Web positioning pin hole and bushing interference fit plastic deformation analysis method

Abstract

The invention provides a web positioning pin hole and bushing interference fit plastic deformation analysis method. The method comprises the following steps: step 1, establishing a finite element model; 2, simulating an interference assembly contact state; 3, calculating an equivalent stress field; 4, tracking the displacement of the inner diameter section; and 5, correcting the size of the tool. Finite element analysis is adopted for simulating the contact state, equivalent stress analysis and displacement field tracking, so that a high-risk area is accurately positioned, the plastic deformation critical condition is judged, and the inner diameter reduction amount is quantified; the technical problem that plastic flow caused by plastic deformation in interference fit affects the dimensional stability and the fatigue life of an assembly is solved. According to the method, selection and optimization of the non-standard part assembly process can be guided, and a reference basis is provided for improving the product quality and interchangeability and reducing the production cost.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of computer-aided design using finite element method, and particularly relates to a method for analyzing plastic deformation of interference fit between a web positioning pin hole and a bushing. BACKGROUND

[0002] The interference assembly process plays an important role in mechanical connection technology and is widely used in the automobile, mold and machine tool industries. The process forms a tight fit with contact normal pressure between the contained part and the containing part through elastic deformation. The pressing process can be decomposed into two coupled effects: 1. elastic extrusion deformation of the material under the action of normal pressure. 2. self-locking effect generated by residual contact pressure after assembly is completed.

[0003] At present, due to the elastic deformation of the material itself, the contained part produces an inner diameter shrinkage [σ] after assembly is completed. In actual processing, since the assembly size is difficult to measure directly, enterprises often meet the tolerance requirements by improving product quality rather than directly evaluating product quality after assembly. However, such shrinkage deformation not only changes the stress distribution state of the fitting surface, causing plastic flow, but also affects the dimensional stability and fatigue life of the assembly.

[0004] For example, the plastic deformation area cannot recover to the original size through elastic rebound, resulting in that the inner diameter of the bushing is smaller than the design value. The size of the web positioning pin hole, pin and other matching tooling is based on the design inner diameter of the bushing. The reduction of the inner diameter will directly cause that the web positioning pin hole cannot be inserted or the gap is too large, reducing interchangeability. In batch production, if the inner diameter of the bushing is discrete due to plastic deformation, the web positioning pin hole needs to be made separately for each set of components, resulting in the need to increase the trial assembly, repair and other processes, prolong the assembly cycle, reduce the universality of tooling and increase the complexity of inventory management. Moreover, non-standard fit may cause problems such as vibration and wear, shortening the service life of the product. In the interference assembly, the contact pressure between the bushing and the web positioning pin hole is non-uniformly distributed along the axial and radial directions, causing high stress areas at the geometric discontinuities such as the edge and transition fillet of the bushing. The bushing simultaneously bears radial compressive stress, tangential tensile stress and axial friction force, and the multi-axial stress state is complex. It is difficult to accurately calculate the plastic deformation of the nonlinear material by using traditional analytical formulas. In view of this, the following technical scheme is proposed. SUMMARY

[0005] The technical problem solved by the present application is to provide a method for analyzing plastic deformation of interference fit between a web positioning pin hole and a bushing, which uses finite element analysis to simulate the contact state, equivalent stress analysis and displacement field tracking, so as to accurately locate the high-risk area, determine the critical condition of plastic deformation and quantify the inner diameter shrinkage. The technical problem of plastic flow caused by plastic deformation of interference fit, affecting the dimensional stability and fatigue life of the assembly is solved.

[0006] The technical scheme adopted by the present application is: a web positioning pin hole and bushing interference fit plastic deformation analysis method, comprising the following steps: Step 1, establishing a finite element model: according to the actual geometric size and material parameters of the sub-plate positioning pin hole and the bushing, a three-dimensional finite element analysis model containing contact pairs is constructed.

[0007] Step 2, simulate the interference assembly contact state: in the model, apply a radial interference displacement boundary condition matching the actual interference amount, define the outer surface of the sub-plate positioning pin hole and the inner surface of the bushing as frictional contact, and set the friction coefficient.

[0008] Step 3, calculate the equivalent stress field: based on the von Mises yield criterion, the equivalent stress distribution cloud of the bushing in the assembly process is obtained by finite element solution, and the plastic deformation area where the equivalent stress [σ v ] exceeds the material yield strength is marked.

[0009] Step 4, track the displacement of the inner diameter section: set displacement tracking points on the inner diameter section of the bushing, extract the radial displacement of each tracking point after assembly, and determine the maximum plastic deformation Δd_max.

[0010] Step 5, correct the tool size: according to the maximum plastic deformation Δd_max, adjust the design size of the sub-plate positioning pin hole and the bushing diameter, so that the actual fit clearance of the sub-plate positioning pin hole and the bushing after assembly meets the preset interchangeability tolerance requirements.

[0011] In the above technical scheme, further: in step 1, the finite element model needs to include the transition fillet features of the bushing and the sub-plate positioning pin hole, and the material parameters include the elastic modulus, the Poisson's ratio and the stress-strain curve.

[0012] In the above technical scheme, further: in step 2, the friction coefficient is in the range of 0.1-0.3 to simulate the lubrication state of the actual assembly surface.

[0013] In the above technical scheme, further: in step 3, by extracting and analyzing the stress curve data, the dynamic change law of the radial stress of the bushing contact surface with the analysis step is obtained.

[0014] In the above technical scheme, further: in step 4, the displacement tracking points are evenly distributed along the inner diameter circumference of the bushing, and the number is not less than 8.

[0015] In the above technical scheme, further: in step 4, the displacement field analysis meets the following conditions: The relationship between the radial shrinkage Δr and the penetration depth h is Δr = α·h^1.2, wherein α is a material-related coefficient; the overall centroid offset of the bushing after assembly is obtained by integrating the particle displacement, and the calculation formula is: Wherein x_i is the axial coordinate of particle i, Δr_i is the radial displacement, and n≥1000.

[0016] In the above technical solution, further: in step 5, the interchangeability tolerance requirement is that the pin and bushing fitting clearance is in the range of 0.01mm-0.05mm.

[0017] In the above technical solution, further: further comprising a plastic deformation experiment verification step: Disassemble the assembled same specification bushing, use a three-coordinate measuring instrument to detect the inner diameter section profile, and obtain the actual plastic deformation Δd_exp; compare Δd_exp with the maximum plastic deformation Δd_max obtained by finite element analysis, if |Δd_exp - Δd_max| / Δd_max ≤15%, the model is valid; the measured plastic deformation range of the bushing contact surface in the experiment is 0.025mm-0.035mm, and the error with the finite element prediction value is controlled within ±0.005mm.

[0018] In the above technical solution, further: in step 5, the diameter of the sub-plate positioning pin hole is designed to satisfy the following optimization rules: The initial design size d_0 is determined according to the designed inner diameter d_s of the bushing, d_0 = d_s - (Δd_max + Δd_safety), wherein Δd_safety is a safety margin, and Δd_safety is 0.01mm-0.02mm; in actual processing, a grouping assembly method is used, the diameter of the sub-plate positioning pin hole is divided into 3-5 groups, and each group has a tolerance band with an overlap of 50%, to compensate for the discreteness of the inner diameter of the bushing; The final fitting clearance Δg is determined by Monte Carlo simulation, which requires Δg to satisfy the normal distribution N(μ, σ 2 ), wherein μ=0.02mm, and σ≤0.008mm.

[0019] In the above technical solution, further: the temperature field influence is also considered in the finite element model, and the plastic deformation is corrected by thermal-mechanical coupling analysis: During assembly, the temperature of the bushing increases ΔT=20℃~50℃, resulting in thermal expansion ΔL=α_T·L·ΔT, wherein α_T is the linear expansion coefficient; The thermal strain ε_T and the mechanical strain ε_M are superimposed to obtain the total strain ε_total=ε_M + ε_T; The corrected plastic deformation amount Δd_corrected=Δd_max·(1+β·ΔT), where β is the temperature correction coefficient, and β takes the range of 0.001 / ℃~0.003 / ℃.

[0020] Advantages of this invention compared to existing technologies: 1. This invention establishes a mechanical model and uses elastoplastic finite element analysis and displacement field analysis to find nodes. This method is effective for the tooling design of interference fit parts and can optimize the uncertainties of some non-standard parts. This method can guide the selection and optimization of assembly processes for non-standard parts and provides a reference for improving product quality, interchangeability and reducing production costs.

[0021] 2. The step-stress curve analysis of this invention can intuitively show the changes in radial stress on the bushing contact surface throughout the assembly process; it can accurately identify key stages in the assembly process and deeply analyze the stress characteristics of these stages; it can determine whether the current assembly process is reasonable; it can predict fatigue, wear and other problems that may occur in parts during long-term use; it can provide important feedback for part design; it can help engineers optimize assembly process parameters; it can verify the accuracy of the finite element model; and it can enhance the credibility of finite element simulation results.

[0022] 3. The invention has no fewer than 8 tracking points, which can ensure a more comprehensive coverage of the deformation of the entire circumference of the bushing, avoiding the omission of deformation information of some key parts due to too few tracking points; it can improve the accuracy of displacement measurement; it can ensure assembly quality; by comparing the actual displacement data measured by the displacement tracking points with the displacement results calculated by the finite element model, the accuracy of the finite element model can be verified; and the parameters of the finite element model can be optimized.

[0023] 4. The Lagrangian description method of this invention uses material coordinates as a basis to describe deformation by following the movement of each mass point. During the bushing interference fit assembly process, it can accurately track the displacement changes of each mass point from the initial state to the assembly process and the final state; improve the accuracy of bushing deformation prediction; improve computational efficiency, improve assembly quality and product performance; ensure the comprehensiveness and accuracy of calculation results; provide reliable data support for evaluating assembly precision and product stability; and by analyzing the contribution of the displacement of each mass point to the centroid offset, we can gain a deeper understanding of the specific reasons for the centroid offset during the assembly process.

[0024] 5. The coordinate measuring machine of this invention detects the inner diameter cross-sectional profile to obtain the actual plastic deformation Δd_exp, and compares it with the maximum plastic deformation Δd_max obtained from finite element analysis, providing an objective and accurate basis for verifying the effectiveness of the finite element model. The plastic deformation of the bushing contact surface measured in the experiment ranged from 0.025mm to 0.035mm, providing direct support for the finite element analysis results. Through experimental verification and finite element analysis, the service life of the product can be evaluated.

[0025] 6. The Monte Carlo simulation of this invention accurately determines the fit clearance, simulates the actual assembly situation, and avoids the deviation that may be caused by relying solely on theoretical calculations; the normal distribution requirement ensures quality stability, thereby improving the quality stability and reliability of the product.

[0026] 7. The finite element model of this invention also considers the influence of the temperature field, which improves the accuracy of the model, better reflects the actual working conditions, accurately reflects the thermal expansion effect, and comprehensively considers the thermo-mechanical coupling effect, which greatly improves the accuracy of the finite element model; enhances the reliability of the results, improves the versatility and adaptability of the model, and provides a reliable basis for actual production; it can more accurately predict the plastic deformation of the bushing at different temperatures, and accurate prediction of the amount of plastic deformation helps to control the assembly quality of the product. Attached Figure Description

[0027] Figure 1(a) is an interference fit assembly diagram of the present invention; Figure 1(b) is an enlarged detail view of part A in Figure 1(a); Figure 2 This is a 2D symmetrical model diagram of the bushing assembly of the present invention; Figure 3(a) is a cloud diagram showing the assembly of the bushing of the present invention; Figure 3(b) shows the cloud-shaped lining of the present invention. Figure 2 ; Figure 4 This is an analysis step-stress curve diagram for the present invention; Figure 5 This is a deformation-depth curve diagram of the present invention; Figure 6 Photos of actual measurement data; Figure 7 This is a flowchart of the method of the present invention; In the diagram: 1-Locking pin hole for the sub-plate, 2-Bushing. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to Figures 1-7. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] (like Figure 7 (As shown) A method for analyzing the plastic deformation of the interference fit between the web locating pin hole and the bushing includes the following steps: Step 1: Establish a finite element model: Based on the actual geometric dimensions and material parameters of the sub-plate positioning pin hole 1 and bushing 2, construct a three-dimensional finite element analysis model that includes the contact pair relationship.

[0030] Among them, bushing 2 is used in the positioning sub-plate of the vertical boring machine. The positioning pin hole 1 of the sub-plate is the precision positioning fixture of the vertical boring machine. The material is cast iron. During mass boring, the pin positioning workpiece needs to be disassembled multiple times, which can easily cause wear and deformation of the positioning sub-plate pin hole. In order to extend the service life of the sub-plate and reduce economic losses, an interference fit bushing 2 is made (as shown in Figure 1).

[0031] This invention constructs a three-dimensional finite element analysis model based on the actual geometric dimensions and material parameters of the sub-plate locating pin hole and the bushing, and considers the contact pair relationship, enabling the model to highly reproduce the actual situation and laying the foundation for subsequent accurate analysis. Considering the specific scenario of the bushing being used in the locating sub-plate of a vertical boring machine, and the problem of wear and deformation of the locating sub-plate due to repeated disassembly of the pin-positioned workpiece during mass boring, an interference fit bushing is specifically manufactured and analyzed to meet actual production needs.

[0032] Step 2: Simulate the interference fit contact state: Apply radial interference displacement boundary conditions that match the actual interference amount in the model, define the outer surface of the subplate positioning pin hole 1 and the inner surface of the bushing 2 as frictional contact, and set the friction coefficient.

[0033] Using Huaxi A-CAE for CAXA 3D (CAXA CAE) software, the distribution of plastic deformation and residual stress can be accurately simulated. For the interference fit analysis of the sub-plate locating pin hole 1 and bushing 2, since this fit is an axisymmetric structure, a 2D axisymmetric model can be used to simplify the press-fit model. By using positional constraints, the computational load can be reduced (e.g., ...). Figure 2As shown in the figure, this approach ensures accuracy while improving computational efficiency. Since the displacement problem during assembly is geometrically nonlinear, it is approximated as a large displacement problem in the finite element analysis. The press head of the press-fitting machine is defined as an analytical rigid body and is not within the scope of this analysis. The sub-plate locating pin hole 1 and bushing 2 are defined as CAX4R axisymmetric linear reduced integral elements, and the friction coefficient between the bushing 2 and the sub-plate locating pin hole 1 is preferably 0.2. To address the geometrically nonlinear displacement problem during model assembly, it is approximated as a large displacement problem. The press head of the press-fitting machine is defined as an analytical rigid body, and the sub-plate locating pin hole and bushing are defined as CAX4R axisymmetric linear reduced integral elements. The friction coefficient is appropriately set to make the simulation more consistent with the actual assembly process.

[0034] Step 3: Calculate the equivalent stress field: Based on the von Mises yield criterion, obtain the equivalent stress distribution cloud map of bushing 2 during assembly through finite element analysis (see Figure 3), and mark the equivalent stress [σ]. v The plastic deformation region exceeding the material's yield strength.

[0035] Post-processing is performed on the results of the above defined model (see...). Figure 4 As can be seen from the analysis step-stress curve, the radial stress on the bushing contact surface increases continuously with the increase of the analysis step. When the bushing 2 is assembled, the radial stress gradually decreases from the contact surface to the axis, and is the largest at the contact surface. When the pressing force is removed, the residual stress on the bushing begins to redistribute, plastic deformation is retained, and a residual stress field is formed.

[0036] Step 4: Tracking the displacement of the inner diameter section: Displacement tracking points are set on the inner diameter section of bushing 2. The radial displacement of each tracking point is extracted after assembly, and the maximum plastic deformation Δd_max is determined. Through displacement field analysis, the movement of the mass points of the bushing during interference fit is understood. The actual measurement results are close to the finite element analysis results, verifying the accuracy of the analysis and providing a reliable basis for subsequent research.

[0037] The displacement field is a vector field describing the positional changes of all particles in a continuous medium under stress or temperature variations. In an interference fit assembly, when bushing 2 is pressed into the locating pin hole 1 of the sub-plate, the particles of bushing 2 move towards the center, and the displacement field exhibits radial contraction (e.g., ...). Figure 5 As shown in the figure, after assembly, the overall centroid offset of bushing 2 is approximately -0.038 mm. The actual measurement results are close to the finite element analysis results and can be used as a reference for subsequent interference fit parts. Notably, the disassembled bushing 2 of the same specification underwent plastic deformation, with a deformation of 0.03 mm (see...). Figure 6 ).

[0038] Step 5: Correct tooling dimensions: Based on the maximum plastic deformation Δd_max, adjust the design dimensions of the sub-plate locating pin hole 1 and bushing 2 diameters so that the actual fit clearance between the sub-plate locating pin hole 1 and bushing 2 after assembly meets the preset interchangeability tolerance requirements. This method can effectively solve the problem of wear and deformation of the locating sub-plate pin hole, extend the service life of the sub-plate, reduce economic losses, and has important guiding significance and application value for actual production.

[0039] In summary, the method of establishing a mechanical model and using elastoplastic finite element analysis and displacement field analysis to find nodes is effective for the tooling design of interference fit parts, and can optimize some uncertainties in non-standard parts. This method can guide the selection and optimization of assembly processes for non-standard parts, providing a reference for improving product quality, interchangeability, and reducing production costs.

[0040] In the above embodiments, further: in step 1, the finite element model needs to include the transition fillet features of the bushing 2 and the sub-plate positioning pin hole 1, and the material parameters include elastic modulus, Poisson's ratio and stress-strain curve.

[0041] It should be noted that in actual mechanical structures, there is usually a transition fillet between the bushing and the locating pin hole of the sub-plate. Incorporating this transition fillet feature into the finite element model allows for a more accurate simulation of the geometry of the actual structure. Compared to a simplified model that ignores the transition fillet, a model including this feature can more realistically reflect the distribution of stress and strain in the structure, avoiding analysis errors caused by geometric simplification, and thus obtaining analysis results that are more consistent with reality.

[0042] The transition fillet is a region prone to stress concentration. During interference fits, stress concentration occurs at the fillet due to geometric changes. By including the transition fillet feature in the finite element model, the stress concentration at this location can be accurately simulated, and potential plastic deformation areas and maximum stress values ​​can be predicted. This is crucial for evaluating the connection strength and reliability between the bushing and the sub-plate locating pin hole, helping to identify potential design flaws early, take corresponding improvement measures, and avoid premature failure due to stress concentration in actual use. Considering the transition fillet feature in the model provides a more accurate basis for structural design.

[0043] The elastic modulus is the ratio of stress to strain in a material during its elastic phase, reflecting the material's resistance to elastic deformation. In finite element analysis, accurately inputting the elastic modulus parameter allows the model to more precisely calculate the elastic deformation of the bushing and sub-plate locating pin holes during interference fit. This is crucial for predicting the initial fit state, contact pressure distribution, and the magnitude and distribution of residual stress after assembly, helping to ensure that the assembly quality meets design requirements.

[0044] Stress-strain curves describe the plastic deformation behavior of materials under different stress levels. By inputting accurate stress-strain curves into a finite element model, the plastic flow and deformation processes of materials during interference fits can be simulated more realistically. This allows for accurate prediction of the size and shape of the plastic deformation region, as well as the impact of plastic deformation on structural performance, such as stiffness reduction and residual stress changes. This is crucial for assessing whether the interference fit between the bushing and the sub-plate locating pin hole will lead to excessive plastic deformation and failure of the material, and for determining a reasonable range of interference.

[0045] Poisson's ratio reflects the ratio of transverse strain to axial strain in a material under uniaxial stress. For some anisotropic materials, the Poisson's ratio may differ in different directions. Specifying the Poisson's ratio parameter allows finite element models to more accurately account for the anisotropic properties of materials, improving the accuracy of the analysis. Even in isotropic materials, accurate Poisson's ratio input helps to more precisely calculate the deformation and stress distribution of structures under complex stress conditions.

[0046] By comprehensively inputting material parameters such as elastic modulus, Poisson's ratio, and stress-strain curves, finite element analysis can more fully consider the mechanical properties of materials. The resulting analysis more accurately reflects the actual situation, improving the reliability and dependability of the analysis results. Engineers can then make more informed decisions based on these accurate analysis results, such as optimizing design parameters, selecting suitable materials, and determining appropriate processing techniques, thereby reducing product development risks and improving product quality.

[0047] In the above embodiments, further: in step 2, the friction coefficient ranges from 0.1 to 0.3 to simulate the lubrication state of the actual assembly surface.

[0048] It should be noted that in the actual interference fit process between the web locating pin hole and the bushing, the assembly surfaces are usually lubricated to some extent. This range of values ​​can cover a variety of common lubrication conditions. Whether grease lubrication, oil film lubrication, or other lubrication methods are used, a friction coefficient range of 0.1 - 0.3 is highly likely to match, thus more realistically simulating the friction situation during actual assembly.

[0049] In interference fit assembly, the magnitude of the pressing force directly affects the ease of assembly and the stress on the bushing and locating pin hole. By setting an appropriate range of friction coefficients, the finite element model can more accurately calculate the pressing force required to press the bushing into the locating pin hole. This helps engineers to rationally select pressing equipment and formulate pressing processes before actual assembly, avoiding problems such as equipment damage due to excessive pressing force or assembly failure due to insufficient pressing force.

[0050] The coefficient of friction affects the stress distribution and deformation of the bushing during the pressing process. Simulations within the friction coefficient range of 0.1 to 0.3 can more accurately predict the elastic and plastic deformation of the bushing and locating pin holes during assembly.

[0051] Based on accurate friction coefficient simulation, engineers can more rationally design the diameter dimensions of the sub-plate locating pin holes and bushings. By simulating the actual fit after assembly under different friction coefficients, appropriate interference fits can be determined, ensuring that the actual fit clearance after assembly meets the preset interchangeability tolerance requirements. This avoids the problem of oversized or undersized dimensions due to uncertain friction coefficients, improving the versatility and interchangeability of parts and reducing production costs.

[0052] Accurate friction coefficient simulation helps assess the impact of residual stress and plastic deformation generated during assembly on the service life of parts. An inappropriate friction coefficient value can lead to inaccurate simulated residual stress distribution, making it impossible to accurately predict potential failure modes such as fatigue cracks and wear during use. A range of 0.1–0.3 makes the simulation results more reliable, providing a basis for adopting appropriate heat treatment processes and surface treatment measures, thereby improving product service life.

[0053] By simulating assembly conditions under different friction coefficients, the impact of varying lubrication states on the assembly process and results can be understood. This helps engineers select appropriate lubrication methods and lubricants in actual production and optimize lubrication processes. During actual assembly, parameters such as the actual indentation force and assembly deformation can be compared with the simulation results based on the friction coefficient range. If the actual parameters deviate significantly from the simulation results, it may indicate problems such as poor lubrication or out-of-tolerance part dimensions during assembly, facilitating timely quality checks and adjustments to ensure product quality consistency and stability.

[0054] In the above embodiments, further: in step 3, the equivalent stress field is calculated by extracting the analysis step-stress curve data (such as...). Figure 4 This allows us to obtain the dynamic variation of radial stress on the bushing contact surface with each analysis step.

[0055] It should be noted that the analysis step-stress curve can visually demonstrate the changes in radial stress on the bushing contact surface throughout the assembly process. From the start to the end of press-fitting, and then to the residual stress state after the press-fitting force is removed, the stress value corresponding to each analysis step is accurately recorded. This helps engineers to fully understand the generation, development, and stabilization process of stress during assembly, and to gain a deeper understanding of the mechanical mechanism of the interaction between the bushing and the locating pin hole.

[0056] Different assembly stages correspond to different mechanical states. By analyzing step-stress curves, key stages in the assembly process can be accurately identified, and the stress characteristics of these stages can be analyzed in depth. For example, in the stage where press fitting is about to be completed, the radial stress on the contact surface may reach its maximum value. At this time, the bushing and locating pin holes bear the greatest load, making it a stage prone to plastic deformation and damage. Understanding the stress characteristics of this stage can provide an important basis for optimizing the assembly process and avoiding excessive stress.

[0057] By analyzing the dynamic variation of radial stress on the bushing contact surface during each analysis step, the rationality of the current assembly process can be determined. If the stress changes are too drastic or abnormal peaks occur at certain stages, it may indicate an issue in the assembly process, such as excessive pressing speed or uneven pressing force. Adjusting the assembly process parameters to make stress changes more stable and reasonable can improve assembly quality and reduce component damage and performance degradation caused by improper assembly.

[0058] Stress is a crucial factor affecting the service life of components. By analyzing step-stress curves to obtain the dynamic stress changes at the bushing contact surface, potential fatigue and wear problems during long-term use can be predicted. For example, if high residual stress occurs at the contact surface during assembly, this stress may lead to crack initiation and propagation during subsequent use, thereby reducing the component's service life. Based on the stress variation patterns, corresponding measures, such as heat treatment and surface strengthening, can be taken to improve the component's fatigue resistance and reliability.

[0059] Understanding how the radial stress on the bushing contact surface changes with each analysis step can provide crucial feedback for part design. If excessive stress is found in certain areas, it may be necessary to optimize the structure of the bushing or locating pin holes, such as by adding transition fillets or changing the wall thickness, to reduce stress concentration and improve the strength and stiffness of the part. Furthermore, the material selection can be adjusted based on stress variations, choosing a material more suitable for withstanding that stress level.

[0060] Analyzing step-stress curve data can help engineers optimize assembly process parameters, such as press-in speed, press-in force, and loading method. By simulating stress changes under different process parameters, the optimal combination of process parameters can be found, resulting in a more reasonable stress distribution during assembly and reducing plastic deformation and residual stress.

[0061] The accuracy of the finite element model can be verified by comparing the dynamic variation law of radial stress on the bushing contact surface obtained by analyzing the step-stress curve with the actual measurement data. If the simulation results are consistent with the actual measurement results, it indicates that the model can well reflect the actual assembly process and mechanical behavior, providing a reliable basis for subsequent analysis and prediction. If there is a large deviation, the model needs to be corrected and improved, such as adjusting material parameters and boundary conditions, to improve the accuracy of the model.

[0062] Accurate analysis of step-stress curve data can enhance the credibility of finite element simulation results. In engineering practice, decision-makers tend to trust simulation results supported by actual data. Comparison and verification with actual measurement data can make simulation results more convincing and provide a more reliable basis for engineering decisions.

[0063] In the above embodiment, further: in step 4, the displacement tracking points are evenly distributed along the inner diameter circumference of the bushing, and the number is not less than 8.

[0064] It should be noted that the inner diameter of the bushing undergoes complex deformation during interference fit assembly. Distributing displacement tracking points evenly along the circumference of the bushing's inner diameter allows for monitoring of this deformation from multiple angles. At least eight tracking points ensure comprehensive coverage of the bushing's deformation across its entire circumference, preventing the omission of deformation information from critical areas due to insufficient tracking points. Deformation may vary at different locations on the bushing's inner diameter, potentially due to uneven stress during assembly or localized changes in material properties. Multiple evenly distributed displacement tracking points can accurately identify these localized deformation differences across the bushing's inner diameter. By comparing displacement data from different tracking points, it becomes possible to determine whether the deformation at certain specific locations on the bushing's inner diameter is larger or smaller, providing detailed information for in-depth analysis of the bushing's deformation mechanism.

[0065] Measurement results from a single displacement tracking point may contain certain errors, which could stem from factors such as the accuracy of the measuring equipment and environmental influences. By evenly distributing multiple displacement tracking points along the inner circumference of the bushing and comprehensively analyzing the displacement data from these points, methods such as averaging and curve fitting can be used to reduce measurement errors and improve the accuracy of displacement measurements. The data from multiple displacement tracking points corroborate each other, enhancing the reliability of the displacement measurement results.

[0066] In interference fit assembly, the uniformity of the fit between the bushing and the locating pin hole is crucial to the assembly quality. By monitoring the displacement changes of displacement tracking points evenly distributed along the circumference of the bushing's inner diameter, the uniformity of the force applied to the bushing during assembly can be assessed. If the displacement changes at each tracking point are basically consistent, it indicates a relatively uniform assembly process and a good fit between the bushing and the locating pin hole. If the displacement changes at each tracking point differ significantly, it may indicate uneven force distribution during assembly, such as skewed pressing force or insufficient machining accuracy of the bushing or locating pin hole, requiring timely adjustments and improvements. The data from the displacement tracking points can also be used to detect potential defects during assembly, such as the ovality or out-of-roundness of the bushing's inner diameter. When assembly defects exist in the bushing, abnormal displacement changes will appear at different positions on its inner diameter. By analyzing data from multiple displacement tracking points, these defects can be accurately detected, and their impact on assembly quality can be assessed.

[0067] Comparing the actual displacement data measured at displacement tracking points with the displacement results calculated by the finite element model can verify the accuracy of the finite element model. If the model's calculation results match the actual measurement data, it indicates that the model can effectively simulate the assembly process and deformation of the bushing. If there are significant deviations, the model needs to be corrected and improved, such as adjusting material parameters and boundary conditions. At least eight displacement tracking points provide abundant comparative data, which helps to more comprehensively and accurately verify the accuracy of the finite element model. Based on the measurement data from the displacement tracking points, the parameters of the finite element model can be optimized.

[0068] In the above embodiments, further: in step 4, during the tracking of the inner diameter section displacement, the displacement field analysis satisfies the following conditions: The displacement of the bushing mass point is defined using the Lagrange description method. The radial shrinkage Δr is related to the indentation depth h by the formula Δr = α·h^1.2, where α is the material correlation coefficient. After assembly, the overall centroid offset of the bushing is obtained by integrating the mass point displacement, and the calculation formula is as follows: Where x_i is the axial coordinate of particle i, Δr_i is the radial displacement, and n≥1000.

[0069] It should be noted that the Lagrangian description method uses material coordinates as its basis, describing deformation by following the motion of each particle. During the interference fit assembly of the bushing, it can accurately track the displacement changes of each particle from its initial state to the assembly process and its final state. Furthermore, the Lagrangian description method has unique advantages in handling large deformation problems; it is not affected by severe mesh distortion, thus ensuring the accuracy of the calculation. Compared to the Eulerian description method, the Lagrangian method does not require consideration of the fluid convection term, avoiding errors and complexities introduced by convection calculations. This allows for a more accurate simulation of the large deformation of the bushing during assembly, ensuring the reliability of the displacement analysis results. The Lagrangian description method also allows for convenient application of boundary conditions at the material boundaries.

[0070] The relationship between radial shrinkage Δr and indentation depth h is Δr = α·h^1.2. The material correlation coefficient α in this equation reflects the characteristics of the bushing material; different materials have different α values. α can be determined through experiments or material testing, allowing this equation to accurately describe the radial shrinkage behavior of a bushing made of a specific material during interference fit. The exponent 1.2 is set based on research into numerous actual assembly cases and material mechanical properties. It can well fit the trend of the bushing's radial shrinkage with indentation depth, matching the observed deformation and improving the accuracy of bushing deformation prediction. Compared to some complex constitutive relations, the equation Δr = α·h^1.2 is simple in form and easy to implement in numerical calculations. In finite element analysis or other numerical simulation methods, using this concise equation can significantly reduce the computational load and improve computational efficiency. At the same time, it still provides relatively accurate radial shrinkage information, reducing computational complexity and cost while ensuring computational accuracy. This formula clarifies the quantitative relationship between radial shrinkage and indentation depth. Engineers can control the radial shrinkage Δr by adjusting the indentation depth h based on the final bushing dimensions required by the design and the fit clearance after assembly. This provides an important theoretical basis for optimizing assembly process parameters, helps to achieve precise fit between the bushing and the locating pin hole, and improves assembly quality and product performance.

[0071] By dividing the bushing into n ≥ 1000 mass points and integrating the axial coordinate x_i and radial displacement Δr_i of each mass point to calculate the center of mass offset, the influence of the deformation of all mass points on the overall center of mass position during assembly can be comprehensively considered. This calculation method avoids the problem of inaccurate center of mass offset calculation due to neglecting local deformation, ensuring the comprehensiveness and accuracy of the calculation results. Increasing the number of mass points n can more finely describe the deformation distribution of the bushing, thereby improving the calculation accuracy of the center of mass offset. When n ≥ 1000, it can better approximate the actual deformation of the bushing, making the integral calculation result closer to the true center of mass offset. Compared with some simplified center of mass calculation methods, this method based on the integration of a large number of mass point displacements can more accurately reflect the overall positional change of the bushing after assembly, providing reliable data support for evaluating assembly accuracy and product stability. By analyzing the contribution of the displacement of each mass point to the center of mass offset, the specific reasons for the center of mass offset during assembly can be understood in depth.

[0072] In the above embodiments, further: in step 5, the interchangeability tolerance requirement is that the clearance between the pin and the bushing is in the range of 0.01mm to 0.05mm.

[0073] It should be noted that a clearance range of 0.01mm - 0.05mm provides reasonable space for assembly operations. A reasonable clearance range facilitates rapid assembly. The fit between pins and bushings is typically used to achieve transmission or positioning functions between parts. A clearance range of 0.01mm - 0.05mm ensures that the pin has adequate movement within the bushing, allowing for the transmission of power or motion without causing inaccurate transmission or unstable positioning due to excessive clearance. Appropriate clearance helps reduce wear between the pin and bushing. The 0.01mm - 0.05mm clearance range provides a certain tolerance for dimensional fluctuations, allowing pins and bushings from different batches to still meet assembly requirements and be interchangeable. This tolerance range is relatively lenient while ensuring the function and performance of the parts, placing less emphasis on processing equipment and processes, and can reduce manufacturing costs to some extent. Although this tolerance range is relatively lenient, it still ensures product quality.

[0074] In the above embodiments, the method further includes a plastic deformation experimental verification step. Disassemble the assembled bushings of the same specifications, use a coordinate measuring machine to detect the inner diameter section profile, and obtain the actual plastic deformation amount Δd_exp; compare Δd_exp with the maximum plastic deformation amount Δd_max obtained by finite element analysis. If |Δd_exp - Δd_max| / Δd_max ≤ 15%, the model validity is verified; in the experiment, the plastic deformation amount of the bushing (2) contact surface was measured to be 0.025mm~0.035mm, and the error with the finite element prediction value was controlled within ±0.005mm.

[0075] It should be noted that the actual plastic deformation Δd_exp was obtained by disassembling an assembled bushing of the same specification and using a coordinate measuring machine to inspect the inner diameter cross-sectional profile. This Δd_exp was then compared with the maximum plastic deformation Δd_max obtained from the finite element analysis. This comparison method, based on actual measurement data and simulated data, provides an objective and accurate basis for verifying the effectiveness of the finite element model. If the comparison results do not meet the given error range, it indicates that the finite element model may have some problems, such as inaccurate material parameter settings, unreasonable boundary condition definitions, or inappropriate mesh generation. Through this experimental verification, potential problems in the model can be identified in a timely manner, providing direction for model correction and improvement.

[0076] The measured plastic deformation of the bushing contact surface ranged from 0.025 mm to 0.035 mm in the experiment, providing direct support for the finite element analysis results. Compared with theoretical analysis and simulation calculations alone, the actual measurement data more realistically reflects the plastic deformation of the bushing during assembly, making the research results more reliable and convincing. The error between the experimentally measured plastic deformation and the finite element prediction was controlled within ±0.005 mm, a very precise error range. This indicates a high degree of consistency between the finite element analysis results and the actual measurement results, further demonstrating the accuracy and reliability of the research method. In practical engineering applications, this high-precision result can provide engineers with more accurate references, helping them make more rational decisions.

[0077] Experimental verification and comparative analysis can reveal the plastic deformation of bushings under different assembly processes. Based on the experimental results, multiple parameters in the assembly process can be comprehensively optimized. The range of plastic deformation at the bushing contact surface measured experimentally can serve as an important basis for product quality control. The amount of plastic deformation is closely related to the service life of the bushing. Excessive plastic deformation may lead to fatigue cracks, accelerated wear, and other problems, shortening the product's service life. Through experimental verification and finite element analysis, the development trend of plastic deformation of the bushing under different operating conditions can be predicted, thereby assessing the product's service life. This helps companies develop reasonable product maintenance and replacement plans, improving product reliability and safety.

[0078] In the above embodiments, further: in step 5, when correcting the tooling dimensions, the diameter design of the sub-plate positioning pin hole 1 satisfies the following optimization rules: The initial design dimension d_0 is determined based on the bushing design inner diameter d_s, d_0 = d_s - (Δd_max + Δd_safety), where Δd_safety is the safety margin, which is 0.01mm to 0.02mm. In actual machining, a group assembly method is adopted, dividing the diameter of the sub-plate positioning pin hole 1 into 3 to 5 groups, with each group's tolerance zone overlapping by 50%, to compensate for the dispersion of the bushing 2 inner diameter. The final fit clearance Δg was determined through Monte Carlo simulation, requiring Δg to satisfy a normal distribution N(μ, σ). 2 ), where μ=0.02mm, σ≤0.008mm.

[0079] It should be noted that the initial design dimensions are reasonably determined, with a safety margin reserved. By reserving this safety margin, it is possible to avoid excessive tightness between the locating pin hole and the bushing due to these uncertainties, thereby reducing problems such as jamming and damage during assembly and improving assembly reliability and success rate. The group assembly method effectively compensates for the variability of the bushing's inner diameter, adapts to batch production differences, and the overlapping tolerance zones enhance flexibility.

[0080] Monte Carlo simulation accurately determines the fit clearance, mimicking real assembly conditions and avoiding deviations that may arise from relying solely on theoretical calculations. The normal distribution requirement ensures quality stability, thus improving product quality stability and reliability.

[0081] In the above embodiments, furthermore: the finite element model also considers the influence of the temperature field, and corrects the amount of plastic deformation through thermo-mechanical coupling analysis. During assembly, the bushing temperature rises by ΔT = 20℃~50℃, resulting in thermal expansion ΔL = α_T·L·ΔT, where α_T is the coefficient of linear expansion. Superimposing the thermal strain ε_T and the mechanical strain ε_M yields the total strain ε_total = ε_M + ε_T; The corrected plastic deformation amount Δd_corrected=Δd_max·(1+β·ΔT), where β is the temperature correction coefficient, and β takes the range of 0.001 / ℃~0.003 / ℃.

[0082] It should be noted that the finite element model also considers the influence of the temperature field, improving model accuracy, better reflecting actual working conditions, accurately reflecting the thermal expansion effect, and comprehensively considering the thermo-mechanical coupling effect, thus greatly improving the accuracy of the finite element model. Optimizing the prediction of plastic deformation enhances the reliability of the results. The influence of temperature on plastic deformation is considered, and the temperature correction coefficient β links temperature changes with the correction of plastic deformation, enhancing the reliability of the prediction results. Since the bushing temperature rises within a range of 20℃ to 50℃ during assembly, this correction method can adapt to this temperature range. At different temperatures, the corrected plastic deformation can be accurately calculated based on the corresponding ΔT and β values. This allows the finite element model to provide relatively accurate prediction results under different temperature conditions, improving the model's versatility and adaptability, and providing a reliable basis for assembly processes under different temperature conditions in actual production. By considering the influence of the temperature field and thermo-mechanical coupling analysis, the plastic deformation of the bushing at different temperatures can be predicted more accurately. Accurate prediction of plastic deformation helps control the assembly quality of the product.

[0083] In traditional assembly process design, neglecting the influence of the temperature field can lead to extensive testing and adjustments to determine suitable assembly process parameters. This is not only time-consuming and labor-intensive but also increases trial-and-error costs. However, by using finite element models and thermo-mechanical coupling analysis that consider the influence of the temperature field, the plastic deformation of the bushing can be accurately predicted during the design phase, reducing the number of tests and lowering trial-and-error costs. Accurate model predictions and process parameter adjustments can improve the first-pass yield of assembly and reduce rework and scrap due to assembly quality issues. This helps to shorten production cycles, improve production efficiency, and reduce production costs.

[0084] As can be seen from the above description, the method of finding nodes by establishing a mechanical model and using elastoplastic finite element analysis and displacement field analysis is effective for the tooling design of interference fit parts. It can optimize the uncertainty factors of some non-standard parts. This method can guide the selection and optimization of assembly processes for non-standard parts, and provide a reference for improving product quality, interchangeability and reducing production costs.

[0085] The various embodiments in this specification are described in a related manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0086] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications and equivalent substitutions made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for analyzing the plastic deformation of the web locating pin hole and the bushing interference fit, characterized in that, Includes the following steps: Step 1: Establish a finite element model: Based on the actual geometric dimensions and material parameters of the sub-plate positioning pin hole (1) and bushing (2), construct a three-dimensional finite element analysis model that includes the contact pair relationship; Step 2, Simulate the interference fit contact state: Apply radial interference displacement boundary conditions that match the actual interference amount in the model, define the outer surface of the sub-plate positioning pin hole (1) and the inner surface of the bushing (2) as frictional contact, and set the friction coefficient; Step 3: Calculate the equivalent stress field: Based on the von Mises yield criterion, obtain the equivalent stress distribution cloud map of the bushing (2) during the assembly process through finite element solution, and mark the equivalent stress [σ]. v The plastic deformation region exceeding the material's yield strength; Step 4: Track the displacement of the inner diameter section: Set displacement tracking points on the inner diameter section of the bushing (2), extract the radial displacement of each tracking point after assembly, and determine the maximum plastic deformation Δd_max; Step 5: Correct tooling dimensions: Based on the maximum plastic deformation Δd_max, adjust the design dimensions of the sub-plate positioning pin hole (1) and bushing (2) diameter so that the actual fit clearance between the sub-plate positioning pin hole (1) and bushing (2) after assembly meets the preset interchangeability tolerance requirements.

2. The analytical method according to claim 1, characterized in that: In step 1, the finite element model must include the transition fillet features of the bushing (2) and the positioning pin hole (1) of the sub-plate, and the material parameters include the elastic modulus, Poisson's ratio and stress-strain curve.

3. The analytical method according to claim 1, characterized in that: In step 2, the coefficient of friction is taken in the range of 0.1 to 0.3 to simulate the lubrication state of the actual assembly surface.

4. The analytical method according to claim 1, characterized in that: In step 3, the equivalent stress field is calculated, and the dynamic variation law of the radial stress on the bushing contact surface with the analysis step is obtained by extracting the analysis step-stress curve data.

5. The analytical method according to claim 1, characterized in that: In step 4, the displacement tracking points are evenly distributed along the inner diameter circumference of the bushing, with a number of no less than 8.

6. The analytical method according to claim 1, characterized in that: In step 4, during the tracking of the inner diameter section displacement, the displacement field analysis satisfies the following conditions: The displacement of the bushing mass point is defined using the Lagrange description method. The radial shrinkage Δr is related to the indentation depth h by the formula Δr = α·h^1.2, where α is the material correlation coefficient. After assembly, the overall centroid offset of the bushing is obtained by integrating the mass point displacement, and the calculation formula is as follows: Where x_i is the axial coordinate of particle i, Δr_i is the radial displacement, and n≥1000.

7. The analytical method according to claim 1, characterized in that: In step 5, the interchangeability tolerance requirement is that the clearance between the pin and the bushing is within the range of 0.01mm to 0.05mm.

8. The analytical method according to claim 1, characterized in that, It also includes a plastic deformation experimental verification step: Disassemble the assembled bushings of the same specifications, use a coordinate measuring machine to detect the inner diameter section profile, and obtain the actual plastic deformation amount Δd_exp; compare Δd_exp with the maximum plastic deformation amount Δd_max obtained by finite element analysis. If |Δd_exp - Δd_max| / Δd_max ≤ 15%, the model validity is verified; in the experiment, the plastic deformation amount of the bushing (2) contact surface was measured to be 0.025mm~0.035mm, and the error with the finite element prediction value was controlled within ±0.005mm.

9. The analytical method according to claim 1, characterized in that: In step 5, when correcting the tooling dimensions, the diameter design of the sub-plate locating pin hole (1) must meet the following optimization rules: The initial design dimension d_0 is determined based on the bushing design inner diameter d_s, d_0 = d_s - (Δd_max + Δd_safety), where Δd_safety is the safety margin, Δd_safety is 0.01mm~0.02mm; in actual processing, the group assembly method is adopted, the diameter of the sub-plate positioning pin hole (1) is divided into 3 to 5 groups, and the tolerance zone of each group overlaps by 50% to compensate for the dispersion of the bushing (2) inner diameter; The final fit clearance Δg was determined through Monte Carlo simulation, requiring Δg to satisfy a normal distribution N(μ, σ). 2 ), where μ=0.02mm, σ≤0.008mm.

10. The analytical method according to claim 1, characterized in that: The finite element model also considers the influence of the temperature field, and corrects the amount of plastic deformation through thermo-mechanical coupling analysis: During assembly, the bushing temperature rises by ΔT = 20℃~50℃, resulting in thermal expansion ΔL = α_T·L·ΔT, where α_T is the coefficient of linear expansion. Superimposing the thermal strain ε_T and the mechanical strain ε_M yields the total strain ε_total = ε_M + ε_T; The corrected plastic deformation amount Δd_corrected=Δd_max·(1+β·ΔT), where β is the temperature correction coefficient, and β takes the range of 0.001 / ℃~0.003 / ℃.

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