Shaft tolerance sensitivity analysis method and system based on virtual assembly

Abstract

This invention relates to the field of mechanical design and manufacturing technology, specifically to a method and system for sensitivity analysis of shaft tolerances based on virtual assembly. The method includes: establishing a part deviation model using small displacement screw theory, constructing an assembly pose transfer chain, and establishing a linear mapping equation between part source deviations and assembly errors using the Jacobian matrix; extracting the sensitivity index of each tolerance term by performing partial derivative analysis on the mapping equation, thereby identifying key geometric elements and optimizing tolerance allocation. This invention significantly improves analysis efficiency by replacing large-scale random sampling with analytical differentiation. It can accurately characterize the cumulative effect of spatial nonlinear tolerances such as coaxiality and perpendicularity. While ensuring assembly accuracy, it effectively relaxes non-critical tolerance requirements, reduces manufacturing accuracy requirements and production costs, and achieves a scientific balance between assembly quality and economy.

Description

Technical Field

[0001] This invention relates to the field of mechanical design and manufacturing technology, and in particular to a method and system for analyzing the tolerance sensitivity of rotating shafts based on virtual assembly. Background Technology

[0002] With the widespread application of precision mechanical equipment such as high-precision spindles and aerospace rotor systems, the assembly accuracy of shaft systems has become a key factor determining the operational stability and service life of equipment. In current engineering design processes, tolerance analysis techniques are typically used to predict and control assembly errors to ensure the dynamic performance of the system under high-speed rotation. This type of analysis usually relies on dimensional chain calculation models, evaluating the cumulative effect of manufacturing deviations in parts to provide a theoretical basis for optimizing design schemes. However, with the continuous increase in assembly accuracy requirements, existing technologies still have significant room for optimization in handling deviation transmission under complex spatial constraints of shafts, the coupling correlation of multi-source geometric tolerances, and sensitivity quantitative analysis for refined design, making it difficult to meet the assembly accuracy control requirements of high-precision equipment.

[0003] Existing tolerance analysis schemes mostly employ extreme value methods or root sum of squares methods. While these methods are well-suited for handling one-dimensional linear dimensional chains, their mathematical analytical depth is relatively limited when characterizing the combined effects of three-dimensional spatial form and position tolerances such as coaxiality and perpendicularity. They also fall short in depicting spatial pose deviations during the actual assembly process of shafts. Furthermore, existing virtual assembly simulation methods typically rely on large-scale random sampling using the Monte Carlo method. This approach requires significant computational resources to obtain statistical results and lacks intuitive and efficient analytical support for revealing the contribution of specific part tolerances to the final assembly error (i.e., sensitivity). Due to the lack of quantitative identification mechanisms for key influencing factors, designers often tend to adopt conservative strategies when allocating tolerances, ensuring assembly quality by improving the overall machining accuracy of parts. This, to some extent, increases manufacturing costs and limits the economic efficiency and scientific rigor of tolerance design. Therefore, there is an urgent need for a shaft tolerance sensitivity analysis method and system that can achieve accurate three-dimensional spatial tolerance mapping, possess efficient computational capabilities, and accurately locate key influencing factors. Summary of the Invention

[0004] To achieve the above objectives, this invention proposes a method and system for tolerance sensitivity analysis of rotating shafts based on virtual assembly. It uses Small Displacement Torsor (SDT) to provide a unified mathematical representation of the three-dimensional geometric tolerances in the rotating shaft assembly, constructs a spatial pose transfer chain for the assembly using a homogeneous transformation matrix, and establishes a linear mapping equation between part source deviations and assembly functional requirements based on the Jacobian matrix. By performing partial derivative analysis on the mapping equation, the contribution index of each tolerance term to the assembly error is extracted, thereby identifying the key geometric elements affecting the assembly accuracy of the rotating shaft and providing a quantitative basis for the scientific allocation of tolerances, thus solving the problems in the aforementioned background technology.

[0005] On the one hand, the present invention provides a method for tolerance sensitivity analysis of rotating shafts based on virtual assembly, comprising the following steps: The geometric topology data, assembly constraints, and preset tolerance design scheme of the rotating shaft assembly are obtained. The geometric topology data is obtained by extracting features from the computer-aided design model of components such as the rotating shaft, bearing, bushing, and housing; the assembly constraints include coaxial constraints, end face contact constraints, and radial positioning constraints between mating surfaces; the preset tolerance design scheme includes the dimensional tolerances, coaxiality tolerances, perpendicularity tolerances, and cylindricity tolerances of each part.

[0006] Based on the small displacement screw theory, a micro-deviation characterization model for the geometric elements of a part is established. This model abstracts the deviation of the actual surface of the part relative to its nominal surface into a six-dimensional vector, composed of three translational deviation components and three rotational deviation components. For different geometric tolerances in the rotating shaft assembly, a mapping function is used to transform them into corresponding screw parameter ranges, forming a part-level error source matrix.

[0007] A spatial pose transfer chain model of the rotating assembly is constructed. A local coordinate system is established at the assembly feature center of each part, and a homogeneous transformation matrix for each local coordinate system relative to the global reference coordinate system is defined. The homogeneous transformation matrix is ​​constructed by multiplying the nominal pose matrix by a deviation transformation matrix containing small displacement screw parameters. The transformation matrices of each part are chained together according to the assembly path to obtain the comprehensive pose transformation equation of the assembly end effector relative to the reference coordinate system.

[0008] An error propagation mapping equation based on the Jacobian matrix is ​​established. The integrated pose transformation equation is expanded using a first-order differential, ignoring higher-order infinitesimals, and the total deviation of the assembly is expressed as a linear weighted sum of the source deviation vectors of each part. The mapping formula is as follows: in, This represents the spatial pose deviation vector at the end of the rotating shaft assembly. This represents the total number of parts in the assembly chain. For the first Jacobian matrix corresponding to each part For the first The small displacement spinor deviation vectors of each component. The Jacobian matrix is ​​constructed by taking the partial derivatives of the kinematic variables and geometric parameters in the transformation matrix, and is used to characterize the amplification or reduction effect of the deviation of each component in the spatial chain.

[0009] Perform tolerance sensitivity analysis calculations. Based on the Jacobian matrix mapping equation, define the tolerance sensitivity index. The sensitivity index is obtained by calculating the absolute value of the partial derivative of the assembly error modulus with respect to the tolerance parameter of a specific part. The specific calculation process includes: performing singular value decomposition on the Jacobian matrix, extracting the principal deviation directions, and calculating the projection intensity of each tolerance term on the principal deviation directions. Sensitivity Index The calculation formula is as follows: in, Indicates the first The first part Tolerance value, The sign represents the partial derivative. By normalizing the sensitivity indices of all tolerance terms, key tolerance terms with sensitivity values ​​greater than a preset threshold are identified.

[0010] The tolerance optimization allocation logic is executed based on the sensitivity analysis results. The identified critical tolerance items are defined as high-precision control elements, and according to the preset cost-tolerance function, while keeping the total assembly deviation within the predetermined acceptable range, the numerical range of non-critical tolerance items is increased and the numerical range of critical tolerance items is reduced, generating an optimized tolerance allocation scheme.

[0011] As one embodiment of the present invention, the establishment of the micro-deviation characterization model for the geometric elements of the part specifically includes: for the mating journal of the rotating shaft, mapping its coaxiality deviation to a rotational screw component about the radial axis and a translational screw component along the radial direction; for the bearing positioning end face, mapping its perpendicularity deviation to two rotational screw components about orthogonal axes within the end face. By defining boundary constraints for the deviation screw, the tolerance band width is transformed into the extreme values ​​of the screw components.

[0012] As one embodiment of the present invention, the spatial pose transfer chain model for constructing the rotating shaft assembly includes: establishing a first local coordinate system at the intersection of the geometric axis of the rotating shaft and the reference end face; establishing a second local coordinate system at the center of the inner ring of the mating bearing; and describing the mating clearance and pose deviation between parts by calculating the rotation matrix and translation vector of the transformation from the first local coordinate system to the second local coordinate system.

[0013] In one embodiment of the present invention, the Jacobian matrix is ​​constructed using a spinor coordinate transformation method. The differential operators of each transformation stage in the assembly chain are mapped to a unified base coordinate system. The rotation operators and position vector operators of the transformation matrix are extracted and combined to form a six-row, six-column sub-Jacobi matrix. For a rotating shaft system with multi-branch constraints, the Jacobian matrices of each branch are fused using the kinematic principles of parallel mechanisms to form a constrained Jacobian matrix.

[0014] In one embodiment of the present invention, the tolerance sensitivity analytical calculation further includes performing an interaction effect assessment. By calculating the second-order partial derivative matrix (Hessian matrix), the nonlinear coupling relationship between part tolerance terms is identified. When the cross-sensitivity coefficient of two tolerance terms exceeds a predetermined correlation threshold, the two tolerance terms are marked as co-optimization terms and adjusted in conjunction with each other in subsequent tolerance allocations.

[0015] In one embodiment of the present invention, the tolerance optimization allocation logic employs the Lagrange multiplier method to solve a constrained optimization problem. With minimizing the total manufacturing cost as the objective function and the constraint condition that the assembly error limit is less than a preset assembly accuracy index, the optimal value of each tolerance term is iteratively calculated using the sensitivity exponent as the gradient search direction.

[0016] According to another aspect of the present invention, a shaft tolerance sensitivity analysis system based on virtual assembly is provided, comprising: The multi-dimensional data integration module is used to acquire the geometric topology data, assembly constraint relationships, and preset tolerance design schemes of the shaft assembly; the module is equipped with a standard data interface for reading the geometric parameters and initial tolerance grades of the parts from an external database.

[0017] The spatial deviation modeling module, connected to the multidimensional data integration module, is used to establish a micro-deviation characterization model of the geometric elements of the part based on the small displacement screw theory, and to uniformly transform various geometric tolerances into six-degree-of-freedom screw parameters.

[0018] The transfer chain construction module is used to establish a spatial pose transfer chain model of the rotating shaft assembly according to the assembly sequence, and generate the system kinematic equations composed of local coordinate system transformation matrices.

[0019] The Jacobi mapping engine, connected to the transfer chain construction module and the spatial deviation modeling module, is used to construct the Jacobi matrix by performing differential transformation on the spatial pose transfer chain model, and to establish a linear mapping equation between the part source deviation and the total assembly error.

[0020] The sensitivity analysis module is used to perform partial derivative operations on the Jacobi mapping equation, calculate the sensitivity index of each tolerance term, and prioritize the tolerance terms according to the magnitude of the sensitivity index.

[0021] The key factor identification module is used to compare the sensitivity index with a preset threshold to identify key tolerance items that have a significant impact on assembly accuracy.

[0022] The tolerance dynamic optimization module is used to perform reverse allocation and optimization of tolerances based on sensitivity analysis results and a preset cost model, and output the adjusted tolerance design scheme.

[0023] The results visualization module is used to display sensitivity analysis results, error distribution curves, and tolerance optimization suggestions in a graphical interface.

[0024] In one embodiment of the present invention, the spatial deviation modeling module has a built-in geometric tolerance screw mapping library. This library contains the corresponding logic for coaxiality, symmetry, parallelism, perpendicularity, and screw parameters. When the user inputs a specific tolerance type, the module automatically calls the corresponding operator to generate the deviation screw matrix.

[0025] In one embodiment of the present invention, the Jacobian mapping engine employs a combination of symbolic and numerical computation. A symbolic Jacobian matrix expression is generated during the model building phase, and specific geometric parameters are substituted into it for numerical solution during the analysis phase, thereby improving computational efficiency.

[0026] In one embodiment of the present invention, the sensitivity analysis module is equipped with a statistical analysis unit. This unit calculates the statistical sensitivity at a predetermined confidence level by introducing a tolerance distribution probability density function, thereby evaluating the impact of tolerance distribution characteristics on the assembly result.

[0027] In one embodiment of the present invention, the tolerance dynamic optimization module includes a multi-criteria decision submodule. This submodule allows users to set weights among manufacturing accuracy, assembly cost, and system lifespan, and provides compromise tolerance allocation suggestions by solving a multi-objective optimization model.

[0028] In one embodiment of the present invention, the system further includes a virtual assembly simulation verification module. This module uses Monte Carlo sampling technology to perform small-scale random simulations on the optimized tolerance scheme, and verifies the accuracy of the analysis model by comparing the consistency between the simulation results and the sensitivity prediction results.

[0029] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention transforms the complex three-dimensional form and position tolerance analysis in shaft assembly into an analytical problem of linear algebraic equations by introducing small displacement screw theory and Jacobian matrix mapping mechanism. Compared with traditional extreme value methods or root sum method, this invention can accurately characterize the cumulative effect of spatial nonlinear tolerances such as coaxiality and perpendicularity, significantly improving the mathematical depth of pose deviation characterization. Due to the use of an analytical differentiation method based on the Jacobian matrix, this invention does not require large-scale Monte Carlo random sampling when obtaining sensitivity results, greatly reducing computational resource consumption and significantly improving sensitivity analysis efficiency. Simultaneously, the sensitivity index constructed by this invention can quantitatively identify key component elements affecting assembly accuracy, changing the previous reliance on experience for conservative tolerance allocation by designers. By finely controlling key elements and relaxing tolerance requirements for non-key elements, this invention effectively reduces the machining accuracy requirements and manufacturing process costs of parts while ensuring the assembly quality of the shaft system, achieving a scientific balance between assembly accuracy and economy. Furthermore, the system architecture provided by this invention has good scalability and can adapt to precision spindle systems with different topologies, providing efficient theoretical support and technical means for the refined design of high-precision spindles and aerospace rotor equipment.

[0030] Attached Figure Description Figure 1 This is a schematic diagram of the core principle of error propagation in this invention; Figure 2 This is a flowchart illustrating the logic of spatial deviation modeling, assembly pose transfer chain construction, and tolerance sensitivity analysis optimization in this invention. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Those skilled in the art, guided by the spirit of this invention, can derive other embodiments, all of which will fall within the protection scope of this invention.

[0032] This invention provides a method for tolerance sensitivity analysis of rotating shafts based on virtual assembly, comprising the following steps: S1: Obtain the geometric topology data, assembly constraint relationships, and preset tolerance design scheme of the shaft assembly; the geometric topology data includes the shaft journal dimensions, the geometric features of the bearing inner and outer rings, and the housing bore diameter parameters; the assembly constraint relationships include the interference / clearance fit constraints between the journal and the bearing inner ring, the positioning constraints between the bearing end face and the bushing, and the coaxial constraints of the housing support hole; the preset tolerance design scheme includes the upper limit of the dimensional tolerance of the parts, the allowable value of coaxiality deviation, the perpendicularity tolerance zone, and the cylindricity error range.

[0033] In step S1, geometric topology data is obtained by parsing the 3D CAD model of the shaft system. The system extracts B-Rep (boundary representation) features of key components such as shafts, bearings, gears, and seals, generating nominal geometric parameter matrices for each mating surface. Assembly constraint relationships are automatically extracted by the assembly semantic recognition module. For example, the coincidence of the shaft centerline and the bearing inner hole centerline is defined as a coaxial constraint, and the contact between the shaft shoulder plane and the bearing end face is defined as a surface contact constraint. The locking state of each degree of freedom is determined according to the mating properties. Preset tolerance design schemes are derived from initial design manuscripts or industry standard databases. After structured processing, they are stored in the assembly information model as deviation attributes. Each tolerance includes tolerance type, datum element, measured element, and tolerance zone value.

[0034] S2: Based on the geometric topology data and the assembly constraint relationship, a micro-deviation characterization model of the part's geometric elements is established by calling the small displacement spinor theory.

[0035] In step S2, the minute deviation characterization model serves as the core mathematical description tool, abstracting the pose deviation of the actual surface of a part relative to its nominal surface into a six-dimensional vector. This vector contains three translational deviation components and three rotational deviation components. For shaft assemblies, different types of form and position tolerances are converted into screw parameters through a predefined mapping function. For example, the coaxiality tolerance of the shaft journal is mapped to a minute rotational screw component about the radial axis and a minute translational screw component along the radial direction; the perpendicularity tolerance of the bearing housing end face is mapped to rotational screw components about two orthogonal axes within the end face. When establishing the model, the tolerance band width is defined by defining boundary constraints for the deviation screw. The extreme value range of the converted spinor components The error sources of all parts together constitute a part-level deviation feature library, which serves as the input source for subsequent spatial chain transmission.

[0036] S3: Construct a spatial pose transfer chain model for the rotating shaft assembly. The transfer chain model includes the homogeneous transformation matrix of the local coordinate system of each part relative to the global reference coordinate system.

[0037] In step S3, the transfer chain construction module establishes a local coordinate system at the assembly feature center of each part (such as the midpoint of the axis centerline or the center of the positioning end face). The spatial relationship between the coordinate systems is determined by the homogeneous transformation matrix. Description. The homogeneous transformation matrix is ​​derived from the nominal pose matrix. With the deviation transformation matrix containing small displacement spinor parameters Multiplication constitutes, that is Deviation transformation matrix A small displacement approximation is used, ignoring higher-order infinitesimals of second order and above. Following the assembly process path, all transformation matrices from the reference part (e.g., housing) to the end effector part (e.g., spindle end) are chained together to generate the overall assembly pose function. This function describes the actual spatial pose of the assembly end effector under manufacturing errors, forming a geometric closed loop for deviation propagation.

[0038] S4: Differentiate and expand the spatial pose transfer chain model to establish an error transfer mapping equation based on the Jacobian matrix, and obtain the total assembly deviation vector.

[0039] In step S4, the error propagation mapping equation is obtained by performing a first-order Taylor expansion on the integrated pose transformation equation. The total pose deviation of the assembly is expressed as a linear weighted sum of the source deviation vectors of each part, and its mapping formula is as follows: in, This represents the spatial pose deviation vector at the end of the rotating shaft assembly. This represents the total number of parts in the assembly chain. For the first The small displacement spinor deviation vector of each part. For the first The Jacobian matrix corresponds to each part. The Jacobian matrix is ​​constructed using the screw coordinate transformation method, mapping the differential operators of each transformation level to a unified global coordinate system. For a rotating shaft system with multi-branch constraints, the system calls a parallel constraint fusion algorithm to extract the rotation operators and position vector operators of each branch transformation matrix and combine them into a constraint Jacobian matrix, thereby accurately characterizing the geometric amplification or reduction effect of each part's deviation in the spatial chain.

[0040] S5: Perform tolerance sensitivity analytical calculation based on the Jacobian matrix mapping equation to obtain the sensitivity index of each tolerance term.

[0041] In step S5, the sensitivity index is not a fixed constant, but rather reflects the contribution of a specific tolerance item to assembly error. The calculation strategy follows these principles: Define the sensitivity index. For the assembly error vector magnitude relative to the first The first part Tolerance value The absolute value of the partial derivative: During the calculation process, singular value decomposition is performed on the Jacobian matrix to identify the principal deviation direction of the assembly error (i.e., the eigenvector direction corresponding to the maximum singular value), and the projection intensity of each tolerance term on the principal deviation direction is used as the core basis for sensitivity evaluation. Furthermore, the system introduces an interaction effect evaluation operator, which identifies the degree of nonlinear coupling between different tolerance terms by calculating the second-order partial derivative matrix (Hessian matrix). The cross-sensitivity coefficient is determined by the Hessian matrix, specifically: the second-order partial derivative elements of the Hessian matrix H. The absolute value of is used to characterize the nonlinear coupling strength between the j-th tolerance of the i-th part and the q-th tolerance of the p-th part. When this absolute value exceeds a predetermined correlation threshold, it is determined that there is a significant coupling relationship between the two tolerances.

[0042] S6: Prioritize all tolerance items according to the sensitivity index and identify key tolerance items whose sensitivity values ​​exceed the preset calibration trigger threshold.

[0043] In step S6, key factor identification is achieved through a dynamic threshold filtering algorithm. Starting from all tolerance terms involved in the calculation, it is performed according to the sensitivity index. Arrange from largest to smallest. Calibrate trigger threshold. Adaptive adjustments are made based on the assembly precision level of the shaft system. The sorted tolerance list is then iterated through. The items marked "high-precision control elements" are typically core tolerance items (such as journal coaxiality) that affect spindle runout or rotational accuracy; Smaller items are labeled as "insensitive tolerance items". In this way, a directed acyclic contribution map is formed, which clarifies the set of tolerance elements to be optimized.

[0044] S7: Based on the preset tolerance design scheme and the key tolerance items, the tolerance items are re-estimated using tolerance optimization allocation logic to generate an optimized tolerance allocation scheme.

[0045] In step S7, tolerance optimization allocation employs a constrained optimization solution based on the Lagrange multiplier method. A mathematical model is established with the objective function of minimizing total manufacturing cost and the constraint that the total assembly error is less than a preset accuracy target. The weight of each tolerance term is determined by its sensitivity index. Decision. The weighting coefficients in the optimization formula. The calculation is as follows: in, This is the cost adjustment coefficient; This is the sensitivity index for the tolerance term; This is the machining difficulty coefficient for the part to which the tolerance item belongs. Its value is obtained by calculating the manufacturing tolerance limit of the part under the current process conditions, and then normalizing it and mapping it to the interval [1.0, 5.0]. The machining difficulty coefficient... The calculation is as follows: For the machining center to which the target part belongs, the residual is calculated based on its historical machining accuracy standard deviation; the process capability index is calculated by taking the most recent 30 batches of valid data points to form a sliding window. Difficulty level The linear normalization method is used: Normalize to the interval [1.0, 5.0], where and For historical data The minimum and maximum values.

[0046] S8: Perform consistency verification on the optimized tolerance allocation scheme. The consistency verification includes numerical boundary compliance determination, logical conflict detection, and manufacturing feasibility assessment.

[0047] In step S8, numerical boundary compliance is determined by the geometric boundary checker, verifying whether the optimized tolerance values ​​are within the material mechanical limits and machine tool machining limits of the part. Logical conflict detection is performed by the constraint consistency checker, conducting a full combinatorial traversal test on the updated tolerance set to ensure there are no contradictory geometric constraints (e.g., internal hole tolerance is greater than external diameter tolerance). Manufacturing feasibility assessment refers to the process capability manual; if a critical tolerance item is compressed to an order of magnitude that existing equipment cannot achieve (e.g., below 0.001mm), the verification is deemed unsuccessful. After all three verifications pass, the tolerance database undergoes an atomic update operation; if any verification fails, the parameters are stored in the pending review area, and a manual review task is generated and pushed to the senior process engineer's terminal.

[0048] S9: Implement dynamic reliability management based on statistical characteristics for all tolerance elements in the rotating shaft system. When the statistical confidence level of any tolerance element is lower than the preset lower confidence limit, it is automatically marked as a state to be analyzed and included in the next round of sensitivity analysis.

[0049] In step S9, the confidence management module maintains a confidence function that fluctuates with the production batch. ,in This represents the cumulative number of production units since the last comprehensive verification of this tolerance scheme. The attenuation rate is set according to the tolerance sensitivity level. For critical tolerances (high sensitivity): the lower confidence limit is set to 0.85; for ordinary tolerances (medium sensitivity): the lower confidence limit is set to 0.75; for insensitive tolerances (low sensitivity): the lower confidence limit is set to 0.60. For sensitivity index For critical tolerance terms >1.0, set γ = 0.01; for sensitivity index 0.5 ≤ For general tolerance terms ≤ 1.0, set γ = 0.005; for the sensitivity index For non-sensitive tolerances <0.5, γ=0.002 is set. The above parameters can be adjusted according to the actual quality control needs of the enterprise. When the distribution characteristics of the actual processing data drift, causing the confidence level of the tolerance unit to fall below the lower limit, the system automatically triggers a new round of sensitivity analysis and tolerance calibration to achieve proactive prevention and control of assembly quality risks.

[0050] The above-described methods and steps constitute a complete closed loop for shaft tolerance analysis. Correspondingly, the shaft tolerance sensitivity analysis system based on virtual assembly includes a multi-dimensional data integration module, a spatial deviation modeling module, a transfer chain construction module, a Jacobi mapping engine, a sensitivity analysis module, a key factor identification module, a tolerance dynamic optimization module, a result visualization module, and a virtual assembly simulation verification module.

[0051] The multi-dimensional data integration module integrates a CAD data parsing unit, an assembly constraint database interface, and a tolerance standard library. The CAD data parsing unit supports standard formats such as STEP and IGES and has automatic feature recognition capabilities. The assembly constraint database interface interfaces with the enterprise's PDM system via API to achieve real-time synchronization of design parameters.

[0052] The spatial deviation modeling module has a built-in geometrical tolerance screw mapping library. This library covers mathematical conversion operators between geometrical tolerances such as coaxiality, perpendicularity, parallelism, and symmetry, and six-degree-of-freedom screw parameters. When the user inputs the tolerance zone type, the module automatically generates the corresponding deviation screw matrix.

[0053] The Jacobian mapping engine employs an architecture that combines symbolic and numerical computation. The engine incorporates a two-layer recursive differential operator with a node embedding dimension of 256. Symbolic Jacobian matrix expressions are generated during the model building phase, and specific part geometric parameters are substituted into these expressions during the analysis phase for numerical solutions, thereby improving computational efficiency while maintaining accuracy.

[0054] The sensitivity analysis module is equipped with a statistical analysis unit. This unit introduces the tolerance distribution probability density function to calculate the statistical sensitivity at a 99.73% confidence level. The key factor identification module implements dynamic threshold scheduling, with the threshold update cycle occurring before the start of each weekly production task. The tolerance dynamic optimization module encapsulates a Lagrange solver, supports multi-criteria decision-making, and allows users to set weights between processing costs and assembly accuracy.

[0055] The virtual assembly simulation verification module uses Monte Carlo sampling techniques to perform small-scale (e.g., 500) random simulations on the optimized tolerance scheme. By comparing the error distribution curve generated by the simulation with the theoretical median value predicted by the Jacobi model, a compliance index is calculated. If the compliance is below 95%, the system automatically prompts for correction of the Jacobi linearization error.

[0056] Example: Taking the tolerance calibration of the bearing support assembly of a high-precision spindle system as an example, this embodiment details how to trigger and complete the sensitivity analysis and optimization of relevant tolerances when the system detects excessive radial runout of the spindle. The spindle assembly topology data is obtained, including the spindle, front / rear bearings, and bearing housings. In the preset scheme, the coaxiality tolerance of the spindle journal is 0.005mm, and the coaxiality of the bearing housing bore is 0.008mm. Actual measurement revealed that the radial runout at the spindle end was 0.012mm, exceeding the design requirement of 0.010mm.

[0057] Based on the small displacement screw theory, the coaxiality of the spindle journal is mapped to screw. The coaxiality of the bearing housing bore is mapped to spinor. Construct a spatial pose transfer chain from the bearing housing to the end of the spindle. Construct the Jacobian matrix and establish the mapping equation. .

[0058] Sensitivity calculations were performed to obtain the sensitivity index of the spindle journal coaxiality. Sensitivity index of bearing housing bore coaxiality .because (Set key thresholds) trigger the optimization process.

[0059] Analysis revealed that the spindle journal error contributed significantly more to the total runout than the bearing housing error. Recent data from the spindle machining center were collected to calculate the spindle machining difficulty coefficient. .

[0060] The parameters were re-estimated using the weighted least squares method. The model suggests that if the coaxiality tolerance of the spindle journal is reduced from 0.005 mm to 0.003 mm, while the perpendicularity tolerance of the insensitive bearing positioning end face is relaxed (from 0.010 mm to 0.015 mm), the total cost will only increase by 2%, but the assembly runout is expected to be reduced to 0.009 mm.

[0061] Consistency verification was performed, and the 0.003mm deviation was found to be within the machining capability range of the high-precision grinding machine, and did not cause any logical conflict with the existing bearing tolerances. Upon successful verification, the system automatically updated the tolerance design scheme for the spindle assembly and issued a process adjustment instruction to the production department.

[0062] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for tolerance sensitivity analysis of rotating shafts based on virtual assembly, characterized in that, Includes the following steps: Step S1: Obtain the geometric topology data, assembly constraints, and preset tolerance design scheme of the rotating shaft assembly; Step S2: Based on the geometric topology data and assembly constraints, use the small displacement screw theory to establish a micro-deviation characterization model for the geometric elements of the parts; Step S3: Construct a spatial pose transfer chain model for the rotating shaft assembly, which includes the homogeneous transformation matrix of the local coordinate system of each part relative to the global reference coordinate system; Step S4: Perform differential expansion on the spatial pose transfer chain model, establish an error transfer mapping equation based on the Jacobian matrix, and obtain the total assembly deviation vector; Step S5: Perform tolerance sensitivity analytical calculation based on the Jacobian matrix mapping equation to obtain the sensitivity index of each tolerance term; Step S6: Based on the sensitivity index, all tolerance items are prioritized, and key tolerance items whose sensitivity values ​​exceed the preset calibration trigger threshold are identified; Step S7: Based on the preset tolerance design scheme and the key tolerance items, the tolerance items are re-estimated using tolerance optimization allocation logic to generate an optimized tolerance allocation scheme; Step S8: The optimized tolerance allocation scheme is subjected to consistency verification, which includes numerical boundary compliance judgment, logic conflict detection, and manufacturing feasibility assessment; Step S9: Reliability dynamic management based on statistical characteristics is implemented for all tolerance units in the shaft system. When the statistical confidence level of any tolerance unit is lower than the preset lower confidence limit, it is automatically marked as a state to be analyzed and included in the next round of sensitivity analysis process.

2. The method for analyzing the tolerance sensitivity of rotating shafts based on virtual assembly according to claim 1, characterized in that, The step S2, establishing a micro-deviation characterization model for the geometric elements of the part, specifically includes: abstracting the pose deviation of the actual surface of the part relative to the nominal surface into a six-dimensional vector, which consists of three translational deviation components and three rotational deviation components; for the mating journal of the rotating shaft, mapping its coaxiality tolerance to a rotational screw component about the radial axis and a translational screw component along the radial direction; for the bearing positioning end face, mapping its perpendicularity tolerance to a rotational screw component about two orthogonal axes within the end face; and defining boundary constraints for the deviation screw, defining the tolerance band width... The extreme value range of the converted spinor components .

3. The method for analyzing the tolerance sensitivity of rotating shafts based on virtual assembly according to claim 1, characterized in that, The step S3 of constructing the spatial pose transfer chain model of the rotating shaft assembly specifically includes: establishing a local coordinate system at the assembly feature center of each part; and defining the homogeneous transformation matrix between each local coordinate system. The homogeneous transformation matrix From the nominal pose matrix With the deviation transformation matrix containing small displacement spinor parameters Multiplication constitutes the result, and the calculation formula is as follows: The transformation matrices at each level are chained together according to the assembly process path to generate the overall assembly pose function describing the actual spatial pose of the assembly end.

4. The method for analyzing the tolerance sensitivity of rotating shafts based on virtual assembly according to claim 1, characterized in that, The step S4 of establishing the error propagation mapping equation based on the Jacobian matrix specifically includes: performing a first-order Taylor expansion on the overall assembly pose function, expressing the total deviation of the assembly as a linear weighted sum of the source deviation vectors of each part, and the mapping formula is as follows: in, This represents the spatial pose deviation vector at the end of the rotating shaft assembly. This represents the total number of parts in the assembly chain. For the first Jacobian matrix corresponding to each part For the first The small displacement spinor deviation vector of each part; the Jacobian matrix By constructing a spinor coordinate transformation method, the differential operator of each level of transformation is mapped to a unified global coordinate system.

5. The method for analyzing the tolerance sensitivity of rotating shafts based on virtual assembly according to claim 1, characterized in that, The tolerance sensitivity analysis calculation performed in step S5 specifically includes: calculating the sensitivity index. It is defined as the magnitude of the assembly error vector relative to the first... The first part Tolerance value The absolute value of the partial derivative is calculated using the following formula: Singular value decomposition is performed on the Jacobian matrix to identify the main deviation direction of the assembly error, and the projection intensity of each tolerance term on the main deviation direction is calculated. The degree of nonlinear coupling between different tolerance terms is identified by calculating the Hessian matrix. When the cross sensitivity coefficient of two tolerance terms exceeds a predetermined correlation threshold, it is determined that there is a coupling relationship and collaborative optimization is performed.

6. The method for analyzing the tolerance sensitivity of rotating shafts based on virtual assembly according to claim 1, characterized in that, The tolerance optimization allocation logic in step S7 specifically includes: using the Lagrange multiplier method to solve a mathematical model with the objective function of minimizing the total manufacturing cost and the constraint that the total assembly error is less than a preset accuracy index; and based on the weight coefficients of each tolerance term... The optimal value is calculated iteratively, and the weighting coefficients are... The calculation formula is: in, This is the cost adjustment coefficient. The sensitivity index. The processing difficulty coefficient; Calculate the process capability index of the machining center to which the target part belongs. The formula is as follows: ,and It is normalized and mapped to the interval [1.0, 5.0].

7. The method for analyzing the tolerance sensitivity of rotating shafts based on virtual assembly according to claim 1, characterized in that, The implementation of dynamic reliability management in step S9 specifically includes: maintaining the confidence function that fluctuates with production batches. ,in To calculate the cumulative number of units produced, The attenuation rate is set according to the tolerance sensitivity level; different preset confidence limits are set for critical tolerance items, ordinary tolerance items and non-sensitive tolerance items; when the actual processing data causes the statistical confidence of the tolerance unit to be lower than the preset confidence limit, a new round of sensitivity analysis and tolerance calibration process is triggered.

8. A system for analyzing the tolerance sensitivity of rotating shafts based on virtual assembly, characterized in that, include: The multi-dimensional data integration module is used to acquire the geometric topology data, assembly constraint relationships, and preset tolerance design schemes of the rotating shaft assembly; The spatial deviation modeling module is used to establish a micro-deviation characterization model of the geometric elements of the part based on the small displacement screw theory, and to convert the form and position tolerances into six-degree-of-freedom screw parameters; the transfer chain construction module is used to establish a spatial pose transfer chain model of the rotating shaft assembly and generate the system kinematic equations; the Jacobian mapping engine is used to perform differential transformation on the spatial pose transfer chain model to construct the Jacobian matrix and establish a linear mapping equation between the part source deviation and the total assembly error. The sensitivity analysis module is used to perform partial derivative operations on the linear mapping equation and calculate the sensitivity index of each tolerance term; The key factor identification module is used to identify key tolerance items that affect assembly accuracy based on the sensitivity index. The tolerance dynamic optimization module is used to optimize the allocation of tolerances based on sensitivity analysis results and a preset cost model. The results visualization module is used to display sensitivity analysis results, error distribution curves, and tolerance optimization suggestions.

9. The shaft tolerance sensitivity analysis system based on virtual assembly according to claim 8, characterized in that, The spatial deviation modeling module has a built-in geometric tolerance screw mapping library, which includes mathematical conversion operators for coaxiality, parallelism, perpendicularity, symmetry, and screw parameters. The Jacobian mapping engine adopts an architecture that combines symbolic and numerical computation. In the model building stage, it generates symbolic Jacobian matrix expressions, and in the analysis stage, it substitutes specific geometric parameters to perform numerical solutions.

10. The shaft tolerance sensitivity analysis system based on virtual assembly according to claim 8, characterized in that, It also includes a virtual assembly simulation verification module, which uses Monte Carlo sampling technology to perform random simulations on the optimized tolerance allocation scheme, and verifies the accuracy of the analysis model by comparing the consistency between the simulation results and the prediction results of the Jacobi mapping engine.

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