinates of the end face center p c (x c ,y c ,z c The expression for the coordinates of the three points on the circle is:

[0039]

[0040] In the formula, parameter M x M y M z The expression for M in terms of the coordinates of the three points is:

[0041]

[0042] M = v x [(y1-y2)(z1-z3)-(y1-y3)(z1-z2)]+v y [(x1-x3)(z1-z2)-(x1-x2)(z1-z3)]+vz [(x1-x2)(y1-y3)-(x1-x3)(y1-y2)]

[0043] The expression for parameter D in the formula is:

[0044]

[0045] Further, in step S4, the statistical distribution mean of the pose deviations of the component intersection holes and mating surfaces is obtained using the maximum likelihood estimation algorithm, specifically including:

[0046] Let M be the batches of measured sample data for the offset of a certain intersection hole position on the fuselage section, namely x1, x2, ... x M The N simulation sample data obtained by combining the Monte Carlo simulation algorithm with the assembly deviation accumulation and transfer model of the fuselage section in the previous processing and assembly process are y1, y2, ... y N Based on the two sets of data, the optimal estimate of the statistical distribution mean u is constructed using the maximum likelihood criterion and expressed as follows:

[0047]

[0048] The statistical distribution mean of the offset of the intersection hole position is estimated based on the above expression; the statistical distribution mean of the axial deviation and mating surface normal deviation of the intersection hole of the fuselage section is estimated using the same method.

[0049] Furthermore, in step S5, the specific process includes the following steps:

[0050] Suppose a component on an aircraft fuselage has m intersection holes and n mating surfaces that mate with another reference component. The coordinates of the center of the end faces of the m intersection holes in the initial pose of this component are p1, p2, ... p. m The direction vectors of the hole axis are s1, s2, ... s m The normal vectors of the n mating surfaces are n1, n2, ... n. n The center of the intersection hole end face on the corresponding reference component is p. t1 ,p t2 ,…p tm The direction vector of the hole axis is n t1 ,n t2 ,…n tn The normal vector of the mating surface is n t1 ,n t2 ,…n tn Using the overlap of these intersecting holes and the parallelism of the mating surface normal vector as a benchmark, the transformation relationship of the component from its initial pose to its optimal pose is calculated. This transformation relationship includes the rotation matrix R and the translation vector t, expressed as:

[0051]

[0052] In the formula, matrices U and V are obtained by performing singular value decomposition on matrix M, which is constructed from the coordinates of the center of the end face of the fuselage intersection hole, the hole axis, and the normal vector coordinates of the mating surface.

[0053]

[0054] By employing the above technical solution, the present invention provides a coordinated assembly method for large aircraft components that takes into account accumulated errors in previous manufacturing processes, which has at least the following beneficial effects:

[0055] (1) The present invention corrects the pose by considering the transmission law of manufacturing error in the preceding processing and assembly of components, and fully considers the important influence of the cumulative error of a single large component in the preceding component assembly stage on the key geometric elements of its mating area.

[0056] (2) This invention, by considering the impact of cumulative errors in the preceding manufacturing process on the fit elements of the long-span docking area of ​​large aircraft components, reveals the deviation distribution law of the fit elements of the docking area under the action of multiple error sources in the preceding manufacturing process. The optimal positioning attitude of the component is calculated based on the fit elements of the docking area with the mean deviation. Compared with the traditional assembly process that uses the feature points on the component far away from the docking area as the reference for positioning the component, it can effectively improve the coordination accuracy of the fit between multiple components in the docking area. Attached Figure Description

[0057] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0058] Figure 1 This is a schematic diagram of a coordinated assembly method for large aircraft components that takes into account the cumulative errors of previous manufacturing processes, according to the present invention.

[0059] Figure 2 This is a schematic diagram of the fuselage section in an embodiment of the present invention;

[0060] Figure 3 This is a schematic diagram showing the positioning of the bulkhead parts in the pre-assembly of the fuselage section in an embodiment of the present invention;

[0061] Figure 4 This is a schematic diagram of the process route for the fuselage section in the preliminary assembly process of an embodiment of the present invention;

[0062] Figure 5 Based on the machining tolerance of the connecting holes of the parts and the tolerance of the tooling positioning pin holes, combined with the assembly deviation cumulative transmission model and Monte Carlo simulation, the distribution of deviations in the center of the end face of multiple intersection holes and the direction of the hole axis on the mating surface of the fuselage section is obtained.

[0063] Figure 6 This is a schematic diagram showing how the normal vector of the wing-fuselage mating surface and the end face circle of the intersection hole are determined by the coordinates of three points in space.

[0064] Figure 7 This is a schematic diagram illustrating the statistical distribution mean of the deviation of the mating elements in the component docking area, which is estimated by integrating measured data points and Monte Carlo simulation data points in the sample space.

[0065] Figure 8 It is a comparison of the deviations of the component's mating elements relative to its theoretical pose after positioning the component using the component's feature points and the mating elements with the average deviation as references. Detailed Implementation

[0066] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0067] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0068] Please refer to Figures 1-8 This illustrates a specific implementation of the present embodiment. This embodiment considers the influence of multiple error sources in the preceding manufacturing process of large aircraft assembly components on the deviation of key geometric elements in the component mating area. It integrates simulation data of the deviation transmission mechanism model with measured sample data of multiple batches of components to reveal the law of the deviation distribution of component mating elements. The aircraft components are positioned based on the mating elements with the statistical mean of the deviation distribution, which greatly improves the coordination accuracy of multiple components in the mating area.

[0069] Please refer to Figure 1 This embodiment proposes a coordinated assembly method for large aircraft components that considers accumulated errors from previous manufacturing processes. The method includes the following steps:

[0070] S1. Establishment of the single-station assembly deviation model:

[0071] Based on the small rotation error model, establish the mapping relationship between the positioning pin hole axis pose error of the tooling fixture in a single station, the part pose error of the positioned reference part, the hole machining error of the reference part connecting to the non-reference part, and the connection hole error of the non-reference part connecting to the part of the next station, and establish the assembly deviation mapping model in a single station.

[0072] As a preferred embodiment of step S1, the specific process includes:

[0073] by Figure 2 Taking the assembly process of the preceding components of the fuselage section as an example, the mid-fuselage section mainly consists of transverse bulkheads and longitudinal stringers and webs. The fuselage bulkheads generally serve as the positioning reference for the webs and stringers. During assembly, they are typically positioned and supported using four locating pin holes on a tooling. Two of these locating pin holes provide positioning for the bulkheads, while the other two provide auxiliary support. The axial orientation of the two locating pin holes determines the spatial orientation of the bulkhead, which in turn affects the position and axial direction of the connection holes on the bulkheads to the stringers and webs. Their geometric relationships are as follows: Figure 3 As shown.

[0074] The following is established Figure 3 The mapping relationship between the axial orientation error of the locating pin hole and the machining error of the connecting hole of the intermediate tooling fixture and the position deviation and axial deviation of the connecting hole:

[0075] For the overall positioning error of the partition frame caused by tooling, i.e., the part pose error of the positioned reference part, under the assumption of small deviation, a six-dimensional screw quantity is used to characterize the pose error of the partition frame during the preceding assembly process. The screw quantity is composed of three translational parameters t = [u, v, w] along the coordinate axes. T And three rotation parameters about the coordinate axes r = [α, β, γ] T The resulting six-dimensional vector ξ = [r, t] T ,like Figure 3 As shown. For the center of the end face of a locating pin hole on the partition frame, p = [x, y, z] T And the direction vector of the hole axis through p, n = [a, b, c] T When the pose of the partition frame undergoes any minute change, the coordinates of the end face center p and the hole axis direction vector n after the change are p' = [x', y', z']. T and n' = [a', b', c'] T It can be represented as:

[0076]

[0077] The position of the center p of the locating pin hole end face and the direction vector n of the hole axis are combined into a six-dimensional vector ζ, which is used to calculate the pose error of the locating pin hole axis. By performing a simple transformation on the above formula, the mapping relationship between the deviation of vector ζ and the overall positioning error ξ of the partition frame can be obtained.

[0078]

[0079] In the formula, Δp and Δn are the positional error of the center of the mating end face of the locating pin hole and the direction vector error of the hole axis, respectively, and J represents the approximate linear mapping relationship between the two sets of deviations.

[0080] Next, we examine the relationship between the pose errors of the axial axes of multiple locating pin holes in the tooling fixture and the overall pose deviation of the partition frame. The pose errors of the locating pin holes in the tooling fixture can be characterized by the six-dimensional vector Δζ in the above formula, including the position error Δp ​​of the center of the locating pin hole end face and the direction vector error Δn of the hole axis, while the overall pose deviation of the partition frame corresponds to the overall positioning error ξ of the partition frame in the above formula. If the pose errors Δζ of the axial axes of m locating pin holes on the partition frame are known... i Let i = 1, 2, 4, ..., m. Then, to calculate the overall pose deviation ξ of the partition frame, i.e., the pose error of the positioned reference part, we can construct the following system of linear equations by augmenting the Jacobian matrix J row-wise:

[0081]

[0082] In the formula J i J is the Jacobian matrix corresponding to the i-th locating pin hole. A It is J i The augmented Jacobian matrix represents the pose error Δζ of the axes of all m locating pin holes. A The mapping relationship of the overall pose deviation ξ of the frame; based on the least squares optimization objective, through the augmented Jacobian matrix J A The generalized inverse form further represents the pose error Δζ of the m locating pin hole axes. A Mapping relationship to the overall pose deviation of the partition frame:

[0083]

[0084] Based on the positional error of the locating pin hole axis in the tooling fixture, the machining error of the connecting hole positions in the preceding mechanical parts of the partition frame is further integrated to establish a mapping relationship between the connecting hole position error, the locating pin hole axis position error, and the connecting hole machining error under a single station. Let p be a connecting hole position on the partition frame that mates with the stringer. i p caused by machining error of connecting hole i The initial position offset of the theoretical point in the relative numerical model is δ. i The initial axial deviation of the connecting hole is vi The positional error Δζ of the partition frame along the axes of the m positioning pin holes is then... A Under the influence of the non-reference part, the connection hole position error E between the non-reference part and the part at the next station is reduced. i Represented as:

[0085]

[0086] The above formula is the assembly deviation mapping model under a single workstation, where e pi e represents the position vector deviation of the connecting hole. ni This indicates the normal deviation of the connection hole position.

[0087] S2, Multi-station assembly deviation transmission model:

[0088] S2. Based on the assembly deviation mapping model established in step S1 under a single workstation, the connection hole position error transmission relationship of the assembly parts connection under multiple workstations is constructed based on the state space model. Then, the position and orientation error of the positioning pin hole axis of the tooling fixture and the hole position machining error of the part connection under each workstation are obtained to the position and orientation deviation transmission relationship of the intersection holes and mating surfaces of the aircraft large components. An assembly deviation cumulative transmission model of the aircraft large components in the previous processing and assembly process is established. The position and orientation deviation of the intersection holes includes position offset and axial deviation, and the position and orientation deviation of the mating surfaces includes normal deviation.

[0089] As a preferred embodiment of step S2, the specific process includes:

[0090] Based on the assembly deviation mapping model under a single workstation, the deviation transmission relationship between mating and connecting components under a multi-workstation model is further established. Similar to the assembly deviation modeling of a single workstation, considering that aircraft structural components are mainly assembled by riveting and bolting with hole-axis constraints, the assembly deviation of a multi-workstation model is still transmitted in the form of hole-to-hole position vector and normal deviation mapping, such as... Figure 4 As shown.

[0091] Suppose that the assembly part at the j-th station in a certain series branch uses the assembly part at the (j-1)-th station as the positioning reference, and they are connected through n connecting holes. The positional error of these connecting holes is denoted as E. 1j E 2j ,…E nj The positional error E of the i-th connecting hole of the (j+1)-th assembly on the j-th assembly is... i,j+1 for:

[0092]

[0093] In the formula δ i,j+1 and v i,j+1These are the positional offset and axial deviation of the i-th connection hole position relative to assembly j+1 caused by machining errors in the connection hole positions of assembly j; J i,j+1 J is the Jacobian matrix representing the mapping relationship between the part pose error of assembly j and the position error of the i-th connecting hole; A,j+1 This is the augmented Jacobian matrix composed of the n connection hole position errors of assembly j-1 and j to the pose error of assembly j. Thus, for an assembly connection relationship of p components connected in series from the inside out, the transmission relationship of the fuselage section from the initial bulkhead component's connection hole position machining error and the tooling fixture's positioning pin hole axis pose error to the pose deviation of the i-th wing-body intersection hole on the component is:

[0094]

[0095] In the formula E i,p+1 It is the positional deviation of the i-th intersection hole on the fuselage section after p+1 assembly processes, δ i,p+1 and v i,p+1 These are the offset of the intersection hole position and the axial deviation caused by the forming error of the i-th part (web plate) under the p+1-th process, respectively. The normal deviation of the mating surface of the large aircraft component is obtained by averaging the axial deviation of all the intersection holes on it, thereby completing the establishment of the assembly deviation accumulation and transmission model of the fuselage section in the previous processing and assembly process.

[0096] S3. Obtain a large number of samples of fit element deviations in the fuselage section docking area through Monte Carlo simulation:

[0097] Within the tolerance zone of tooling pin hole positioning and part connection hole machining at each workstation, a large amount of deviation source data is randomly generated using the Monte Carlo simulation algorithm. Using the assembly deviation accumulation and transmission model established in step S2, several simulation sample data of the positional deviations of the component intersection holes and mating surfaces are obtained. The distribution of the collected sample point intersection hole end face center deviation and hole axis direction deviation data is as follows: Figure 5 As shown.

[0098] S4. Estimate the mean values ​​of mating elements in the fuselage section docking area by integrating measured sample data and simulation samples:

[0099] Digital measurement equipment was used to collect the coordinates of multiple points in the docking area of ​​multiple batches of aircraft components. The positional deviation data of the component intersection holes and mating surfaces were calculated using the point coordinates. The calculated measured sample data was then fused with the simulation sample data obtained in step 3. The maximum likelihood estimation algorithm was used to obtain the statistical distribution mean of the positional deviation of the component intersection holes and mating surfaces.

[0100] As a preferred embodiment of step S4, the specific process of calculating the component fit element deviation data through point coordinates includes:

[0101] First, determine the direction vector of the hole axis and the coordinates of the center of the end face circle of the intersection hole based on the coordinates of three points on the circle. Let the coordinates of the three points collected on the circle of the end face of a certain intersection hole be p1(x1,y1,z1), p2(x2,y2,z2), and p3(x3,y3,z3), as follows: Figure 6 As shown, the direction vector of the hole axis is s(s x ,s y ,s z The analytical expression for the coordinates of these three points on the circle is:

[0102]

[0103] The expression for parameter C in the formula with respect to the coordinates of the three points is:

[0104]

[0105] End face center coordinates p c (x c ,y c ,z c The expression for the coordinates of the three points on the circle is:

[0106]

[0107] In the formula, parameter M x M y M z The expression for M in terms of the coordinates of the three points is:

[0108]

[0109] M = v x [(y1-y2)(z1-z3)-(y1-y3)(z1-z2)]+v y [(x1-x3)(z1-z2)-(x1-x2)(z1-z3)]+v z [(x1-x2)(y1-y3)-(x1-x3)(y1-y2)]

[0110] The expression for parameter D in the formula is:

[0111]

[0112] Calculate the axial deviation and end face center deviation of the intersection hole according to the above expressions, that is, the axial deviation and positional offset of the intersection hole.

[0113] Similar to the algorithm described above for determining the hole axis direction vector based on three points on the end face circle, the specific algorithm for determining the mating surface normal vector based on the coordinates of three points on the mating surface is as follows:

[0114] Let the coordinates of three points collected on the mating surface be q1(x1′,y1′,z1′), q2(x2′,y2′,z2′), and q3(x3′,y3′,z3′), then the normal vector n(n x ,n y ,n z )for:

[0115]

[0116] The expression for parameter C' in the formula is:

[0117]

[0118] Calculate the normal deviation of the mating surface based on the above expression.

[0119] As a preferred embodiment of step S4, obtaining the statistical distribution mean of the component fit element deviation using the maximum likelihood estimation algorithm specifically includes:

[0120] The coordinates of multiple points on the end face circles of the intersection holes and the mating surfaces of the wing-body components of multiple batches of fuselage sections are collected according to the above formula. The direction vector of the hole axis, the coordinates of the end face circle center, and the normal vector of the mating surface of the corresponding intersection holes of multiple batches of fuselage components are calculated. The simulation sample data obtained in step S3 are then fused to estimate the statistical distribution mean and variance of the hole axis pose and the mating surface normal vector of the intersection holes. The specific method is as follows:

[0121] Let M be the batches of measured sample data for the offset of a certain intersection hole position on the fuselage section, namely x1, x2, x3, x4, x5, x6, x7, x8, x9, x1, x1, x9, x1, x1, x2, x1, x1, x2, x3, x1, x1, x2, x3, x1, x1, x2, x3, x4, x1, x1, x2, x3 ... 2,… x M Their distribution in the sample space is as follows Figure 7 The red scatter dots shown represent N simulation sample data points obtained through Monte Carlo simulation combined with a multi-station assembly deviation transfer model for fuselage components, namely y1, y2, y3, y4, y5, y6, y7, y8, y9, y1, y1, y1, y2, y3, y4, y5, y6, y7, y8, y9, y1 ...1, y1, y1, y1, y1, y1, y1, y1, y1, y1, 2,… y N Their distribution in the sample space is as follows Figure 7 The green scatter plots are shown. Based on the two sets of data, according to the maximum likelihood criterion, the optimal estimates of the mean and variance of the distribution of the hole position offset at the intersection point, u and σ, should cause the likelihood functions corresponding to the two sets of sample data to reach their extreme values, i.e.:

[0122]

[0123] In the formula, L is a bivariate likelihood function with respect to the mean u and variance σ, constructed from simulated and measured sample data. By taking the logarithm of the likelihood function, the optimization model is transformed into:

[0124]

[0125] According to the necessary condition for extrema, let the partial derivatives of the logarithm of the likelihood function with respect to u and σ be zero:

[0126]

[0127] The optimal estimate of the statistical distribution mean of the offset of the hole at this intersection point can be obtained from the above formula:

[0128]

[0129] The statistical distribution mean of the offset of the intersection hole position is estimated based on the above expression; the statistical distribution mean of the axial deviation and mating surface normal deviation of the intersection hole of the fuselage section is estimated using the same method.

[0130] S5. Position the fuselage section based on the pose of the intersection hole with the average deviation and the normal vector of the mating surface:

[0131] Using the statistical distribution mean of the pose deviations of the component intersection holes and mating surfaces obtained in step 4, and taking the axis of the intersection hole, the center of the end face, and the normal vector of the mating surface with the statistical distribution mean of the deviation as the reference, the singular value decomposition algorithm is used to solve the transformation relationship of the component from the initial pose to the optimal pose, thereby improving the coordination between the components.

[0132] As a preferred embodiment of step S5, it specifically includes:

[0133] like Figure 2 As shown, the fuselage section has 6 intersection holes and 1 mating plane that mates with the wing, which serves as a reference. Let the coordinates of the center of the end face of the 6 intersection holes on the fuselage section in its initial pose be p1, p2, ..., p6, the direction vectors of the hole axes be s1, s2, ..., s6, and the normal vector of the mating surface be n; the center of the end face of the intersection hole on the corresponding reference component is p. t1 ,p t2 ,…p t6 The direction vector of the hole axis is n t1 ,n t2 ,…n t6 The normal vector of the mating surface is n t The least-squares optimization model for solving the motion of the component from its initial pose to its optimal pose, based on the overlap of these intersection holes and the parallelism of the mating surface normal, is as follows:

[0134]

[0135] In the formula, R and t represent the rotation matrix and translation vector of the fuselage section relative to its initial pose, respectively, in the global coordinate system. To solve this optimization model, the partial derivative of the objective function f with respect to the translation vector t is set to zero:

[0136]

[0137] Substituting the expression for the translation vector t into the expression for the objective function f yields a single-objective optimization model for the rotation matrix R:

[0138]

[0139] In the formula p' i and p' ti They are p i and p ti Decentralized coordinates:

[0140]

[0141] Further transformation of the objective function f(R) yields:

[0142]

[0143] In the formula, trace(·) represents the trace of the matrix, i.e., the sum of the diagonal elements; matrix M is a real symmetric matrix, so it can always be orthogonally diagonalized, i.e., there exist orthogonal matrices U and V and a diagonal matrix D such that:

[0144] M = UDV T

[0145] The method of solving for matrices U and V from matrix M is the singular value decomposition algorithm, a widely used and very mature standard method, which will not be elaborated here. Substituting the expression for M into the objective function above, the optimization model is finally transformed into:

[0146]

[0147] In the formula r ii and d ii These are orthogonal matrices V T RU and the diagonal elements of the diagonal matrix D. Clearly, when r... 11 =r 22 =r 33 =1, that is, V T When RU is the identity matrix, the above equation satisfies the maximization objective, and we have:

[0148] R = VU T

[0149] In summary, the expression for the transformation relationship of the fuselage segment from its initial pose to its optimal pose, i.e., the rotation matrix R and the translation vector t, is as follows:

[0150]

[0151] In the formula, matrices U and V are obtained by performing singular value decomposition on matrix M, which is constructed from the coordinates of the center of the end face of the fuselage intersection hole, the hole axis, and the normal vector of the mating surface.

[0152]

[0153] This application also provides a simulation verification method:

[0154] Using the assembly scenario of large components such as the fuselage section and wing of a certain type of aircraft as a verification example, the rotation matrix and translation vector of the components from the initial pose to the optimal pose are calculated based on the coordinates of feature points on the fuselage section in the digital model and the offset intersection holes and mating surfaces in the wing-fuselage mating area. The coordinates of the fuselage section intersection hole axis and mating surface normal vector under the initial pose are transformed according to the calculated two sets of rotation matrices and translation vectors. The angular and distance errors of the transformed fuselage intersection hole axis and mating surface normal vector relative to the intersection hole axis and mating surface normal vector on the wing are compared... Figure 8 As shown, compared to the traditional strategy of positioning components based on feature points far from the docking area, the strategy proposed in this invention, which uses the offset intersection holes and mating surfaces as references to change the attitude of the fuselage segments, can effectively improve the coordination accuracy of the mating of the wing-fuselage intersection holes and docking surfaces.

[0155] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0156] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0157] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for coordinated assembly of large aircraft components considering accumulated errors in preceding manufacturing processes, characterized in that, Includes the following steps: S1. Based on the small rotation error model, establish the mapping relationship between the positioning pin hole axis pose error of the tooling fixture in a single station, the part pose error of the positioned reference part, the hole machining error of the reference part connecting to the non-reference part, and the connection hole error of the non-reference part connecting to the part of the next station, and establish an assembly deviation mapping model in a single station; Step S1 specifically includes the following steps: S11. Based on the small rotation error model, define the mapping relationship between the pose error of a single positioning pin hole axis and the pose error of the positioning reference part: ； Where Δp and Δn represent the positional error of the center of the mating end face of the locating pin hole and the direction vector error of the hole axis, respectively; u, v, and w are the coordinates representing the positional error of the located part; α, β, and γ are the Euler angles representing the spatial attitude error of the located part; and J is the part pose error vector representing the reference part being located. Position error vector of the locating pin hole axis The Jacobian matrix of the mapping relationship; S12. Based on the mapping relationship obtained in S11, the mapping relationship between the pose errors of multiple positioning pin hole axes and the pose errors of the reference part being positioned is derived: ； In the formula J i J is the Jacobian matrix corresponding to the i-th locating pin hole. A It is J i The augmented Jacobian matrix characterizes the pose error of the axes of all m locating pin holes. The part pose error of the reference part being positioned The mapping relationship; S13. Based on the least squares optimization objective, by augmenting the Jacobian matrix J... A The generalized inverse form further represents the pose error of the m locating pin hole axes. Mapping relationship between the part pose error and the positioning reference part: ； S14. Based on the positional error of the locating pin hole axis, further integrate the machining error of the holes connecting the reference part and the non-reference part. Let a certain connecting hole on the reference part be... Caused by machining errors of the connecting holes The initial position offset of the theoretical point in the relative numerical model is: The initial axial deviation of the connecting hole is The positional error of the reference part along the axis of the m locating pin holes is... Under the influence of the reference part, the connection hole position error between the non-reference part connected to the reference part and the part connected to the next station is reduced. Represented as: ； The above formula is the assembly deviation mapping model under a single workstation, where e pi e represents the position vector deviation of the connecting hole position on a non-reference part. ni Indicates the normal deviation of the connection hole position; S2. Based on the assembly deviation mapping model established in step S1 under a single workstation, the connection hole position error transmission relationship of the assembly parts under multiple workstations is constructed based on the state space model. This allows for the acquisition of the position deviation transmission relationship between the positioning pin hole axis pose error of the tooling fixture and the hole position machining error of the part connection at each workstation and the position deviation transmission relationship between the intersection holes and mating surfaces of the aircraft's large components. This establishes an assembly deviation accumulation transmission model for the aircraft's large components during the preceding machining and assembly process. The position deviation of the intersection holes includes position offset and axial deviation, and the position deviation of the mating surfaces includes normal deviation. Step S2 specifically includes the following steps: S21. Suppose that the assembly part at the j-th station in a certain series branch takes the assembly part at the (j-1)-th station as the positioning reference, and they are connected through n connecting holes. The positional error of these connecting holes is denoted as E. 1j E 2j , …E nj The positional error E of the i-th connecting hole of the (j+1)-th assembly on the j-th assembly is... i, j+1 for: ， In the formula and These are the positional offset and axial deviation of the i-th connecting hole position of assembly j+1 caused by the machining error of the hole position of assembly j; J i, j+1 J is the Jacobian matrix representing the mapping relationship between the part pose error of assembly j and the position error of the i-th connecting hole; A, j+1 It is the augmented Jacobian matrix composed of the positional errors of the n connecting holes of assembly j-1 and j to the positional errors of the parts of assembly j; S22. For an assembly connection of p components connected in series from the inside out, the transmission relationship of the initial hole machining error and the axial pose error of the positioning pin hole of the tooling fixture to the pose deviation of the i-th intersection hole on the component is as follows: ， In the formula E i, p+1 It is the pose deviation vector of the i-th intersection hole on the large aircraft component after p+1 assembly processes. and These are the position offset and axial deviation of the i-th intersection hole caused by the machining forming error of the last part participating in the assembly in the p+1th process, respectively. The normal deviation of the mating surface of the large aircraft component is obtained by averaging the axial deviation of all the intersection holes on it, thereby completing the establishment of the assembly deviation accumulation and transmission model of the large components of the aircraft fuselage section in the previous machining and assembly process. S3. Within the tolerance zone of tooling pin hole positioning and part connection hole machining at each workstation, a large amount of deviation source data is randomly generated using the Monte Carlo simulation algorithm. Using the assembly deviation cumulative transmission model established in step S2, several simulation sample data of the positional deviation of the component intersection hole and mating surface are obtained. S4. Use digital measurement equipment to collect the coordinates of multiple points in the docking area of ​​multiple batches of aircraft components. Calculate the pose deviation data of the component intersection hole and mating surface through the point coordinates. Then, fuse the measured sample data obtained by the calculation with the simulation sample data obtained in step S3. Use the maximum likelihood estimation algorithm to obtain the statistical distribution mean of the pose deviation of the component intersection hole and mating surface. S5. Using the statistical distribution mean of the pose deviations of the component intersection holes and mating surfaces obtained in step S4, and taking the axis of the intersection hole with the deviation statistical distribution mean, the center of the end face, and the normal vector of the mating surface as the reference, the singular value decomposition algorithm is used to solve the transformation relationship of the component from the initial pose to the optimal pose, thereby improving the coordination between the components.

2. The method for coordinated assembly of large aircraft components considering cumulative errors in preceding manufacturing processes, as described in claim 1, is characterized in that: In step S4, the calculation of the pose deviation between the component intersection hole and the mating surface using point coordinates specifically includes the following steps: S41. Based on the coordinates of three points on the end face circle of a certain intersection hole, construct analytical expressions for the hole axis direction vector and the end face circle center coordinates of the intersection hole with respect to these three point coordinates, and then calculate the hole axis direction deviation and end face circle center deviation of the intersection hole, that is, the axial deviation and position offset of the intersection hole. S42. Based on the coordinates of the three points on the mating surface, construct an analytical expression for the normal vector of the mating surface with respect to these three coordinates, and then calculate the normal deviation of the mating surface. The calculation method for the normal vector of the mating surface is the same as that for calculating the direction vector of the hole axis in step S41.

3. The method for coordinated assembly of large aircraft components considering cumulative errors in preceding manufacturing processes, as described in claim 2, is characterized in that: In step S41, the analytical expressions for the hole axis direction vector and the end face center coordinates of the intersection hole with respect to these three point coordinates are constructed respectively. The specific process includes the following steps: S411. Suppose the coordinates of three points collected on the end face of a hole at a certain intersection are p1(x1, y1, z1), p2(x2, y2, z2), and p3(x3, y3, z3), then the direction vector of the hole axis s(s x , s y , s z The analytical expression for the coordinates of these three points on the circle is: ； The expression for parameter C in the formula with respect to the coordinates of the three points is: ； S412, coordinates of the center of the end face p c (x c , y c , z c The expression for the coordinates of the three points on the circle is: ； In the formula, parameter M x M y M z The expression for M in terms of the coordinates of the three points is: ； The expression for parameter D in the formula is: 。 4. The method for coordinated assembly of large aircraft components considering cumulative errors in preceding manufacturing processes, as described in claim 2, is characterized in that: In step S4, obtaining the statistical distribution mean of the pose deviations of the component intersection holes and mating surfaces using the maximum likelihood estimation algorithm specifically includes: Let M be the batches of measured sample data for the offset of a certain intersection hole position on the fuselage section, respectively, x1, x2, x3, x4, x5, x6, x7, x8, x9, x1, x9, x1, x1, x9, x1, x1, x2, x1, x1, x2, x3 ...3, x4, x1, x2, x3, x3, x4, x1, x2, x3, x4, x1, x2, x3, x4, x1, x2, x3, x4, x1, x2, x3, x4, x3, x4, x1, x2, x3, x4, x3, x4, x3, x4, x3, x4, x3, x4, x3, x4, x3, x4, x3, x4, x3, x4, x5, x1, x2, 2, … x M The N simulation sample data obtained by combining the Monte Carlo simulation algorithm with the assembly deviation accumulation and transfer model of the fuselage section in the previous processing and assembly process are y1, y2, y3, y4, y5, y6, y7, y8, y9, y1, y1, y1, y2, y3, y4, y5, y6, y7, y8, y9, y1, y1, y2, y1, y2, y3, y1, y2, y3, y4, y1, y2, y3, y4, y1, y2, y3, y4, y5, y6, y7, y8, y9, y1, y1, y2, y1, y2, y1, y2, y2, y1, y2, y2, y2, y3 ...2, y3, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2, y2 2, … y N Based on the two sets of data, the optimal estimate of the statistical distribution mean u is constructed using the maximum likelihood criterion and expressed as follows: ， The statistical distribution mean of the offset of the intersection hole position is estimated based on the above expression; the statistical distribution mean of the axial deviation and mating surface normal deviation of the intersection hole of the fuselage section is estimated using the same method.

5. The method for coordinated assembly of large aircraft components considering cumulative errors in preceding manufacturing processes, as described in claim 1, is characterized in that: Step S5 specifically includes: Suppose a component on an aircraft fuselage has m intersection holes and n mating surfaces that mate with another reference component. The coordinates of the center of the end faces of the m intersection holes in the initial pose of this component are p1, p2, ... p m The direction vectors of the hole axis are s1, s2, ... s m The normal vectors of the n mating surfaces are n1, n2, ... n. n The center of the intersection hole end face on the corresponding reference component is p. t1 , p t2 ,…p tm The direction vector of the hole axis is n t1 , n t2 ,…n tn The normal vector of the mating surface is n t1 , n t2 ,…n tn Using the overlap of these intersecting holes and the parallelism of the mating surface normal vector as a benchmark, the transformation relationship of the component from its initial pose to its optimal pose is calculated. This transformation relationship includes the rotation matrix R and the translation vector t, expressed as: ， In the formula, matrices U and V are obtained by performing singular value decomposition on matrix M, which is constructed from the coordinates of the center of the end face of the fuselage intersection hole, the hole axis, and the normal vector coordinates of the mating surface. 。

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