Optimization method for meshing clearance of synchronous belt drive based on micro-deformation model of force on tooth profile

Abstract

This invention relates to the field of computer-aided design technology, specifically to a method for optimizing the meshing clearance of synchronous belt drives based on a tooth profile stress micro-deformation model. The method includes: establishing a finite element model of the meshing process between the synchronous pulley and the synchronous belt, and simulating several load conditions. During the simulation, based on the numerical distribution of the simulation data under different load conditions, different process parameters of the synchronous pulley in the initial meshing model are iteratively and collaboratively adjusted. During the adjustment process, a backlash objective function and an interference objective function are set, and the process parameters of the synchronous pulley are optimized by combining the backlash objective function and the interference objective function to obtain a process parameter front solution set composed of several preferred process parameter combinations. The preferred process parameter combinations in the process parameter front solution set are further simulated and verified to determine the final process parameters of the synchronous pulley. This invention effectively improves the optimization effect of the meshing clearance of synchronous belt drives.

Description

Technical Field

[0001] This invention relates to the field of computer-aided design technology, and specifically to a method for optimizing the meshing clearance of synchronous belt drives based on a tooth profile stress micro-deformation model. Background Technology

[0002] Synchronous belt drives are widely used in high-end equipment such as precision machine tools, industrial robots, and automotive engines due to their advantages such as accurate transmission ratio, zero slippage, and low noise. One of their core performance indicators is the meshing clearance (or backlash), which directly affects the transmission accuracy, smoothness, and lifespan. In existing synchronous belt pulley tooth profile design technology, the tooth profile design (such as pressure angle, tooth thickness, and tooth root fillet radius) mainly relies on engineers' empirical formulas and standard manuals. This design does not consider the slight elastic deformation of the synchronous belt teeth under stress. This is because synchronous belts are usually composed of a rubber matrix and reinforcing cords. When transmitting torque, the belt teeth will bend and compress towards the tooth root. Therefore, this slight deformation of the tooth profile under stress will significantly change the theoretical meshing clearance.

[0003] To optimize the meshing clearance of synchronous belt drives, simulation is commonly used to optimize the tooth profile and dimensions of the synchronous pulleys. However, a balance between backlash and interference exists during the optimization process. To avoid the tooth surfaces jamming during meshing (i.e., interference), traditional designs reserve a large backlash; however, excessive backlash leads to increased transmission backlash and decreased positioning accuracy. Conversely, if backlash is excessively reduced in pursuit of accuracy, interference can easily occur due to slight deformation of the tooth profile during actual operation, causing abnormal wear, noise, and transmission failure. Summary of the Invention

[0004] This invention provides a method for optimizing the meshing clearance of synchronous belt drives based on a tooth profile stress micro-deformation model, in order to solve the existing problem that traditional synchronous belt pulley tooth profile design does not consider tooth profile stress micro-deformation, resulting in difficulty in accurately balancing backlash and interference.

[0005] The synchronous belt drive meshing clearance optimization method based on the tooth profile stress micro-deformation model of the present invention adopts the following technical solution: One embodiment of the present invention provides a method for optimizing the meshing clearance of synchronous belt drives based on a tooth profile stress micro-deformation model. The method includes the following steps: A finite element model of the meshing process of the synchronous pulley and the synchronous belt is established as the initial meshing model. Several load conditions are set to simulate the meshing process of the initial meshing model. During the simulation, several simulation data under each load condition are obtained. Based on the numerical distribution of simulation data under different load conditions, the different process parameters of the synchronous pulley in the initial meshing model are iteratively and collaboratively adjusted. During the adjustment process, the backlash objective function and the interference objective function are set, and the process parameters of the synchronous pulley are optimized by combining the backlash objective function and the interference objective function, so as to obtain the process parameter front solution set composed of several optimized process parameters. The optimal process parameter combinations in the solution set of the process parameter frontier are further simulated and verified to determine the final process parameters of the synchronous pulley.

[0006] Furthermore, the specific method for obtaining the initial meshing model is as follows: Collect the geometric and material parameters, as well as the operating parameters, of the timing pulley and timing belt; Based on the aforementioned geometric and material parameters, a 2D tooth profile curve is imported into the finite element software. The pulley is defined as a linear elastic material and the synchronous belt as a hyperelastic material. Frictional contact is set between the pulley tooth surface and the belt tooth surface. The meshing contact area is adaptively refined to establish a 2D finite element meshing model as the initial meshing model.

[0007] Furthermore, the initial meshing model is simulated under several load conditions, and simulation data under each load condition is obtained during the simulation process. The specific methods include: Three load conditions are set: no-load, rated load, and overload. The boundary conditions of the three load conditions are applied to the 2D finite element meshing model respectively to simulate the dynamic meshing process. Under each load condition, at least one complete meshing cycle is simulated. During the simulation, the real-time backlash value, tooth profile micro-deformation, contact stress distribution, and interference region area under each working condition are monitored and recorded in real time as the simulation data.

[0008] Furthermore, the specific method for iteratively and collaboratively adjusting different process parameters of the synchronous pulley in the initial meshing model based on the numerical distribution of simulation data under different load conditions includes: Several sets of process parameter combinations are generated as the initial population; Substitute each set of process parameters into the initial meshing model for simulation, and calculate the corresponding side clearance objective function value and interference objective function value; Based on two objective function values, the population is subjected to selection, crossover, and mutation operations to generate a new generation of population, and the process is repeated until the preset number of iterations is reached.

[0009] Furthermore, the specific methods for performing selection, crossover, and mutation operations on the population based on two objective function values ​​are as follows: In the selection operation, the fitness of an individual is calculated based on the side gap objective function value and the interference objective function value corresponding to that individual. In crossover and mutation operations, a guiding rule based on the coupling law of process parameters is introduced to adjust the process parameters of the generated offspring individuals in order to guide the population to perform iterative search in the parameter space.

[0010] Furthermore, the specific method for obtaining the side gap objective function is as follows: Based on the real-time backlash value and the tooth profile micro-deformation, the effective backlash under each working condition is calculated; the average effective backlash within a complete meshing cycle under each working condition is calculated as the average effective backlash. The side clearance fluctuation is calculated based on the difference between the average effective side clearance under different load conditions; the penalty parameter for excessively small side clearance is determined based on the average effective side clearance under overload conditions, combined with the preset safe side clearance threshold and penalty sensitivity. A side clearance objective function is constructed by combining the average effective side clearance, side clearance fluctuation, and the penalty parameter for excessively small side clearance.

[0011] Furthermore, the specific method for obtaining the interference objective function is as follows: Based on the area of ​​the interference region and the contact stress distribution, the interference stress concentration at each sampling time under each load condition is calculated; based on the area of ​​the interference region and the interference stress concentration, the condition interference degree under each load condition is calculated. The operating condition coefficients for each load condition are preset, and the interference degree of all load conditions is combined to construct the interference objective function.

[0012] Furthermore, the specific method for obtaining the interference stress concentration is as follows: Preset allowable stress of material, when under load conditions Next moment When the area of ​​the interference region is 0, it will be under load conditions. Next moment The interference stress concentration is set to 1; Under load conditions Next moment When the area of ​​the interference region is greater than 0, according to the load condition Next moment The stress difference factor is obtained by calculating the difference between the maximum contact stress and the allowable stress of the material. Based on this stress difference factor, the stress under load conditions can be determined. Next moment The interference stress concentration, wherein the stress difference factor is positively correlated with the interference stress concentration.

[0013] Furthermore, the specific method for obtaining the solution set of the process parameter front is as follows: The set of all non-dominated process parameter combinations during the iteration process is taken as the process parameter front solution set; the non-dominated process parameter combination refers to the combination in the population that is superior to this combination in both the side gap objective function value and the interference objective function value.

[0014] Furthermore, the specific method for obtaining the final process parameters is as follows: For each optimal combination of process parameters in the solution set of the process parameter frontier, a corresponding 3D finite element meshing model is established. The 3D finite element meshing model is subjected to simulation conditions including thermodynamic boundary conditions and long-term time-varying load spectrum to perform long-term operation simulation. During long-term simulation, the time-varying side clearance changes, fatigue stress accumulation, and thermal deformation compatibility are monitored. Based on long-term simulation results, the optimal combination of process parameters with the best overall performance under the conditions of satisfying the set side clearance range and no interference was selected as the final process parameters.

[0015] The beneficial effects of the technical solution of this invention are as follows: Traditional tooth profile design ignores the minute elastic deformation of the synchronous belt under stress, while the embodiments of this invention calculate the effective backlash to reflect the actual clearance state after the belt teeth are bent and compressed under stress, fundamentally overcoming the blind spot of traditional theoretical calculations and improving the accuracy of meshing clearance optimization; in addition, by constructing a backlash objective function and an interference objective function for multi-objective collaborative optimization, the backlash objective function not only pursues the minimization of clearance but also introduces backlash fluctuation and excessively small backlash penalty parameters under overload conditions, effectively preventing the risk of extreme interference caused by pursuing accuracy and ensuring transmission smoothness; at the same time, the interference objective function integrates interference area, stress concentration, and time duration, penalizing interference damage and ensuring While achieving high positioning accuracy, it avoids meshing jamming and abnormal wear. Considering the nonlinear coupling relationship between different process parameters of the synchronous belt pulley and meshing performance, iterative optimization of the process parameters avoids the stress amplification problem that may be caused by independent adjustment of a single parameter. This allows for efficient iteration within the parameter space, resulting in the optimal process parameter front set. In the early stage of optimization, a 2D finite element model is used for multi-condition simulation and large-scale optimization, effectively reducing computational costs. In the later stage, a 3D model is established for verification on a small number of front set solutions, which not only improves optimization efficiency but also ensures the fatigue resistance, thermal deformation compatibility, and time-varying backlash stability of the finally determined process parameters in long-term operation, effectively improving the optimization effect on the meshing clearance of the synchronous belt drive. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart illustrating the steps of the synchronous belt drive meshing clearance optimization method based on the tooth profile stress micro-deformation model of the present invention. Figure 2 This is a schematic diagram of the meshing process of a timing belt and a timing pulley, provided as an embodiment of the present invention. Detailed Implementation

[0018] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of the synchronous belt drive meshing clearance optimization method based on a tooth profile stress micro-deformation model proposed in this invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0019] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0020] The following description, in conjunction with the accompanying drawings, details the specific scheme of the synchronous belt drive meshing clearance optimization method based on the tooth-shaped stress micro-deformation model provided by this invention.

[0021] Please see Figure 1 The diagram illustrates a flowchart of a synchronous belt drive meshing clearance optimization method based on a tooth profile stress micro-deformation model, according to an embodiment of the present invention. The method includes the following steps: Step S001: Establish a finite element model of the meshing process of the synchronous pulley and the synchronous belt as the initial meshing model, and set several load conditions to simulate the meshing process of the initial meshing model. During the simulation, obtain several simulation data under each load condition.

[0022] It should be noted that since the force along the width direction of synchronous belt meshing is usually basically uniform, and a 3D finite element model of the meshing process between the synchronous pulley and the synchronous belt would have a certain degree of computational redundancy, in order to reduce the computational cost in optimizing the process parameters of the synchronous pulley through finite element simulation, the finite element model established in this embodiment of the invention is a 2D model, which shows the sides of the synchronous pulley and the synchronous belt during meshing operation, such as... Figure 2 The diagram shows the meshing process of the timing belt and timing pulley. Figure 2 Includes timing pulley and timing pulley Furthermore, the two synchronous pulleys are linked by the synchronous belt, thus rotating at different speeds. and rotational speed It rotates.

[0023] In addition, the forces exerted on the synchronous pulley and synchronous belt during long-term continuous operation are dynamically changing and are also affected by different load levels. Therefore, in order to ensure that the subsequent process parameter optimization results can enable the synchronous pulley to meet different working conditions during use, the embodiments of the present invention further set multiple load conditions to cover the actual working boundary.

[0024] Specifically, in one embodiment, the method for obtaining the initial meshing model is as follows: collecting the geometric and material parameters and operating parameters of the synchronous pulley and the synchronous belt; based on the geometric and material parameters, importing 2D tooth profile curves into the finite element software, defining the pulley as a linear elastic material and the synchronous belt as a hyperelastic material, setting frictional contact between the pulley tooth surface and the belt tooth surface, and performing adaptive mesh refinement on the meshing contact area to establish a 2D finite element meshing model as the initial meshing model.

[0025] As an optional embodiment, the geometric and material parameters include: the number of teeth, standard tooth profile, and material of the synchronous pulley; the tooth profile dimensions of the synchronous belt, the hardness of the rubber matrix, and the elastic modulus of the cord material.

[0026] For example, the synchronous pulley can have 30 teeth, the standard tooth profile can be circular arc tooth HTD8M, the material can be 45 steel with an elastic modulus of 206000MPa and a Poisson's ratio of 0.3; the tooth profile of the synchronous belt matches that of the synchronous pulley, the rubber matrix hardness is Shore A70, and the elastic modulus of the cord material is 120000MPa.

[0027] As an optional embodiment, the operating parameters include: load range, operating temperature range, and friction coefficient of the meshing surfaces of the belt teeth and gear teeth.

[0028] For example, for the load range, the load is set to 0 when unloaded and can be 100 when under rated load. When overloaded, its load can be 120. The operating temperature range is -10℃ to 60℃; the friction coefficient of the meshing surface between the belt teeth and the gear teeth can be 0.3.

[0029] It should be noted that the above parameter values ​​are only examples in one specific embodiment of the present invention. In other embodiments, they can be adjusted accordingly based on the specific design requirements of the actual synchronous belt drive system and the data provided by the material supplier. The embodiments of the present invention do not impose specific limitations.

[0030] In one embodiment, the initial meshing model is simulated under several load conditions, and simulation data under each load condition is obtained during the simulation. The specific method includes: setting three load conditions: no-load, rated load, and overload; applying boundary conditions of the three load conditions to the 2D finite element meshing model respectively, and performing dynamic meshing process simulation. Under each load condition, at least one complete meshing cycle is simulated; during the simulation, the real-time backlash value, tooth profile micro-deformation, contact stress distribution, and interference region area under each condition are monitored and recorded in real time as the simulation data.

[0031] As an optional embodiment, the specific method for establishing the 2D finite element meshing model is as follows: extract the three-dimensional cross-sections of the synchronous pulley and the belt teeth, and establish a planar meshing model of their sides; import the 2D tooth profile curves of the pulley and the belt teeth into the finite element software Abaqus; define the pulley as a linear elastic material, and define the synchronous belt as an elasto-plastic material or a hyperelastic material through the Mooney-Rivlin model to accurately simulate the nonlinear deformation of rubber under stress; define face-to-face contact between the pulley tooth surface and the belt tooth surface, with the normal behavior being hard contact and the tangential behavior setting the friction coefficient; use a mesh with a minimum size of less than or equal to 0.1 mm in and around the meshing contact area to accurately capture contact stress and deformation, and use a mesh with a size of 0.5 mm in areas far from the contact area to improve calculation speed; the software can be set to automatically adjust the mesh density according to the deformation during the calculation process.

[0032] It should be noted that since the 2D model ignores the force gradient in the width direction, it may introduce errors to some extent. Therefore, when applying the load, an equivalent force correction factor in the width direction is introduced. For example, if bench testing reveals that the actual contact stress is 5% higher on average than the 2D simulation, then it can be set that... Multiply the loads in the 2D model by To correct the calculation results; among which The equivalent force correction factor in the width direction can be obtained through a small number of preliminary tests or more precise 3D simulation comparisons. In addition, the equivalent force correction factor in the width direction can also be estimated empirically based on the width-to-diameter ratio of the synchronous belt and the pulley flange structure. For conventional flat belt pulleys, the factor can be between 1.0 and 1.1. When the width of the synchronous belt is greater than 50mm and there is no flange, the factor can be between 1.05 and 1.1. The load in the 2D model is multiplied by the correction factor to compensate for the uneven force in the width direction.

[0033] As an optional embodiment, the specific method for setting several load conditions and performing simulation is as follows: setting three load conditions: no-load, rated load, and overload; applying boundary conditions of the three load conditions to the 2D finite element meshing model respectively, and performing dynamic meshing process simulation. Under each load condition, at least one complete meshing cycle is simulated, specifically 10 complete meshing cycles, to ensure data stability; during the simulation process, the real-time backlash value, tooth profile micro-deformation, contact stress distribution, and interference region area under each condition are monitored and recorded in real time as the simulation data.

[0034] It should be noted that the real-time backlash value is the minimum distance between the non-working tooth surfaces of the belt tooth and the gear tooth measured at each meshing moment; the tooth profile micro-deformation is the elastic deformation displacement generated along the tooth surface normal direction at the backlash measurement point of the non-working tooth surface of the belt tooth in the follower coordinate system; the contact stress distribution is the extraction of the maximum contact stress value and its distribution cloud map of the meshing contact area; the interference region area is used to check whether the mesh of the belt tooth and the gear tooth penetrates during the meshing process. If there is no penetration, the interference region area is 0; if there is penetration, the area of ​​the penetration region is calculated.

[0035] Thus, the initial meshing model and simulation data under different load conditions were obtained through the above method.

[0036] Step S002: Based on the numerical distribution of each simulation data under different load conditions, the different process parameters of the synchronous pulley in the initial meshing model are iteratively and collaboratively adjusted. During the adjustment process, the backlash objective function and the interference objective function are set, and the process parameters of the synchronous pulley are optimized by combining the backlash objective function and the interference objective function to obtain the process parameter front solution set composed of several optimized process parameters.

[0037] It should be noted that excessively small tooth profile deviations in synchronous pulleys can easily lead to meshing jamming, while excessively large deviations will fail to meet the small clearance requirements. Furthermore, the influence of different process parameters of synchronous pulleys on the meshing performance between the pulley and the synchronous belt is not a simple additive relationship, but a more complex nonlinear one. For example, when the pressure angle of the synchronous pulley increases, its lateral separation increases, while when the tooth thickness decreases, the bending cross-section decreases. When these two factors act individually, they may both lead to an increase in contact stress. However, when they coexist, the degree of stress surge is not a simple sum of the stress increment caused by the pressure angle and the stress increment caused by the tooth thickness. Rather, it may be amplified multiple times due to stress concentration caused by abrupt changes in deformation modes. Therefore, in order to effectively balance between minimum side clearance and no meshing interference, this embodiment of the invention uses a collaborative optimization method for the process parameters of the synchronous pulley to satisfy the strong coupling relationship between the process parameters, thereby determining the solution set of the process parameter front.

[0038] Specifically, in one embodiment, the method of iteratively and collaboratively adjusting different process parameters of the synchronous pulley in the initial meshing model according to the numerical distribution of each simulation data under different load conditions includes: generating several sets of process parameter combinations as an initial population; substituting each set of process parameter combinations into the initial meshing model for simulation, calculating the corresponding side clearance objective function value and interference objective function value; performing selection, crossover, and mutation operations on the population based on the two objective function values ​​to generate a new generation population, iterating until a preset number of iterations is reached.

[0039] As an optional embodiment, the process parameters include pressure angle, tooth thickness offset, and tooth root fillet radius, wherein the pressure angle is set to a range of 14° to 20°; the tooth thickness offset is an increase or decrease based on the standard tooth thickness, with a corresponding range of -0.3mm to +0.3mm; and the tooth root fillet radius is set to a range of 0.5mm to 1.5mm.

[0040] It should be noted that the above-mentioned range of design variables is only an example in a specific embodiment of the present invention. In other embodiments, adjustments can be made according to the actual design standards and processing capabilities of the synchronous pulley. The embodiments of the present invention do not impose specific limitations.

[0041] In one embodiment, the specific method for performing selection, crossover, and mutation operations on the population based on two objective function values ​​is as follows: in the selection operation, the fitness of an individual is calculated based on the side gap objective function value and the interference objective function value corresponding to the individual; in the crossover and mutation operation, a guiding rule based on the coupling law of process parameters is introduced to adjust the process parameters of the generated offspring individuals in order to guide the population to perform iterative search in the parameter space.

[0042] Specifically, the guiding rule includes: when the pressure angle variation of a progeny exceeds a preset safety limit, the tooth thickness offset of that progeny is reduced in conjunction with a preset inverse proportional coefficient to avoid local stress concentration caused by a single parameter mutation. The preset safety limit is set based on the machining accuracy and deformation sensitivity of the pressure angle, for example, it can be set to 0.5°; the preset inverse proportional coefficient is used to characterize the tooth thickness's sensitivity to pressure angle changes, and can be set to 0.5 to 1.0; the specific calculation method for the in conjunction reduction is: calculating the reduction in tooth thickness offset. ,in It is an inverse proportional coefficient. This represents the actual increase in the variation of the pressure angle. As a preset safety upper limit, the tooth thickness offset of the offspring individual is reduced by this reduction amount based on the original mutation result. .

[0043] In one embodiment, the specific method for obtaining the backlash objective function is as follows: based on the real-time backlash value and the tooth profile micro-deformation, calculate the effective backlash under each working condition; calculate the average effective backlash within a complete meshing cycle under each working condition as the average effective backlash; calculate the backlash fluctuation based on the difference between the average effective backlash under different load conditions; determine the excessively small backlash penalty parameter based on the average effective backlash under overload conditions, combined with a preset safe backlash threshold and penalty sensitivity; and construct the backlash objective function by combining the average effective backlash, backlash fluctuation, and excessively small backlash penalty parameter.

[0044] As an optional embodiment, the specific method for calculating the average effective side clearance can be: ,in These represent no-load, rated load, and overload conditions, respectively. Indicates load condition The average effective backlash is denoted by T; T represents the total number of sampling times within a complete meshing cycle. Indicates under load conditions Next moment The effective side clearance, and ,in Indicates under load conditions Next moment Real-time side clearance value, Indicates under load conditions Next moment The amount of micro-deformation of the tooth profile.

[0045] When synchronous belt teeth are subjected to force, they undergo bending and compression micro-deformation towards the tooth root, resulting in a reduction in the actual effective backlash. Therefore, the difference between the real-time backlash value and the amount of tooth profile micro-deformation is taken as the effective backlash, which can more realistically reflect the clearance state during meshing.

[0046] As an optional embodiment, the specific calculation method for the side clearance fluctuation can be:

[0047] in, Indicates the side clearance fluctuation; This represents the average effective side clearance when the load condition is no load. This represents the average effective side clearance when the load condition is the rated load; This represents the average effective side clearance under overload conditions. This represents the absolute value function.

[0048] The backlash fluctuation reflects the change in load conditions that usually occur when the timing belt and timing pulley mesh during actual operation. Therefore, this is achieved by calculating the difference in the average effective backlash between adjacent load conditions to reflect the degree of backlash change when switching between different loads. Excessive fluctuation will lead to unstable transmission backlash and affect transmission smoothness.

[0049] As an optional embodiment, the specific calculation method for the excessively small side clearance penalty parameter can be as follows:

[0050] in, This represents the penalty parameter for excessively small backlash; This indicates the preset safety clearance threshold; This represents the average effective side clearance under overload conditions. This indicates the preset penalty sensitivity; This represents an exponential function with the natural constant as its base.

[0051] It should be noted that the purpose of constructing the backlash objective function is to minimize the backlash, but it is necessary to take into account stability and prevent interference risks caused by excessively small backlash under overload conditions. Therefore, a penalty term for excessively small backlash is introduced. When the average effective backlash under overload conditions is less than the preset safe backlash threshold, an exponential penalty is applied to the objective function to guide the optimization algorithm away from the dangerous area. In specific embodiments, the safe backlash threshold can be set according to the minimum allowable backlash of the synchronous belt model, for example, it can be 0.02mm to 0.05mm. The preset penalty sensitivity is used to control the penalty intensity and can be set to 1 to 10 according to the tolerance for overload interference.

[0052] As an optional embodiment, the specific calculation method of the side gap objective function can be:

[0053] in, Describe the objective function for the side gap; This represents the average effective backlash for all load conditions. This indicates the preset safety clearance threshold; Indicates the side clearance fluctuation; This represents the penalty parameter for excessively small backlash; and This indicates the preset first and second weights.

[0054] It should be noted that, in one embodiment of the present invention, the first weight and the second weight can be set to 0.4 and 0.6 respectively, and in other embodiments they can be adjusted according to the actual situation.

[0055] In one embodiment, the specific method for obtaining the interference objective function is as follows: based on the area of ​​the interference region and the contact stress distribution, calculate the interference stress concentration at each sampling time under each load condition; based on the area of ​​the interference region and the interference stress concentration, calculate the condition interference degree under each load condition; preset the condition coefficients for each load condition, and combine the condition interference degrees of all load conditions to construct the interference objective function.

[0056] As an optional embodiment, the specific calculation method for the interference stress concentration can be:

[0057] in, Indicates under load conditions Next moment Interference stress concentration; Indicates under load conditions Next moment The maximum contact stress; This indicates the preset allowable stress of the material; Indicates under load conditions Next moment The area of ​​the interference region; This represents an exponential function with the natural constant as its base.

[0058] It should be noted that the destructiveness of interference depends not only on the size of the interference area, but also on the level of contact stress at the time of interference. With the same interference area, the greater the contact stress, the more severe the cutting and crushing wear on the toothed belt. When there is no interference, the interference area is 0, and a stress concentration of 1 does not affect the results. When interference occurs, the contact stress is often extremely high; the greater the stress exceeds the allowable stress, the larger the exponential term, and the more the interference stress concentration increases sharply, thus severely penalizing this parameter combination in the objective function. Furthermore, the preset allowable material stress is the allowable contact stress of the synchronous toothed belt material, obtained through material tensile and compressive tests based on the hardness of the rubber matrix and the characteristics of the cord material; for example, it can be set to 8MPa to 15MPa.

[0059] As an optional embodiment, the specific calculation method for the working condition interference degree can be:

[0060] in, Indicates load condition The degree of interference under operating conditions; Indicates under load conditions Next moment The area of ​​the interference region; Indicates under load conditions Next moment Interference stress concentration; This represents the total number of sampling moments within a complete meshing cycle.

[0061] The interference degree of the working condition is calculated by averaging the accumulated time series data, which integrates the amplitude of the interference, the severity of the stress, and the duration of the time, thereby enabling a comprehensive assessment of the interference risk under a specific working condition.

[0062] As an optional embodiment, the specific calculation method of the interference objective function can be: ,in This represents the objective function of interference. Indicates the preset load conditions The operating condition coefficient, and .

[0063] Since interference is an absolutely unacceptable destructive factor in synchronous belt drives and must be strictly eliminated, the interference levels under all operating conditions are weighted and summed, with the overload condition given the highest weight. This ensures that the optimization process strongly repels interference under any operating condition, especially extreme conditions. Furthermore, the operating condition coefficients for different load conditions are... ,in , respectively, represent no-load, rated load and overload conditions, and can be specifically set to 0.25, 0.35 and 0.4, so as to ensure that the timing pulley and timing belt meet the meshing clearance requirements in actual operation during transmission meshing. In other embodiments, the condition coefficient can be adjusted according to the actual situation. The embodiments of the present invention do not make specific limitations.

[0064] In one embodiment, the specific method for obtaining the process parameter front solution set is as follows: the set of all non-dominated process parameter combinations during the iteration process is taken as the process parameter front solution set; the non-dominated process parameter combination refers to the combination in the population that is superior to this combination in both the side gap objective function value and the interference objective function value.

[0065] Thus, the solution set of the process parameter front is obtained through the above method.

[0066] Step S003: Further simulate and verify the optimal process parameter combinations in the solution set of the process parameter frontier to determine the final process parameters of the synchronous pulley.

[0067] It should be noted that although the process parameter front set obtained by simulation using a 2D finite element model can effectively balance the minimum backlash and no meshing interference at the stress distribution level, in order to ensure that the final process parameters not only balance backlash and interference in transient mechanics, but also withstand the test of thermodynamics and time-varying effects in long-term operation, this embodiment of the invention further establishes a 3D finite element model for simulation verification. In this way, only a very small number of candidate schemes need to be calculated at high cost and high fidelity, and the computational resources are fully bearable.

[0068] Specifically, in one embodiment, the method for obtaining the final process parameters is as follows: for each preferred combination of process parameters in the solution set of the process parameter frontier, a corresponding 3D finite element meshing model is established; a simulation condition including thermodynamic boundary conditions and a long-term time-varying load spectrum is applied to the 3D finite element meshing model to perform long-term operation simulation; during the long-term simulation, the time-varying backlash change, fatigue stress accumulation, and thermal deformation compatibility are monitored; based on the long-term simulation results, the process parameter combination with the best comprehensive performance under the condition of satisfying the set backlash range and no interference is selected as the final process parameters.

[0069] Specifically, selecting the optimal combination of process parameters includes: obtaining the time-varying meshing backlash, peak fatigue stress, and maximum thermal deformation displacement during the simulation process, and normalizing them respectively; using preset weighting coefficients to perform a linear weighted summation of the three normalized indicators to calculate the comprehensive penalty score for each parameter combination; and selecting the process parameter combination with the lowest comprehensive penalty score as the final process parameters. In one embodiment, 40%, 30%, and 30% are respectively used as the corresponding weighting coefficients for the time-varying meshing backlash, peak fatigue stress, and maximum thermal deformation displacement. In other embodiments, these can be adjusted according to actual conditions, and this embodiment of the invention does not impose specific limitations.

[0070] This concludes the embodiment.

[0071] It should be noted that the embodiments used in this example The model is only used to represent negative correlations and the results of the constraint model output are in Within this range, in specific implementations, other models with the same purpose can be substituted; this embodiment is merely an example. The description will be based on a model, without making specific limitations on it. This refers to the input of the model.

[0072] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the meshing clearance of synchronous belt drives based on a tooth profile stress micro-deformation model, characterized in that, The method includes the following steps: A finite element model of the meshing process of the synchronous pulley and the synchronous belt is established as the initial meshing model. Several load conditions are set to simulate the meshing process of the initial meshing model. During the simulation, several simulation data under each load condition are obtained. Based on the numerical distribution of simulation data under different load conditions, the different process parameters of the synchronous pulley in the initial meshing model are iteratively and collaboratively adjusted. During the adjustment process, the backlash objective function and the interference objective function are set, and the process parameters of the synchronous pulley are optimized by combining the backlash objective function and the interference objective function, so as to obtain the process parameter front solution set composed of several optimized process parameters. The optimal process parameter combinations in the solution set of the process parameter frontier are further simulated and verified to determine the final process parameters of the synchronous pulley.

2. The method for optimizing the meshing clearance of synchronous belt drives based on the tooth profile stress micro-deformation model according to claim 1, characterized in that, The specific method for obtaining the initial meshing model is as follows: Collect the geometric and material parameters, as well as the operating parameters, of the timing pulley and timing belt; Based on the aforementioned geometric and material parameters, a 2D tooth profile curve is imported into the finite element software. The pulley is defined as a linear elastic material and the synchronous belt as a hyperelastic material. Frictional contact is set between the pulley tooth surface and the belt tooth surface. The meshing contact area is adaptively refined to establish a 2D finite element meshing model as the initial meshing model.

3. The method for optimizing the meshing clearance of synchronous belt drives based on the tooth profile stress micro-deformation model according to claim 2, characterized in that, The method involves setting several load conditions to simulate the meshing process of the initial meshing model, and obtaining several simulation data under each load condition during the simulation process. The specific methods include: Three load conditions are set: no-load, rated load, and overload. The boundary conditions of the three load conditions are applied to the 2D finite element meshing model respectively to simulate the dynamic meshing process. Under each load condition, at least one complete meshing cycle is simulated. During the simulation, the real-time backlash value, tooth profile micro-deformation, contact stress distribution, and interference area under each working condition are monitored and recorded in real time as the simulation data.

4. The method for optimizing the meshing clearance of synchronous belt drives based on the tooth profile stress micro-deformation model according to claim 1, characterized in that, The method for iteratively and collaboratively adjusting different process parameters of the synchronous pulley in the initial meshing model based on the numerical distribution of simulation data under different load conditions includes: Several sets of process parameter combinations are generated as the initial population; Each set of process parameters is substituted into the initial meshing model for simulation, and the corresponding side clearance objective function value and interference objective function value are calculated. Based on two objective function values, selection, crossover, and mutation operations are performed on the population to generate a new generation of population, iterating until the preset number of iterations is reached.

5. The method for optimizing the meshing clearance of synchronous belt drives based on the tooth profile stress micro-deformation model according to claim 4, characterized in that, The specific methods for performing selection, crossover, and mutation operations on the population based on two objective function values ​​are as follows: In the selection operation, the fitness of an individual is calculated based on the side gap objective function value and the interference objective function value corresponding to that individual. In crossover and mutation operations, a guiding rule based on the coupling law of process parameters is introduced to adjust the process parameters of the generated offspring individuals in order to guide the population to perform iterative search in the parameter space.

6. The method for optimizing the meshing clearance of synchronous belt drives based on the tooth profile stress micro-deformation model according to claim 3, characterized in that, The specific method for obtaining the side gap objective function is as follows: Based on the real-time backlash value and the tooth profile micro-deformation, the effective backlash under each working condition is calculated; the average effective backlash within a complete meshing cycle under each working condition is calculated as the average effective backlash. The side clearance fluctuation is calculated based on the difference between the average effective side clearance under different load conditions. Based on the average effective side clearance under overload conditions, and combined with the preset safe side clearance threshold and penalty sensitivity, the penalty parameters for excessively small side clearance are determined. A side clearance objective function is constructed by combining the average effective side clearance, side clearance fluctuation, and the penalty parameter for excessively small side clearance.

7. The method for optimizing the meshing clearance of synchronous belt drives based on the tooth profile stress micro-deformation model according to claim 3, characterized in that, The specific method for obtaining the interference objective function is as follows: Based on the area of ​​the interference region and the contact stress distribution, the interference stress concentration at each sampling time under each load condition is calculated; based on the area of ​​the interference region and the interference stress concentration, the condition interference degree under each load condition is calculated. The operating condition coefficients for each load condition are preset, and the interference degree of all load conditions is combined to construct the interference objective function.

8. The method for optimizing the meshing clearance of synchronous belt drives based on the tooth profile stress micro-deformation model according to claim 7, characterized in that, The specific method for obtaining the interference stress concentration is as follows: Preset allowable stress of material, when under load conditions Next moment When the area of ​​the interference region is 0, it will be under load conditions. Next moment The interference stress concentration is set to 1; Under load conditions Next moment When the area of ​​the interference region is greater than 0, according to the load condition Next moment The stress difference factor is obtained by calculating the difference between the maximum contact stress and the allowable stress of the material. Based on this stress difference factor, the stress under load conditions can be determined. Next moment The interference stress concentration, wherein the stress difference factor is positively correlated with the interference stress concentration.

9. The method for optimizing the meshing clearance of synchronous belt drives based on the tooth profile stress micro-deformation model according to claim 1, characterized in that, The specific method for obtaining the solution set of the process parameter front is as follows: The set of all non-dominated process parameter combinations during the iteration process is taken as the process parameter front solution set; the non-dominated process parameter combination refers to the combination in the population that is superior to this combination in both the side gap objective function value and the interference objective function value.

10. The method for optimizing the meshing clearance of synchronous belt drives based on the tooth profile stress micro-deformation model according to claim 1, characterized in that, The specific method for obtaining the final process parameters is as follows: For each optimal combination of process parameters in the solution set of the process parameter frontier, a corresponding 3D finite element meshing model is established. The 3D finite element meshing model is subjected to simulation conditions including thermodynamic boundary conditions and long-term time-varying load spectrum to perform long-term operation simulation. During long-term simulation, the time-varying side clearance changes, fatigue stress accumulation, and thermal deformation compatibility are monitored. Based on long-term simulation results, the optimal combination of process parameters with the best overall performance under the conditions of satisfying the set side clearance range and no interference was selected as the final process parameters.

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