Precision allocation method for multi-branch closed-loop transmission chain considering precision-rigidity coupling

Abstract

The application discloses a kind of multi-branch closed-loop transmission chain precision distribution methods considering precision-rigidity coupling, comprising: clear multi-branch closed-loop transmission chain end multi-station output index, establish geometric error transmission model;Sobol global sensitivity analysis is used to identify key geometric error term and carry out initial precision distribution;Introduce working load, establish elastic structure equation, analyze the influence of load transmission and elastic deformation on end error;Multi-objective optimization model containing position accuracy, attitude accuracy and structure stiffness cost is constructed, and Pareto solution set is solved and the optimal scheme is selected using TOPSIS method;Output geometric error final allowable value, structure stiffness configuration and manufacturable engineering control index.The application realizes the collaborative design of geometric precision and structure stiffness, and significantly improves the end execution precision of transmission chain and design economy.

Description

Technical Field

[0001] This invention belongs to the field of precision design and analysis technology for complex mechanical transmission systems. Specifically, it relates to a precision allocation method for multi-branch closed-loop transmission chains that considers precision-rigid coupling. It is particularly suitable for complex transmission chains with common input, branch transmission, converged output and terminal multi-station output characteristics, such as the main transmission system of multi-axis CNC machine tools, the parallel drive system of heavy machinery, and the multi-actuator of aerospace equipment. It can achieve the coordinated optimization and allocation of geometric precision and structural stiffness in the design stage. Background Technology

[0002] In modern high-end mechanical equipment, such as multi-axis CNC machine tools, heavy-duty forging presses, and aerospace actuation systems, to meet the requirements of high power transmission and synchronous action of multiple actuators, their transmission systems typically employ a multi-branch closed-loop transmission structure composed of complex gear trains, transmission shaft systems, and end effectors. This type of transmission chain is characterized by long transmission links, numerous error sources, and strong coupling relationships between branches. The overall output accuracy at its end (such as multi-axis linkage spatial error and synchronization error of multiple actuators) directly determines the machining quality and working performance of the equipment. Therefore, conducting scientific and systematic accuracy allocation for multi-branch closed-loop transmission chains is a key technical aspect in ensuring the final accuracy and operational stability of complex equipment.

[0003] Existing accuracy analysis methods for transmission systems can be mainly classified into the following categories.

[0004] (1) Geometric tolerance chain and linear error propagation method: This type of method is commonly used in engineering practice. Its core idea is to regard the system as a series error propagation chain, and synthesize the errors of each component loop based on the small perturbation assumption and the principle of linear superposition. However, this type of method is difficult to accurately describe the branching, merging and coupling effects of errors in multi-branch and closed-loop structures. For example, the error on one branch may affect other branches through the merging point, producing a nonlinear "geometric lever amplification effect", which traditional linear methods cannot effectively quantify.

[0005] (2) Error source tracing method based on single factor analysis: This type of method studies the impact trend of individual error sources on the final accuracy by changing them one by one. Although it can initially identify key error sources, it cannot answer in-depth engineering decision-making questions such as "which error sources contribute to the output error, what is the proportion of the interaction and coupling effect between each error source, and which positions should be tightened first" when multiple error sources coexist in actual working conditions.

[0006] (3) Optimization allocation methods focusing on geometric accuracy: Some existing studies attempt to use global sensitivity analysis (such as the Sobol method) to quantify the influence weight of geometric error sources and allocate tolerances accordingly. These methods improve the targeting of allocation to a certain extent. However, they generally narrowly interpret "accuracy" as "geometric accuracy" and ignore the key factor of working load. Under actual working conditions, transmission shafts, supports and other related components will produce non-negligible elastic deformation when subjected to huge working loads. This "force-induced error" will be superimposed on geometric error, and even affect the accuracy of the entire link in a closed-loop structure through the "load feedback" effect. Existing geometric accuracy allocation methods do not consider this coupling effect of "accuracy-rigidity".

[0007] In summary, existing precision allocation techniques have the following significant technical defects: (1) Model distortion: They fail to adequately characterize the complex error coupling and transmission relationships of multi-branch closed-loop transmission chains, making it difficult to accurately describe the geometric lever amplification effect of errors; (2) Information fragmentation: Single-factor analysis or first-order sensitivity analysis cannot provide the comprehensive influence weight of multiple error sources, especially the interaction between errors, on the final precision, resulting in insufficient basis for allocation decisions; (3) Incomplete consideration of factors: Most methods remain at the level of pure geometric error analysis, severing the inherent physical connection between "precision" and "rigidity", and failing to consider the decisive influence of elastic deformation under working load on the final precision; (4) Detached from engineering practicality: The final allocation result is often an abstract statistical value of error terms, which is difficult to directly and effectively transform into specific engineering indicators to guide the processing, assembly, and verification of parts, such as bearing seat hole position accuracy, support hole coaxiality, and stiffness configuration of key components.

[0008] Therefore, there is an urgent need to propose a more advanced and systematic method for precision allocation. This method should be able to deeply integrate the geometric characteristics and structural rigidity of the transmission chain, and realize positive, quantitative, and collaborative design from macroscopic precision indicators to microscopic executable engineering indicators, so as to fill the gap in existing technologies. Summary of the Invention

[0009] In view of this, the purpose of this invention is to provide a method for allocating the accuracy of a multi-branch closed-loop transmission chain that considers the coupling of accuracy and rigidity. By establishing a coupling model of geometric error and elastic deformation, and combining global sensitivity analysis and multi-objective decision-making, the method achieves the coordinated optimization allocation of accuracy indicators and structural stiffness, and provides executable engineering indicators for manufacturing and assembly.

[0010] To achieve the above objectives, the present invention provides the following technical solution: A method for accuracy allocation in a multi-branch closed-loop drive train considering accuracy-rigid coupling includes the following steps: Step 1: Define the research object and end output indicators. For multi-branch closed-loop transmission chains with common input, branch transmission, converge output and terminal multi-station output characteristics, identify its branching position, converge position and terminal output component, and select multiple work points on the terminal output component as end evaluation points to determine the output accuracy requirements that each evaluation point must meet. Step 2: Unify coordinate representation and error modeling. Establish a global fixed coordinate system and a local coordinate system. Select key geometric error terms that affect the accuracy of the end effector. Based on the transmission relationship of the transmission chain, establish an error mapping model from the key geometric error terms to multiple end output evaluation points. Use the geometric error with the largest absolute value among the multiple output evaluation points as the unified evaluation index. Step 3: Sobol sensitivity analysis and initial precision allocation. The Sobol global sensitivity analysis method is used to quantify the contribution of each geometric error item to the unified evaluation index and the error of a single end output evaluation point, so as to obtain the total effect index. In accordance with the principle of "strict control of high sensitivity items and moderate relaxation of low sensitivity items", the initial precision allocation is carried out for position / meshing error items and angle error items respectively, and the initial allowable value of each error item is determined. Step 4: Load transfer and elastic error analysis. Based on the initial accuracy allocation results, the working load is introduced to establish an elastic structural equation that includes the overall stiffness matrix and nodal load vectors. The deflection and rotation angle of key loaded components are calculated, and weak stiffness areas are identified based on the improvement rate of the synchronous output error of the multi-station end based on the addition of supports or the improvement of local constraint stiffness. Step 5: Consider the multi-objective decision-making of accuracy and stiffness, establish a set of design variables that simultaneously include error allocation variables and structural stiffness variables, construct the objective functions of position accuracy, attitude accuracy, and structural stiffness, use a multi-objective optimization algorithm to solve the Pareto candidate scheme set, and select the optimal structure-accuracy combination scheme from them through a comprehensive decision-making method; Step Six: Output the allocation results. Based on the optimal structure-precision combination scheme, determine the final allowable value of each key geometric error item, the support reinforcement or local stiffness adjustment result of key load-bearing components, and convert the allocation results at the error item level into manufacturing and assembly control indicators.

[0011] Furthermore, in step two, the geometric error output model for the i-th terminal output evaluation point is: in: Indicates the first Geometric vertical error of each end output evaluation point; Indicates the first Vertical position error of a key transmission component; Indicates the first A key transmission component revolves around a local Axis attitude error; Indicates the first The equivalent error of a key transmission pair; Indicates the first The vertical position error of a key transmission component is transmitted to the first... The influence coefficient of each end output evaluation point; Indicates the first The attitude error of the key transmission component is transmitted to the first The influence coefficient of each end output evaluation point; Indicates the first The equivalent error of the key transmission pair is transmitted to the first... The influence coefficient of each end output evaluation point; Indicates the quantity of key transmission components; Indicates the number of key transmission pairs.

[0012] Furthermore, in step two, the unified evaluation index is expressed as follows: in: This represents the most unfavorable geometric output error under multi-station synchronization constraints. Indicates the first Geometric vertical error of each end output evaluation point; This indicates the number of evaluation points at the end of the output.

[0013] Furthermore, in step three, the total effect index of the j-th geometric error term on the r-th output evaluation quantity is calculated using the Jansen estimation formula: in: Indicates the first The geometric error term affects the first... The total effect index of each output evaluation quantity; A and B are two independent sampling matrices; Representation matrix The Row samples; Indicates the matrix The Column replacement with matrix The The resulting mixture matrix after column division; Represents the mixture matrix The Row samples; Indicates the first One output evaluation function; Indicates the first The variance of each output evaluation quantity; Indicates the first Geometric error output for each evaluation point; Indicates the number of samples.

[0014] Furthermore, in step three, the allowable value for the position / meshing error term in the initial accuracy allocation... Allowable values ​​for angle-related error terms They are determined in the following ways respectively: in: Indicates the first Initial allowable values ​​for each positional error term; This represents the total allowable error for positional errors; Indicates the first Weighting of each location-type error term; Indicates the first Each geometric error term affects the unified evaluation index. The total effect index; Indicates the number of position-related error terms; Indicates the first Initial allowable values ​​for each positional error term; This represents the total allowable error for positional errors; Indicates the first Weights are assigned to the insensitivity of each angle-type error term. Indicates the number of angle-related error terms; Indicates the first Each geometric error term affects the unified evaluation index. The total effect index; To prevent small positive quantities with a denominator of zero; This is the sensitivity adjustment coefficient.

[0015] Furthermore, in step four, the elastic structure equation is expressed as: in The overall stiffness matrix of the key load-bearing components of the transmission chain after discretization; The nodal displacement vector; The nodal load vector is formed by the terminal working load, the equivalent force of the transmission pair, and the load return action. The improvement rate is defined as: in: Indicates candidate position Improvement rate of multi-station synchronous output error; This represents the maximum total output error under the initial structure; Indicates the candidate position The maximum total output error after adding supports or increasing the stiffness of local constraints.

[0016] Furthermore, in step five, the design variable set is represented as follows: in: Indicates the joint design variables of structure and precision; Indicates the scaling factor for position / engagement type errors; Indicates the scaling factor for angle-type error assignment; Indicates the first Equivalent stiffness scaling factor for a key load-bearing component or key support area; Indicates the first New support locations or local reinforcement locations on key load-bearing components; Position accuracy objective function Attitude accuracy objective function and structural stiffness objective function They are represented as follows: in: This represents the objective function for positional accuracy. Indicate candidate solutions Next The total output error of each end output evaluation point; Indicates the number of evaluation points in the final output; This indicates the end-position error control index; Represents the attitude accuracy objective function; Indicate candidate solutions The overall attitude error of the lower terminal output component or key output stage; Indicates attitude error control parameters; Represents the objective function for structural stiffness; This indicates the number of key load-bearing components involved in structural optimization; Indicates the first Recommended reinforcement locations determined based on the support location scanning results on key load-bearing components; Indicates the first The effective length of a key load-bearing component; , , and These are all weighting coefficients used to adjust the influence of error allocation scaling, stiffness adjustment, and support position offset on the structural cost objective.

[0017] Furthermore, the multi-objective optimization problem can be expressed as: The constraints include error tolerance constraints, variable upper and lower bound constraints, and terminal output accuracy constraints: in: Indicate candidate solutions Next Allowable values ​​for each key error term; and They represent the first The lower and upper limits of manufacturing or assembly feasibility for each key error item; and Indicates the scaling factor for position / engagement type error allocation. The lower and upper limits of the value; and These represent the scaling factors for angle-type error allocation. The lower and upper limits of the value; , They represent the first Equivalent stiffness scaling factor for key load-bearing components The lower and upper limits of the value; and They represent the first Additional supports or local reinforcements may be placed on key load-bearing components. The lower and upper limits of the value.

[0018] Furthermore, the Pareto optimization method is used to solve for the candidate solution set, and the TOPSIS comprehensive decision method is used to select the optimal solution from the Pareto candidate solutions, where the comprehensive proximity of the i-th candidate solution is expressed as: in: Indicates the first The overall relevance of each candidate solution; and They represent the first The distance from each candidate solution to the ideal optimal solution and the ideal worst solution.

[0019] Furthermore, in step six, the output manufacturing and assembly control indicators include: Requirements for the consistency of the support hole axis, the positional accuracy of the support hole, or the local installation error of the critical mounting position relative to the reference axis, which are transformed from shaft position errors; The parallelism or inclination requirements of the common axis of the support holes relative to the assembly reference axis, which is transformed from shaft attitude errors; Requirements for gear mounting position error, gear pair center distance error, end face runout, radial runout, or meshing installation relationship error converted from the equivalent error of the transmission pair; In addition, new support locations, support stiffness levels, local reinforcement requirements for key shaft segments, or support arrangement adjustment requirements are derived from the results of structural stiffness optimization.

[0020] The beneficial effects of this invention are as follows: This invention considers a precision allocation method for multi-branch closed-loop transmission chains with precision-rigid coupling, and has the following technical advantages: (1) The model is closer to the physical essence: By establishing a unified evaluation index that includes the largest absolute value (most unfavorable error) among multiple output evaluation points and the elastic structure equation under working load, the “geometric lever amplification” and “load feedback” effects of the multi-branch closed-loop transmission chain are quantified in the accuracy allocation, overcoming the defect of the traditional method that separates the analysis of accuracy and stiffness. (2) More scientific decision-making basis: Sobol global sensitivity analysis is used to quantify the comprehensive contribution of each error source and its coupling effect to the end error, and position / angle errors are classified and allocated according to sensitivity, which solves the engineering problem of "which errors should be strictly controlled first" and avoids the cost waste caused by blindly tightening tolerances; (3) Better design results: Through multi-objective collaborative optimization, the end position accuracy, attitude accuracy and structural adjustment cost are taken as optimization objectives. By using Pareto solution set and TOPSIS decision, the optimal balance of "accuracy-stiffness-cost" is achieved, avoiding the sacrifice of overall performance by optimizing only one aspect. (4) More practical for engineering: The abstract error allocation results are directly transformed into specific indicators that can be manufactured, assembled and verified, such as the consistency of the support hole axis, parallelism and installation relationship error, and the support stiffness configuration and reinforcement position suggestions are output, which fills the gap between theoretical design and engineering implementation.

[0021] In summary, this invention establishes a coupled model of geometric error and elastic deformation, combined with global sensitivity analysis and multi-objective decision-making, to achieve coordinated optimization of accuracy indicators and structural stiffness allocation, and provides executable engineering indicators for manufacturing and assembly. This significantly improves the end-efficiency execution accuracy and design reliability of multi-branch closed-loop transmission chains, while reducing trial production iteration costs and manufacturing difficulty. Attached Figure Description

[0022] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 A flowchart illustrating the precision allocation method for multi-branch closed-loop drive trains considering precision-rigid coupling in this invention; Figure 2 This is a simplified diagram of the transmission chain mechanism; Figure 3 The results are as follows: (a) Sobol analysis of several errors for output point 1 (x=290mm); (b) Sobol analysis of several errors for output point 2 (x=862mm); (c) Sobol analysis of several errors for output point 3 (x=1506mm); (d) Sobol analysis of geometric error for the maximum output comprehensive index. Figure 4 Assign results to the initial precision; Figure 5 For verification results; Figure 6 The curves are: (a) the deflection and rotation angle curves of the key shaft segments; (b) the deflection curve of crankshaft 2; (c) the deflection curve of camshaft 13; (d) the deflection curve of camshaft 14; and (d) the rotation angle curve of camshaft 14. Figure 7 To add support improvement rate; (a) is the full-axis scan improvement rate distribution of crankshaft 2; (b) is the full-axis scan improvement rate distribution of camshaft 13; (c) is the full-axis scan improvement rate distribution of camshaft 14; Figure 8 Comparison of deflection and rotation curves for key shaft segments; (a) Crankshaft 2 deflection curve; (b) Camshaft 13 deflection curve; (c) Camshaft 14 deflection curve; (d) Camshaft 14 rotation curve; Figure 9 For Pareto candidate solution set; Figure 10 TOPSIS overall score; Figure 11 Results of key variable precision assignment; (a) Summary of output metrics; (b) Distribution of improvement rate across the entire axis scan; (c) Overall output comparison; (d) Key variable assignment. Detailed Implementation

[0023] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0024] This embodiment considers a precision allocation method for a multi-branch closed-loop transmission chain with precision-rigid coupling. The aim is to parametrically model geometric error sources such as shaft installation error, shaft deflection error, and gear pair error, under the premise of unified transmission structure and end-effector functional indicators. An error transmission model is established based on the transmission structure of the multi-branch closed-loop transmission chain. Under the condition that multiple error sources exist simultaneously, global sensitivity analysis is used to quantify the contribution of each error source to the end-effector functional error. Based on the initial precision allocation results, a working load is introduced to calculate the end-effector error caused by elastic deformation. Collaborative optimization is performed through support position, support stiffness, and error allocation coefficients, ultimately outputting an upper limit of geometric precision and structural stiffness configuration that meets the precision requirements of the end-effector.

[0025] Specifically, such as Figure 1 As shown, this embodiment considers a precision allocation method for multi-branch closed-loop transmission chains with precision-rigid coupling, including the following steps.

[0026] Step 1: Define the research subjects and the final output indicators.

[0027] For multi-branch closed-loop transmission chains with characteristics of common input, branch transmission, convergence output, and multi-station terminal output, the transmission chain object to be allocated accuracy and its power transmission relationship are first identified. After identifying the transmission chain object, the branching positions, convergence positions, and terminal output components in the transmission chain are identified based on the power flow direction and structural connection relationship. Through this step, the complex whole machine transmission system is transformed into an accuracy allocation object composed of input segment, branch segment, and terminal output segment, enabling subsequent error modeling to be carried out along the actual transmission path and avoiding the problems of double counting of common segment errors or omission of branch segment errors.

[0028] Furthermore, based on the end-function requirements of the transmission chain, several workstations are selected as end-evaluation points on the terminal output component, and the output accuracy requirements that each evaluation point needs to meet are determined. For multi-station synchronous output transmission chains, if the output error of any workstation exceeds the allowable range, it may cause the accuracy of the end-effector of the entire transmission chain to fail to meet the requirements. Therefore, this step uses the synchronous output requirements of multiple workstations as a unified evaluation index for subsequent sensitivity analysis, initial accuracy allocation, load transfer and elasticity error analysis, and accuracy-rigidity integrated decision-making.

[0029] Step 2: Unified Coordinate Representation and Error Modeling. Establish a global fixed coordinate system and a local coordinate system, select key geometric error terms that affect the accuracy of the end effector, and establish an error mapping model from the key geometric error terms to multiple end effector output evaluation points based on the transmission relationship of the transmission chain. The geometric error with the largest absolute value among the multiple output evaluation points is used as the unified evaluation index.

[0030] Specifically, after clarifying the research object of the multi-branch closed-loop transmission chain, a unified coordinate expression system and geometric error modeling method are established. This step is used to unify the installation error, attitude error, and transmission pair error in the transmission chain under the same error transmission framework, so that the errors in different branch paths can be superimposed according to the actual power transmission relationship.

[0031] First, a global fixed coordinate system and several local coordinate systems are established based on the structural topology of the transmission chain. The global fixed coordinate system is used to uniformly describe the installation and attitude errors of multiple end-output evaluation points; the local coordinate systems are established at the reference sections of each component to describe the local installation and attitude errors of each transmission component itself. This coordinate system allows for a unified expression of the error propagation relationships between different transmission paths, different components, and different output points, avoiding the problems of double-counting errors in common segments or omissions of errors in branch segments due to inconsistent coordinate references.

[0032] Secondly, key error terms affecting the accuracy of the end effector are selected. For transmission chains that mainly generate output deviations in the vertical plane, the geometric error model should at least include the vertical position error of the transmission components, the attitude error in the force plane, and the equivalent installation error or equivalent transmission error of the key gear transmission pairs.

[0033] Then, based on the common input, branch transmission, convergence transmission, and terminal output relationships of the transmission chain, an error mapping model is established from the key geometric error term to multiple terminal output evaluation points. For the i-th terminal output evaluation point, its geometric error output model is: in: Indicates the first Geometric vertical error of each end output evaluation point; Indicates the first Vertical position error of a key transmission component; Indicates the first A key transmission component revolves around a local Axis attitude error; Indicates the first The equivalent error of a key transmission pair; Indicates the first The vertical position error of a key transmission component is transmitted to the first... The influence coefficient of each end output evaluation point; Indicates the first The attitude error of the key transmission component is transmitted to the first The influence coefficient of each end output evaluation point; Indicates the first The equivalent error of the key transmission pair is transmitted to the first... The influence coefficient of each end output evaluation point; Indicates the quantity of key transmission components; Indicates the number of key transmission pairs.

[0034] Considering that excessive error at any output point may lead to the end effector failing to meet accuracy requirements, the geometric error with the largest absolute value among multiple output evaluation points is used as a unified evaluation index. Specifically, the unified evaluation index is expressed as follows: in: This represents the most unfavorable geometric output error under multi-station synchronization constraints. Indicates the first Geometric vertical error of each end output evaluation point; This indicates the number of evaluation points at the end of the output. This evaluation metric is used for subsequent Sobol sensitivity analysis, initial precision allocation, and geometric error verification.

[0035] Step 3: Sobol sensitivity analysis and initial precision allocation.

[0036] After completing the unified coordinate representation and error modeling, the Sobol global sensitivity analysis method is used to quantify the contribution of each geometric error term to the unified evaluation index and the error of a single end-point output evaluation point, obtaining the total effect index, identifying key geometric error terms in the multi-branch closed-loop transmission chain, and allocating initial precision based on the sensitivity results. Following the principle of "strict control of high-sensitivity terms and moderate relaxation of low-sensitivity terms," ​​initial precision allocation is performed for position / meshing error terms and angle error terms respectively, determining the initial allowable value for each error term. This step is used to quantify the contribution of each geometric error term to the error of a single end-point output point and the comprehensive error of multi-station synchronization under the condition of multiple error sources coexisting, and further converts the contribution ranking into the allowable value for each error term.

[0037] First, the key geometric error terms involved in the sensitivity analysis are grouped into an error variable vector: in: This represents the key geometric error vector of a multi-branch closed-loop drive train. Indicates the first One geometric error term; This indicates the number of geometric error terms involved in the sensitivity analysis.

[0038] For multiple evaluation points on the terminal output component, establish a single-point evaluation function for each: in: Indicates the first Geometric error output for each evaluation point; Represents the relationship between the key geometric error vector and the first... Mapping function for geometric error of each output evaluation point; Indicates the first Geometric vertical error of each output evaluation point; This indicates the number of evaluation points at the end of the output.

[0039] Considering the requirement for multi-station synchronous output in multi-branch closed-loop transmission chains, a comprehensive evaluation function under multi-station synchronous constraints is further constructed: in: This represents the comprehensive evaluation quantity under multi-station synchronous constraints. This represents the mapping function from the key geometric error vector to the overall output error; This represents the most unfavorable geometric output error among multiple evaluation points.

[0040] Subsequently, two sets of independent sampling matrices are constructed: In the formula, Indicates the number of samples; This represents the number of input error terms. (Matrix) sum matrix Each row in the table represents a set of geometric error samples.

[0041] For the Construct a hybrid sampling matrix with geometric error terms. Hybrid sampling matrix Indicates the matrix The Column replacement with matrix The The resulting mixture matrix. Using this mixture matrix, we can examine the first error term while keeping the remaining error term samples unchanged. The impact of changes in each error term on the output error.

[0042] For any output evaluation quantity ,in: The Jansen estimator is used to calculate the first... The geometric error term affects the first... The total effect index of each output evaluation quantity: in: Indicates the first The geometric error term affects the first... The total effect index of each output evaluation quantity; A and B are two independent sampling matrices; Representation matrix The Row samples; Indicates the matrix The Column replacement with matrix The The resulting mixture matrix after column division; Represents the mixture matrix The Row samples; Indicates the first One output evaluation function; Indicates the first The variance of each output evaluation quantity; Indicates the first Geometric error output for each evaluation point; Indicates the number of samples.

[0043] Total effect index Used to characterize the Each geometric error term affects the output evaluation quantity. The overall contribution includes both the independent effect of the error term and its coupling effect with other error terms. When The larger the value, the more significant the impact of the error term on the corresponding output evaluation quantity, and it should be given priority control in subsequent accuracy allocation.

[0044] Initial accuracy allocation is mainly based on comprehensive evaluation quantity. Corresponding total effect index As the basis for ranking. Each individual evaluation metric. Corresponding total effect index It can be used to help determine the sensitivity differences of different output points to the same error source.

[0045] After obtaining the total effect index of each geometric error term, the initial accuracy is allocated according to the principle of "strict control of high-sensitivity terms and moderate relaxation of low-sensitivity terms". Considering that position errors, meshing errors and angle errors belong to different physical quantities, position / meshing error allocation models and angle error allocation models are established separately to avoid direct mixing and allocation of error terms with different dimensions.

[0046] For position-related error terms, let the set of error terms be: In the formula, Represents the set of position-related error terms; Indicates the first One position / engagement error term; Indicates the number of position-related error terms.

[0047] Based on the total effect index corresponding to the comprehensive evaluation quantity, the first... The insensitivity weights for each positional error term are: in: Indicates the first Weighting of each location-type error term; Indicates the first Each geometric error term affects the unified evaluation index. The total effect index; To prevent small positive quantities with a denominator of zero; This represents the sensitivity adjustment coefficient. As shown in the formula above, the larger the total effect index, the smaller the weighting of the anti-sensitivity distribution, and the smaller the corresponding allowable error value.

[0048] Total allowable error for a given location Under the conditions, the first The allowable value for each positional error term is defined as follows: in: Indicates the first Initial allowable values ​​for each positional error term; This represents the total allowable error for positional errors.

[0049] For angle-related error terms, let the set of error terms be: In the formula, Represents the set of angle-related error terms; Indicates the first An angle-related error term; Indicates the number of angle-related error terms.

[0050] Based on the total effect index corresponding to the comprehensive output, the first... The weights for the insensitivity of each angle-type error term are as follows: in: Indicates the first Weights are assigned to the insensitivity of each angle-type error term. Indicates the first Each geometric error term affects the unified evaluation index. The total effect index.

[0051] Total allowable error for a given angle category Under the conditions, the first The allowable values ​​for each angle-type error term are defined as follows: in: Indicates the first Initial allowable values ​​for each angle-type error term; This represents the total allowable amount of angular error.

[0052] After completing the initial precision allocation, the allowable values ​​of each error term are re-substituted into the geometric error propagation model, and back-substitution verification is performed on multiple output evaluation points. For the first... The geometric error output after the allocation of each output evaluation point can be expressed as: in: Indicates the first The geometric error output of each output evaluation point after initial precision allocation; This represents the initial precision allocation vector, which consists of the allowable values ​​for each error term.

[0053] Furthermore, the error with the largest absolute value among multiple output evaluation points is taken as the geometric verification result after initial allocation: in: This represents the most unfavorable geometric output error under multi-station synchronous constraints after initial precision allocation.

[0054] like If the geometric error control index is met, then the initial accuracy allocation result will be used as the input for subsequent load transfer and elastic error analysis; if If the geometric error control targets are not met, adjust the total allowable amount of position / meshing errors. Total allowable error for angles or sensitivity adjustment coefficient Then, the initial accuracy allocation and verification are redone until the geometric error control requirements are met.

[0055] Step 4: Load transfer and elastic error analysis. Based on the initial accuracy allocation results, the working load is introduced to establish an elastic structural equation that includes the overall stiffness matrix and nodal load vectors. The deflection and rotation angle of key load-bearing components are calculated, and weak stiffness areas are identified based on the improvement rate of the synchronous output error of the multi-station end based on the addition of supports or the improvement of local constraint stiffness.

[0056] Specifically, after completing the Sobol sensitivity analysis and initial accuracy allocation, the influence of elastic error under working load is further considered. This step is used to determine whether the transmission chain can still meet the accuracy requirements of the end effector under actual load, provided that the geometric error meets the initial control requirements, and to identify the stiffness-weak areas that significantly affect the multi-station output error of the end effector.

[0057] For multi-branch closed-loop drive trains, the working load borne by the terminal output component not only directly causes local deflection and rotation of the terminal output section, but also transmits it to the confluence section through gear pairs, further affecting the elastic response of the upstream drive train. Therefore, it is necessary to establish a load transfer and elastic error model in addition to the geometric error model.

[0058] In modeling, critical long shafts and end-output components in the transmission chain, which are subject to loads, are represented as beam element models. Constraints at support locations are represented as support stiffness, and load transfer between gear pairs or other transmission pairs is represented as concentrated forces, concentrated moments, or equivalent nodal loads. This leads to the discretized elastic structural equations: in: This represents the overall stiffness matrix after discretization of the key load-bearing components of the transmission chain. Represents the nodal displacement vector; This represents the nodal load vector formed by the terminal working load, the equivalent force of the transmission pair, and the load return effect.

[0059] After obtaining the nodal displacement vectors, interpolation is performed on each beam element using the Euler-Bernoulli beam element shape function to obtain the nth... The beam element in axial position Deflection function at: in: Indicates the first The beam element in axial position Deflection at the point; Indicates the first The shape function matrix of a beam element; Indicates the first The nodal displacement vectors corresponding to each beam element.

[0060] Axial position of each beam element The angle of rotation at a given point is obtained by differentiating the deflection function with respect to the axial coordinate: in: Indicates the first The beam element in axial position The angle of rotation at the point is determined by splicing the deflection and rotation functions of each beam element according to their axial positions. This yields the overall deflection and rotation curves of the key load-bearing component along the axial direction.

[0061] To identify weak stiffness areas in the transmission chain, candidate support locations or local reinforcement locations on key load-bearing components are used as structural optimization variables, with the error improvement rate as the evaluation index. Let the maximum total output error under multi-station synchronous constraints in the initial structure be... In the candidate position The maximum total output error after adding supports or increasing local constraint stiffness is The error improvement rate of the candidate position is then defined as: in: Indicates candidate position Improvement rate of multi-station synchronous output error; This represents the maximum total output error under the initial structure; Indicates the candidate position The maximum total output error after adding supports or increasing the stiffness of local constraints.

[0062] when The larger the value, the more significant the improvement in the output accuracy of the multi-station output at the candidate location due to support reinforcement or local stiffness enhancement. Therefore, this candidate location should be prioritized in subsequent structural optimization and multi-objective decision-making. By scanning different candidate locations along the axial direction of the critical load-bearing component, the relationship between the support reinforcement location and the error improvement rate can be obtained, thereby identifying stiffness-weak areas in the critical load-bearing component.

[0063] Step 5: Consider the multi-objective decision-making of accuracy and stiffness, establish a set of design variables that simultaneously include error allocation variables and structural stiffness variables, construct the objective functions of position accuracy, attitude accuracy, and structural stiffness, use a multi-objective optimization algorithm to solve the Pareto candidate scheme set, and select the optimal structure-accuracy combination scheme from them through a comprehensive decision-making method.

[0064] Specifically, after completing the initial accuracy allocation, load transfer, and elasticity error analysis, if multiple structural-accuracy combination schemes exist that meet or closely approximate the accuracy requirements of the end effector, a multi-objective decision-making model considering accuracy and rigidity is further established. This step is used to comprehensively weigh the end-effector position error, end-effector attitude error, and structural design, avoiding problems such as excessive structural reinforcement, overly stringent manufacturing and assembly requirements, or insufficient engineering feasibility of the scheme due to solely reducing output error through a single objective.

[0065] First, establish the accuracy-rigidity joint design variables. Specifically, the accuracy-rigidity joint design variables include both error allocation variables and structural stiffness variables. The error allocation variables describe the overall contraction or relaxation of allowable values ​​for positional and angular errors, while the structural stiffness variables describe the local support stiffness variations of key load-bearing components and the locations of candidate support reinforcements. The design variable set can be represented as: in: Indicates the joint design variables of structure and precision; This represents the scaling factor for position / meshing error allocation, used to reflect the overall contraction or relaxation of allowable values ​​for position and meshing errors; This represents the scaling factor for angular error allocation, used to reflect the overall contraction or relaxation of the allowable value for angular errors; Indicates the first Equivalent stiffness scaling factor for a key load-bearing component or key support area; Indicates the first New support locations or local reinforcement locations on key load-bearing components.

[0066] For any candidate solution The allowable values ​​for position / engagement errors and angle errors can be obtained by scaling the initial allocation results; the elastic error is calculated by substituting the corresponding support stiffness and support position into the elastic error model. Therefore, each candidate scheme simultaneously contains geometric accuracy allocation information and structural stiffness enhancement information.

[0067] Secondly, a position accuracy target is established. For a multi-station synchronous output structure with multiple end-point output evaluation points, the maximum value of the total output error at each evaluation point represents the most unfavorable position error under this candidate scheme. This value is then normalized to the allowable position error to obtain the position accuracy target function: in: This represents the objective function for positional accuracy. Indicate candidate solutions Next The total output error of each end output evaluation point; Indicates the number of evaluation points in the final output; This indicates the end position error control index. The smaller the value, the better the multi-station synchronous position error control effect under this scheme.

[0068] Then, an attitude accuracy target is established. For terminal output components or critical output stages, the comprehensive attitude error is used to characterize the stability of the terminal output, and this is normalized with the allowable attitude error to obtain the attitude accuracy target function: in: Represents the attitude accuracy objective function; Indicate candidate solutions The overall attitude error of the lower terminal output component or key output stage; This indicates the attitude error control index. The smaller the value, the better the stability of the terminal's output posture.

[0069] Furthermore, a structural stiffness target is established. This target reflects the structural design difficulties caused by error distribution shrinkage, support stiffness adjustment, and support position deviation from the recommended region, and is written as: in: Represents the objective function for structural stiffness; This indicates the number of key load-bearing components involved in structural optimization; Indicates the first Recommended reinforcement locations determined based on the support location scanning results on key load-bearing components; Indicates the first The effective length of a key load-bearing component; , , and These are all weighting coefficients used to adjust the influence of error allocation scaling, stiffness adjustment, and support position offset on the structural cost objective. The smaller the value, the smaller the structural adjustment range and the lower the implementation cost of the solution.

[0070] Therefore, a multi-objective optimization problem considering accuracy and rigidity is constructed: The constraints of this optimization problem should simultaneously satisfy the allowable error value, the upper and lower bounds of the variables, and the final output accuracy constraint: in: Indicate candidate solutions Next Allowable values ​​for each key error term; and They represent the first The lower and upper limits of manufacturing or assembly feasibility for each key error item; and Indicates the scaling factor for position / engagement type error allocation. The lower and upper limits of the value; and These represent the scaling factors for angle-type error allocation. The lower and upper limits of the value; , They represent the first Equivalent stiffness scaling factor for key load-bearing components The lower and upper limits of the value; and They represent the first Additional supports or local reinforcements may be placed on key load-bearing components. The lower and upper limits of the value.

[0071] After obtaining the multi-objective optimization model, the Pareto optimization method is used to solve for the candidate solution set. Each solution in the Pareto candidate solution set represents a compromise solution that cannot be completely dominated by other solutions in terms of position accuracy, attitude accuracy, and structural design difficulty. To select the optimal solution that meets design preferences from multiple Pareto candidate solutions, the TOPSIS comprehensive decision method is further used for ranking.

[0072] Let the first The objective value vector of the Pareto candidate solutions is: in: For the first A vector of target values ​​for Pareto candidate solutions; The objective function for structural stiffness The One Pareto candidate solution; The attitude accuracy objective function The One Pareto candidate solution; The objective function for structural stiffness The One Pareto candidate solution.

[0073] Given position accuracy weights, attitude accuracy weights, and structural cost weights: in: , and These represent the weights of the position accuracy target, attitude accuracy target, and structural cost target in the comprehensive decision-making process.

[0074] After constructing a decision matrix from the Pareto candidate solutions and performing dimensionless processing, the ideal optimal solution and the ideal worst solution are constructed respectively. Let the first... The distances from each candidate solution to the ideal optimal solution and the ideal worst solution are respectively and Then the overall similarity of the candidate solution is: In the formula, Indicates the first Overall relevance of each candidate solution. The larger the value, the closer the candidate solution is to the ideal optimal solution and the further away it is from the ideal worst solution. Therefore, it is more suitable as a precision-rigid integrated optimization solution under the current design preference.

[0075] Through the aforementioned multi-objective decision-making process, a superior scheme that balances the synchronous positional accuracy of multiple terminal workstations, the stability of the terminal output attitude, and the difficulty of structural design can be selected from multiple feasible structure-precision combination schemes. The error allocation coefficient, the stiffness scaling coefficient of key load-bearing components, and the locations of additional supports or local reinforcements corresponding to this scheme will serve as the basis for the final precision allocation result and the conversion of engineering control indicators.

[0076] Step Six: Output the allocation results. Based on the optimal structure-precision combination scheme, determine the final allowable value of each key geometric error item, the support reinforcement or local stiffness adjustment result of key load-bearing components, and convert the allocation results at the error item level into manufacturing and assembly control indicators.

[0077] Specifically, after completing the multi-objective decision-making process considering accuracy and rigidity, the final accuracy allocation and structural optimization results of the multi-branch closed-loop drive train are output. This step is used to transform the optimization results obtained from the aforementioned sensitivity analysis, initial accuracy allocation, elasticity error analysis, and multi-objective decision-making into engineering control indicators that can be used for manufacturing, assembly, and verification.

[0078] First, based on the optimal structure-accuracy combination scheme obtained through multi-objective decision screening, the final allowable values ​​for each key error term are determined. Let the final selected scheme be: The corresponding final error allocation vector can then be expressed as: in: This indicates the final error allocation result; Indicates the first The final allowable value for each key error term; This indicates the number of critical error terms involved in the precision allocation.

[0079] For schemes that also include structural optimization variables, the results of support reinforcement or local stiffness adjustment for key load-bearing components are further output: in: This represents the final structural optimization result; This indicates the equivalent stiffness configuration of the h-th critical load-bearing component or critical support region; This indicates the location of a new support or local reinforcement on the h-th critical load-bearing component; This indicates the number of key load-bearing components involved in structural optimization.

[0080] After obtaining the final error allocation vector, the allocation results at the error term level are further transformed into executable manufacturing and assembly control indicators. For shaft position errors, these can be transformed into requirements for the consistency of support hole axes, the positional accuracy of support holes, or the local installation error requirements of key mounting positions relative to the reference axis; for shaft attitude errors, these can be transformed into requirements for the parallelism or inclination of the common axis of support holes relative to the assembly reference axis; for transmission pair equivalent errors, these can be transformed into requirements for gear mounting position errors, gear pair center distance errors, end face runout, radial runout, or meshing installation relationship errors; and for structural stiffness optimization results, these can be transformed into requirements for new support positions, support stiffness levels, local reinforcement requirements for key shaft segments, or support arrangement adjustment requirements.

[0081] Therefore, the final output should include at least the following: (1) The final allowable value of each key geometric error term; (2) The final allocation results of positional errors and angular errors; (3) The location of support reinforcement or local stiffness configuration of key load-bearing components; (4) Final error verification results of multiple end output evaluation points; (5) Manufacturing and assembly control indicators obtained from the conversion of error terms; (6) Recommendations on the corresponding bearing fit, support hole accuracy, installation relationship error and running accuracy level.

[0082] By using the above output method, the accuracy requirements of the end actuator of the multi-branch closed-loop transmission chain can be back-reasoned step by step to specific error items, key support structures and engineering manufacturing assembly control objects. This allows the accuracy allocation results to no longer remain at the theoretical error weight level, but to directly serve the parts processing, assembly control, support arrangement and accuracy allocation.

[0083] The following examples further illustrate the specific implementation and technical effects of the precision allocation method for multi-branch closed-loop transmission chains that considers precision-rigid coupling in this invention.

[0084] This embodiment takes a complex transmission chain in a certain device as an example to illustrate the specific application process of the present invention in a multi-branch closed-loop transmission chain with the characteristics of common input, split transmission, converged output and terminal multi-station output.

[0085] Specifically, this drive chain is responsible for continuing to transmit power after the current converges and driving the multi-station output at the terminal. Its power transmission route includes two branches: one is servo motor → pulley → flywheel → main shaft 1 (gear 1) → crankshaft 2 (gear 2) → shaft 3 → reversing shaft 9 → shaft 11 → camshaft 13 → camshaft 14 → end-effector; the other is servo motor → pulley → flywheel → main shaft 1 (gear 1) → crankshaft 2 (gear 2) → shaft 4 → reversing shaft 10 → shaft 12 → camshaft 13 → camshaft 14 → end-effector. The two branches diverge at crankshaft 2 and converge at camshaft 13, then continue to transmit power to camshaft 14 via a gear pair. A simplified diagram of the mechanism is shown below. Figure 2 As shown.

[0086] To retain the error sources and load-bearing components that have the most significant impact on the end output accuracy in this transmission chain, crankshafts 2, 3, and 4, reversing shafts 9, 10, 11, and 12, camshafts 13 and 14, and their related cylindrical and bevel gear pairs are selected as the accuracy allocation objects.

[0087] The basic error transmission relationship is as follows: the installation error of crankshaft 2 is transmitted to the left and right branches through the split section, and then transmitted to camshaft 13 through reversing shafts 9-11 and 10-12. The combined error formed after the two branches converge at camshaft 13 continues to be transmitted to camshaft 14. At the same time, the local displacement and rotation angle generated by camshaft 14 under working load further affect the terminal multi-station output error.

[0088] To evaluate the terminal output accuracy of the transmission chain in this embodiment, three output evaluation points are selected on the camshaft 14. The axial positions of the three evaluation points relative to the left end reference section of the camshaft 14 are 290 mm, 862 mm and 1506 mm, respectively. The vertical output error of the three output evaluation points is examined, and the simultaneous satisfaction of the accuracy requirements of the three output evaluation points is taken as the unified control target.

[0089] Error modeling revolves around two questions: first, how the installation error of crankshaft 2 is transmitted to camshaft 14 via the left and right branch paths and the camshaft 13 confluence section; second, how the errors of the camshaft 13 confluence section, the 13-14 stage transmission pair, and the camshaft 14 itself manifest as different vertical output deviations at the three output evaluation points. Considering that the main error response of this transmission chain is concentrated in the vertical plane, the model retains the vertical position error and the tilt error in the force plane, and no longer simultaneously develops errors in other directions.

[0090] To facilitate a unified description of error terms, a global fixed coordinate system and a local axis coordinate system are established. Among them, The coordinate system is global, with the origin located at the center of camshaft 14; , , , , , , , and These are the local coordinate systems for crankshafts 2, 3, 4, 9, 10, 11, 12, 13, and 14, respectively, with the origin located at the center of the reference section on the left end of each shaft.

[0091] Define the vertical position error and the local error of the reference section at the left end of crankshaft 2. The tilt errors of the shafts are respectively and The vertical position errors of axes 3, 4, 9, 10, 11, 12, 13, and 14 are respectively... , , , , , , and Its local The tilt errors of the shafts are respectively , , , , , , and Meanwhile, the equivalent mounting or transmission errors for gear pairs 3 / 4, 5 / 6, 17 / 18, 20 / 21, 18 / 19, and 21 / 22 are defined as follows: , , , , and .

[0092] Since the common input segment error affects both the left and right branches simultaneously, the errors of the splitting segment and the reversing segment will first converge at camshaft 13, and then continue to be transmitted to camshaft 14 through the 13-14 stage transmission pair. The position error and attitude error of camshaft 14 will be further amplified according to the axial position of the output point. Therefore, the first stage error of camshaft 14... The vertical output error of each output evaluation point can be expressed as: in: Indicates camshaft 14th Local vertical error of each output evaluation point; Indicates the first The axial distance from each output evaluation point to the reference section at the left end of the camshaft 14, where , , ; This indicates the axial distance from the reference mounting position of camshaft 14 to the left end reference section; Indicates the first The first critical error term is propagated to the second... The influence coefficients at each output evaluation point are determined by applying small perturbations to each of the three output points and calculating the error increments, thereby obtaining the degree of influence of each error term on different output evaluation points.

[0093] Considering that this transmission chain is a three-station synchronous output structure, if the positional error of any one of the three output points is too large, it will become the weak point of the entire chain. Therefore, the local vertical error with the largest absolute value among the three output points is taken as the unified evaluation quantity, defined as: After establishing the error model, Sobol global sensitivity analysis was used to identify key geometric error terms. Since this transmission chain uses the vertical errors of the three output evaluation points of camshaft 14 as evaluation indicators, respectively... , and As a single-point output quantity, and taking the most unfavorable output error under the three-station synchronous constraint as the value. As a comprehensive output, the corresponding output evaluation function can be written as: in: This is the key geometric error vector of the transmission chain in this embodiment; , and These represent the geometric error output values ​​for the three output evaluation points, respectively. This represents the overall output under multi-station synchronous constraints.

[0094] No. The total effect exponent of each error term on the single-point output and the combined output is calculated using the Jansen formula: in: The number of samples; and There are two independent sampling matrices; Indicates the matrix The Column replacement with matrix The The resulting mixture matrix after column division; The variance of the corresponding output quantity; The larger it is, the more likely it is to be the first The error term affects the first... The greater the overall contribution of each output evaluation metric, the better.

[0095] Since the goal of subsequent precision allocation is not to ensure that a single output evaluation point meets the standard, but to ensure that all three output evaluation points simultaneously meet the control requirements under synchronous constraints, the initial precision allocation is mainly based on the overall output quantity. The corresponding total effect index was used as the ranking criterion. The sensitivity analysis results are as follows: Figure 3 As shown.

[0096] After obtaining the total effect index of each error term, the initial accuracy is allocated according to the principle of "strict control of high-sensitivity terms and moderate relaxation of low-sensitivity terms". Considering that positional errors, meshing errors and angular errors belong to different physical quantities, allowable values ​​for positional / meshing errors and allowable values ​​for angular errors are set separately to avoid direct mixing and allocation of different physical quantities.

[0097] For position / engagement error terms, the weighting of their insensitivity assignment is defined as follows: in: For the first Weighting of each position / engagement error term; To prevent small quantities with a denominator of zero; This represents the sensitivity adjustment coefficient. As shown in the formula above, the larger the total effect exponent, the smaller the weighting, and consequently, the smaller the allowable value. This represents the total allowable error at a given position / meshing type. Under the conditions, the first The allowable values ​​for each position / engagement error term are: For angle-related error terms, the weighting of their insensitivity is defined as follows: Total allowable error for a given angle category Under the conditions, the first The allowable values ​​for each angle-type error term are: The initial precision allocation results are as follows Figure 4As shown. Substituting the allowable values ​​of each error term into the geometric error model of the transmission chain in this embodiment, the vertical errors of the three output work points of the camshaft 14 are recalculated. At this time, the... The verification results for each output workstation can be written as: in: , , , , , and These represent the allowable values ​​for each error term obtained according to the Sobol results; Indicates the number of allocations after the first allocation. Local vertical error of each output work point.

[0098] Furthermore, the local error with the largest absolute value among the three output work points is taken as the verification result, i.e. Verification results are as follows Figure 5 As shown, it can be seen that the verification results meet the control indicators when only considering geometric errors. However, it is still necessary to further analyze whether the elastic error plus the geometric error will exceed the allowable error value under the action of working load.

[0099] Starting from the dual-load condition at the end of camshaft 14. Camshaft 14 in and Each of the camshafts 14 and 13 is subjected to a 5 kN vertical downward load. This dual load not only acts directly on the camshaft 14 body, causing local deflection and rotation of the camshaft 14, but is also transmitted in the reverse direction to the camshaft 13 through the gear pair, and further fed back to the upstream split section. Therefore, the elastic error of the transmission chain in this embodiment is not determined independently by any one shaft, but is jointly determined by the load on the end of the camshaft 14, the deformation of the camshaft 13 confluence section, the gear pair transmission, and the stiffness of the crankshaft 2 split section.

[0100] In terms of modeling methodology, a solution strategy of "beam elements + equivalent support stiffness" is adopted. Let the overall stiffness matrix of the discretized system be... The node load vector is Then the nodal displacement vector satisfy: in: The nodal load vector is formed by the dual loads of the camshaft 14 and the equivalent forces of each gear pair.

[0101] After obtaining the nodal degrees of freedom, the deflection function within the element is obtained by interpolating the Euler-Bernoulli beam element shape function for each beam element: in: Indicates the first Axial position within each beam unit Deflection at the point; The shape function matrix represents the element; This represents the nodal displacement vector corresponding to this element. The axial position of each axis... The angle of rotation at a given point is obtained by differentiating the deflection function with respect to the axial coordinate: By concatenating the deflection and rotation functions of each unit according to their axial positions, the overall axial deflection curves of crankshaft 2, camshaft 13, and camshaft 14 can be obtained. and turning curve ,like Figure 6 As shown.

[0102] It can be seen that, under the initial configuration, the main areas of weak stiffness are concentrated in the crankshaft 2 flow splitter region, the camshaft 13 flow collector region, and the camshaft 14 terminal output region. Among these, the crankshaft 2 flow splitter region determines the level of common elastic error, the camshaft 13 flow collector region determines the amplification of the flow error to the terminal output, and the camshaft 14 directly determines the local deflection and attitude changes at the three output evaluation points. To identify the most worthy priority reinforcement locations, candidate support positions on crankshaft 2, camshaft 13, and camshaft 14 are used as structural design variables, and the comprehensive output error improvement rate is used as the evaluation index. Let's assume a certain candidate position... After adding supports or increasing the stiffness of local constraints, the most unfavorable total error among the three output evaluation points is reduced from... Reduced to The improvement rate is then defined as: in: The comprehensive error with the largest absolute value among the three output evaluation points under the initial structure; For in position The maximum overall error after adding supports or increasing local stiffness; The larger the value, the more significant the improvement in multi-station synchronous output error due to the enhanced support at that location. The results of the improvement rate analysis for the newly added support locations on crankshaft 2, camshaft 13, and camshaft 14 are as follows: Figure 7 As shown.

[0103] The scanning results of the newly added support locations show that the improvement rates of crankshaft 2, camshaft 13, and camshaft 14 all exhibit a "high in the middle and low at both ends" characteristic. The improvement effect of adding supports to crankshaft 2 is significant in the approximately 400 mm-900 mm range, peaking around 800 mm, indicating that this section corresponds to the critical weak points in the concentrated area of ​​the splitter gear and the common input section. Camshaft 13 shows a generally high improvement rate in the approximately 300 mm-1500 mm range, indicating that the area near the confluence gear mounting area and gear meshing area needs focused reinforcement. Camshaft 14 maintains a consistently high improvement rate in the approximately 600 mm-1500 mm range, peaking around 1100 mm, indicating that the long span section in the middle of the terminal output shaft and the load-bearing area are the most critical weak points in stiffness throughout the entire chain. Therefore, structural optimization should not adopt a uniform support arrangement. Instead, it should prioritize directional reinforcement around the crankshaft 2 flow distribution transition area, the camshaft 13 flow junction area, and the camshaft 14 load area and intermediate station area. The optimized structural rotation angle and deflection curves are as follows: Figure 8 As shown in the figure, the optimized curves indicate that the peak deflection and peak rotation angle of the common input section of crankshaft 2, the merging section of camshaft 13, and the terminal output section of camshaft 14 are significantly reduced, thereby effectively compressing the elastic error amplification effect in the transmission chain.

[0104] After completing the geometric accuracy redistribution and structural reinforcement, multiple feasible structure-accuracy combination schemes still exist. Different schemes cannot simultaneously achieve optimal performance in terms of positional errors at the three output evaluation points, attitude errors at the terminal output stage, and structural implementation costs. Therefore, a comprehensive evaluation through multi-objective decision-making is necessary. Based on the optimized structural form, the design variable set is defined as follows: in: Indicates the scaling factor for position / engagement type errors; Indicates the scaling factor for angle-type error assignment; , and These represent the equivalent stiffness scaling factors for the key sections of crankshaft 2, camshaft 13, and camshaft 14, respectively. , and These represent the newly added support positions for crankshaft 2, camshaft 13, and camshaft 14, respectively.

[0105] Establish the objective function for positional accuracy: Establish the attitude accuracy objective function: Establish the objective function for structural stiffness: Therefore, a multi-objective optimization model is established: This model is used to find an engineering-acceptable optimal range of compromises between the three-station synchronous position error, the terminal attitude error, and the structural design difficulty.

[0106] Figure 9 The Pareto candidate solution set obtained by multi-objective optimization in this embodiment is presented, and further comprehensive evaluation is performed using the TOPSIS method. Let the... The objective value vector of the candidate solutions is: Given position accuracy weights, attitude accuracy weights, and stiffness weights: After constructing the Pareto candidate solutions into a decision matrix and making it dimensionless, the ideal optimal solution and the ideal worst solution are constructed respectively, and the th... Distance from each candidate solution to both and And calculate the overall similarity: when The larger the value, the closer the solution is to the ideal optimal solution and the further it is from the ideal worst solution, thus making it more suitable as the optimal candidate solution under the current design preferences. This step allows for the selection of a superior solution from multiple feasible options that balances the accuracy of key mounting positions, the overall attitude stability of crankshaft 2, and the cost of structural implementation. The TOPSIS comprehensive score results are as follows: Figure 10 As shown.

[0107] The scoring results show that among the multiple Pareto candidate solutions, the optimal solution selected by TOPSIS comprehensive evaluation is candidate solution number 1, with a comprehensive score of 0.9129. This indicates that the solution has a good balance among the three objectives of position accuracy, attitude accuracy, and structural cost. The corresponding optimal design variable combination is shown in Table 1. Table 1. TOPSIS Optimal Design Variable Combinations and Their Engineering Implications The distribution result of the transmission chain is as follows: Figure 11 As shown.

[0108] Substituting the initial accuracy allocation results into the error propagation model for calculation, the maximum position error of the three output work points is approximately 2.7 μm, and the maximum attitude error is approximately 2.3 μrad. This indicates that, from the perspective of geometric error alone, the initial allocation result of the transmission chain in this embodiment is already at a low level. After superimposing the load, the total output error under the initial structure is approximately 720 μm, far exceeding the allowable index; after optimization, the total output error has been significantly reduced to approximately 15 μm, and further reduced to approximately 12 μm under the Pareto-TOPSIS optimal scheme, meeting the control index of 16 μm. Through the addition of support optimization and comprehensive decision-making, the total system error has been compressed by orders of magnitude. From the key variable allocation results, under the optimal scheme, and It is still at the highest control level, indicating that the equivalent meshing and installation error of the 11th / 12th axis to the camshaft 13th bus stage has the most direct impact on the terminal multi-station output, and therefore needs to be strictly controlled first. Secondly, this indicates that the attitude error of the camshaft 13 busbar section remains the key factor determining the error amplification; simultaneously, , , as well as , The error terms related to intermediate commutation stages and terminal output stages also maintained a high weight.

[0109] Furthermore, to ensure that the optimized accuracy allocation results can directly serve actual manufacturing and assembly control, it is necessary to further transform the allocation results at the error term level into specific installation locations and process control quantities. For the drivetrain in this embodiment, This can be converted into the parallelism requirement between the common axis formed by the support hole of camshaft 13 and the assembly reference axis; This can be converted into the parallelism requirement between the common axis of the crankshaft 2 support holes and the assembly reference axis; , and This can be converted into the consistency requirements of the axes of the two main support holes of crankshaft 2, camshaft 13, and camshaft 14, respectively. , , and This can then be transformed into local installation error control of the gear mounting positions at the merging and terminal stages. Based on the above approach, the actual accuracy distribution results of this transmission chain can be obtained, as shown in Table 2.

[0110] Table 2. Actual accuracy distribution results of the transmission chain in this embodiment. The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for accuracy allocation in a multi-branch closed-loop drive train considering accuracy-rigid coupling, characterized in that: Includes the following steps: Step 1: Define the research object and end output indicators. For multi-branch closed-loop transmission chains with common input, branch transmission, converge output and terminal multi-station output characteristics, identify its branching position, converge position and terminal output component, and select multiple work points on the terminal output component as end evaluation points to determine the output accuracy requirements that each evaluation point must meet. Step 2: Unify coordinate representation and error modeling. Establish a global fixed coordinate system and a local coordinate system. Select key geometric error terms that affect the accuracy of the end effector. Based on the transmission relationship of the transmission chain, establish an error mapping model from the key geometric error terms to multiple end output evaluation points. Use the geometric error with the largest absolute value among the multiple output evaluation points as the unified evaluation index. Step 3: Sobol sensitivity analysis and initial precision allocation. The Sobol global sensitivity analysis method is used to quantify the contribution of each geometric error item to the unified evaluation index and the error of a single end output evaluation point, so as to obtain the total effect index. Initial precision allocation is performed on position / meshing error items and angle error items respectively to determine the initial allowable value of each error item. Step 4: Load transfer and elastic error analysis. Based on the initial accuracy allocation results, the working load is introduced to establish an elastic structural equation that includes the overall stiffness matrix and nodal load vectors. The deflection and rotation angle of key loaded components are calculated, and weak stiffness areas are identified based on the improvement rate of the synchronous output error of the multi-station end based on the addition of supports or the improvement of local constraint stiffness. Step 5: Consider the multi-objective decision-making of accuracy and stiffness, establish a set of design variables that simultaneously include error allocation variables and structural stiffness variables, construct the objective functions of position accuracy, attitude accuracy, and structural stiffness, use a multi-objective optimization algorithm to solve the Pareto candidate scheme set, and select the optimal structure-accuracy combination scheme from them through a comprehensive decision-making method; Step Six: Output the allocation results. Based on the optimal structure-precision combination scheme, determine the final allowable value of each key geometric error item, the support reinforcement or local stiffness adjustment result of key load-bearing components, and convert the allocation results at the error item level into manufacturing and assembly control indicators.

2. The accuracy allocation method for multi-branch closed-loop transmission chains considering accuracy-rigid coupling according to claim 1, characterized in that: In step two, the geometric error output model for the i-th terminal output evaluation point is: in: Indicates the first Geometric vertical error of each end output evaluation point; Indicates the first Vertical position error of a key transmission component; Indicates the first A key transmission component revolves around a local Axis attitude error; Indicates the first The equivalent error of a key transmission pair; Indicates the first The vertical position error of a key transmission component is transmitted to the first... The influence coefficient of each end output evaluation point; Indicates the first The attitude error of the key transmission component is transmitted to the first The influence coefficient of each end output evaluation point; Indicates the first The equivalent error of the key transmission pair is transmitted to the first... The influence coefficient of each end output evaluation point; Indicates the quantity of key transmission components; Indicates the number of key transmission pairs.

3. The accuracy allocation method for multi-branch closed-loop transmission chains considering accuracy-rigid coupling according to claim 1, characterized in that: In step two, the unified evaluation index is expressed as follows: in: This represents the most unfavorable geometric output error under multi-station synchronization constraints. Indicates the first Geometric vertical error of each end output evaluation point; This indicates the number of evaluation points at the end of the output.

4. The accuracy allocation method for multi-branch closed-loop transmission chains considering accuracy-rigid coupling according to claim 1, characterized in that: In step three, the total effect index of the j-th geometric error term on the r-th output evaluation quantity is calculated using the Jansen estimator: in: Indicates the first The geometric error term affects the first... The total effect index of each output evaluation quantity; A and B are two independent sampling matrices; Representation matrix The Row samples; Indicates the matrix The Column replacement with matrix The The resulting mixture matrix after column division; Represents the mixture matrix The Row samples; Indicates the first One output evaluation function; Indicates the first The variance of each output evaluation quantity; Indicates the first Geometric error output for each evaluation point; Indicates the number of samples.

5. The accuracy allocation method for multi-branch closed-loop transmission chains considering accuracy-rigid coupling according to claim 1, characterized in that: In step three, the allowable values ​​for position / meshing error terms in the initial accuracy allocation. Allowable values ​​for angle-related error terms They are determined in the following ways respectively: in: Indicates the first Initial allowable values ​​for each positional error term; This represents the total allowable error for positional errors; Indicates the first Weighting of each location-type error term; Indicates the first Each geometric error term affects the unified evaluation index. The total effect index; Indicates the number of position-related error terms; Indicates the first Initial allowable values ​​for each positional error term; This represents the total allowable error for positional errors; Indicates the first Weights are assigned to the insensitivity of each angle-type error term. Indicates the number of angle-related error terms; Indicates the first Each geometric error term affects the unified evaluation index. The total effect index; To prevent small positive quantities with a denominator of zero; This is the sensitivity adjustment coefficient.

6. The accuracy allocation method for multi-branch closed-loop transmission chains considering accuracy-rigid coupling according to claim 1, characterized in that: In step four, the elastic structure equation is expressed as: in The overall stiffness matrix of the key load-bearing components of the transmission chain after discretization; The nodal displacement vector; The nodal load vector is formed by the terminal working load, the equivalent force of the transmission pair, and the load return action. The improvement rate is defined as: in: Indicates candidate position Improvement rate of multi-station synchronous output error; This represents the maximum total output error under the initial structure; Indicates the candidate position The maximum total output error after adding supports or increasing the stiffness of local constraints.

7. The accuracy allocation method for multi-branch closed-loop transmission chains considering accuracy-rigid coupling according to claim 1, characterized in that: In step five, the design variable set is represented as follows: in: Indicates the joint design variables of structure and precision; Indicates the scaling factor for position / engagement type errors; Indicates the scaling factor for angle-type error assignment; Indicates the first Equivalent stiffness scaling factor for a key load-bearing component or key support area; Indicates the first New support locations or local reinforcement locations on key load-bearing components; Position accuracy objective function Attitude accuracy objective function and structural stiffness objective function They are represented as follows: in: This represents the objective function for positional accuracy. Indicate candidate solutions Next The total output error of each end output evaluation point; Indicates the number of evaluation points in the final output; This indicates the end-position error control index; Represents the attitude accuracy objective function; Indicate candidate solutions The overall attitude error of the lower terminal output component or key output stage; Indicates attitude error control parameters; Represents the objective function for structural stiffness; This indicates the number of key load-bearing components involved in structural optimization; Indicates the first Recommended reinforcement locations determined based on the support location scanning results on key load-bearing components; Indicates the first The effective length of a key load-bearing component; , , and These are all weighting coefficients used to adjust the influence of error allocation scaling, stiffness adjustment, and support position offset on the structural cost objective.

8. The accuracy allocation method for multi-branch closed-loop transmission chains considering accuracy-rigid coupling according to claim 7, characterized in that: The multi-objective optimization problem is represented as: The constraints include error tolerance constraints, variable upper and lower bound constraints, and terminal output accuracy constraints: in: Indicate candidate solutions Next Allowable values ​​for each key error term; and They represent the first The lower and upper limits of manufacturing or assembly feasibility for each key error item; and Indicates the scaling factor for position / engagement type error allocation. The lower and upper limits of the value; and These represent the scaling factors for angle-type error allocation. The lower and upper limits of the value; , They represent the first Equivalent stiffness scaling factor for key load-bearing components The lower and upper limits of the value; and They represent the first Additional supports or local reinforcements may be placed on key load-bearing components. The lower and upper limits of the value.

9. The accuracy allocation method for multi-branch closed-loop transmission chains considering accuracy-rigid coupling according to claim 8, characterized in that: The Pareto optimization method is used to solve for the candidate solution set, and the TOPSIS comprehensive decision method is used to select the optimal solution from the Pareto candidate solutions. The comprehensive proximity of the i-th candidate solution is expressed as: in: Indicates the first The overall relevance of each candidate solution; and They represent the first The distance from each candidate solution to the ideal optimal solution and the ideal worst solution.

10. The accuracy allocation method for multi-branch closed-loop transmission chains considering accuracy-rigid coupling according to claim 1, characterized in that: In step six, the output manufacturing and assembly control indicators include: Requirements for the consistency of the support hole axis, the positional accuracy of the support hole, or the local installation error of the critical mounting position relative to the reference axis, which are transformed from shaft position errors; The parallelism or inclination requirements of the common axis of the support holes relative to the assembly reference axis, which is transformed from shaft attitude errors; Requirements for gear mounting position error, gear pair center distance error, end face runout, radial runout, or meshing installation relationship error converted from the equivalent error of the transmission pair; In addition, new support locations, support stiffness levels, local reinforcement requirements for key shaft segments, or support arrangement adjustment requirements are derived from the results of structural stiffness optimization.

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