A multi-objective optimization design method, system, and storage medium for double-row tapered roller hub bearing structures.

Abstract

This invention discloses a multi-objective optimization design method, system, and storage medium for double-row tapered roller hub bearings, belonging to the field of hub bearing design and optimization. The method includes: constructing a mechanical model of the double-row tapered roller hub bearing; establishing force and moment balance equations; solving for the contact loads between the rollers and raceways, and between the rollers and flanges, using an iterative method; establishing a multi-objective optimization function; calculating radial stiffness, PV value, and fatigue life; setting optimization constraints; performing multi-objective optimization using an algorithm; initializing a population that satisfies the constraints; obtaining the Pareto solution set through selection, crossover, and mutation iterative calculations; selecting the optimal structural parameters through a weighted evaluation function; and completing the multi-objective optimization design of the hub bearing. This invention solves the problem in traditional double-row tapered roller hub bearing design practice where it is difficult to determine the optimal variable values ​​due to the contradictory relationships between variables, thus reducing the time required to evaluate the internal loads and stresses of the bearing.

Description

Technical Field

[0001] This invention belongs to the field of wheel hub bearing design and optimization, specifically relating to a multi-objective bearing optimization design method, system, and storage medium for improving the radial stiffness, roller-flange PV value, and bearing fatigue life of wheel hub bearings. Technical Background

[0002] Wheel bearings are core load-bearing components of automotive chassis systems, located between the steering knuckle and the wheel hub. They bear the critical tasks of transmitting vehicle weight, withstanding complex alternating loads (including radial force, axial force, and bending moment), and providing precise guidance for wheel rotation. With the popularization of new energy vehicles and the deepening of lightweight automotive design, modern automobiles have placed unprecedentedly stringent requirements on the comprehensive performance of wheel bearings. Specifically, high radial stiffness is fundamental to ensuring vehicle handling stability and steering precision, directly affecting the driver's "road feel" and the overall NVH (noise, vibration, and harshness) performance of the vehicle. The contact stress level between the rollers and the flanges directly relates to the internal friction state and temperature distribution of the bearing; excessive contact stress is a major cause of flange wear, galling, and even premature bearing failure. The fatigue life of the bearing directly determines the product's reliability and maintenance costs, and is a core indicator for measuring its service durability. Therefore, how to simultaneously improve these three performance aspects during the design phase has become a core challenge in the field of wheel bearing design.

[0003] In traditional wheel hub bearing design practice, engineers typically rely on empirical formulas, standard manuals, and analogies to determine the main structural parameters of the bearing, such as rolling element diameter, pitch circle diameter, and contact angle. However, this traditional design method has significant limitations: First, there are often contradictory relationships between various performance indicators. For example, simply increasing the rolling element diameter to improve radial stiffness may alter the geometry of the contact area between the roller end face and the flange, leading to an abnormal increase in contact stress. Second, existing numerical simulation-aided design methods face a trade-off between efficiency and accuracy. While finite element analysis can accurately assess stiffness and stress distribution under given structural parameters, simulation experiments require enormous computational resources and time to handle multi-parameter design spaces. Finally, most existing publicly available technical solutions involve single-objective optimization or optimize ball bearings or single-row tapered roller bearings. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-objective optimization design method, system, and storage medium for double-row tapered roller hub bearing structures, which solves the problem of difficulty in determining an optimal variable value due to the contradictory relationships between variables in traditional double-row tapered roller hub bearing design practice, and reduces the time spent evaluating the internal load and stress of the bearing.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] On one hand, the present invention provides a multi-objective optimization design method for a double-row tapered roller hub bearing structure, comprising:

[0007] The mechanical equilibrium model of the bearing is obtained by performing force analysis on a single roller based on a computer system, and the mechanical model of the bearing is obtained by combining the relationship between load and deformation.

[0008] The obtained bearing mechanical model is used to solve for the load and deformation of a single roller. By summing the stiffness of the rollers in a single row bearing in parallel, the overall stiffness of the single row bearing is obtained. Then, by summing the stiffness of the two rows of bearings in parallel, the stiffness of the entire double-row tapered roller bearing is obtained.

[0009] Based on the obtained bearing mechanical model, the contact load between each roller and the baffle is solved, and the roller-baffle contact stress P is obtained according to Hertz point contact theory. Multiplying it by the relative sliding speed V between the roller and the baffle, the roller-baffle PV value is obtained.

[0010] Based on the obtained bearing mechanical model, the contact load and equivalent load between each roller and raceway are solved. Then, the rated load of the bearing is obtained based on the structural parameters of the bearing. The fatigue life of the bearing is calculated based on the equivalent load and the rated load.

[0011] Based on the obtained bearing radial stiffness, roller-flange PV value, and bearing fatigue life, the NSGA-II algorithm is used to optimize the bearing with the pitch circle diameter, average roller diameter, outer ring contact angle, center distance between the two rows of bearings, and roller half-cone angle as variables. Finally, an optimal variable is determined to maximize the bearing stiffness, minimize the roller-flange PV value, and maximize the bearing fatigue life.

[0012] The aforementioned multi-objective optimization design method for a double-row tapered roller hub bearing structure includes the following steps for force analysis of individual rollers: decomposing the contact load between each roller and the outer ring into components along the bearing axial and radial directions, considering the balance of force and torque, and accumulating the radial, axial, and torque components of all rollers to balance the external force, thereby obtaining the mechanical equilibrium model of the bearing.

[0013] The aforementioned multi-objective optimization design method for a double-row tapered roller hub bearing structure includes the following steps for constructing the mechanical equilibrium model of the bearing:

[0014] Under radial load F r Axial load F a Under the action of bending moment load M, the j-th roller of the m-th bearing generates a contact load Q with the outer ring. emj Contact load Q is generated with the inner ring. imj The contact load Q generated with the inner ring large flange fmj αe α i α f These are the contact angles between the roller and the outer raceway, the inner raceway, and the inner raceway flange, respectively.

[0015] Q emj The components in the radial and axial directions are:

[0016] ;

[0017] ;

[0018] Among them, ϕ j κ represents the azimuth angle of the j-th roller from the first roller, m is the column where the roller is located, when m=1, κ=1; when m=2, κ=-1;

[0019] The formula for calculating the resisting moment about the bearing center generated by the roller contact load under external load is as follows:

[0020] ;

[0021] Where, d c d is the center distance between the two rows of bearings. m The bearing pitch circle diameter;

[0022] Treating the roller-inner ring as an isolated body in the mechanical analysis, when considering the balance of the bearing system, the Q of each roller is... emj By superimposing the radial and axial components of the force and considering the balance of force and torque, the mechanical equilibrium equation of the bearing is obtained, as follows:

[0023] ;

[0024] Where Z represents the number of rollers in each row of bearings.

[0025] The aforementioned multi-objective optimization design method for a double-row tapered roller hub bearing structure includes solving the contact load between each roller and the baffle by: obtaining the relationship between the contact deformation and the contact load between the roller and the raceway based on the relationship between load and deformation under Hertzian contact theory; and obtaining the contact load between the roller and the raceway and between the roller and the baffle by using an iterative method and writing a program in MATLAB software.

[0026] The aforementioned multi-objective optimization design method for a double-row tapered roller hub bearing structure includes the following relationship between load and deformation:

[0027] Under external load, treating the roller-inner ring as a separate body in the mechanical analysis, and considering the outer rings of the two rows of bearings as a single unit and the two inner rings as another single unit, then under external load, the inner ring has a radial displacement δ relative to the outer ring. r axial displacement δa Angle θ;

[0028] The j-th roller in column m is radially displaced by δ from the inner ring. r The resulting radial displacement δ mrj for:

[0029] ;

[0030] The j-th roller in column m is radially displaced by δ from the inner ring. a The resulting axial displacement δ maj for:

[0031] ;

[0032] Where K is an auxiliary calculation coefficient;

[0033] The relative rotation angle between the inner and outer rings produced by θ at the j-th roller in the m-th column is:

[0034] ;

[0035] The radial and axial displacements caused by the angular displacement θ at the j-th roller in the m-th column are:

[0036] ;

[0037] ;

[0038] When a certain axial preload is applied to the bearing, the amount of roller displacement under the action of the preload alone is:

[0039] ;

[0040] Where F0 is the magnitude of the axial preload, K ne Contact coefficient: ;

[0041] The total normal contact deformation at the bearing roller-raceway contact point is:

[0042] ;

[0043] The roller normal contact load is obtained as follows:

[0044] .

[0045] The aforementioned multi-objective optimization design method for a double-row tapered roller hub bearing structure includes: selecting the bearing fatigue life L. 10 PV value and radial stiffness K of the inner ring large flange r To optimize the objective function;

[0046] The LP lifetime calculation formula is as follows:

[0047] ;

[0048] Among them, Q c The rated dynamic load of the raceway is related to the bearing geometry; Q e The equivalent loads for the inner and outer rings are related to the external load; Q c The calculation formula is as follows:

[0049] ;

[0050] In this diagram, the upper "+" symbol is used for the inner raceway, and the lower "-" symbol is used for the outer raceway; λ is a coefficient caused by roller edge load and eccentric load, with a value of 0.7; α is the contact angle, which is α for the outer raceway. e The inner raceway is α i ; Where is the average diameter of the rollers; γ is an auxiliary calculation coefficient, and the formula is as follows:

[0051] ;

[0052] For the equivalent load Q of the inner ring eu The formula is as follows:

[0053] ;

[0054] Among them, Q imj ε is the contact load between the j-th roller in column m and the inner raceway, and ε is a coefficient related to the rotational state of the bearing ring relative to the external load.

[0055] Based on the LP life calculation formula and the rated dynamic load Q of the raceway... c Equivalent load Q of the inner ring eu The fatigue life of the inner ring is obtained using the following formula:

[0056] ;

[0057] Similarly, the equivalent dynamic load and fatigue life of the outer ring can be obtained as follows:

[0058] ;

[0059] ;

[0060] Obtain bearing fatigue life L 10 The formula is as follows:

[0061] ;

[0062] Among them, L u1 L u2L represents the lifespan of the inner and outer raceways on the left column. v1 L v2 For the life of the inner and outer raceways of the right column, b m This is a correction factor;

[0063] The formula for the PV value of the inner ring large flange is as follows:

[0064] ;

[0065] in, The contact load between the j-th roller in column m and the inner ring flange; This is the maximum diameter of the inner raceway; The average diameter of the roller; Let n be the half-length and half-width of the contact ellipse formed by the contact between the roller and the flange; n is the bearing speed.

[0066] Radial stiffness K r The formula is as follows:

[0067] ;

[0068] in, This is the stiffness coefficient; The contact angle between the roller and the outer raceway; It represents the normal contact displacement between the j-th roller in column m and the outer raceway.

[0069] The second invention provides a system comprising:

[0070] Memory, used to store computer programs / instructions;

[0071] A processor for executing the computer program / instructions to implement the steps of the multi-objective optimization design method for the double-row tapered roller hub bearing structure as described in any one of the claims.

[0072] The third invention provides a storage medium storing a computer program / instructions thereon, which, when executed by a processor, implements the steps of the multi-objective optimization design method for the double-row tapered roller hub bearing structure described in any one of the claims.

[0073] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0074] This invention constructs a static model of a double-row tapered roller hub bearing. Based on this model, it builds a radial stiffness model, a roller-flange PV value model, and a bearing fatigue life model. Then, using the NSGA-II algorithm, with the above three models as objective functions and the pitch circle diameter, average roller diameter, outer ring contact angle, center distance between the two rows of bearings, and roller half-cone angle as variables, the bearing is optimized. This solves the problem in traditional double-row tapered roller hub bearing design practice where it is difficult to determine an optimal variable value due to the contradictory relationships between the variables. At the same time, it solves the problem of using finite element analysis to evaluate the internal load and stress consumption time of the bearing. Attached Figure Description

[0075] Figure 1 This is a schematic diagram of the force analysis of the double-row tapered roller bearing of the present invention;

[0076] Figure 2 This is a schematic diagram of the internal structure dimensions of the double-row tapered roller bearing of the present invention;

[0077] Figure 3 Flowchart of the mechanical solution of this invention;

[0078] Figure 4 The contact geometry diagram of the tapered roller flange of this invention;

[0079] Figure 5 The optimized flowchart of this invention;

[0080] Figure 6 The Pareto solution set of this invention;

[0081] Figure 7 The bearing contact stress cloud diagrams before and after optimization in this invention;

[0082] Figure 8 Schematic diagram of the wheel hub bearing fatigue testing machine of the present invention;

[0083] Figure 9 Failure diagrams of the hub bearing and inner ring after testing according to this invention. Detailed Implementation

[0084] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0085] The term "and / or" simply describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. Additionally, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0086] Example 1:

[0087] This embodiment provides a multi-objective optimization design method for a double-row tapered roller hub bearing structure, including: Step 1: Performing force analysis on a single roller based on a computer system to obtain the bearing's...

[0088] The mechanical equilibrium model is used to solve for the bearing mechanical model by combining the relationship between load and deformation.

[0089] Step 2: Using the obtained bearing mechanical model, solve for the load and deformation of a single roller. By summing the stiffness of the rollers in a single row bearing in parallel, obtain the overall stiffness of the single row bearing. Then, sum the stiffness of the two rows of bearings in parallel to obtain the stiffness of the entire double-row tapered roller bearing.

[0090] Step 3: Based on the obtained bearing mechanical model, solve for the contact load between each roller and the baffle, and then obtain the roller-baffle contact stress P according to Hertz point contact theory. Multiply the roller-baffle relative sliding speed V to obtain the roller-baffle PV value.

[0091] Step 4: Based on the obtained bearing mechanical model, solve for the contact load and equivalent load between each roller and raceway. Then, based on the bearing's structural parameters, calculate the bearing's rated load. Finally, calculate the bearing's fatigue life based on the equivalent load and rated load.

[0092] Step 5: Based on the obtained bearing radial stiffness, roller-flange PV value and bearing fatigue life, the NSGA-II algorithm is used to optimize the bearing with the pitch circle diameter, average roller diameter, outer ring contact angle, center distance between the two rows of bearings, and roller half-cone angle as variables. Finally, an optimal variable is determined to maximize the bearing stiffness, minimize the roller-flange PV value, and maximize the bearing fatigue life.

[0093] The construction of the mechanical model for wheel hub bearings includes: Figure 1 As shown, under radial load F r Axial load F a Under the action of bending moment load M, the j-th roller of the m-th bearing generates a contact load Q with the outer ring. emj Contact load Q is generated with the inner ring. imj The contact load Q generated with the inner ring large flange fmj α e α i α fThese are the contact angles between the roller and the outer raceway, the inner raceway, and the inner raceway flange, respectively.

[0094] Based on geometric relationships, Q emj The components in the radial and axial directions are:

[0095]

[0096]

[0097] In the formula ϕ j κ represents the azimuth angle of the j-th roller from the first roller, and m is the column where the roller is located. When m=1, κ=1; when m=2, κ=-1.

[0098] Under external load, the resisting moment about the bearing center generated by the roller contact load can be determined by equation (3):

[0099]

[0100] In the formula d c d is the center distance between the two rows of bearings. m For the bearing pitch circle diameter, such as Figure 2 As shown.

[0101] By treating the roller-inner ring as an isolated body for mechanical analysis, when considering the balance of the bearing system, it is only necessary to consider the Q of each roller. emj By superimposing the radial and axial components of the force and considering the balance of force and torque, the mechanical equilibrium equation of the bearing can be obtained as follows:

[0102]

[0103] In the formula, Z represents the number of rollers in each row of bearings.

[0104] Under external load, treating the roller-inner ring as a separate body in the mechanical analysis, and considering the outer rings of the two rows of bearings as a single unit and the two inner rings as another single unit, then under external load, the inner ring has a radial displacement δ relative to the outer ring. r axial displacement δ a Angle θ.

[0105] At this time, the j-th roller in the m-th column is radially displaced by δ from the inner ring. r The resulting radial displacement δ mrj for:

[0106]

[0107] The j-th roller in column m is radially displaced by δ from the inner ring. a The resulting axial displacement δ maj for:

[0108]

[0109] Since the relative rotation angle between the inner and outer rings produced by θ at the j-th roller in the m-th column is:

[0110]

[0111] Therefore, the radial and axial displacements generated by the angular displacement θ at the j-th roller in the m-th column are:

[0112]

[0113]

[0114] Generally, a certain axial preload is applied to the bearing, and the displacement of the roller under the action of the preload can be calculated by equation (10).

[0115]

[0116] In the formula, F0 is the magnitude of the axial preload, and K ne The contact coefficient is denoted as .

[0117]

[0118] In summary, the total normal contact deformation at the bearing roller-raceway contact point is:

[0119]

[0120] According to Hertzian line contact theory, the roller normal contact load can be obtained as follows:

[0121]

[0122] Equation (4) is based on δ r δ a For a system of nonlinear equations with θ as an unknown, the solution can be obtained using an iterative method. The solution process is as follows: Figure 3 As shown.

[0123] The optimization objective function includes: selecting the bearing fatigue life L. 10 PV value and radial stiffness K of the inner ring large flange rTo optimize the objective function.

[0124] 1. According to the LP lifetime calculation formula:

[0125]

[0126] In the formula Q c The rated dynamic load of the raceway is related to the bearing geometry; Q e The equivalent loads of the inner and outer rings are related to the external load.

[0127]

[0128] In the formula, the upper symbol is used for the inner raceway, and the lower symbol is used for the outer raceway; λ is the coefficient caused by roller edge load and eccentric load, with a value of 0.7; α is the contact angle, and α is the outer raceway angle. e The inner raceway is α i .

[0129]

[0130] For the equivalent load Q of the inner ring eu :

[0131]

[0132] In the formula Q imj ε is the contact load between the j-th roller in column m and the inner raceway. ε is a coefficient related to the rotational state of the bearing ring relative to the external load, which is 4 for the rotating ring (inner ring) and 4.5 for the stationary ring (outer ring).

[0133] From equations (14), (15), and (17), the fatigue life of the inner ring can be obtained as follows:

[0134]

[0135] Similarly, the equivalent dynamic load and fatigue life of the outer ring can be obtained as follows:

[0136]

[0137]

[0138] The overall fatigue life of a double-row tapered roller bearing is:

[0139]

[0140] In the formula Lu1 L u2 L represents the lifespan of the inner and outer raceways on the left column. v1 L v2 For the life of the inner and outer raceways of the right column, b m The correction factor is set to 1.11.

[0141] 2. The PV value of the flange reflects the degree of risk of scuffing between the large flange of the bearing inner ring and the end face of the roller.

[0142] The evaluation index is the value obtained by multiplying the contact stress by the sliding speed V.

[0143] The geometric relationship between the inner ring large flange and the large end face of the tapered roller is as follows: Figure 4 As shown. In Figure 4 In the diagram, point D is the contact point, point C is the intersection of the flange and the raceway generatrix, the oil groove length along the flange is CM, O1 is the center of the roller ball base surface, O is the vertex of the bearing outer ring end face, O1D is perpendicular to CD, SR is the radius of the roller ball base surface, d2 is the diameter of the inner ring large flange, and d... i D is the maximum diameter of the inner raceway. w1 The diameter of the large end of the roller.

[0144] Depend on Figure 4 The location of the contact point can be obtained from the geometric relationships in the diagram:

[0145]

[0146] The contact stress P between the inner ring large flange and the roller end face can be calculated by equation (23):

[0147]

[0148] In the formula, a and b are the half-length and half-width of the contact ellipse, respectively.

[0149] The relative sliding speed is calculated using equation (24):

[0150]

[0151] The PV value of the roller-edge guard is:

[0152]

[0153] 3. The radial stiffness of a bearing is defined as:

[0154]

[0155] The radial stiffness of the single-row bearing can be obtained by summing the radial stiffnesses of the rollers in parallel. The radial stiffness of the entire double-row tapered roller bearing can be obtained by summing the radial stiffnesses of the two rows of bearings in parallel. Combining equations (4), (12), and (26), the formula for calculating the radial stiffness of the bearing is as follows:

[0156]

[0157] Among them, the constraints include: when designing wheel hub bearings, certain constraints are usually imposed on the design variables due to considerations such as ring strength, cage strength, operational flexibility and geometric constraints.

[0158] The bearing pitch circle diameter should meet the following requirements:

[0159]

[0160]

[0161] In the formula, e is the shift parameter, which is taken as 0.07 in this paper.

[0162] The average diameter of the rollers should meet the following requirements:

[0163]

[0164]

[0165] In the formula: , σ max The maximum contact stress that the material can withstand.

[0166] Overall constraints are satisfied:

[0167]

[0168]

[0169]

[0170] The PV value needs to meet the constraints of grease lubrication:

[0171]

[0172] To ensure that the deformation at the contact point between the inner ring flange and the large end face of the roller does not exceed the oil groove, the following conditions must be met:

[0173]

[0174] To ensure that the contact point between the inner ring large flange and the large end face of the roller is in a reasonable position, the following must be met:

[0175]

[0176] To ensure that the optimized bearing meets the requirements of low carbon emissions and energy conservation, a constraint is added to the friction torque of the optimized bearing to ensure that the friction torque of the optimized bearing is less than that of the unoptimized bearing. The Palmgren friction torque calculation model is used, and the calculation formula is as follows:

[0177]

[0178]

[0179]

[0180]

[0181] In equations (38)-(41), M′ is the total frictional torque; M1 is the bearing load frictional torque; M v F is the bearing viscous friction torque; f1 is a coefficient related to bearing type and load; F β X is the equivalent dynamic load; Y is the radial load factor and axial load factor, which can be selected from the bearing manual; f0 is a coefficient related to the bearing type and lubrication method; v is the kinematic viscosity of the lubricant; and n is the bearing speed.

[0182] The implementation of the algorithm includes:

[0183] Figure 5 The flowchart shows the multi-objective algorithm for wheel hub bearings. Due to the numerous constraints, a population that satisfies the constraints is randomly generated during the initialization phase to increase optimization efficiency.

[0184] For the NSGA-II algorithm, the population size, number of iterations, mutation probability, and crossover probability all affect the distribution of the Pareto front solution set. After continuous debugging, the population size was finally set to 200, the maximum number of iterations to 100, the crossover probability to 0.9, and the mutation probability to 0.1. The Pareto front solution set obtained is evaluated using Equation (42) to find an optimal solution.

[0185]

[0186] In the formula L 10 ′、PV′、K r ′ represents the data before optimization, L 10 PV, K r To optimize the data, ϖ1, ϖ2, and ϖ3 are weights applied, prioritizing fatigue life, then PV value, and finally stiffness. Therefore, ϖ1=0.5, ϖ2=0.4, and ϖ3=0.1.

[0187] The above calculation process will be implemented using MATLAB programming. To verify the effectiveness of this design optimization method, this invention provides a calculation example.

[0188] Taking the 363020X1C double-row tapered roller hub bearing as an example, the loading conditions are: radial load 58480N, axial load 18145N, bending moment 6350N·m, and speed 500r / min. The bearing structural parameters are shown in the table below:

[0189] Table 1: Parameter Table of 363020X1C Wheel Hub Bearing

[0190] Number of single-row rollers 24 effective length of roller 28.3mm Roller large end diameter 15.5mm roller small end diameter 14.018mm Roller-outer raceway contact angle 13.833° Roller-inner raceway contact angle 10.833° Stick - Large side contact angle 78.567° Center distance between two rows of bearings 81mm Bearing pitch circle diameter 65mm elastic modulus 206 GPa Poisson's ratio 0.3 Inner ring large flange diameter 125mm Maximum diameter of inner raceway 111.29mm Bearing outer diameter 156mm bearing inner diameter 100mm Outer ring width 33mm Roller ball base radius 270mm Oil groove overrun groove dimensions 1.2mm

[0191] The range of values ​​for the optimization variables is shown in the table below:

[0192] Table 2: Range of values ​​for optimization variables

[0193] Pitch circle diameter 122-142mm average roller diameter 12.76-16.76mm Roller-outer raceway contact angle 12.5-14.5° Center distance between two rows of bearings 76-88mm Roller half cone angle 1-2°

[0194] The bearing parameters before and after optimization are shown in the table below:

[0195] Table 3: Optimized front and rear wheel hub bearing parameters

[0196] Pitch circle diameter 130 mm 124 mm average roller diameter 14.76 mm 15.16 mm Roller - Outer Ring Contact Angle 13.833° 13.92° Center distance between two rows of bearings 81 mm 86 mm Roller half cone angle 1.5° 1.26° radial stiffness <![CDATA[4918049 N·mm -1 ]]> <![CDATA[5019438 N·mm -1 ]]> PV value 142MPa·m / s 106 MPa·m / s Fatigue life <![CDATA[17×10 6 r]]> <![CDATA[20×10 6 r]]> Frictional torque 4.8 N·m 4.6 N·m

[0197] Figure 6 This is the Pareto front solution set calculated by the algorithm.

[0198] The bearing parameters before and after optimization show that the radial stiffness of the optimized bearing increased by 2.1%, the PV value decreased by 25.3%, and the fatigue life increased by 17.6%.

[0199] Finite element method and experimental methods were used to test the bearing performance before and after optimization, thereby verifying the effectiveness of the design optimization method.

[0200] Finite element verification:

[0201] Figure 7 To perform finite element method (FEM) simulation analysis of the contact stress cloud diagram of the bearings before and after optimization under the above working conditions, the following steps were taken: Figure 7The optimized bearing showed a 35% reduction in maximum contact stress on the outer ring, an 18.5% reduction in maximum contact stress on the rollers, an 18.9% reduction in maximum contact stress on the inner ring raceway, and a 17.5% reduction in maximum contact stress on the inner ring large flange. The overall maximum contact stress of the optimized bearing was improved, demonstrating the effectiveness of the optimization method.

[0202] Experimental verification:

[0203] Further experimental verification was conducted to optimize the bearing life before and after the optimization. A fatigue life simulation test was performed on the 363020X1C wheel hub bearing unit using the PLS-150 automotive wheel hub bearing dynamic simulation testing machine. Figure 8 As shown. Two sets of bearing samples are required to undergo a 1000-hour timed truncated test. Here, number 1# represents the unoptimized model, and number 2# represents the optimized model. The load spectrum is from data from a certain vehicle axle company, and the test conditions are shown in the table below:

[0204] Table 4: Bearing Fatigue Test Conditions

[0205] 1 400 105 0 60 2 400 135 0 10 3 400 105 -15.7 12.5 4 400 105 -26.2 2.5 5 400 105 11.6 12.5 6 400 105 26.3 2.5

[0206] The method involved cyclic loading and oil circulation lubrication. The fatigue test results are shown in the table below:

[0207] Table 5: Bearing fatigue test results

[0208] 1# 1000h Inner raceway spalling and failure 2# 1000h Not expired

[0209] Before optimization, the bearing experienced inner ring raceway spalling failure; after testing, the bearing... Figure 9 As shown in the fatigue test results table, the bearing before optimization failed after 1000 hours, while the optimized bearing did not fail, indicating an improvement in fatigue life.

[0210] Example 2:

[0211] This embodiment provides a system, including:

[0212] Memory, used to store computer programs / instructions;

[0213] A processor is configured to execute the computer program / instructions to implement the steps of the multi-objective optimization design method for the double-row tapered roller hub bearing structure described in any of the preceding claims.

[0214] Example 3:

[0215] This embodiment provides a storage medium storing a computer program / instruction, which, when executed by a processor, implements the steps of the multi-objective optimization design method for the double-row tapered roller hub bearing structure described in any of the preceding embodiments.

[0216] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0217] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0218] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0219] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0220] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A multi-objective optimization design method for a double-row tapered roller hub bearing structure, characterized in that, include: The mechanical equilibrium model of the bearing is obtained by performing force analysis on a single roller based on a computer system, and the mechanical model of the bearing is obtained by combining the relationship between load and deformation. Based on the obtained bearing mechanical model, the load and deformation of a single roller are solved. By summing the stiffness of the rollers in a single row bearing in parallel, the overall stiffness of the single row bearing is obtained. Then, by summing the stiffness of the two rows of bearings in parallel, the stiffness of the entire double-row tapered roller bearing is obtained. Based on the obtained bearing mechanical model, the contact load between each roller and the baffle is solved, and the roller-baffle contact stress P is obtained according to Hertz point contact theory. Multiplying it by the relative sliding speed V between the roller and the baffle, the roller-baffle PV value is obtained. Based on the obtained bearing mechanical model, the contact load and equivalent load between each roller and raceway are solved. Then, the rated load of the bearing is obtained based on the structural parameters of the bearing. The fatigue life of the bearing is calculated based on the equivalent load and the rated load. Based on the obtained bearing radial stiffness, roller-flange PV value, and bearing fatigue life, the NSGA-II algorithm is used to optimize the bearing with the pitch circle diameter, average roller diameter, outer ring contact angle, center distance between the two rows of bearings, and roller half-cone angle as variables. Finally, an optimal variable is determined to maximize the bearing stiffness, minimize the roller-flange PV value, and maximize the bearing fatigue life.

2. The multi-objective optimization design method for double-row tapered roller hub bearing structure according to claim 1, characterized in that, The force analysis of a single roller includes: decomposing the contact load between each roller and the outer ring into components along the bearing axial and radial directions, and considering the balance of force and torque, accumulating the radial, axial and torque components of all rollers and balancing them with the external force to obtain the mechanical balance model of the bearing.

3. The multi-objective optimization design method for double-row tapered roller hub bearing structure according to claim 1, characterized in that, The steps for constructing the mechanical equilibrium model of the bearing include: Under the action of radial load F r , axial load F a , bending moment load M, the jth roller of the mth row of bearings produces contact load Q emj with the outer ring, contact load Q imj with the inner ring, and contact load Q fmj with the large flange of the inner ring e , α i , α f are the contact angles of the roller with the outer ring raceway, the inner ring raceway, and the large flange of the inner ring, respectively Q emj The components in the radial and axial directions are: ； ； Among them, ϕ j κ represents the azimuth angle of the j-th roller from the first roller, m is the column where the roller is located, when m=1, κ=1; when m=2, κ=-1; The formula for calculating the resisting moment about the bearing center generated by the roller contact load under external load is as follows: ； Where, d c d is the center distance between the two rows of bearings. m The bearing pitch circle diameter; Treating the roller-inner ring as an isolated body in the mechanical analysis, when considering the balance of the bearing system, the Q of each roller is... emj By superimposing the radial and axial components of the force and considering the balance of force and torque, the mechanical equilibrium equation of the bearing is obtained, as follows: ； Where Z represents the number of rollers in each row of bearings.

4. The multi-objective optimization design method for double-row tapered roller hub bearing structure according to claim 1, characterized in that, The solution for the contact load between each roller and the baffle includes: based on the relationship between load and deformation under Hertzian contact theory, the relationship between the contact deformation and contact load between the roller and the raceway is obtained. The contact load between the roller and the raceway and between the roller and the baffle can be obtained by writing a program in MATLAB software using an iterative method.

5. The multi-objective optimization design method for double-row tapered roller hub bearing structure according to claim 1, characterized in that, The relationship between the load and deformation includes: Under external load, treating the roller-inner ring as a separate body in the mechanical analysis, and considering the outer rings of the two rows of bearings as a single unit and the two inner rings as another single unit, then under external load, the inner ring has a radial displacement δ relative to the outer ring. r axial displacement δ a Angle θ; The j-th roller in column m is radially displaced by δ from the inner ring. r The resulting radial displacement δ mrj for: ； The j-th roller in column m is radially displaced by δ from the inner ring. a The resulting axial displacement δ maj for: ； Where K is an auxiliary calculation coefficient; The relative rotation angle between the inner and outer rings produced by θ at the j-th roller in the m-th column is: ； The radial and axial displacements caused by the angular displacement θ at the j-th roller in the m-th column are: ； ； When a certain axial preload is applied to the bearing, the amount of roller displacement under the action of the preload alone is: ； Where F0 is the magnitude of the axial preload, K ne Contact coefficient: ; The total normal contact deformation at the bearing roller-raceway contact point is: ； The roller normal contact load is obtained as follows: 。 6. The multi-objective optimization design method for double-row tapered roller hub bearing structure according to claim 1, characterized in that, include: Select bearing fatigue life L 10 PV value and radial stiffness K of the inner ring large flange r To optimize the objective function; The LP lifetime calculation formula is as follows: ； Among them, Q c The rated dynamic load of the raceway is related to the bearing geometry; Q e The equivalent loads for the inner and outer rings are related to the external load; Q c The calculation formula is as follows: ； In this diagram, the upper "+" symbol is used for the inner raceway, and the lower "-" symbol is used for the outer raceway; λ is a coefficient caused by roller edge load and eccentric load, with a value of 0.7; α is the contact angle, which is α for the outer raceway. e The inner raceway is α i ; Where is the average diameter of the rollers; γ is an auxiliary calculation coefficient, and the formula is as follows: ； For the equivalent load Q of the inner ring eu The formula is as follows: ； Among them, Q imj ε is the contact load between the j-th roller in column m and the inner raceway, and ε is a coefficient related to the rotational state of the bearing ring relative to the external load. Based on the LP life calculation formula and the rated dynamic load Q of the raceway... c Equivalent load Q of the inner ring eu The fatigue life of the inner ring is obtained using the following formula: ； Similarly, the equivalent dynamic load and fatigue life of the outer ring can be obtained as follows: ； ； Obtain bearing fatigue life L 10 The formula is as follows: ； Among them, L u1 L u2 L represents the lifespan of the inner and outer raceways on the left column. v1 L v2 For the life of the inner and outer raceways of the right column, b m This is a correction factor; The formula for the PV value of the inner ring large flange is as follows: ； in, The contact load between the j-th roller in column m and the inner ring flange; This is the maximum diameter of the inner raceway; The average diameter of the roller; Let n be the half-length and half-width of the contact ellipse formed by the contact between the roller and the flange; n is the bearing speed. Radial stiffness K r The formula is as follows: ； in, This is the stiffness coefficient; The contact angle between the roller and the outer raceway; It represents the normal contact displacement between the j-th roller in column m and the outer raceway.

7. A system, characterized in that, include: Memory, used to store computer programs / instructions; A processor is configured to execute the computer program / instructions to implement the steps of the multi-objective optimization design method for the double-row tapered roller hub bearing structure as described in any one of claims 1 to 6.

8. A storage medium having a computer program / instruction stored thereon, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the multi-objective optimization design method for the double-row tapered roller hub bearing structure as described in any one of claims 1 to 6.

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