Structural parameter design method of thermally constrained steel angular contact ball bearing

Abstract

The invention belongs to the field of structural design of high-bearing-capacity steel angular contact ball bearings, and particularly relates to a structural parameter design method of a thermal constraint steel angular contact ball bearing. According to the method, aiming at the characteristic of high bearing capacity of the steel angular contact ball bearing, the diameter and the number of rolling bodies, the curvature radius coefficient of an inner raceway groove, the curvature radius coefficient of an outer raceway groove, the width of a retainer lintel and the like are used as design target parameters; the coupling effect of factors such as external load conditions, working rotating speed, material performance, bearing capacity, fatigue life and heating conditions is comprehensively considered, multivariable constraint conditions and a multi-objective function are established, and therefore the multivariable structure parameter design method is formed. According to the method, iteration is carried out according to actual working conditions, and calculation design of structural parameters of the steel angular contact ball bearing meeting the working conditions is achieved. According to the method, calculation verification is carried out by taking multiple sets of foreign bearings as verification pieces, and a result calculated and designed by adopting the method is very consistent with a surveying and mapping value, so that the method is scientific and reliable.

Description

Technical Field

[0001] The invention belongs to the field of high-load angular contact ball bearing structure design, and in particular relates to a structural parameter design method for a thermally constrained steel angular contact ball bearing. Background Art

[0002] Bearings are an important part of machinery. They are widely used in machinery. Bearings can be seen in any mechanical equipment. Bearings are high-precision industrial products. They require the support of many scientific theories, such as material science, mathematics, physics, etc. At the same time, they also require precision processing and measurement technology, heat treatment technology, computer technology and other fields of technology to serve them. Therefore, the quality of bearings not only determines the use and service performance of the host equipment, but also reflects the scientific and technological level of a country. At present, my country has become a major bearing country, accounting for a large share of both the export and import of bearings. However, the products of my country's bearing companies are mainly concentrated in the middle and low-end markets, and there are still large shortcomings in the field of high-end and high-precision bearings, and they cannot compete in the market with world-renowned bearing companies such as SKF, FAG, NSK, etc. This has led to the need for a large number of imports of high-end bearings used in various fields in my country, which has become a major problem that needs to be solved in my country. One of the key reasons for this situation is that we do not have a deep enough understanding of the characteristics of current high-end bearings, lack the underlying physical understanding, and are weak in the concepts, methods, and procedures of structural design. This leads to a gap between theoretical design and bench testing and mass production in practical applications, ultimately forcing us to rely on foreign companies to provide design and continuous supply.

[0003] Current research has found that high-precision machine tool bearings will fail and retire due to reduced precision long before reaching their fatigue life. This shows that the key factor affecting the service performance of high-precision machine tool bearings is no longer fatigue, but the stability of their precision. Therefore, the previous design concept of excessive pursuit of the longest fatigue life is no longer applicable. For high-precision machine tool bearings, their operating speed has been greatly increased, making the bearings more prone to frictional heating and thus causing precision failure. The frictional heating phenomenon is difficult to observe directly, but it can be converted into the calculation of the bearing roll ratio. The so-called roll ratio refers to the ratio of the angular velocity of the rolling element's rotation around the normal of the contact surface to the angular velocity of its revolution. It can be used to study the degree of sliding and heating of the rolling element. The larger the value, the more severe the frictional heating, that is, the worse the precision stability. In addition, the introduction of the PV value, an important indicator for measuring bearing wear power consumption and heat generation, can achieve effective regulation of the heat generation of the inner and outer raceways of high-speed rotating bearings, thereby further ensuring the precision stability of the bearings under high-speed operation. In view of this, we propose to comprehensively consider various important factors that affect the accuracy and stability of bearings, introduce the PV value of the bearing to measure the heat generation of the inner and outer raceways, and use the roll ratio of the bearing as the final constraint objective function, so as to establish a structural parameter calculation design scheme for steel angular contact ball bearings. We hope that this work can play a positive role in promoting the independent design and manufacturing of high-end bearings in my country. Summary of the invention

[0004] In view of the shortcomings of the current design of steel angular contact ball bearing structures according to working conditions, the purpose of the present invention is to provide a structural parameter design method for a thermally constrained steel angular contact ball bearing to solve the problem of difficult structural design of steel angular contact ball bearings.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for designing structural parameters of a thermally constrained steel angular contact ball bearing comprises the following steps:

[0007] Step S1: Establishing the objective function of structural design;

[0008] Step S2: Establish multivariable constraints;

[0009] Step S3: Propose a structural calculation design method for steel angular contact ball bearings taking heating conditions into consideration.

[0010] The structural parameter design method of the thermally constrained steel angular contact ball bearing, in step S1, establish X = (x1, x2, f e ,f i ,g,B)’s objective function:

[0011] Take X=(x1,x2,f e ,f i,g,B) as design variables, x1 is the rolling element diameter, x2 is the number of rolling elements, f e is the outer raceway groove curvature radius coefficient, f i is the inner raceway groove curvature radius coefficient, g is the cage pocket clearance, and B is the cage beam width; according to the requirement that the friction and wear of steel angular contact ball bearings should be as low as possible, the following objective function is constructed:

[0012] min f1(x)=(1-rcosu)tan(ut)+rsinu (1)

[0013] In the above formula (1), minf1(x) represents the minimum roll ratio, r = x1 / D0, D0 is the pitch circle diameter, u is the working contact angle, and t is the deflection angle.

[0014] The structural parameter design method of the thermally constrained steel angular contact ball bearing, in step S2, constructs X=(x1, x2, f e ,f i ,g,B)’s multivariate constraints:

[0015] (1) Multivariable constraints on carrying capacity

[0016] The structure of the steel angular contact ball bearing needs to meet the load-bearing requirements and establish the following load-bearing capacity constraints:

[0017] R1(x)=C or >[C or ] (2)

[0018] R2(x)=C r >[C r ] (3)

[0019] In the above formulas (2) and (3), C or and C r They are the rated static load and rated dynamic load, [C or ] and [C r ] are the rated static load and rated dynamic load required by the working conditions;

[0020] (2) Multivariable constraints on safety factor

[0021] The bearing is subjected to load during operation and needs to meet certain safety indicators:

[0022] R3(x)=C oa / F a >S a (4)

[0023] R4(x)=C 0r / F r >Sr (5)

[0024] In the above formulas (4) and (5), C oa and C or is the static load rating of the axial and radial directions, F a and F r are the axial force and radial force, S a and S r are the axial and radial safety factors;

[0025] (3) Structural association multivariate constraints

[0026] In steel angular contact ball bearings, the rolling elements are separated by cages, the cage beam width is B, the rolling element pitch circle circumference is expressed as (g+B+x1)x2, g is the cage pocket clearance, and the rolling element pitch circle circumference is also expressed as πD0, so the following relationship exists:

[0027] πD0=(x1+B+g)x2 (6)

[0028] For steel angular contact ball bearings, the requirements for the cage beam width B are usually: B>1mm and B>0.1x1, thus establishing the following constraints:

[0029] R5(x)=πD0 / x2-g-x1≥1.0 (7)

[0030] R6(x)=πD0 / x2-g-x1≥0.1x1 (8)

[0031] Among them, the cage pocket clearance g = 0.004x1 + 0.12;

[0032] (4) Rated life constraints

[0033] Steel angular contact ball bearings need to achieve a certain rated life in the service environment, and the calculation formula is as follows:

[0034]

[0035] In the above formula, L 10 is the rated life, a1 is the reliability life correction factor, a ISO is the life correction factor based on the life calculation system method, n is the bearing speed, C0 is the rated dynamic load, and P0 is the equivalent dynamic load;

[0036] The following rated life constraints are established:

[0037]

[0038] In the above formula (10), L0 is the fatigue life value required to be achieved;

[0039] (5) Friction torque constraint condition

[0040] The rotational motion of the bearing is hindered by the friction torque, which is calculated as follows:

[0041]

[0042] In the above formula (11), M is the friction torque, f0 is a coefficient related to the bearing type and lubrication method, v0 is the lubricant viscosity, n is the bearing speed, f1 is a coefficient related to the bearing structure, equivalent static load and rated static load, and F β is the load related to the bearing type and external load;

[0043] The following friction torque constraint condition is established:

[0044]

[0045] In the above formula (12), M max It is the upper limit of the friction torque allowed for the bearing operation;

[0046] (6) Stiffness requirement constraints

[0047] The structure of steel angular contact ball bearings must meet the stiffness requirements of the working conditions, and the following stiffness requirements constraints are established:

[0048]

[0049] In the above formulas (13) and (14), δ a and δ r are the axial and radial deformations, α is the contact angle, G amin and G rmin are the required stiffness values ​​in the axial and radial directions respectively;

[0050] (7) Lubrication constraints

[0051] According to the research results proposed by Hamrock B J and Dowson D, the following lubrication constraints are established:

[0052]

[0053] In the above formula (15), U, W, G, R x , E0, K are velocity parameter, load parameter, viscosity pressure index, equivalent curvature radius, equivalent elastic modulus and ellipticity, respectively, h min is the required minimum oil film thickness value;

[0054] (8) Thermal constraints of the inner and outer raceways of bearings

[0055] Steel angular contact ball bearings usually bear large loads at a certain speed, and temperature rise is also an important factor affecting service performance; PV value is an important indicator to measure bearing friction power consumption and heat generation. P is the contact stress between the rolling element and the ring, and V is the rolling linear velocity in the contact area. The PV value of the bearing is introduced to represent the heat generation of the bearing. Under the condition that other conditions remain unchanged, the higher the PV value, the higher the bearing temperature rise; the heat dissipation of the inner raceway is not as good as that of the outer raceway. In order to make the temperatures of the inner and outer raceways as close as possible, the heat generation of the inner raceway needs to be lower than that of the outer raceway:

[0056] P i V i <P e V e (16)

[0057] This constructs the constraints:

[0058] R 12 (x) = P i V i -P e V e ≤0 (17)

[0059] In addition, in steel angular contact ball bearings, the groove curvature radius coefficient of the inner and outer raceways is required to be between 0.510 and 0.550, thereby establishing the following constraints:

[0060] R 13 (x) = f i -0.550<0 (18)

[0061] R 14 (x) = f i -0.510>0 (19)

[0062] R 15 (x) = f e -0.550<0 (20)

[0063] R 16 (x) = f e -0.510>0 (21).

[0064] The structural parameter design method of the thermally constrained steel angular contact ball bearing, in step S3, the structural calculation design method of the steel angular contact ball bearing comprises the following steps:

[0065] (1) The rated dynamic load, rated static load and inner and outer diameters of the bearing under actual working conditions are used as initial input data;

[0066] (2) Calculate and filter through multivariable constraint formulas (2)-(21) to obtain a set of values ​​X1=(x1, x2, fe ,f i ,g,B);

[0067] (3) Using the objective function formula (1), the value set X1 = (x1, x2, f e ,f i ,g,B) to screen and determine the optimal value that satisfies the objective function, and finally obtain the optimal structural parameters.

[0068] The design idea of ​​the present invention is:

[0069] The present invention discloses a method for designing the structural parameters of a heat-constrained steel angular contact ball bearing. Starting from the actual service conditions of the bearing, the structural parameters of the bearing are coupled and comprehensively considered. Through the requirements of load distribution, material properties, load-bearing capacity, fatigue life, and operation stability, the actual production and processing conditions and the accumulated relevant experience are integrated, and the heating conditions of the bearing operation are introduced to establish a design framework of a multi-objective function under multivariable constraints, so as to realize the accurate design of the structural parameters of the steel angular contact ball bearing. The design method is derived from the thermodynamic physical principle of the bearing, which is completely different from the current empirical design. The method is scientific and universal, and can design a steel angular contact ball bearing structure that meets the requirements according to the given actual working conditions.

[0070] The advantages and beneficial effects of the present invention are:

[0071] The present invention proposes a method for designing the structural parameters of a heat-constrained steel angular contact ball bearing. The method takes the rolling element diameter, quantity, outer raceway groove curvature radius coefficient, inner raceway groove curvature radius coefficient, cage pocket clearance, cage lintel width, etc. as design target parameters, comprehensively considers the coupling effects of factors such as external load conditions, operating speed, material properties, load-bearing capacity, fatigue life, and heating conditions, establishes multivariable constraint conditions and multi-objective functions, and thus forms a multivariable structural parameter design method. The method is iterated according to actual working conditions to achieve the calculation and design of the structural parameters of the steel angular contact ball bearing that meets the working conditions, which will have a positive role in promoting the independent structural design and production of steel angular contact bearings in my country. DETAILED DESCRIPTION

[0072] In the specific implementation process, the present invention proposes a structural parameter design method for a thermally constrained steel angular contact ball bearing, which considers the structural parameters of the bearing in a coupled and comprehensive manner to determine the optimal value of each structural parameter, including the following steps:

[0073] Step S1: Establish X = (x1, x2, f e ,f i ,g,B)

[0074] Take X=(x1,x2,f e ,f i ,g,B) as design variables, x1 is the rolling element diameter (mm), x2 is the number of rolling elements (pieces), f e is the outer raceway groove curvature radius coefficient, f i is the inner raceway groove curvature radius coefficient, g is the cage pocket clearance (mm), and B is the cage beam width (mm); according to the design requirements of high running stability of steel angular contact ball bearings, the following objective function is constructed:

[0075] minf1(x)=(1-rcosu)tan(ut)+rsinu (1)

[0076] In the above formula (1), minf1(x) represents the minimum spin-to-roll ratio, r=x1 / D0, D0 is the pitch circle diameter (mm), u is the working contact angle (°), and t is the deflection angle (°).

[0077] Step S2: construct X = (x1, x2, f e ,f i ,g,B) multivariate constraints

[0078] (1) Multivariable constraints on carrying capacity

[0079] The structure of the steel angular contact ball bearing needs to meet the load-bearing requirements and establish the following load-bearing capacity constraints:

[0080] R1(x)=C or >[C or ] (2)

[0081] R2(x)=C r >[C r ] (3)

[0082] In the above formulas (2) and (3), C or and C r They are the rated static load (N) and the rated dynamic load (N), [C or ] and [C r ] are the rated static load (N) and rated dynamic load (N) required by the working conditions;

[0083] (2) Multivariable constraints on safety factor

[0084] The bearing is subjected to load during operation and needs to meet certain safety indicators:

[0085] R3(x)=C oa / F a >S a (4)

[0086] R4(x)=C 0r / F r >S r (5)

[0087] In the above formulas (4) and (5), C oa and C or is the static load rating of the axial and radial directions (N), F a and F r is the axial force (N) and radial force (N), S a and S r are the axial and radial safety factors (values ​​are taken according to actual working conditions);

[0088] (3) Structural association multivariate constraints

[0089] In steel angular contact ball bearings, the rolling elements are separated by cages, the cage beam width is B, the rolling element pitch circle circumference can be expressed as (g+B+x1)x2, g is the cage pocket clearance, and the rolling element pitch circle circumference can also be expressed as πD0, so there is the following relationship:

[0090] πD0=(x1+B+g)x2 (6)

[0091] For steel angular contact ball bearings, the requirements for the cage beam width B are usually: B>1mm and B>0.1x1, thus establishing the following constraints:

[0092] R5(x)=πD0 / x2-g-x1≥1.0 (7)

[0093] R6(x)=πD0 / x2-g-x1≥0.1x1 (8)

[0094] Among them, the cage pocket clearance g = 0.004x1 + 0.12.

[0095] (4) Rated life constraints

[0096] Angular contact bearings need to achieve a certain rated life in the service environment, and the calculation formula is as follows:

[0097]

[0098] In the above formula, L 10 is the rated life (h), a1 is the reliability life correction factor (a1 in the embodiment is 1), a ISO is the life correction factor based on the life calculation system method (a in the embodiment ISO Take value 1), n ​​is the bearing speed (rpm), C0 is the rated dynamic load (N), P0 is the equivalent dynamic load (N);

[0099] The following rated life constraints are established:

[0100]

[0101] In the above formula (10), L0 is the fatigue life value required to be achieved (h);

[0102] (5) Friction torque constraint condition

[0103] The rotational motion of the bearing is hindered by the friction torque, which is calculated as follows:

[0104]

[0105] In the above formula (11), M is the friction torque (N*mm), f0 is a coefficient related to the bearing type and lubrication method (the value of f0 in the embodiment is 2), and v0 is the viscosity of the lubricant (mm 2 / s), n is the bearing speed (rpm), f1 is a coefficient related to the bearing structure, equivalent static load and rated static load (f1 in the embodiment refers to GB / T24609-2023), F β is the load related to the bearing type and external load (N);

[0106] The following friction torque constraint condition is established:

[0107]

[0108] In the above formula (12), M max is the upper limit of the friction torque allowed for the bearing operation (N*mm);

[0109] (6) Stiffness requirement constraints

[0110] The structure of steel angular contact ball bearings must meet the stiffness requirements of the working conditions, and the following stiffness requirements constraints are established:

[0111]

[0112] In the above formulas (13) and (14), δ a and δ r are the axial and radial deformations (mm), α is the contact angle (°), G amin and G rmin are the required stiffness values ​​in the axial and radial directions (N / mm);

[0113] (7) Lubrication constraints

[0114] According to the research results proposed by Hamrock B J and Dowson D, the following lubrication constraints are established:

[0115]

[0116] In the above formula (15), U, W, G, R x , E0, and K are speed parameter, load parameter, viscosity pressure index (depending on the properties of the lubricant), equivalent radius of curvature (mm), equivalent elastic modulus (Pa), and ellipticity (ratio of the contact semi-minor axis to the semi-major axis), respectively. min is the required minimum oil film thickness value (mm);

[0117] (8) Thermal constraints of the inner and outer raceways of bearings

[0118] Steel angular contact ball bearings usually bear large loads at a certain speed, and temperature rise is also an important factor affecting service performance; PV value is an important indicator to measure bearing friction power consumption and heat generation. P is the contact stress between the rolling element and the ring, and V is the rolling linear velocity in the contact area. The PV value of the bearing is introduced to represent the heat generation of the bearing. Under the condition that other conditions remain unchanged, the higher the PV value, the higher the bearing temperature rise. The heat dissipation of the inner raceway is not as good as that of the outer raceway. In order to make the temperatures of the inner and outer raceways as close as possible, the heat generation of the inner raceway needs to be lower than that of the outer raceway:

[0119] P i V i <P e V e (16)

[0120] This constructs the constraints:

[0121] R 12 (x) = P i V i -P e V e ≤0 (17)

[0122] In addition, in steel angular contact ball bearings, the groove curvature radius coefficient of the inner and outer raceways is required to be between 0.510 and 0.550, thereby establishing the following constraints:

[0123] R 13 (x) = f i -0.550<0 (18)

[0124] R 14 (x) = f i -0.510>0 (19)

[0125] R 15 (x) = f e -0.550<0 (20)

[0126] R 16 (x) = f e-0.510>0 (21)

[0127] Step S3: Propose a structural parameter design method for a thermally constrained steel angular contact ball bearing, comprising the following steps:

[0128] (1) The rated static load, rated dynamic load and inner and outer diameters of the bearing under actual working conditions are used as initial input data;

[0129] (2) Calculate and filter through multivariable constraint formulas (2)-(21) to obtain a set of values ​​X1=(x1, x2, f e ,f i ,g,B);

[0130] (3) Using the objective function formula (1), the value set X1 = (x1, x2, f e ,f i ,g,B) to screen and determine the optimal value that satisfies the objective function, and finally obtain the optimal structural parameters.

[0131] Implementation calculation case:

[0132] For several sets of imported steel angular contact ball bearings from a certain country, the structural parameters are calculated and designed according to their respective service conditions (rated dynamic load, rated static load, fatigue life and stiffness, etc.), and compared and verified with the actual surveying values. The results of the calculation and design using the present invention and the actual surveying data are shown in Table 1. By comparison, it is found that the calculation results of the design method proposed by the present invention are very consistent with the actual measured values.

[0133] Table 1 Comparison of the calculated values ​​of a foreign imported steel angular contact ball bearing with the actual survey value

[0134]

[0135]

[0136] It can be seen from the implementation calculation case that the calculation design results of the present invention are in good agreement with the actual surveying and mapping values, which shows that the design method of the present invention is scientific and reliable. This method will have a positive role in promoting the independent structural design and production of steel angular contact bearings in my country.

Claims

1. A method for designing structural parameters of a thermally constrained steel angular contact ball bearing, characterized in that: The following steps are involved: Step S1: Establishing the objective function of structural design; Step S2: Establish multivariable constraints; Step S3: Propose a structural calculation design method for steel angular contact ball bearings taking heating conditions into consideration.

2. The structural parameter design method of the thermally constrained steel angular contact ball bearing according to claim 1, characterized in that: In step S1, establish X=(x1,x2,f e ,f i ,g,B)’s objective function: Take X=(x1,x2,f e ,f i ,g,B) as design variables, x1 is the rolling element diameter, x2 is the number of rolling elements, f e is the outer raceway groove curvature radius coefficient, f i is the inner raceway groove curvature radius coefficient, g is the cage pocket clearance, and B is the cage beam width; according to the requirement that the friction and wear of steel angular contact ball bearings should be as low as possible, the following objective function is constructed: minf1(x)=(1-rcosu)tan(ut)+rsinu (1) In the above formula (1), minf1(x) represents the minimum roll ratio, r = x1 / D0, D0 is the pitch circle diameter, u is the working contact angle, and t is the deflection angle.

3. The structural parameter design method of the thermally constrained steel angular contact ball bearing according to claim 1 or 2, characterized in that: In step S2, construct X=(x1,x2,f e ,f i ,g,B)’s multivariate constraints: (1) Multivariable constraints on carrying capacity The structure of the steel angular contact ball bearing needs to meet the load-bearing requirements and establish the following load-bearing capacity constraints: R1(x)=C or >[C or ] (2) R2(x)=C r >[C r ] (3) In the above formulas (2) and (3), C or and C r They are the rated static load and rated dynamic load, [C or ] and [C r ] are the rated static load and rated dynamic load required by the working conditions; (2) Multivariable constraints on safety factor The bearing is subjected to load during operation and needs to meet certain safety indicators: R3(x)=C oa / F a >S a (4) R4(x)=C 0r / F r >S r (5) In the above formulas (4) and (5), C oa and C or is the static load rating of the axial and radial directions, F a and F r are the axial force and radial force, S a and S r are the axial and radial safety factors; (3) Structural association multivariate constraints In steel angular contact ball bearings, the rolling elements are separated by cages, the cage beam width is B, the rolling element pitch circle circumference is expressed as (g+B+x1)x2, g is the cage pocket clearance, and the rolling element pitch circle circumference is also expressed as πD0, so the following relationship exists: πD0=(x1+B+g)x2 (6) For steel angular contact ball bearings, the requirements for the cage beam width B are usually: B>1mm and B>0.1x1, thus establishing the following constraints: R5(x)=πD0 / x2-g-x1≥1.0 (7) R6(x)=πD0 / x2-g-x1≥0.1x1 (8) Among them, the cage pocket clearance g = 0.004x1 + 0.12; (4) Rated life constraints Steel angular contact ball bearings need to achieve a certain rated life in the service environment, and the calculation formula is as follows: In the above formula, L 10 is the rated life, a1 is the reliability life correction factor, a ISO is the life correction factor based on the life calculation system method, n is the bearing speed, C0 is the rated dynamic load, and P0 is the equivalent dynamic load; The following rated life constraints are established: In the above formula (10), L0 is the fatigue life value required to be achieved; (5) Friction torque constraint condition The rotational motion of the bearing is hindered by the friction torque, which is calculated as follows: In the above formula (11), M is the friction torque, f0 is a coefficient related to the bearing type and lubrication method, v0 is the lubricant viscosity, n is the bearing speed, f1 is a coefficient related to the bearing structure, equivalent static load and rated static load, and F β is the load related to the bearing type and external load; The following friction torque constraint condition is established: In the above formula (12), M max It is the upper limit of the friction torque allowed for the bearing operation; (6) Stiffness requirement constraints The structure of steel angular contact ball bearings must meet the stiffness requirements of the working conditions, and the following stiffness requirements constraints are established: In the above formulas (13) and (14), δ a and δ r are the axial and radial deformations, α is the contact angle, G amin and G rmin are the required stiffness values ​​in the axial and radial directions respectively; (7) Lubrication constraints According to the research results proposed by Hamrock B J and Dowson D, the following lubrication constraints are established: In the above formula (15), U, W, G, R x , E0, K are velocity parameter, load parameter, viscosity pressure index, equivalent curvature radius, equivalent elastic modulus and ellipticity, respectively, h min is the required minimum oil film thickness value; (8) Thermal constraints of the inner and outer raceways of bearings Steel angular contact ball bearings usually bear large loads at a certain speed, and temperature rise is also an important factor affecting service performance; PV value is an important indicator to measure bearing friction power consumption and heat generation. P is the contact stress between the rolling element and the ring, and V is the rolling linear velocity in the contact area. The PV value of the bearing is introduced to represent the heat generation of the bearing. Under the condition that other conditions remain unchanged, the higher the PV value, the higher the bearing temperature rise; the heat dissipation of the inner raceway is not as good as that of the outer raceway. In order to make the temperatures of the inner and outer raceways as close as possible, the heat generation of the inner raceway needs to be lower than that of the outer raceway: P i In i <P e In e (16) This constructs the constraints: R 12 (x)=P i V i -P e V e ≤0 (17) In addition, in steel angular contact ball bearings, the groove curvature radius coefficient of the inner and outer raceways is required to be between 0.510 and 0.550, thereby establishing the following constraints: R 13 (x)=f i -0.550<0 (18) R 14 (x)=f i -0.510>0 (19) R 15 (x)=f e -0.550<0 (20) R 16 (x)=f e -0.510>0 (21)。 4. The structural parameter design method of the thermally constrained steel angular contact ball bearing according to claim 3, characterized in that: In step S3, the structural calculation and design method of the steel angular contact ball bearing includes the following steps: (1) The rated dynamic load, rated static load and inner and outer diameters of the bearing under actual working conditions are used as initial input data; (2) Calculate and filter through multivariable constraint formulas (2)-(21) to obtain a set of values ​​X1=(x1, x2, f e ,f i ,g,B); (3) Using the objective function formula (1), the value set X1 = (x1, x2, f e ,f i ,g,B) to screen and determine the optimal value that satisfies the objective function, and finally obtain the optimal structural parameters.

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