High-precision positioning method and system for compressor rotor assembly

Abstract

The invention discloses a high-precision positioning method and system for compressor rotor assembly, relates to the technical field of assembly positioning, and realizes comprehensive perception of invisible physical quantities such as temperature and stress by acquiring and preprocessing an instantaneous assembly data set Rds through a sensor array. A CAD physical simulation model is constructed, positioning deviation caused by the heat effect and the force effect is predicted, a prediction error vector set Epr is generated, and active prediction of errors is achieved. And performing nonlinear coupling calculation on the prediction error vector set Epr to generate a final compensation vector Vc, and calculating a compensation target point Pc after the amplitude of the final compensation vector Vc is evaluated to be feasible so as to ensure the physical authenticity and the performability of a compensation scheme. Simulation assembly is executed in a CAD physical simulation model, a final residual error f is utilized to carry out iterative optimization on a system prediction model, a physical trial and error process is transferred to a virtual space, the system is endowed with self-learning and self-adaptive capabilities, and long-term high-precision stability is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of assembly positioning, and in particular to a high-precision positioning method and system for compressor rotor assembly. Background Art

[0002] In the field of advanced manufacturing technology, precision assembly is one of the core links that determine the performance and reliability of high-end equipment. In particular, in the manufacturing process of high-performance rotating machinery such as aircraft engines, large gas turbines, and turbochargers for new energy vehicles, the assembly accuracy of their core components is directly related to the success or failure of the entire system. The heart of these machines is usually a rotor system that needs to operate stably at extremely high angular velocities. Therefore, during the assembly stage of the rotor parts, how to achieve high-precision relative position determination between the various components, that is, the core issue to be solved by "A high-precision positioning method and system for compressor rotor assembly", has become a key technical bottleneck to ensure the performance of the entire machine, improve operating efficiency and extend service life.

[0003] In the current rotor assembly process, traditional positioning methods have significant limitations. Most processes rely on high-precision but rigid physical fixtures. Although this method guarantees positioning accuracy to a certain extent, it lacks flexibility for different product models and has difficulty dealing with dynamic and hidden error sources during the assembly process. Specifically, existing technologies generally ignore the thermal deformation effects caused by small fluctuations in ambient temperature and heat conduction, and fail to effectively quantify and compensate for the force-induced deformation caused by the small torsional stress exerted on the parts by the clamping force during the clamping and fixing process. These errors, which exist in the real world but are difficult to measure and control using traditional methods, will directly lead to insufficient assembly positioning accuracy after assembly is completed. In addition, traditional assembly verification mostly relies on the trial assembly and subsequent testing of physical samples. This "assemble first, inspect later" model lacks process prediction and feedforward control. Once the assembly fails due to unreasonable parameters, it will result in the scrapping of expensive precision components and huge cost investment. Summary of the Invention

[0004] In view of the deficiencies in the prior art, the present invention provides a high-precision positioning method and system for compressor rotor assembly, which solves the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solutions: A high-precision positioning method for compressor rotor assembly, comprising the following steps:

[0006] S1, by setting up a sensor array in the assembly area, collecting the instantaneous raw data set Raw of the environment and component status and preprocessing it to obtain the instantaneous assembly data set Rds;

[0007] S2. Based on the instantaneous assembly dataset Rds, a CAD physical simulation model is constructed and an ideal target coordinate P is preset. The positioning deviation caused by thermal and force effects is calculated to generate a prediction error vector set Epr.

[0008] S3, based on the prediction error characteristic vector Epr, nonlinear coupling calculation is performed to calculate the mechanical and thermal coupling displacement deviation vector C TF And generate the final compensation vector Vc;

[0009] S4. Evaluate the compensation amplitude based on the final compensation vector Vc and generate a compensation amplitude evaluation result QA. If the compensation amplitude evaluation result QA is false, suspend the compensation calculation and request manual intervention. If the compensation amplitude evaluation result QA is true, calculate the compensation target point Pc after compensation.

[0010] S5. Perform simulated assembly of compensation positioning based on the compensation target point Pc, measure the actual final position Pa of the part in the CAD physical simulation model, compare it with the ideal target coordinate P, calculate the final residual error f, and use the final residual error f for iterative optimization.

[0011] Preferably, S1 includes S11;

[0012] S11. Before the assembly action begins, an advanced sensor array installed in the assembly area takes an instantaneous "physical snapshot" of the assembly unit to collect the instantaneous raw data set Raw of the environment and component status;

[0013] The instantaneous raw data set, Raw, includes the three-dimensional laser point cloud data P of the assembly environment and rotor collected by a laser three-dimensional coordinate measuring machine; the original part path thermal gradient vector ▽RT measured by a non-contact infrared thermal imaging array, reflecting the uneven temperature distribution inside the part; the clamping torsional strain scalar γc measured by a fiber Bragg grating sensor embedded in the inner wall of the flexible clamp, representing the degree of slight distortion caused by the clamping force; and the material anisotropy tensor km retrieved from the part database based on the read part RFID information, describing the differences in the material's mechanical and thermal properties in different directions.

[0014] The thermal imaging array sensor coordinate system of the original part path thermal gradient vector ▽RT in the instantaneous raw data set Raw is aligned with the Cartesian coordinate system of the machine tool, and the noise is filtered out by combining with a Gaussian filter to obtain the part path thermal gradient vector ▽T and generate the preprocessed instantaneous assembly data set Rds.

[0015] Preferably, S2 includes S21 and S22;

[0016] S21. Import the 3D laser point cloud data P in the instantaneous assembly dataset Rds into CAD software, generate a CAD physical simulation model, and preset an ideal target coordinate P=[x, y, z], where x represents the preset ideal target coordinate of the rotor on the X-axis, y represents the preset ideal target coordinate of the rotor on the Y-axis, and z represents the preset ideal target coordinate of the rotor on the Z-axis;

[0017] In the CAD physical simulation model, a thermally induced displacement deviation effect algorithm is constructed based on the part path thermal gradient vector ▽T and the material anisotropy tensor km in the instantaneous assembly dataset Rds. The accumulated thermal deformation is calculated by integrating along the part path. The exponential function exp is used to simulate the physically realistic nonlinear relationship between temperature gradient and expansion, completing the vectorization of the nonlinear expansion effect. By multiplying it with the material anisotropy tensor km and the preset system thermal response transfer matrix MT, the directional differences in the material and the response characteristics of the entire machine tool structure are incorporated into the calculation. The thermally induced displacement deviation vector △PT in the machine tool coordinate system is obtained, representing the predicted displacement values ​​of the X, Y, and Z axes caused by the thermal effect.

[0018] The algorithm expression of thermally induced displacement deviation effect is as follows:

[0019] ;

[0020] Where MT represents the preset system thermal response transfer matrix, that is, the response characteristics of the mechanical system to heat input, ∫ represents the integral operation, α represents the principal thermal expansion coefficient of the material in the part database, L represents the virtual path predefined in the CAD physical simulation model, that is, the path of heat transfer along the part, and |▽T| represents the modulo operation on the thermal gradient vector ▽T of the part path.

[0021] Preferably, S22, based on the clamping torsional strain scalar γc in the instantaneous assembly data set Rds, a force-induced displacement deviation effect algorithm is constructed, by decomposing a tiny clamping torsional strain scalar γc into coupled displacements in three-dimensional space, and expressing the physical effects in different directions in a column vector respectively, the axial displacement is modeled as a term proportional to the square of the clamping torsional strain scalar γc, and the lateral displacement is modeled as a geometric effect caused by the part geometry and torsion angle, and accurately described by trigonometric functions and the part database, and the deformation vector calculated in the local coordinate system of the part is multiplied by the preset system force response transfer matrix MF to obtain the force-induced displacement deviation vector △PF in the global coordinate system of the machine tool, which represents the predicted value of the X, Y, and Z axis displacement caused by the clamping force;

[0022] The algorithm expression of force-induced displacement deviation effect is as follows:

[0023] ;

[0024] Where MF represents the preset system force response transfer matrix, that is, the response characteristics of the mechanical system to the clamping force, μ represents the Poisson's ratio of the material in the part database, G represents the shear modulus of the material in the part database, R represents the characteristic radius of the part in the part database, sin represents the sine function, and cos represents the cosine function;

[0025] According to the thermally induced displacement deviation vector △PT and the force-induced displacement deviation vector △PF, a prediction error vector set Epr is generated.

[0026] Preferably, S3 includes S31;

[0027] S31. Based on the prediction error vector set Epr, a mechanical-thermal coupling displacement deviation effect algorithm is constructed. Through the outer product of the thermal-induced displacement deviation vector △PT and the force-induced displacement deviation vector △PF, the interaction relationship tensor between the thermal effect and the force effect is constructed to describe the interaction strength and direction of the two deformation sources. Then, the mechanical-thermal coupling displacement deviation vector C is calculated by combining it with the preset system thermal response transfer matrix MT and the force-induced displacement deviation vector △PF. TF , which represents the high-order error caused by the interaction of thermal and force effects;

[0028] The algorithm expression of the mechanical and thermal coupling displacement deviation effect is as follows:

[0029] ;

[0030] Where, β represents the preset coupling effect factor, △PF T represents the transposed vector of the force-induced displacement deviation vector △PF;

[0031] Based on the thermal displacement deviation vector △PT, the force-induced displacement deviation vector △PF and the force-heat coupling displacement deviation vector C TF The vector sum between them is used to calculate the final compensation vector Vc;

[0032] The final compensation vector Vc is calculated as follows:

[0033] ;

[0034] Where Vc represents the final compensation vector that needs to be executed to achieve the ideal target coordinate P, which is calculated based on the comprehensive prediction of the error sources.

[0035] Preferably, S4 includes S41 and S42;

[0036] S41. Based on the final compensation vector Vc, the Euclidean norm of the compensation vector Vc is calculated to simplify the complex three-dimensional compensation instruction into a single scalar value that can represent the total difficulty of compensation, and the norm of the compensation vector ||Vc|| is obtained;

[0037] The calculation formula for the norm of the compensation vector ||Vc|| is as follows:

[0038] ;

[0039] Where Vcx, Vcy, and Vcz represent the components of the final compensation vector Vc on the X, Y, and Z axes, respectively;

[0040] If the norm of the compensation vector ||Vc||> the preset maximum compensable threshold δmax, the compensation amount is determined to be beyond the compensable range, and the compensation amplitude assessment result QA is false. The compensation instruction is suspended and a warning is issued. Manual intervention is requested to check the assembly environment. If the sensor has detection deviation, the sensor is recalibrated. If the sensor does not have detection deviation, professionals in this field adjust the temperature and clamping force of the assembly environment.

[0041] If the norm of the compensation vector ||Vc|| ≤ the preset maximum compensable threshold δmax, the compensation is determined to be feasible, the compensation amplitude evaluation result QA is true, and the compensation instruction can continue to be executed.

[0042] Preferably, S42, based on the compensation amplitude evaluation result QA being true, the manipulator is directed to aim at a deliberately offset compensation target point Pc according to the ideal target coordinates P and the final compensation vector Vc, wherein the offset direction of the compensation target point Pc is opposite to the direction of the final compensation vector Vc and the magnitude is equal, and the compensation target point Pc is calculated by subtracting the final compensation vector Vc from the ideal target coordinates P;

[0043] Among them, the calculation formula of the compensation target point Pc is as follows:

[0044] ;

[0045] The compensation target point Pc is input into the CAD physical simulation model as the final target coordinate.

[0046] Preferably, S5 includes S51 and S52;

[0047] S51. Performing simulated assembly of compensation positioning in the CAD physical simulation model based on the compensation target point Pc. Performing simulated collision detection during the simulated assembly process to implement feasibility testing of the assembly path. After the simulated assembly is completed, performing physical property simulation to simulate the offset position of the part and the assembly environment after cooling, and measuring the actual final position Pa of the part in the CAD physical simulation model.

[0048] Based on the actual final position Pa of the part measured in the CAD physical simulation model, the vector difference with the ideal target coordinate P is calculated to calculate the final residual error f;

[0049] Among them, the final residual error f is calculated as follows:

[0050] ;

[0051] Where f represents the error remaining after this compensation, which serves as the basis for evaluating the performance of a single compensation.

[0052] If the final residual error f≤the preset residual error threshold fth, the error is considered to be within an acceptable range and no iterative optimization is required.

[0053] If the final residual error f> the preset residual error threshold fth, it is determined that the error is beyond the acceptable range and iterative optimization is required.

[0054] Preferably, in S52, when the error exceeds the acceptable range, based on the final residual error f, a system response transfer matrix optimization algorithm is constructed for the preset system thermal response transfer matrix MT and the system force response transfer matrix MF in combination with the gradient descent idea, and a correction matrix is ​​obtained by calculating the outer product of the final residual error f and the prediction error vector set Epr. At the same time, the correction matrix is ​​normalized by using the square of the modulus of the prediction error vector set Epr, and multiplied by the preset interest rate η to obtain a specific correction term, and the step size of each optimization is controlled. The correction term is subtracted from the original preset system response transfer matrix to obtain a new system response transfer matrix;

[0055] Among them, the system response transfer matrix optimization algorithm expression is as follows:

[0056] ;

[0057] ;

[0058] Where MT' represents the system thermal response transfer matrix after iterative optimization, MF' represents the system force response transfer matrix after iterative optimization, ηT represents the learning rate of the preset system thermal response transfer matrix MT, ηF represents the learning rate of the preset system force response transfer matrix MF, △PT T The transposed vector of the thermally induced displacement deviation vector △PT, △PF T represents the transposed vector of the force-induced displacement deviation vector △PF, || 2 Indicates the square operation of the vector modulus, and λ represents the regularization term to prevent the denominator from being zero, specifically 1*10 -8 ;

[0059] The iteratively optimized system thermal response transfer matrix MT' and the iteratively optimized system force response transfer matrix MF' are written into the system preset parameters, overwriting the original system thermal response transfer matrix MT and the system force response transfer matrix MF.

[0060] A high-precision positioning system for compressor rotor assembly, comprising an assembly data acquisition module, an error prediction module, an error compensation module, a compensation point evaluation and calculation module, and a simulation assembly and iterative optimization module;

[0061] The assembly data acquisition module sets up a sensor array in the assembly area to collect the instantaneous raw data set Raw of the environment and component status and preprocesses it to obtain the instantaneous assembly data set Rds;

[0062] The error prediction module builds a CAD physical simulation model based on the instantaneous assembly data set Rds and presets an ideal target coordinate P, calculates the positioning deviation caused by thermal and force effects, and generates a prediction error vector set Epr;

[0063] The error compensation module calculates the mechanical and thermal coupling displacement deviation vector C by performing nonlinear coupling calculation based on the predicted error eigenvector Epr TF And generate the final compensation vector Vc;

[0064] The compensation point evaluation calculation module evaluates the compensation amplitude based on the final compensation vector Vc and generates a compensation amplitude evaluation result QA. When the compensation amplitude evaluation result QA is false, the compensation calculation is suspended and manual intervention is requested. When the compensation amplitude evaluation result QA is true, the compensation target point Pc after compensation is calculated.

[0065] The simulation assembly and iterative optimization module performs simulated assembly of compensation positioning based on the compensation target point Pc, measures the actual final position Pa of the part in the CAD physical simulation model, compares it with the ideal target coordinate P, calculates the final residual error f, and uses the final residual error f for iterative optimization.

[0066] The present invention provides a high-precision positioning method and system for compressor rotor assembly, which has the following beneficial effects:

[0067] (1) Through the sensor array, the thermal gradient, clamping strain and other previously ignored physical states of the assembly unit are fully perceived. On this basis, the system uses a built-in advanced algorithm that couples multiple physical field effects to accurately quantify the key error sources of thermal and force effects. These prediction errors are further nonlinearly coupled and calculated, and after a rigorous safety assessment, a feedforward, high-precision compensation instruction is generated. This series of core prediction and compensation links is mainly carried out in the CAD physical simulation model, thereby ensuring extremely high accuracy while avoiding the huge cost of physical trial and error. Ultimately, the present invention achieves assembly accuracy far exceeding that of traditional processes, significantly improving the performance, reliability and service life of compressor products.

[0068] (2) The sensor array takes an instantaneous physical snapshot of the assembly unit, comprehensively collects and pre-processes the instantaneous raw data set including three-dimensional point cloud, thermal gradient and clamping strain. This overcomes the blind spot of traditional methods in perceiving "invisible" error sources such as temperature change and clamping stress, and provides an unprecedented, high-fidelity data foundation for accurate analysis. Then, a CAD physical simulation model is constructed based on the instantaneous raw data set. Using physical algorithms, the thermal displacement deviation vector △PT caused by thermal effect and the force displacement deviation vector △PF caused by force effect are quantitatively calculated. This process transforms the core contradiction of assembly from "passive detection error" to "active prediction error", accurately predicting potential positioning deviation before physical action occurs, thereby fundamentally solving the problems of high cost, low efficiency and high risk brought about by traditional processes relying on physical trial and error.

[0069] (3) By constructing a nonlinear mechanical and thermal coupling model algorithm, a final compensation vector Vc that is closer to physical reality is generated. Before the instruction is generated, the amplitude of the compensation vector is evaluated to see if it exceeds the preset maximum compensable threshold δmax, thereby establishing a key safety barrier for physical execution. By completing simulated assembly and error verification in a virtual environment, zero-risk and zero-cost process iteration is achieved. It uses the final residual error f to iteratively optimize the internal physical response model through the gradient descent idea, which gives the system the self-learning ability of "getting more accurate with use". This ability ensures that the system can continue to learn and improve itself, continuously improve the accuracy of monitoring and the intelligence of decision-making, and ensure that its ultra-high precision is a dynamic performance of sustainable evolution. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 This is a schematic diagram of the steps of a high-precision positioning method for assembling a compressor rotor according to the present invention;

[0071] Figure 2 This is a schematic block diagram of a high-precision positioning system for compressor rotor assembly according to the present invention;

[0072] Figure 3 The data processing flow chart is shown in Figure 2. DETAILED DESCRIPTION

[0073] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0074] Example 1

[0075] The present invention provides a high-precision positioning method for compressor rotor assembly. Figure 1 , including the following steps:

[0076] S1, by setting up a sensor array in the assembly area, collecting the instantaneous raw data set Raw of the environment and component status and preprocessing it to obtain the instantaneous assembly data set Rds;

[0077] S2. Based on the instantaneous assembly dataset Rds, a CAD physical simulation model is constructed and an ideal target coordinate P is preset. The positioning deviation caused by thermal and force effects is calculated to generate a prediction error vector set Epr.

[0078] S3, based on the prediction error characteristic vector Epr, nonlinear coupling calculation is performed to calculate the mechanical and thermal coupling displacement deviation vector C TF And generate the final compensation vector Vc;

[0079] S4. Evaluate the compensation amplitude based on the final compensation vector Vc and generate a compensation amplitude evaluation result QA. If the compensation amplitude evaluation result QA is false, suspend the compensation calculation and request manual intervention. If the compensation amplitude evaluation result QA is true, calculate the compensation target point Pc after compensation.

[0080] S5. Perform simulated assembly of compensation positioning based on the compensation target point Pc, measure the actual final position Pa of the part in the CAD physical simulation model, compare it with the ideal target coordinate P, calculate the final residual error f, and use the final residual error f for iterative optimization.

[0081] In this embodiment, by setting up a sensor array in the assembly area and collecting the instantaneous raw data set Raw containing thermal gradient and strain information, the subtle deformation errors caused by the dynamic thermal and force effects in the traditional process are converted into a set of predicted error vectors Epr that can be quantified and analyzed, thus making up for the defect that traditional fixtures cannot deal with hidden error sources. Secondly, based on the predicted error vector set Epr, the force-heat coupling displacement deviation vector C is calculated. TFThe final compensation vector Vc is generated, and the compensation amplitude is evaluated based on the final compensation vector Vc and the compensation amplitude evaluation result QA is generated. After evaluating its feasibility, the compensation target point Pc is calculated to ensure the physical authenticity and feasibility of the compensation scheme. Then, the entire process until the actual final position Pa is measured through simulated assembly is completed in the CAD physical simulation model, which changes the traditional high-cost model of "physical trial assembly first, then inspection". The trial-and-error risk that may cause expensive parts to be scrapped is completely transferred to the zero-cost virtual space, realizing feedforward error prediction and correction. Finally, by iteratively optimizing the system using the final residual error f, an intelligent self-learning closed loop is established to ensure that the system accuracy will not degrade due to long-term use, but can continue to self-improve. This is essentially different from traditional fixed physical tooling and fundamentally guarantees the long-term stability and reliability of high-precision positioning.

[0082] Example 2

[0083] This embodiment is explained in Example 1, please refer to Figure 1 and Figure 3 , specifically: S1 includes S11;

[0084] S11. Before the assembly action begins, the system uses the advanced sensor array set up in the assembly area to take an instantaneous "physical snapshot" of the assembly unit and collect the instantaneous raw data set Raw of the environment and component status;

[0085] The instantaneous raw data set, Raw, includes the three-dimensional laser point cloud data P of the assembly environment and rotor collected by a laser three-dimensional coordinate measuring machine; the original part path thermal gradient vector ▽RT measured by a non-contact infrared thermal imaging array, reflecting the uneven temperature distribution inside the part; the clamping torsional strain scalar γc measured by a fiber Bragg grating sensor embedded in the inner wall of the flexible clamp, representing the degree of slight distortion caused by the clamping force; and the material anisotropy tensor km retrieved from the part database based on the read part RFID information, describing the differences in the material's mechanical and thermal properties in different directions.

[0086] The thermal imaging array sensor coordinate system of the original part path thermal gradient vector ▽RT in the instantaneous raw data set Raw is aligned with the Cartesian coordinate system of the machine tool. A Gaussian filter is used to remove noise to obtain the part path thermal gradient vector ▽T and generate the preprocessed instantaneous assembly data set Rds.

[0087] S2 includes S21 and S22;

[0088] S21. Import the 3D laser point cloud data P in the instantaneous assembly dataset Rds into CAD software, generate a CAD physical simulation model, and preset an ideal target coordinate P=[x, y, z], where x represents the preset ideal target coordinate of the rotor on the X-axis, y represents the preset ideal target coordinate of the rotor on the Y-axis, and z represents the preset ideal target coordinate of the rotor on the Z-axis;

[0089] In the CAD physical simulation model, a thermally induced displacement deviation effect algorithm is constructed based on the part path thermal gradient vector ▽T and the material anisotropy tensor km in the instantaneous assembly dataset Rds. The accumulated thermal deformation is calculated by integrating along the part path. The exponential function exp is used to simulate the physically realistic nonlinear relationship between temperature gradient and expansion, completing the vectorization of the nonlinear expansion effect. By multiplying it with the material anisotropy tensor km and the preset system thermal response transfer matrix MT, the directional differences in the material and the response characteristics of the entire machine tool structure are incorporated into the calculation. The thermally induced displacement deviation vector △PT in the machine tool coordinate system is obtained, representing the predicted displacement values ​​of the X, Y, and Z axes caused by the thermal effect.

[0090] The algorithm expression of thermally induced displacement deviation effect is as follows:

[0091] ;

[0092] Where MT represents the preset system thermal response transfer matrix, that is, the response characteristics of the mechanical system to heat input, ∫ represents the integral operation, α represents the principal thermal expansion coefficient of the material in the part database, L represents the virtual path predefined in the CAD physical simulation model, that is, the path of heat transfer along the part, and |▽T| represents the modulo operation of the thermal gradient vector ▽T of the part path;

[0093] S22. Based on the clamping torsional strain scalar γc in the instantaneous assembly data set Rds, a force-induced displacement deviation effect algorithm is constructed. By decomposing a tiny clamping torsional strain scalar γc into coupled displacements in three-dimensional space, the physical effects in different directions are expressed in a column vector. The axial displacement is modeled as a term proportional to the square of the clamping torsional strain scalar γc, and the lateral displacement is modeled as a geometric effect caused by the part geometry and torsion angle. These are accurately described using trigonometric functions and the part database. The deformation vector calculated in the part's local coordinate system is multiplied by the preset system force response transfer matrix MF to obtain the force-induced displacement deviation vector △PF in the machine tool's global coordinate system, which represents the predicted displacement values ​​of the X, Y, and Z axes caused by the clamping force.

[0094] The algorithm expression of force-induced displacement deviation effect is as follows:

[0095] ;

[0096] Where MF represents the preset system force response transfer matrix, that is, the response characteristics of the mechanical system to the clamping force, μ represents the Poisson's ratio of the material in the part database, G represents the shear modulus of the material in the part database, R represents the characteristic radius of the part in the part database, sin represents the sine function, and cos represents the cosine function;

[0097] According to the thermally induced displacement deviation vector △PT and the force-induced displacement deviation vector △PF, a prediction error vector set Epr is generated.

[0098] In this embodiment, a sensor array actively collects a multimodal instantaneous raw dataset (Raw) consisting of three-dimensional laser point cloud data P, the original part path thermal gradient vector ▽RT, the clamping torsional strain scalar γc, and the material anisotropy tensor km. The original part path thermal gradient vector ▽RT is then preprocessed through coordinate alignment and Gaussian filtering to obtain the instantaneous assembly dataset Rds. This overcomes the limitations of traditional methods that rely solely on geometric dimensions, achieving high-fidelity characterization of invisible physical states such as thermal and stress fields, and providing a distortion-free data source for subsequent accurate predictions. When calculating and predicting the thermally induced displacement deviation vector △PT, a nonlinear integration algorithm containing an exponential function is used to simulate the heat accumulation and nonlinear expansion effects. The material anisotropy tensor km and the preset system thermal response transfer matrix MT are then combined for matrix transformation to obtain the thermally induced displacement deviation vector △PT in the machine tool coordinate system, thereby quantifying the complex influence of material directionality and thermal effects. When calculating the predicted force-induced displacement error vector △PF, a coupled mechanical model is used to decompose the single clamping torsional strain scalar γc in three-dimensional space into axial displacement related to strain energy and lateral displacement related to geometric torsion. This is then corrected by the Poisson's ratio μ of the part material. Ultimately, this is transformed using the preset system force response transfer matrix MF to obtain the force-induced displacement error vector △PF in the machine tool's global coordinate system, thereby quantifying the complex influence of material properties and force effects. This modeling and quantification approach, based on deep physical mechanisms, ensures the accuracy and physical authenticity of the generated prediction error vector set Epr.

[0099] Example 3

[0100] This embodiment is explained in Example 2, please refer to Figure 1 and Figure 3 , specifically: S3 includes S31;

[0101] S31. Based on the prediction error vector set Epr, a mechanical-thermal coupling displacement deviation effect algorithm is constructed. Through the outer product of the thermal-induced displacement deviation vector △PT and the force-induced displacement deviation vector △PF, the interaction relationship tensor between the thermal effect and the force effect is constructed to describe the interaction strength and direction of the two deformation sources. Then, the mechanical-thermal coupling displacement deviation vector C is calculated by combining it with the preset system thermal response transfer matrix MT and the force-induced displacement deviation vector △PF. TF , which represents the high-order error caused by the interaction of thermal and force effects;

[0102] The algorithm expression of the mechanical and thermal coupling displacement deviation effect is as follows:

[0103] ;

[0104] Where, β represents the preset coupling effect factor, △PF T represents the transposed vector of the force-induced displacement deviation vector △PF;

[0105] Based on the thermal displacement deviation vector △PT, the force-induced displacement deviation vector △PF and the force-heat coupling displacement deviation vector C TF The vector sum between them is used to calculate the final compensation vector Vc;

[0106] The final compensation vector Vc is calculated as follows:

[0107] ;

[0108] Where Vc represents the final compensation vector that needs to be executed to achieve the ideal target coordinate P, which is calculated based on the comprehensive prediction of the error source;

[0109] The specific example of the final compensation vector Vc is as follows:

[0110] System thermal response transfer matrix MT: ;

[0111] Thermally induced displacement deviation vector △PT: mm, force-induced displacement deviation vector △PF: mm;

[0112] Coupling effect influence factor β: 0.001;

[0113] Mechanical and thermal coupling displacement deviation vector C TF The calculation is as follows:

[0114] ;

[0115] mm;

[0116] The final compensation vector Vc is calculated as follows:

[0117] mm;

[0118] S4 includes S41 and S42;

[0119] S41. Based on the final compensation vector Vc, the Euclidean norm of the compensation vector Vc is calculated to simplify the complex three-dimensional compensation instruction into a single scalar value that can represent the total difficulty of compensation, and the norm of the compensation vector ||Vc|| is obtained;

[0120] The calculation formula for the norm of the compensation vector ||Vc|| is as follows:

[0121] ;

[0122] Where Vcx, Vcy, and Vcz represent the components of the final compensation vector Vc on the X, Y, and Z axes, respectively;

[0123] If the norm of the compensation vector ||Vc||> the preset maximum compensable threshold δmax, the compensation amount is determined to be beyond the compensable range, and the compensation amplitude assessment result QA is false. The compensation instruction is suspended and a warning is issued. Manual intervention is requested to check the assembly environment. If the sensor has detection deviation, the sensor is recalibrated. If the sensor does not have detection deviation, professionals in this field adjust the temperature and clamping force of the assembly environment.

[0124] If the norm of the compensation vector ||Vc|| is less than or equal to the preset maximum compensable threshold δmax, the compensation is deemed feasible, the compensation amplitude evaluation result QA is true, and the compensation instruction can be executed.

[0125] S42. Based on the compensation amplitude evaluation result QA being true, the manipulator is directed to aim at a deliberately offset compensation target point Pc according to the ideal target coordinates P and the final compensation vector Vc. The offset direction of the compensation target point Pc is opposite to the direction of the final compensation vector Vc and the same in magnitude. The compensation target point Pc is calculated by subtracting the final compensation vector Vc from the ideal target coordinates P.

[0126] Among them, the calculation formula of the compensation target point Pc is as follows:

[0127] ;

[0128] The compensation target point Pc is input into the CAD physical simulation model as the final target coordinate.

[0129] In this embodiment, an interaction tensor is constructed by calculating the mathematical outer product of the thermally induced displacement deviation vector △PT and the force-induced displacement deviation vector △PF. The technical significance of this tensor is that the correlation between the two error vectors in each axis is quantified. In the precision mechanical assembly scenario of metal materials, the influence of temperature on mechanical properties such as material stiffness and yield strength is generally considered to be more significant and common than the influence of mechanical stress on the thermal expansion coefficient of the material. Therefore, the thermal effect is used as a modulator of the force effect. Based on this, combined with the system thermal response transfer matrix MT, the force-induced displacement deviation vector △PF is transformed to calculate the force-thermal coupling displacement deviation vector CTF that can characterize the complex physical phenomenon of the mechanical response of the system changing due to the thermal state. Finally, by vector summing the main effect with this high-order coupling term, the final compensation vector Vc obtained can cope with complex working conditions where the traditional model cannot handle and the physical fields are intertwined. Its operational safety is reflected in a rigorous decision-making process based on the idea of ​​feedforward control. Before generating a command, the system first calculates the Euclidean norm of the compensation vector, ||Vc||, simplifying a complex three-dimensional vector into a single scalar representing the compensation difficulty. This scalar is then compared to the maximum compensable threshold δmax, representing the physical limits of the system, to generate a compensation magnitude assessment result, QA. This process, essentially a constraint check within the control system, ensures that the compensation command remains within the equipment's safe operating envelope and is key to the system's operational self-checking and self-protection capabilities. Only when this assessment is true is the feedforward compensation calculation performed to generate the final compensation target point, Pc. This Pc is then input as the final target coordinate into the CAD physical simulation model, awaiting simulated assembly.

[0130] Example 4

[0131] This embodiment is explained in Example 3, please refer to Figure 1 and Figure 3 ,Specifically: S5 includes S51 and S52;

[0132] S51. Performing simulated assembly of compensation positioning in the CAD physical simulation model based on the compensation target point Pc. Performing simulated collision detection during the simulated assembly process to implement feasibility testing of the assembly path. After the simulated assembly is completed, performing physical property simulation to simulate the offset position of the part and the assembly environment after cooling, and measuring the actual final position Pa of the part in the CAD physical simulation model.

[0133] Based on the actual final position Pa of the part measured in the CAD physical simulation model, the vector difference with the ideal target coordinate P is calculated to calculate the final residual error f;

[0134] Among them, the final residual error f is calculated as follows:

[0135] ;

[0136] Where f represents the error remaining after this compensation, which serves as the basis for evaluating the performance of a single compensation.

[0137] If the final residual error f≤the preset residual error threshold fth, the error is considered to be within an acceptable range and no iterative optimization is required.

[0138] If the final residual error f> the preset residual error threshold fth, it is determined that the error is beyond the acceptable range and iterative optimization is required;

[0139] S52. When the error exceeds the acceptable range, a system response transfer matrix optimization algorithm is constructed based on the final residual error f and the gradient descent idea for the preset system thermal response transfer matrix MT and the system force response transfer matrix MF. A correction matrix is ​​obtained by calculating the outer product of the final residual error f and the set of prediction error vectors Epr. The correction matrix is ​​normalized by the square of the modulus of the set of prediction error vectors Epr and multiplied by the preset interest rate η to obtain a specific correction term. The step size of each optimization is controlled, and the correction term is subtracted from the original preset system response transfer matrix to obtain a new system response transfer matrix.

[0140] Among them, the system response transfer matrix optimization algorithm expression is as follows:

[0141] ;

[0142] ;

[0143] Where MT' represents the system thermal response transfer matrix after iterative optimization, MF' represents the system force response transfer matrix after iterative optimization, ηT represents the learning rate of the preset system thermal response transfer matrix MT, ηF represents the learning rate of the preset system force response transfer matrix MF, △PT T The transposed vector of the thermally induced displacement deviation vector △PT, △PF T represents the transposed vector of the force-induced displacement deviation vector △PF, || 2 Indicates the square operation of the vector modulus, and λ represents the regularization term to prevent the denominator from being zero, specifically 1*10 -8 ;

[0144] The iteratively optimized system thermal response transfer matrix MT' and the iteratively optimized system force response transfer matrix MF' are written into the system preset parameters, overwriting the original system thermal response transfer matrix MT and the system force response transfer matrix MF.

[0145] In this embodiment, a completely virtualized verification closed loop is constructed by completing the final assembly simulation in a CAD physical simulation model and obtaining the actual final position Pa. This eliminates the costly and risky physical trial assembly required to verify parameters in traditional processes, allowing process optimization and iteration to be performed infinitely in a low-cost, low-risk environment. By iteratively optimizing the preset system thermal response transfer matrix MT and system force response transfer matrix MF using the final residual error f, a correction matrix is ​​generated by calculating the outer product of the final residual error f and the set of prediction error vectors Epr. This correction matrix is ​​normalized and multiplied by a preset learning rate η to control the step size of each optimization. Ultimately, the system subtracts this calculated correction term from the original system thermal response transfer matrix MT and system force response transfer matrix MF to obtain the updated iteratively optimized system thermal response transfer matrix MT' and iteratively optimized system force response transfer matrix MF', giving the system true self-evolution capability. This gradient-descent-based optimization algorithm transforms the system from a static tool with fixed performance after leaving the factory into a dynamic intelligent agent that learns from minor errors in each mission and continuously updates its understanding of its physical properties. This capability ensures that the system can automatically adapt to gradual changes such as mechanical wear and environmental changes caused by long-term use, ensuring that its ultra-high precision is a "living" performance that can be maintained and developed sustainably.

[0146] Example 5

[0147] A high-precision positioning system for compressor rotor assembly, please refer to Figure 2 ,Specifically: including assembly data acquisition module, error prediction module, error compensation module, compensation point evaluation calculation module and simulation assembly and iterative optimization module;

[0148] The assembly data acquisition module sets up a sensor array in the assembly area to collect the instantaneous raw data set Raw of the environment and component status and preprocesses it to obtain the instantaneous assembly data set Rds;

[0149] The error prediction module builds a CAD physical simulation model based on the instantaneous assembly data set Rds and presets an ideal target coordinate P, calculates the positioning deviation caused by thermal and force effects, and generates a prediction error vector set Epr;

[0150] The error compensation module calculates the mechanical and thermal coupling displacement deviation vector C by performing nonlinear coupling calculation based on the predicted error eigenvector Epr TF And generate the final compensation vector Vc;

[0151] The compensation point evaluation calculation module evaluates the compensation amplitude based on the final compensation vector Vc and generates a compensation amplitude evaluation result QA. When the compensation amplitude evaluation result QA is false, the compensation calculation is suspended and manual intervention is requested. When the compensation amplitude evaluation result QA is true, the compensation target point Pc after compensation is calculated.

[0152] The simulation assembly and iterative optimization module performs simulated assembly of compensation positioning based on the compensation target point Pc, measures the actual final position Pa of the part in the CAD physical simulation model, compares it with the ideal target coordinate P, calculates the final residual error f, and uses the final residual error f for iterative optimization.

[0153] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A high-precision positioning method for compressor rotor assembly, characterized by: The following steps are involved: S1, by setting up a sensor array in the assembly area, collecting the instantaneous raw data set Raw of the environment and component status and preprocessing it to obtain the instantaneous assembly data set Rds; S2. Based on the instantaneous assembly dataset Rds, a CAD physical simulation model is constructed and an ideal target coordinate P is preset. The positioning deviation caused by thermal and force effects is calculated to generate a prediction error vector set Epr. S3, based on the prediction error characteristic vector Epr, nonlinear coupling calculation is performed to calculate the mechanical and thermal coupling displacement deviation vector C TF And generate the final compensation vector Vc; S4. Evaluate the compensation amplitude based on the final compensation vector Vc and generate a compensation amplitude evaluation result QA. If the compensation amplitude evaluation result QA is false, suspend the compensation calculation and request manual intervention. If the compensation amplitude evaluation result QA is true, calculate the compensation target point Pc after compensation. S5. Perform simulated assembly of compensation positioning based on the compensation target point Pc, measure the actual final position Pa of the part in the CAD physical simulation model, compare it with the ideal target coordinate P, calculate the final residual error f, and use the final residual error f for iterative optimization.

2. A high-precision positioning method for compressor rotor assembly according to claim 1, characterized in that: S1 includes S11; S11. Before the assembly process begins, an advanced sensor array installed in the assembly area takes an instantaneous "physical snapshot" of the assembly unit, collecting an instantaneous raw data set of the environment and component status. The instantaneous raw data set, Raw, includes the three-dimensional laser point cloud data P of the assembly environment and rotor collected by a laser three-dimensional coordinate measuring machine; the original part path thermal gradient vector ▽RT measured by a non-contact infrared thermal imaging array, reflecting the uneven temperature distribution inside the part; the clamping torsional strain scalar γc measured by a fiber Bragg grating sensor embedded in the inner wall of the flexible clamp, representing the degree of slight distortion caused by the clamping force; and the material anisotropy tensor km retrieved from the part database based on the read part RFID information, describing the differences in the material's mechanical and thermal properties in different directions. The thermal imaging array sensor coordinate system of the original part path thermal gradient vector ▽RT in the instantaneous raw data set Raw is aligned with the Cartesian coordinate system of the machine tool, and the noise is filtered out by combining with a Gaussian filter to obtain the part path thermal gradient vector ▽T and generate the preprocessed instantaneous assembly data set Rds.

3. The high-precision positioning method for compressor rotor assembly according to claim 2, characterized in that: S2 includes S21 and S22; S21. Import the 3D laser point cloud data P in the instantaneous assembly dataset Rds into CAD software, generate a CAD physical simulation model, and preset an ideal target coordinate P=[x, y, z], where x represents the preset ideal target coordinate of the rotor on the X-axis, y represents the preset ideal target coordinate of the rotor on the Y-axis, and z represents the preset ideal target coordinate of the rotor on the Z-axis; In the CAD physical simulation model, a thermally induced displacement deviation effect algorithm is constructed based on the part path thermal gradient vector ▽T and the material anisotropy tensor km in the instantaneous assembly dataset Rds. The accumulated thermal deformation is calculated by integrating along the part path. The exponential function exp is used to simulate the physically realistic nonlinear relationship between temperature gradient and expansion, completing the vectorization of the nonlinear expansion effect. By multiplying it with the material anisotropy tensor km and the preset system thermal response transfer matrix MT, the directional differences in the material and the response characteristics of the entire machine tool structure are incorporated into the calculation. The thermally induced displacement deviation vector △PT in the machine tool coordinate system is obtained, representing the predicted displacement values ​​of the X, Y, and Z axes caused by the thermal effect. The algorithm expression of thermally induced displacement deviation effect is as follows: ； Where MT represents the preset system thermal response transfer matrix, that is, the response characteristics of the mechanical system to heat input, ∫ represents the integral operation, α represents the principal thermal expansion coefficient of the material in the part database, L represents the virtual path predefined in the CAD physical simulation model, that is, the path of heat transfer along the part, and |▽T| represents the modulo operation on the thermal gradient vector ▽T of the part path.

4. A high-precision positioning method for compressor rotor assembly according to claim 3, characterized in that: S22. Based on the clamping torsional strain scalar γc in the instantaneous assembly data set Rds, a force-induced displacement deviation effect algorithm is constructed. By decomposing a tiny clamping torsional strain scalar γc into coupled displacements in three-dimensional space, the physical effects in different directions are expressed in a column vector. The axial displacement is modeled as a term proportional to the square of the clamping torsional strain scalar γc, and the lateral displacement is modeled as a geometric effect caused by the part geometry and torsion angle. These are accurately described using trigonometric functions and the part database. The deformation vector calculated in the part's local coordinate system is multiplied by the preset system force response transfer matrix MF to obtain the force-induced displacement deviation vector △PF in the machine tool's global coordinate system, which represents the predicted displacement values ​​of the X, Y, and Z axes caused by the clamping force. The algorithm expression of force-induced displacement deviation effect is as follows: ； Where MF represents the preset system force response transfer matrix, that is, the response characteristics of the mechanical system to the clamping force, μ represents the Poisson's ratio of the material in the part database, G represents the shear modulus of the material in the part database, R represents the characteristic radius of the part in the part database, sin represents the sine function, and cos represents the cosine function; According to the thermally induced displacement deviation vector △PT and the force-induced displacement deviation vector △PF, a prediction error vector set Epr is generated.

5. The high-precision positioning method for compressor rotor assembly according to claim 4, characterized in that: S3 includes S31; S31. Based on the prediction error vector set Epr, a mechanical-thermal coupling displacement deviation effect algorithm is constructed. Through the outer product of the thermal-induced displacement deviation vector △PT and the force-induced displacement deviation vector △PF, the interaction relationship tensor between the thermal effect and the force effect is constructed to describe the interaction strength and direction of the two deformation sources. Then, the mechanical-thermal coupling displacement deviation vector C is calculated by combining it with the preset system thermal response transfer matrix MT and the force-induced displacement deviation vector △PF. TF , which represents the high-order error caused by the interaction of thermal and force effects; The algorithm expression of the mechanical and thermal coupling displacement deviation effect is as follows: ； Where, β represents the preset coupling effect factor, △PF T represents the transposed vector of the force-induced displacement deviation vector △PF; Based on the thermal displacement deviation vector △PT, the force-induced displacement deviation vector △PF and the force-heat coupling displacement deviation vector C TF The vector sum between them is used to calculate the final compensation vector Vc; The final compensation vector Vc is calculated as follows: ； Where Vc represents the final compensation vector that needs to be executed to achieve the ideal target coordinate P, which is calculated based on the comprehensive prediction of the error sources.

6. The high-precision positioning method for compressor rotor assembly according to claim 5, characterized in that: S4 includes S41 and S42; S41. Based on the final compensation vector Vc, the Euclidean norm of the compensation vector Vc is calculated to simplify the complex three-dimensional compensation instruction into a single scalar value that can represent the total difficulty of compensation, and the norm of the compensation vector ||Vc|| is obtained; The calculation formula for the norm of the compensation vector ||Vc|| is as follows: ； Where Vcx, Vcy, and Vcz represent the components of the final compensation vector Vc on the X, Y, and Z axes, respectively; If the norm of the compensation vector ||Vc||> the preset maximum compensable threshold δmax, the compensation amount is determined to be beyond the compensable range, and the compensation amplitude assessment result QA is false. The compensation instruction is suspended and a warning is issued. Manual intervention is requested to check the assembly environment. If the sensor has detection deviation, the sensor is recalibrated. If the sensor does not have detection deviation, professionals in this field adjust the temperature and clamping force of the assembly environment. If the norm of the compensation vector ||Vc|| ≤ the preset maximum compensable threshold δmax, the compensation is determined to be feasible, the compensation amplitude evaluation result QA is true, and the compensation instruction can continue to be executed.

7. A high-precision positioning method for compressor rotor assembly according to claim 6, characterized in that: S42. Based on the compensation amplitude evaluation result QA being true, the manipulator is directed to aim at a deliberately offset compensation target point Pc according to the ideal target coordinates P and the final compensation vector Vc. The offset direction of the compensation target point Pc is opposite to the direction of the final compensation vector Vc and the same in magnitude. The compensation target point Pc is calculated by subtracting the final compensation vector Vc from the ideal target coordinates P. Among them, the calculation formula of the compensation target point Pc is as follows: ； The compensation target point Pc is input into the CAD physical simulation model as the final target coordinate.

8. The high-precision positioning method for compressor rotor assembly according to claim 7, characterized in that: S5 includes S51 and S52; S51. Performing simulated assembly of compensation positioning in the CAD physical simulation model based on the compensation target point Pc. Performing simulated collision detection during the simulated assembly process to implement feasibility testing of the assembly path. After the simulated assembly is completed, performing physical property simulation to simulate the offset position of the part and the assembly environment after cooling, and measuring the actual final position Pa of the part in the CAD physical simulation model. Based on the actual final position Pa of the part measured in the CAD physical simulation model, the vector difference with the ideal target coordinate P is calculated to calculate the final residual error f; Among them, the final residual error f is calculated as follows: ； Where f represents the error remaining after this compensation, which serves as the basis for evaluating the performance of a single compensation. If the final residual error f≤the preset residual error threshold fth, the error is considered to be within an acceptable range and no iterative optimization is required. If the final residual error f> the preset residual error threshold fth, it is determined that the error is beyond the acceptable range and iterative optimization is required.

9. The high-precision positioning method for compressor rotor assembly according to claim 8, characterized in that: S52. When the error exceeds the acceptable range, a system response transfer matrix optimization algorithm is constructed based on the final residual error f and the gradient descent idea for the preset system thermal response transfer matrix MT and the system force response transfer matrix MF. A correction matrix is ​​obtained by calculating the outer product of the final residual error f and the set of prediction error vectors Epr. The correction matrix is ​​normalized by the square of the modulus of the set of prediction error vectors Epr and multiplied by the preset interest rate η to obtain a specific correction term. The step size of each optimization is controlled, and the correction term is subtracted from the original preset system response transfer matrix to obtain a new system response transfer matrix. Among them, the system response transfer matrix optimization algorithm expression is as follows: ； ； Where MT' represents the system thermal response transfer matrix after iterative optimization, MF' represents the system force response transfer matrix after iterative optimization, ηT represents the learning rate of the preset system thermal response transfer matrix MT, ηF represents the learning rate of the preset system force response transfer matrix MF, △PT T The transposed vector of the thermally induced displacement deviation vector △PT, △PF T represents the transposed vector of the force-induced displacement deviation vector △PF, || 2 Indicates the square operation of the vector modulus, and λ represents the regularization term to prevent the denominator from being zero, specifically 1*10 -8 ; The iteratively optimized system thermal response transfer matrix MT' and the iteratively optimized system force response transfer matrix MF' are written into the system preset parameters, overwriting the original system thermal response transfer matrix MT and the system force response transfer matrix MF.

10. A high-precision positioning system for compressor rotor assembly, applied to a high-precision positioning method for compressor rotor assembly according to any one of claims 1 to 9, characterized in that: It includes assembly data acquisition module, error prediction module, error compensation module, compensation point evaluation calculation module and simulation assembly and iterative optimization module; The assembly data acquisition module sets up a sensor array in the assembly area to collect the instantaneous raw data set Raw of the environment and component status and preprocesses it to obtain the instantaneous assembly data set Rds; The error prediction module builds a CAD physical simulation model based on the instantaneous assembly data set Rds and presets an ideal target coordinate P, calculates the positioning deviation caused by thermal and force effects, and generates a prediction error vector set Epr; The error compensation module calculates the mechanical and thermal coupling displacement deviation vector C by performing nonlinear coupling calculation based on the predicted error eigenvector Epr TF And generate the final compensation vector Vc; The compensation point evaluation calculation module evaluates the compensation amplitude based on the final compensation vector Vc and generates a compensation amplitude evaluation result QA. When the compensation amplitude evaluation result QA is false, the compensation calculation is suspended and manual intervention is requested. When the compensation amplitude evaluation result QA is true, the compensation target point Pc after compensation is calculated. The simulation assembly and iterative optimization module performs simulated assembly of compensation positioning based on the compensation target point Pc, measures the actual final position Pa of the part in the CAD physical simulation model, compares it with the ideal target coordinate P, calculates the final residual error f, and uses the final residual error f for iterative optimization.

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