An ultra-high temperature heavy load tapered roller bearing optimization design method and system based on NSGA-III algorithm

Abstract

The application discloses an optimization design method and system for super-high-temperature heavy-load tapered roller bearings based on an NSGA-III algorithm, belongs to the field of optimization design of rolling bearings, and solves the problems that the maximum equivalent stress of a tapered roller bearing is over limited, a friction coefficient is increased, and a roller is skewed under the super-high-temperature heavy-load working condition of a hypersonic aircraft, the problems are coupled with each other, plastic deformation, lubrication failure and damage of a retainer are caused, and traditional optimization methods are difficult to deal with the complex coupling relationship, and the existing NSGA-III algorithm lacks adaptability improvement for the super-high-temperature working condition. The method comprises the following steps: obtaining initial parameters of a bearing structure, collecting working condition parameters of the tapered roller bearing and NSGA-III algorithm parameters; establishing an optimization model for the super-high-temperature heavy-load tapered roller bearing, comprising the following steps: determining a target function; determining design variables; determining constraint conditions; and performing joint simulation optimization on the design variables of the tapered roller bearing by using the NSGA-III algorithm. The application is suitable for the optimization design scene of the super-high-temperature heavy-load tapered roller bearing.

Description

Technical Field

[0001] This invention relates to the field of rolling bearing optimization design, specifically to an optimization design method for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm. Background Technology

[0002] In the extreme operating conditions of hypersonic vehicles, tapered roller bearings, as core supporting components of power transmission, attitude control, and thermal protection systems, directly determine the reliability of the vehicle and even affect the ultimate success or failure of the mission. Under ultra-high temperature and heavy load conditions, a series of problems become particularly prominent: if the maximum equivalent stress exceeds a reasonable range, it can easily lead to plastic deformation in the contact area between the rolling elements and the raceway of the bearing. This significantly shortens the bearing's fatigue life, exacerbates local wear, and in severe cases, can even cause the bearing to seize. An increase in the bearing's coefficient of friction leads to a sharp increase in frictional heat generation, which not only accelerates the thermal softening of the material but also speeds up lubrication failure, resulting in bearing failures such as sticking and seizing, and significantly reducing its operational stability. When the rollers of a tapered roller bearing become misaligned, it can cause uneven or excessive load distribution on the cage, leading to accelerated cage wear, deformation, and even breakage. This directly affects the bearing's rotational accuracy and overall dynamic performance, resulting in a decrease in the attitude control accuracy of the aircraft. It can be said that early failure of tapered roller bearings under ultra-high temperature and heavy load conditions has become a major technical bottleneck restricting the performance improvement of high-end equipment. These issues, stemming from maximum equivalent stress, bearing friction coefficient, and cage contact load, are interconnected and mutually influential, forming complex coupling relationships that become even more intricate under high-temperature environments. Traditional optimization design methods, relying on a combination of empirical formulas and finite element simulations, struggle to accurately describe and control the complex changes and interactions of these parameters under ultra-high temperature and heavy-load conditions, failing to achieve coordinated optimization of multiple objectives such as bearing load capacity, operational stability, and rotational accuracy. The NSGA-Ⅲ algorithm demonstrates strong global search capabilities and fast convergence speed when facing complex scenarios with multiple design variables, multiple nonlinear constraints, and multiple objective functions. However, this algorithm lacks adaptive improvements for ultra-high temperature and heavy-load conditions, limiting its application in such specific scenarios. Therefore, developing an optimization algorithm that accurately targets maximum equivalent stress, bearing friction coefficient, and cage contact load, adapting to ultra-high temperature and heavy-load conditions, is crucial for improving the performance of tapered roller bearings and overcoming technological bottlenecks in high-end equipment. Summary of the Invention

[0003] This invention provides an optimization design method for ultra-high temperature heavy-load tapered roller bearings based on the NSGA-Ⅲ algorithm. The purpose is to solve the problem that tapered roller bearings face problems such as excessive maximum equivalent stress, increased friction coefficient and roller misalignment under ultra-high temperature heavy-load conditions in hypersonic vehicles. These problems are coupled and lead to plastic deformation, lubrication failure and cage damage. Traditional optimization methods are difficult to handle these complex coupling relationships, and the existing NSGA-Ⅲ algorithm lacks adaptive improvements for ultra-high temperature conditions.

[0004] The present invention proposes an optimization design method for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm, which includes: S1: Based on the model of the tapered roller bearing, obtain the initial parameters of the bearing structure, collect the operating parameters of the tapered roller bearing and the NSGA-Ⅲ algorithm parameters; S2: Establish an optimization model for ultra-high temperature heavy-duty tapered roller bearings, including: S21: Construct a quasi-static model of the tapered roller bearing and determine the objective function; S22: Determine the design variables; S23: Determine the constraints; S3: The design variables of the tapered roller bearing are optimized by joint simulation using the NSGA-Ⅲ algorithm, and the optimization results are obtained.

[0005] Furthermore, a preferred embodiment is provided: the initial parameters of the bearing structure include: the average diameter of the bearing rollers, the effective length of the rollers, the contact angle of the inner raceway, the contact angle of the outer raceway, the contact angle of the flange, the number of rolling elements, the crown, the cage pocket clearance, the flange clearance, and the material parameters.

[0006] Furthermore, a preferred option is provided: the operating parameters include: axial force, radial force, clearance, fit, temperature, and rotational speed of the bearing.

[0007] Furthermore, a preferred solution is provided: S21 includes: constructing a quasi-static model of the tapered roller bearing, calculating the maximum equivalent stress of the rolling elements, the bearing friction coefficient, and the cage contact load, and using these three calculation results as the objective function.

[0008] Furthermore, a preferred solution is provided: the quasi-static model of the tapered roller bearing is solved using the Dogbox-TRF collaborative solution algorithm.

[0009] Furthermore, a preferred embodiment is provided: the constraints include: rolling element equivalent stress constraint, flange root thickness constraint, half-cone angle constraint, roller large end diameter and number constraint, sub-length constraint, inner and outer ring minimum effective wall thickness constraint, large flange root thickness strength constraint, and flange contact height constraint.

[0010] Furthermore, a preferred embodiment is provided, characterized in that S3 includes: S31: Initialize the population for the NSGA-III algorithm and configure parameters, including: population size, number of iterations, crossover probability, and mutation probability; S32: Set the optimization variables, constraints, and objective function; S33: Randomly generate within the solution space containing N The parent population of each individual t is the number of iterations, and a child population is generated. ; S34: Merge the parent and offspring populations to obtain a population size of 2. N new population ,calculate Individual fitness value; S35: Merging populations Perform a fast non-dominated sort, divide the system into non-dominated levels, and select the optimal level based on a reference point. N Individuals constitute the new generation of the parent population; S36: Using Python's parallel computing mode, the fitness function for multi-core parallel computing is called in the parallel pool based on the NSGA-III algorithm; S37: Repeat S33-S36 until the algorithm obtains the optimal solution or reaches the maximum number of iterations, at which point the optimization process ends.

[0011] The present invention also proposes a computer device, the computer device including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the above-described method for optimizing the design of ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm.

[0012] The present invention also proposes a computer-readable storage medium for storing a computer program that executes the above-described method for optimizing the design of ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm.

[0013] This invention also proposes an optimization design system for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm. The system is implemented based on an optimization design method for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm, as described in any one or more of the above-mentioned schemes. The system includes: Parameter acquisition module: used to obtain the initial structural parameters of the tapered roller bearing based on the model of the tapered roller bearing, and to acquire the operating parameters of the tapered roller bearing and the NSGA-Ⅲ algorithm parameters; Ultra-high temperature heavy-duty tapered roller bearing optimization model module: used to construct a quasi-static model of tapered roller bearings, determine the objective function, design variables, and constraints; Simulation optimization module: Used to perform joint simulation optimization of the design variables of tapered roller bearings using the NSGA-Ⅲ algorithm, and obtain the optimization results.

[0014] This invention proposes a co-simulation optimization design method for tapered roller bearings based on the NSGA-Ⅲ algorithm. Based on the quasi-static model of the bearing, the method aims to reduce the maximum equivalent stress, bearing friction coefficient, and cage contact load. Combined with the NSGA-Ⅲ algorithm, an optimization design model for tapered roller bearings is constructed, providing a technical means for the rapid optimization of tapered roller bearing structures.

[0015] This invention is applicable to the optimization design of ultra-high temperature heavy-duty tapered roller bearings. Attached Figure Description

[0016] Figure 1 The flowchart shows an optimization design method for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm, as described in a specific embodiment of the present invention. Figure 2 This is a flowchart of the Dogbox-TRF collaborative solution algorithm described in Specific Embodiment 3 of the present invention. Detailed Implementation

[0017] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application can also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0018] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0019] It should also be understood that the terminology used in this application specification is for the purpose of describing particular embodiments only and is not intended to limit the application. As used in this application specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0020] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0021] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0022] Implementation Method 1: Reference Figure 1 This implementation method is described below.

[0023] An optimization design method for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm, characterized in that the method includes: S1: Based on the model of the tapered roller bearing, obtain the initial structural parameters of the bearing, collect the operating parameters of the tapered roller bearing and the NSGA-Ⅲ algorithm parameters, and provide input for the subsequent establishment of an optimization mathematical model; The initial parameters of the bearing structure include: the average diameter of the bearing rollers. Effective length of roller Inner raceway contact angle Outer raceway contact angle , edge contact angle Number of rolling elements convexity Cage pocket clearance , edge clearance and material parameters; The operating parameters include: the axial force on the bearing. radial force Clearance, fit, temperature, and rotational speed; The NSGA-Ⅲ algorithm parameters include: reference directions, the number of which must be consistent with the number of objective functions; in this implementation, the reference directions are 3; the population size is between 100 and 200; the tournament size in the selection operator is 2 to 4; the distribution index in the crossover operator is 20 to 50, and the crossover probability is between 0.8 and 1.0; the distribution index in the mutation operator is 10 to 30, and the mutation probability is between 0.11 and 0.22. S2: Establish an optimization model for ultra-high temperature heavy-duty tapered roller bearings, including: S21: Construct a quasi-static model of the tapered roller bearing and determine the objective function; S22: Determine the design variables. The design variables that have a direct impact on the objective function are: average diameter of bearing rollers. Effective length of roller Inner raceway contact angle Outer raceway contact angle , edge contact angle Number of rolling elements convexity Cage pocket clearance , edge clearance The above nine parameters are selected as the design variables for this method: ; S23: Determine the constraints; S3: The design variables of the tapered roller bearing are optimized by joint simulation using the NSGA-Ⅲ algorithm, and the optimization results are obtained.

[0024] Implementation Method Two: This embodiment is a further illustrative example of S21 in the optimization design method for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm described in Embodiment 1.

[0025] S21 establishes a quasi-static model to calculate the contact load of the tapered roller bearing under high temperature and heavy load conditions. Based on the obtained rolling element load distribution, it calculates the maximum equivalent stress of the rolling elements, the bearing friction coefficient, and the cage contact load, and uses these three calculation results as the objective function.

[0026] Establish a quasi-static model for tapered roller bearings: Based on the original bearing's geometric parameters, a deformation compatibility model considering temperature and assembly stress is proposed: The inner cylinder bears external pressure, and the outer cylinder bears internal pressure. Assembly stress (initial stress) occurs within this combined cylinder, along with the assembly pressure. The relationship with the radius interference Δ is: (1) in, Indicates the inner diameter of the inner cylinder, Indicates the outer diameter of the outer cylinder, Indicates the outer diameter of the inner cylinder. Indicates the amount of interference. This represents the temperature-dependent elastic modulus of the inner cylinder material. This indicates the temperature-dependent elastic modulus of the outer cylinder material. Poisson's ratio, representing the relationship between the inner cylinder material and temperature, This represents the Poisson's ratio of the outer cylinder material in relation to temperature.

[0027] In part radius At this point, the assembly stress of the inner and outer rings and the deformation caused by rotation. , and for: (2) in, This indicates the fitting stress of the inner ring. This indicates the fitting stress of the outer ring. This represents the temperature-dependent elastic modulus of the bearing. Indicates the inner angular velocity. Poisson's ratio, representing the bearing's temperature dependence, This indicates the temperature-dependent density of the bearing material. Indicates the outer diameter of a cylindrical part. The inner diameter of the cylindrical part is indicated by T; the temperature is indicated by T.

[0028] The amount of raceway deformation caused by temperature is expressed as: (3) in, ΔT represents the coefficient of thermal expansion, and ΔT represents the temperature increment.

[0029] Raceway radius considering assembly, rotational speed, and thermal expansion effects: (4) in, Indicates the first k The azimuth angle of the roller, This indicates the azimuth angle considering the effects of assembly, rotational speed, and thermal expansion. Outer raceway radius, This indicates the azimuth angle considering the effects of assembly, rotational speed, and thermal expansion. The inner raceway radius, Indicates the corresponding azimuth angle The initial dimension of the inner raceway radius, Indicates the corresponding azimuth angle The initial size of the outer raceway radius.

[0030] Based on the vector transformation method and the slicing method, a contact deformation model of the raceway and rollers is established to simulate the interaction between the rollers, raceways, and cages.

[0031] Among them, the contact deformation between the roller and the raceway for:

[0032] (5) In the formula, Indicates the first raceway on the inner raceway after loading. k The radial component of the position vector of the contact point of each roller in the azimuth coordinate system. Indicates the first raceway on the outer track after loading. k The radial component of the position vector of the contact point of each roller in the azimuth coordinate system. Indicates the inner raceway half-cone angle. This indicates the half-cone angle of the outer raceway.

[0033] Contact deformation between the roller and the flange Represented as: (6) In the formula, This represents the x-component of the position vector of the contact point of the flange in the flange contact coordinate system. This indicates the radius of the arc at the large end of the roller.

[0034] Next, the contact load equations between the roller and the outer raceway, the inner raceway, and the cage due to skewness are constructed. The deformation-contact load equations between the roller and the outer raceway and the inner raceway are expressed as follows: (7) In the formula, Indicates raceway contact deformation. k = i , o ; Poisson's ratio, representing the material of the raceway as a function of temperature, Poisson's ratio, representing the temperature-dependent properties of the roller material, This represents the temperature-dependent elastic modulus of the ring material. This indicates the temperature-dependent elastic modulus of the roller material. Indicates contact load, Indicates the effective contact length.

[0035] The deformation-contact load equation between the roller and the flange is expressed as: (8) in, The coefficients are related to the principal curvature difference function at the contact point. Represents the principal curvature and function at the contact point. This represents the combined elastic constant of the two objects. This indicates the contact load between the rolling element and the flange.

[0036] The steps for establishing the quasi-static model of a tapered roller bearing are as follows: Roller force balance equation: (9) (10) in, Indicates the number of slices. Indicates the first roller j Contact load on the inner raceway of each slice Indicates the first roller j Contact load on the outer raceway of each slice Indicates the first j The coordinates of the position of the slice center on the roller axis. This indicates the coordinates of the roller's geometric center on the roller's axis. This indicates the position coordinates of the flange contact point along the roller axis. Indicates the roller tilt angle. Indicates the roller skew angle. Indicates the first j The change in azimuth angle corresponding to each slice , Indicates the first j The distance from the center of each slice to the bearing axis. Indicates the first roller j The diameter of each slice, Indicates the semi-cone angle of the roller. Indicates the pressure angle of the retaining edge. This indicates the angle between the roller axis and the bearing axis. The roller radius indicating the centroid position. Indicates the radius of the arc at the large end of the roller. Indicates the effective contact length. Indicates centrifugal force. This indicates the frictional force between the roller and the inner raceway caused by roller misalignment. This represents the total frictional force between the roller and the outer raceway caused by roller misalignment. This represents the torque on the roller caused by the roller-inner raceway load due to skewness. This represents the torque on the roller caused by the roller-outer raceway load due to skewness. This represents the tilting moment caused by the roller-inner raceway load. This represents the tilting moment caused by the roller-outer raceway load. This indicates the contact force between the roller and the cage pocket. This represents the gyroscopic torque of the roller. This represents the coefficient of friction between the contact surfaces of the roller and the raceway.

[0037] The inner ring force balance equation is expressed as: (11) (12) This represents the transformation matrix from the roller coordinate system to the inner ring coordinate system. This indicates the contact load between the roller and the inner raceway. This indicates the contact load between the roller and the flange. This represents the vector of contact points between the roller and the inner raceway. This represents the vector of the contact point between the roller and the flange.

[0038] Solving the above system of equations will yield the load distribution of the rolling elements.

[0039] The calculation of maximum equivalent stress, friction coefficient, and cage load is further illustrated below with examples: (1) Based on the obtained rolling element load distribution, the equivalent stress of the bearing is calculated using the small strain thermoelastic theory and expressed as a function of the deviatoric strain tensor under the corresponding high temperature condition: (13) In the formula: S represents the deviatoric stress tensor.

[0040] The deviatoric stress tensor S is: (14) In the formula: Represents the stress tensor. This represents a fourth-order unit tensor.

[0041] The stress tensor is: (15) In the formula: Represents the temperature-dependent elastic tensor; This represents the strain tensor.

[0042] (2) The steps for calculating the friction coefficient of tapered roller bearings under high-temperature conditions are as follows: The frictional torque of a tapered roller bearing is expressed as: (16) in, This indicates the total power loss of a dry friction tapered roller bearing. This represents the frictional power loss caused by differential sliding between the rolling elements and the raceways. This represents the frictional power loss caused by sliding friction between the large end face of the rolling element and the inner ring flange. This represents the frictional power loss caused by the sliding friction between the skewed rolling element and the cage pocket. This represents the total frictional torque of a high-temperature dry friction tapered roller bearing. This represents the frictional torque caused by the differential sliding between the rolling elements and the raceways. This represents the frictional torque caused by the sliding friction between the large end face of the rolling element and the inner ring flange. This represents the frictional torque caused by the sliding friction between the skewed rolling element and the cage pocket. This indicates the rotational speed of the inner ring.

[0043] The coefficient of friction of the bearing is: (17) In the formula: The value represents the frictional torque of the tapered roller bearing, d represents the bearing inner diameter, D represents the bearing outer diameter, and P represents the bearing equivalent load.

[0044] (3) By evaluating the stress state of the cage at high temperatures, the initial fit clearance design considering thermal expansion compensation can be deduced to avoid stress overload caused by abnormal clearance and ensure the stability of roller movement. Contact force between the roller and the cage pocket. This can be calculated from the aforementioned model, therefore: (18) in, —Permissible load of the cage under high temperature conditions.

[0045] In summary, the objective function is: (19) Implementation Method 3: Reference Figure 2 This implementation method is described below.

[0046] This embodiment further illustrates the calculation of rolling element load distribution in the ultra-high temperature heavy-duty tapered roller bearing optimization design method based on the NSGA-Ⅲ algorithm described in Embodiment 2.

[0047] This implementation method is based on the Dogbox-TRF collaborative solution algorithm to solve for the contact deformation and displacement between the roller and the raceway, and to obtain the load distribution. The specific calculation process is as follows: Figure 2 As shown.

[0048] The quasi-static model of a tapered roller bearing considering rolling element misalignment is expressed by a system of equations consisting of 4Z+5 equations. Among these, the displacement and rotation of the inner ring relative to the inertial coordinate system are... There are a total of 5 unknowns; in the roller coordinate system, the first... j The displacement and rotation of each rolling element are There are a total of 4Z unknowns.

[0049] The system of equations is solved using a combined algorithm of Dogbox and TRF to obtain the contact load on each rolling element and the contact force between the skewed rolling element and the cage pocket. The specific logic is as follows: (1) Preliminary estimate of inner circle displacement and rolling element displacement Determine the relative positions of the inner ring and the rollers; (2) Use the Dogbox-TRF collaborative solution algorithm to solve the equilibrium equations of the rollers and solve for the displacements of all rollers. ; (3) Use the Dogbox-TRF collaborative solution algorithm to solve the equilibrium equations of the inner ring and determine the displacement of the ring. If the solution converges, the inner loop is in equilibrium, and the current solution is the final solution; if not, use the current loop position and go to step (2).

[0050] The logic of the Dogbox-TRF collaborative solution algorithm is as follows: First, use Dogbox to quickly shrink the solution space to the effective constraint region. If the convergence accuracy tool is reached at this point, output the solution result sol. If the convergence accuracy tool is not reached at this point, use the calculated result sol_Dogbox as the initial data and substitute it into the TRF algorithm for calculation. If the convergence accuracy tool is reached, output the result sol. If it still does not converge, adjust the iteration number iter and the convergence accuracy.

[0051] By combining the Dogbox and TRF algorithms, adjusting the order of computation, and fine-tuning the iteration accuracy and maximum number of iterations, local optima can be effectively avoided, thus improving solution efficiency and accuracy.

[0052] This implementation innovatively proposes a collaborative solution strategy combining the Dogbox and TRF algorithms to solve the nonlinear equations of a high-temperature tapered roller bearing model, overcoming the performance bottleneck of a single algorithm under complex working conditions. The Dogbox algorithm, leveraging its rectangular trust region characteristics and boundary constraint handling advantages, demonstrates high convergence efficiency in exploring local solution spaces with low variable dimensions. Meanwhile, the TRF algorithm, by dynamically adjusting the trust region shape, effectively addresses the ill-conditioned and multi-extremum problems that may arise in the nonlinear equations, maintaining strong robustness in the global solution space search. The organic combination of the two forms a two-layer solution mechanism of "local fine optimization - global robust exploration": the Dogbox algorithm is used to quickly shrink the solution space to the effective constraint region, and then the TRF algorithm is used to accurately locate the global optimal solution in this region. This avoids the convergence lag of the single Dogbox algorithm under high-dimensional variables and overcomes the insufficient optimization efficiency of the TRF algorithm under strong constraints. In the end, it achieves a synergistic improvement in accuracy, efficiency and stability in solving the nonlinear equations of high-temperature tapered roller bearings, and provides a breakthrough numerical solution scheme for bearing performance evaluation under extreme working conditions.

[0053] Implementation Method Four: This embodiment is a further illustrative example of S23 in the optimization design method for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm described in Embodiment 1.

[0054] In S23 of this embodiment, the constraints include: rolling element equivalent stress constraint, flange root thickness constraint, half-cone angle constraint, roller large end diameter and number constraint, sub-length constraint, inner and outer ring minimum effective wall thickness constraint, large flange root thickness strength constraint, and flange contact height constraint.

[0055] Specifically: (1) Equivalent stress constraint of rolling element: The maximum equivalent stress in the inner and outer raceways and the flanges of the rolling elements is less than the yield strength. (20) The expression for yield strength is: (twenty one) In the formula: This represents the initial yield stress at different temperatures, in Pa. The value represents the material's melting temperature, in °C; m represents the thermal softening index. This indicates the thermal softening factor.

[0056] (2) Thickness constraint at the root of the retaining edge: The large-end flange and small-end flange of the inner ring are: (twenty two) in, Indicates the small end flange of the inner ring; Indicates the large end flange of the inner ring; B This refers to the nominal width of the inner ring. , It is a value related to the serial number that can be obtained from a lookup table.

[0057] (3) Half-cone angle constraint: Based on the internal geometry of a tapered roller bearing, the half-cone angle is: (twenty three) According to the tapered roller design method, the half-cone angle must meet the following conditions: (twenty four) (25) in: D Indicates the outer diameter of the bearing; d Indicates the inner diameter of the bearing; E Indicates the nominal smaller inner diameter of the outer ring; C Indicates the nominal width of the outer ring; Indicates the outer raceway contact angle; , The flange dimension of the raceway is obtained by referring to a table.

[0058] (26) (4) Roller large end diameter and quantity constraints: The diameter of the large end of the roller is: (27) The number of rollers in a tapered roller bearing should be less than the number of full complement rollers, and adjacent rollers must not interfere with each other. The clearance between adjacent rollers at their large ends should be [not specified]. J It should be less than a certain value, that is: (28) (29) (5) Sub-length constraint: The roller must have sufficient contact length with the outer raceway, but it must not exceed the chamfers on both sides of the outer raceway, that is: (30) in: , T For bearing assembly height, and It can be obtained by looking up a table.

[0059] Therefore: (31) (6) Minimum effective wall thickness constraints for inner and outer rings: Effective wall thickness at the small end of the inner roller In principle, it should not be less than the effective wall thickness of the outer ring at the large end of the roller. Therefore, the effective wall thickness of the inner and outer rings is a crucial parameter affecting the inner and outer stiffness and strength, as well as the roller diameter and length. However, since the dimensions of the outer ring are standardized, it is permissible to sometimes... Slightly smaller Furthermore, the thickness difference of the inner ring wall must be controlled within the specified range.

[0060] (32) (33) (7) Thickness strength constraint at the root of the large flange: The allowable thickness at the root of the inner ring large flange is: (34) In the above formula [ S The ] is the allowable safety factor obtained from the table lookup. Indicates the maximum radius of the inner raceway. This indicates the rated dynamic load.

[0061] therefore: (35) (8) Edge contact height constraint: Position of the contact point between the base surface of the roller ball and the inner ring large flange h It can be calculated from the aforementioned quasi-static model: Initial contact height between the large end of the roller and the inner ring flange for: (36) When the bearing is under load, the contact point between the large end of the roller and the inner ring flange will shift. The relationship between the contact point and its position is given by the following formula. By solving the above quasi-static model, the displacement of the contact point can be calculated. .

[0062] (37) This represents the transformation matrix from the inertial coordinate system to the edge coordinate system. This represents the initial coordinate vector of the contact point of the flange in the inertial coordinate system.

[0063] Therefore, the contact height between the large end of the roller and the inner ring flange of the tapered roller bearing under load is: (38) The contact point should be controlled within the range of about 1 / 2 of the middle of the large flange to determine the appropriate contact height range. (39) in, This indicates the height of the inner ring large flange.

[0064] In summary, the optimized design model for ultra-high temperature heavy-duty tapered roller bearings is as follows: (40) Implementation Method 5: This embodiment is a further example illustrating S3 in the optimization design method for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm described in Embodiment 1.

[0065] S3 includes: S31: Initialize the population for the NSGA-III algorithm and configure parameters such as population size, number of iterations, crossover probability, and mutation probability; S32: Set the optimization variables, constraints, and objective function. In this invention, the optimization variable is set as the average diameter of the bearing rollers. Effective length of roller Inner raceway contact angle Outer raceway contact angle , edge contact angle Number of rolling elements convexity Cage pocket clearance , edge clearance Each individual in the population is represented as a 9-dimensional vector. The constraint vector is denoted as The objective function vector is denoted as ; S33: Randomly generate within the solution space containing N The parent population of each individual t represents the number of iterations, and genetic algorithms such as selection, crossover, and mutation are used to generate the offspring population. ; S34: Merge the parent and offspring populations to obtain a population size of 2. N new population ,calculate Individual fitness value; S35: Merging populations Perform a fast non-dominated sort, divide the system into non-dominated levels, and select the optimal level based on a reference point. N Individuals constitute the new generation of the parent population; S36: By using Python's parallel mode, multiple solvers are called for parallel computation, improving computational efficiency; S37: Repeat S33-S36 until the algorithm obtains the optimal solution or reaches the maximum number of iterations, at which point the optimization process ends; S38: Determine the target design parameters based on the Pareto optimal solution. For ultra-high temperature and heavy load conditions, the maximum equivalent stress, bearing friction coefficient, and cage contact load are calculated to evaluate the ultimate load capacity of tapered roller bearings.

[0066] Implementation Method Six: An optimization design system for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm is disclosed. The system is implemented based on the optimization design method for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm described in the above embodiments. The system includes: Parameter acquisition module: used to obtain the initial structural parameters of the tapered roller bearing based on the model of the tapered roller bearing, and to acquire the operating parameters of the tapered roller bearing and the NSGA-Ⅲ algorithm parameters; Ultra-high temperature heavy-duty tapered roller bearing optimization model module: used to construct a quasi-static model of tapered roller bearings, determine the objective function, design variables, and constraints; Simulation optimization module: Used to perform joint simulation optimization of the design variables of tapered roller bearings using the NSGA-Ⅲ algorithm, and obtain the optimization results.

[0067] Implementation Method 7: This implementation method takes a certain type of tapered roller bearing as an example. The radial load is 10KN, the axial load is 2KN, the speed is 800r / min, and the temperature is 800℃. The bearing structural parameters and objective function values ​​before and after optimization are shown in Tables 1-4.

[0068] The results in Tables 2 and 4 show that after adopting the optimized bearing design parameters, the maximum equivalent stress of the bearing is reduced by 10.53%, the bearing friction coefficient is reduced by 12.00%, and the cage contact load is reduced by 12.5%, which is sufficient to prove that the optimized design method has a good effect on improving bearing performance.

[0069] Table 1 Original bearing structural parameters

[0070] Table 2 Objective function values ​​before optimization

[0071] Table 3 Optimized bearing structural parameters

[0072] Table 4. Optimized objective function values

Claims

1. A method for optimizing the design of ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm, characterized in that, The method includes: S1: Based on the model of the tapered roller bearing, obtain the initial structural parameters of the bearing, and collect the operating parameters of the tapered roller bearing and the NSGA-Ⅲ algorithm parameters; the initial structural parameters of the bearing include: the average diameter of the bearing rollers, the effective length of the rollers, the contact angle of the inner raceway, the contact angle of the outer raceway, the contact angle of the flange, the number of rolling elements, the crown, the cage pocket clearance, the flange clearance, and the material parameters; the operating parameters include: the axial force, radial force, clearance, fit, temperature, and rotational speed of the bearing; S2: Establish an optimization model for ultra-high temperature heavy-duty tapered roller bearings, including: S21: Construct a quasi-static model of the tapered roller bearing and determine the objective function. The input parameters of this model include: geometric parameters consisting of the average roller diameter, effective roller length, inner raceway contact angle, outer raceway contact angle, flange contact angle, number of rolling elements, crown, cage pocket clearance, and flange clearance; operating parameters consisting of axial force, radial force, clearance, interference fit, temperature, and rotational speed; and material parameters consisting of elastic modulus, Poisson's ratio, density, and coefficient of thermal expansion that vary with temperature. The model corrects the raceway radius by taking into account the interference fit, rotational centrifugal force, and raceway deformation caused by thermal expansion. Based on the corrected raceway radius, a set of force balance equations is established, and the rolling element load distribution is obtained by solving the equations. This yields the maximum equivalent stress of the rolling elements, the bearing friction coefficient, and the cage contact load, which are used as the objective function. S22: Determine the design variables; select the average roller diameter, effective roller length, inner raceway contact angle, outer raceway contact angle, flange contact angle, number of rolling elements, crown, cage pocket clearance, and flange clearance as design variables; S23: Determine the constraints; S3: The design variables of the tapered roller bearing are optimized by joint simulation using the NSGA-Ⅲ algorithm, and the optimization results are obtained.

2. The optimization design method for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm according to claim 1, characterized in that, The quasi-static model of the tapered roller bearing was solved using the Dogbox-TRF collaborative solution algorithm.

3. The optimization design method for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm according to claim 1, characterized in that, The constraints include: rolling element equivalent stress constraint, flange root thickness constraint, half-cone angle constraint, roller large end diameter and number constraint, sub-length constraint, inner and outer ring minimum effective wall thickness constraint, large flange root thickness strength constraint, and flange contact height constraint.

4. The optimization design method for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm according to claim 1, characterized in that, S3 includes: S31: Initialize the population for the NSGA-III algorithm and configure parameters, including: population size, number of iterations, crossover probability, and mutation probability; S32: Set the optimization variables, constraints, and objective function; S33: Randomly generate within the solution space containing N The parent population of each individual t is the number of iterations, and a child population is generated. ; S34: Merge the parent and offspring populations to obtain a population size of 2. N new population ,calculate Individual fitness value; S35: Merging populations Perform a fast non-dominated sort, divide the system into non-dominated levels, and select the optimal level based on a reference point. N Individuals constitute the new generation of the parent population; S36: Using Python's parallel computing mode, the fitness function for multi-core parallel computing is called in the parallel pool based on the NSGA-III algorithm; S37: Repeat S33-S36 until the algorithm obtains the optimal solution or reaches the maximum number of iterations, at which point the optimization process ends.

5. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes an optimization design method for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm according to any one of claims 1-4.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store a computer program that executes the optimization design method for ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm according to any one of claims 1-4.

7. A system for optimizing the design of ultra-high temperature heavy-duty tapered roller bearings based on the NSGA-Ⅲ algorithm, characterized in that, The system is based on the NSGA-Ⅲ algorithm-based optimization design method for ultra-high temperature heavy-duty tapered roller bearings as described in any one of claims 1-4. The system includes: Parameter acquisition module: used to obtain the initial structural parameters of the tapered roller bearing based on the model of the tapered roller bearing, and to acquire the operating parameters of the tapered roller bearing and the NSGA-Ⅲ algorithm parameters; Ultra-high temperature heavy-duty tapered roller bearing optimization model module: used to construct a quasi-static model of tapered roller bearings, determine the objective function, design variables, and constraints; Simulation optimization module: Used to perform joint simulation optimization of the design variables of tapered roller bearings using the NSGA-Ⅲ algorithm, and obtain the optimization results.

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