A method, apparatus and electronic device for optimizing bearing friction torque

Abstract

This application provides a method, apparatus, and electronic device for optimizing bearing friction torque, relating to the field of bearing technology. Based on the initial quantitative parameters, design variables, and boundary constraints of the bearing, an optimization model of the bearing is constructed. The overall deformation of each rolling element in the bearing is determined based on the inner ring deformation parameters. The deformation and force of each segment included in each rolling element are calculated to determine the total load of the rolling elements and the inner ring force parameters. The inner ring deformation parameters are iterated until the force balance of the inner ring is determined based on the inner ring force parameters, meeting the accuracy requirements. Based on the total load of each rolling element corresponding to the converged inner ring deformation parameters, the contact load of each contact surface of the rolling element is determined. Combining the load of each contact surface corresponding to each rolling element with the friction coefficient, the friction torque is determined. With the goal of minimizing the friction torque, the design parameters in the optimization model are determined through iterative optimization using a genetic algorithm. In this way, the limitation of reducing friction solely by improving accuracy is overcome, achieving a reduction in friction torque.

Description

Technical Field

[0001] This application relates to the field of bearing technology, and in particular to a method, apparatus and electronic device for optimizing bearing friction torque. Background Technology

[0002] Traditional methods for optimizing the friction torque of tapered roller bearings often involve improving the bearing's own precision. However, optimizing the bearing's precision is limited by the machining precision of the equipment used to manufacture tapered roller bearings. Furthermore, as precision increases, the cost and difficulty of machining also increase, while the reduction in friction torque remains minimal. Summary of the Invention

[0003] In view of this, this application provides a method, apparatus and electronic device for optimizing the friction torque of tapered roller bearings, aiming to achieve low-cost optimization of the friction torque of tapered roller bearings without relying on breakthroughs in machining accuracy.

[0004] In a first aspect, this application provides a method for optimizing friction torque, the method comprising: An optimization model for the bearing is constructed based on its initial quantity, design variables, and boundary constraints; the boundary constraints are configured according to the rated dynamic load and machining constraints. Based on the optimization model and inner ring deformation parameters, the overall deformation of each rolling element in the bearing is determined; the deformation and force of each slice of each rolling element are calculated by the slicing method to determine the total load of the rolling element and the inner ring force parameters; the inner ring deformation parameters are iterated until the inner ring force balance is determined based on the inner ring force parameters to meet the accuracy requirements; the inner ring deformation parameters include displacement and tilt angle. Based on the total load of each rolling element corresponding to the converged inner ring deformation parameters, determine the contact load of each contact surface of the rolling element in contact with the contact surface. The friction torque is determined by combining the load and friction coefficient of each contact surface of each rolling element; With the goal of minimizing the frictional torque, the design parameters in the optimization model are determined through iterative optimization using a genetic algorithm.

[0005] Optionally, the bearing is a tapered roller bearing; The boundary constraints include: the rated dynamic load being greater than the rated dynamic load before optimization; the ratio of the width of the bearing large flange to the width of the inner ring being greater than a first value; the ratio of the width of the bearing small flange to the width of the inner ring being greater than a second value; the length difference between the large end and the raceway of the rolling element and the length difference between the small end and the raceway of the rolling element being greater than zero; the roller big end clearance being the maximum value between 0.57 and a third value, where the third value is the product of 0.057 and the diameter of the large end of the rolling element; the effective wall thickness of the inner ring being greater than the product of the difference between the bearing outer diameter and the inner diameter and 0.07; the absolute value of the difference between the effective wall thickness of the inner ring and the effective wall thickness of the outer ring being less than the product of the difference between the bearing outer diameter and the bearing inner diameter and 0.02; and the width of the cage beam being greater than the product of a fourth value and the thickness of the cage plate.

[0006] Optionally, the inner ring deformation parameters include the inner ring radial displacement, the inner ring axial displacement, and the inner ring tilt angle; The formulas for calculating the overall deformation of each rolling element include: ; Where, δ j Let δr be the overall deformation of the j-th rolling element, δa be the radial displacement of the inner ring, θ be the tilt angle of the inner ring, dm be the mean diameter of the rolling element, and α be the bearing contact angle. j Let be the circumference angle of the j-th rolling element.

[0007] Optionally, the step of calculating the deformation and stress of each slice of each rolling element using the slice method to determine the total load of the rolling element includes: Each rolling element is divided into multiple slices along its length; Based on the overall deformation of the rolling element and the rolling element shaping curve, the deformation of each slice of the rolling element is calculated. By simultaneously solving the force balance equations and deformation compatibility equations of each rolling element, the force on each slice is obtained, and the total load of the rolling element is obtained by summing the forces on the slices included in the rolling element.

[0008] Optionally, the inner ring force parameters include radial force, axial force, and moment; determining the inner ring force parameters includes: The radial force included in the inner ring force parameters is determined based on the sum of the radial components of the forces exerted by all rolling elements on the inner ring of the bearing. The axial force included in the force parameters of the inner ring is determined based on the sum of the axial component forces of all rolling elements of the bearing on the inner ring. The torque included in the inner ring force parameters is determined based on the sum of the total load torque of all rolling elements in the bearing and the additional torque caused by the force on the slices included in each rolling element.

[0009] Optionally, before determining the frictional torque by combining the load and friction coefficient of each rolling element at each corresponding contact surface, the method further includes: Determine the minimum film thickness ratio of each rolling element to each contact surface; Based on the minimum film thickness ratio of each rolling element to each contact surface, the friction coefficient of each contact surface in contact with the rolling element is solved by a piecewise function of the friction coefficient.

[0010] Optionally, determining the frictional torque by combining the load and friction coefficient of each rolling element at each contact surface further includes: When the inner ring of the bearing rotates, the frictional torque is the sum of the torque generated by the friction between all the rolling elements of the bearing and the outer ring, and the torque generated by the sliding friction between all the rolling elements and the large flange of the inner ring. When the outer ring of a bearing rotates, the frictional torque is the sum of the torque generated by the friction between all the rolling elements and the inner ring, and the torque generated by the sliding friction between all the rolling elements and the large flange of the inner ring.

[0011] Optionally, after determining the frictional torque by combining the load and friction coefficient of each rolling element at each corresponding contact surface, the method further includes: Based on the correction coefficient determined by the experimental data, the friction torque is corrected to obtain the corrected friction torque.

[0012] Secondly, this application provides a friction torque optimization device, the device comprising: A construction unit is used to construct an optimization model of the bearing based on the bearing's initial quantity, design variables, and boundary constraints; the boundary constraints are configured based on the rated dynamic load and machining constraints. The processing unit is used to determine the overall deformation of each rolling element in the bearing based on the optimization model and the inner ring deformation parameters; calculate the deformation and force of each slice of each rolling element using the slicing method to determine the total load of the rolling element and the inner ring force parameters; iterate the inner ring deformation parameters until the inner ring force balance is determined based on the inner ring force parameters to meet the accuracy requirements; the inner ring deformation parameters include displacement and tilt angle; The decomposition unit is used to determine the contact load of the rolling element on each contact surface in contact with the rolling element based on the total load of each rolling element corresponding to the converged inner ring deformation parameters. The calculation unit is used to determine the friction torque by combining the load and friction coefficient of each contact surface of each rolling element; An optimization unit is used to determine the design parameters in the optimization model by iterative optimization using a genetic algorithm, with the goal of minimizing the frictional torque.

[0013] Thirdly, this application provides an apparatus comprising a memory and a processor, the memory for storing instructions or code, and the processor for executing the instructions or code to cause the apparatus to perform a friction torque optimization method as described in any of the first aspects above.

[0014] Fourthly, this application provides a computer storage medium storing code, wherein when the code is executed, a device running the code implements a friction torque optimization method as described in any of the first aspects above.

[0015] This application provides a method, apparatus, and electronic device for optimizing bearing friction torque. The method includes: constructing an optimization model of the bearing based on its initial parameters, design variables, and boundary constraints; the boundary constraints are configured based on rated dynamic load and machining constraints; determining the overall deformation of each rolling element in the bearing based on the optimization model and inner ring deformation parameters; calculating the deformation and force of each slice of each rolling element using a slicing method to determine the total load of the rolling elements and the inner ring force parameters; iterating the inner ring deformation parameters until the inner ring force balance meets the accuracy requirements based on the inner ring force parameters; the inner ring deformation parameters include displacement and tilt angle; determining the contact load of each rolling element on each contact surface based on the total load of each rolling element corresponding to the converged inner ring deformation parameters; determining the friction torque by combining the load of each rolling element on each contact surface with the friction coefficient; and determining the design parameters in the optimization model through iterative optimization using a genetic algorithm, with the goal of minimizing the friction torque. Based on this, this application first iteratively corrects the inner ring deformation parameters until the inner ring is in force equilibrium, determining the load conditions of each slice of the rolling element and the overall bearing. Then, the load of the rolling element is decomposed according to the contact surface. Furthermore, the friction torque is calculated based on the load and friction coefficient of each contact surface. With the goal of minimizing the friction torque, the design parameters in the optimization model are iteratively optimized using a genetic algorithm to determine the optimized design parameters under the boundary constraints of rated dynamic load and machining feasibility. This accurately reproduces the stress and deformation state of the bearing under actual load, making the load distribution obtained after iterative convergence more accurate and closer to actual working conditions, ensuring reliable results. Simultaneously, by aiming for minimum friction torque and combining genetic algorithms with bearing calculation theory, multiple design parameters can be synergistically optimized to achieve global optimization, breaking through the limitations of traditional methods that rely solely on improving precision to reduce friction, and achieving a reduction in friction torque without increasing processing costs. Attached Figure Description

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

[0017] Figure 1 A schematic flowchart illustrating a friction torque optimization method provided in an embodiment of this application; Figure 2 This is a schematic diagram of the structure of a tapered roller bearing provided in an embodiment of this application; Figure 3 A schematic diagram of an iterative analysis process to ensure the accuracy requirements of the inner ring force balance is met, provided for an embodiment of this application; Figure 4 A schematic diagram showing the comparison of frictional torque before and after optimization under the condition of varying bearing axial load and constant rotational speed, provided for an embodiment of this application; Figure 5 A schematic diagram showing the comparison of frictional torque before and after optimization under the condition of constant bearing axial load and changing rotational speed, provided for an embodiment of this application; Figure 6 This is a schematic diagram of a friction torque optimization device provided in an embodiment of this application. Detailed Implementation

[0018] To provide a more detailed understanding of the features and technical content of the embodiments of this disclosure, the implementation of the embodiments of this disclosure will be described in detail below with reference to the accompanying drawings. The accompanying drawings are for illustrative purposes only and are not intended to limit the embodiments of this disclosure. In the following technical description, for ease of explanation, several details are used to provide a full understanding of the disclosed embodiments. However, one or more embodiments may still be implemented without these details. In other cases, well-known structures and devices may be simplified in their depiction to simplify the drawings.

[0019] The terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this disclosure are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of this disclosure described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion.

[0020] Unless otherwise stated, the term "multiple" means two or more.

[0021] In this embodiment of the disclosure, the character " / " indicates that the objects before and after it are in an "or" relationship. For example, A / B means: A or B.

[0022] The term "and / or" describes an association between objects, indicating that three relationships can exist. For example, A and / or B means: A or B, or A and B.

[0023] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0024] See Figure 1 , Figure 1 This application provides a flowchart illustrating a method for optimizing friction torque, specifically a bearing friction torque optimization method, comprising: S101. Based on the initial quantity, design variables, and boundary constraints of the bearing, construct an optimization model for the bearing; the boundary constraints are configured based on the rated dynamic load and machining constraints.

[0025] See Figure 2 The diagram shows a structural schematic of a tapered roller bearing. Based on this, when configuring the initial bearing dimensions, involved variables, and boundary constraints, an example can be given as follows: Optionally, the above initial measurements may include: tapered roller bearing width T, tapered roller bearing inner diameter d, tapered roller bearing outer diameter D, and contact angle α.

[0026] Optionally, the above design variables may include: rolling element large end diameter Dw, rolling element length Ln, and rolling element semi-cone angle. B, inner ring width, C, number of rolling elements, Z.

[0027] Optionally, the above boundary constraints may include: rated dynamic load C r Greater than or equal to the rated dynamic load C before optimization ro And considering the machining constraints that allow for the machining configuration based on the bearing design results.

[0028] Optionally, the above-mentioned rated dynamic load can be calculated using the method in ISO 281-2007.

[0029] Optionally, the processing constraint may include: The ratio of the width a0 of the bearing's large flange to the width B of the inner ring is greater than the first value K. a0 K a0 =0.2.

[0030] ,in The allowable safety factor for the flange is denoted by di, where di is the diameter of the inner ring large flange oil groove.

[0031] The ratio of the width a1 of the bearing small flange to the width B of the inner ring is greater than the second value K. a1 K a1 =0.1.

[0032] The length difference C2min between the large end of the rolling element and the raceway is greater than zero, and the length difference C3min between the small end of the rolling element and the raceway is greater than zero. The roller big end clearance J (the clearance between the big ends of the two rolling elements) is taken as the maximum value between 0.57 and the third value, where the third value is the product of 0.057 and the big end diameter Dw of the rolling element; Inner ring effective wall thickness S i Greater than the product of the difference between the outer diameter D and the inner diameter d of the tapered roller bearing and 0.07; Inner ring effective wall thickness S i With the effective wall thickness S of the outer ring e The absolute value of the difference is less than the product of the difference between the outer diameter D and the inner diameter d of the tapered roller bearing and 0.02; Keep the beam width Cb greater than the fourth value K j The fourth value K is the product of the cage plate thickness S. j The value can be 1.7.

[0033] Specifically, the formula for processing constraints can be comprehensively expressed as follows: (2) S102. Based on the optimization model and inner ring deformation parameters, determine the overall deformation of each rolling element in the bearing; calculate the deformation and force of each slice of each rolling element using the slicing method, and determine the total load of the rolling element and the inner ring force parameters; iterate the inner ring deformation parameters until the inner ring force balance is determined based on the inner ring force parameters to meet the accuracy requirements.

[0034] The inner ring deformation parameters include displacement (inner ring radial displacement δr, inner ring axial displacement δa) and inner ring tilt angle θ. See Figure 3 The diagram shows a flowchart of an iterative analysis to ensure the accuracy of the force balance of the inner ring. The specific implementation of step S102 above can be as follows: Step A1: Assign an initial inner ring deformation parameter, which may include the inner ring radial displacement δr, the inner ring axial displacement δa, and the inner ring tilt angle θ. Step A2: Calculate the overall deformation δj of each rolling element in the bearing.

[0035] (3)

[0036] In the above formula (3), δj is the overall deformation of the j-th rolling element, where j∈[1,2,…,Z], δr is the radial displacement of the inner ring, δa is the axial displacement of the inner ring, θ is the tilt angle of the inner ring, dm is the pitch circle diameter of the rolling element, and α is the bearing contact angle. j Let be the circumference angle of the j-th rolling element.

[0037] Step A3: Based on the effective contact length Lwe of each rolling element, divide the rolling element into multiple slices (e.g., n slices), with the width of each slice l = Lwe / n; Step A4: Based on the overall deformation δ of the j-th rolling element j With rolling element modification curve z λ (y λ ), calculate the deformation δ of the j-th rolling element and the λ-th slice. jλ ; (4) Understandably, after the rolling element is deformed by compression, the actual contact deformation of each slice is the difference between the overall deformation of the rolling element and twice the height of the rolling element shaping curve at that position.

[0038] Step A4: Solve the force balance equations and deformation compatibility equations of each rolling element simultaneously to obtain the force Q on each slice. jλe The total load Q of the rolling element is obtained by summing the forces acting on the slices of the rolling element. je .

[0039] The above force balance equations refer to the first and second equations in the following simultaneous equation (5), where the first equation states that the sum of the contact stresses of each slice of the rolling element integrated over the contact area equals the total load Q borne by the rolling element. je The second equation refers to the force Q acting on a single slice. jλe (The load it bears).

[0040] The above deformation compatibility equation refers to the third equation in the following simultaneous equation (5). The contact deformation on the left side of the third equation, which is derived from the contact stress, is equal to the contact deformation calculated on the right side based on the inner ring deformation parameters and the shaping curve.

[0041] (5)

[0042] In equation (5) above, b jλ The contact half-width of the λ-th slice of the j-th rolling element can be calculated using the Hertz contact formula; qjλmax : The maximum contact stress at the λ-th slice position of the j-th rolling element; D jλ E' is the compliance coefficient, and E′ is the combined elastic modulus of the rolling element and the raceway. The specific formula is as follows: , Where V1 is the Poisson's ratio of the rolling element, E1 is the elastic modulus of the rolling element, V2 is the Poisson's ratio of the raceway, and E2 is the elastic modulus of the raceway.

[0043] Thus, based on steps A3 and A4 above, the slicing method is used to calculate the load on the rolling element segmented along its length. This accurately reflects the stress differences at different positions of the roller and fully considers the true distribution of roller deformation and contact deformation. Compared to the overall calculation method, the load solution is more refined, avoiding overestimation or underestimation of subsequent friction calculations due to simplification, making the final friction torque more reliable.

[0044] Step A5: Determine the radial force Fr, axial force Fa, and torque M included in the inner ring force parameters.

[0045] (6)

[0046] In equation (6) above, y λ Let y be the axial position of the λ-th slice. jc This is the center position of the j-th rolling element along its axis.

[0047] Understandably, in the above formula (6), the radial force included in the inner ring force parameter is determined based on the sum of the radial component forces of all rolling elements included in the bearing on the inner ring; the axial force included in the inner ring force parameter is determined based on the sum of the axial component forces of all rolling elements included in the bearing on the inner ring; and the torque included in the inner ring force parameter is determined based on the sum of the total load torque of each rolling element included in the bearing and the additional torque caused by the force on the slices included in each rolling element.

[0048] Thus, by decomposing the forces on all rolling elements of the bearing in the radial, axial and torque directions, and summing them up, the force parameters of the inner ring (radial force Fr, axial force Fa and torque M) can be obtained.

[0049] Step A6: Based on the actual load borne by the bearing and the force parameters of the inner ring, determine whether the force balance of the inner ring meets the accuracy requirements.

[0050] In one example, the inner ring force parameters (radial force Fr, axial force Fa, and moment M) are determined according to the above steps, and the actual radial force Fr included in the actual load borne by the bearing (the load applied to the bearing from the outside) is set. in Actual axial force Fa in Actual torque M in .

[0051] Determine the actual radial force Fr in The absolute value of the first difference between the radial force Fr and the inner ring force parameter (absolute error of radial force) and the actual radial force Fr in Is the ratio (radial force relative error) less than or equal to a preset first accuracy threshold (e.g., 10)? -3 ).

[0052] Determine the actual axial force Fa in The absolute value of the second difference between the axial force Fa and the inner ring force parameter (absolute error of axial force) and the actual axial force Fa in Is the ratio (relative error of axial force) less than or equal to the preset second accuracy threshold (e.g., 10)? -3 ).

[0053] Determine the actual torque M in The absolute value of the third difference between the torque Fr and the inner ring force parameter (absolute torque error) and the actual torque M in Is the ratio (relative torque error) less than or equal to the preset third precision threshold (e.g., 10)? -3 ).

[0054] Step A7: If the force balance of the inner ring meets the accuracy requirements (e.g., when the above three relative errors are all less than their respective accuracy thresholds), save the force Q of each slice of each rolling element obtained in step A4. jλe and the total load Q of the rolling elements je Otherwise, it indicates that the assigned inner ring deformation is inappropriate. In this case, the inner ring displacement should be reassigned and steps A2-A7 above should be repeated until the inner ring is in force balance and meets the accuracy requirements.

[0055] In this way, by using relative error, compared with absolute error, the magnitude of the error can be linked to the magnitude of the measured quantity itself, which is not affected by the load magnitude. The accuracy standard is uniform and can be applied to a variety of working conditions. There is no need to configure thresholds for different working conditions, which better adapts to different loads and different bearing models.

[0056] Based on the above steps A1-A7, by sequentially assigning inner ring deformation parameters, calculating rolling element deformation, solving inner ring force parameters, and judging balance accuracy, the stress and deformation state of the bearing under actual load can be accurately reproduced, improving data accuracy. The load distribution obtained after iterative convergence is more accurate and closer to actual working conditions, providing a reliable basis for subsequent friction torque calculation and improving torque calculation accuracy.

[0057] S103. Based on the total load of each rolling element corresponding to the inner ring deformation parameters after convergence, determine the contact load of each contact surface of the rolling element in contact with the contact surface.

[0058] In one example, the contact surfaces of the rolling elements in a tapered roller bearing include the inner ring, the outer ring, and the flange. Therefore, based on the total load Q of the j-th rolling element... je (Also the contact load of the j-th rolling element on the outer ring), decompose the inner ring contact load Q of the j-th rolling element on the inner ring. je Outer ring contact load Q ji and the contact load Q of the flange. jf The specific formula can be as follows: (7) In equation (7) above, α is the bearing contact angle, and αi is the inner ring contact angle. This is the contact angle of the retaining edge.

[0059] In this way, the total load of each rolling element is decomposed into inner ring contact load, outer ring contact load, and flange contact load, which facilitates the subsequent calculation of friction on each contact surface and fully covers the main sources of bearing friction.

[0060] S104. Determine the friction torque by combining the load and friction coefficient of each contact surface of each rolling element; In one possible implementation, prior to step S104 above, the following may also be included: The minimum film thickness ratio of each rolling element to each contact surface is determined, and the friction coefficient of each contact surface in contact with the rolling element is solved by a piecewise function of the friction coefficient.

[0061] Optionally, the minimum film thickness ratio can be calculated using the Hamrock-Dowson minimum oil film thickness formula. .

[0062] Optionally, the piecewise function of the friction coefficient can be: (8) In equation (8) above, μ jλ S is the coefficient of drag friction for the λ-th slice in the j-th rolling element; jλ Let λ be the slip ratio of the λ-th slice in the j-th rolling element; Λ is the minimum film thickness ratio, which is optional. d =0.001, Λ bd =0.06, Λ hd =1.5.

[0063] Understandably, the minimum film thickness ratio differs for different contact surfaces of the rolling elements. Therefore, it is necessary to calculate the friction coefficient μ of the outer ring of the rolling element contact separately. jλe The coefficient of friction μ of the inner ring in contact with the rolling elements jλi The coefficient of friction μ of the flange in contact with the rolling element jf.

[0064] In one possible implementation, step S104 above determines the frictional torque M by combining the load and friction coefficient of each rolling element on each contact surface. f ,include: (9) In equation (9) above, j is the j-th rolling element, Z is the total number of rolling elements in the bearing, λ is the λ-th slice on the rolling element, n is the total number of slices included in the rolling element, and Q jλe μ is the contact load between the λ-th slice of the j-th rolling element and the outer ring. jλe Let Q be the coefficient of friction of the λth slice of the j-th rolling element. jf Let μ be the contact load between the j-th rolling element and the flange. jf Let Q be the coefficient of friction at the contact point between the j-th rolling element and the flange. jλi μ is the contact load between the λ-th slice of the j-th rolling element and the outer ring. jλi Let be the friction coefficient of the λth slice of the j-th rolling element.

[0065] Understandably, when the inner ring of a bearing rotates, the frictional torque is the sum of the torque generated by the friction between all rolling elements and the outer ring, and the torque generated by the sliding friction between all rolling elements and the large flange of the inner ring. When the outer ring of a bearing rotates, the frictional torque is the sum of the torque generated by the friction between all rolling elements and the inner ring, and the torque generated by the sliding friction between all rolling elements and the large flange of the inner ring.

[0066] In this way, the torque is calculated separately for inner and outer ring rotation conditions, adapting to different installation and usage scenarios, making the optimization results more universal.

[0067] Optionally, after step S104 above, the method further includes:

[0068] Based on the correction coefficient determined from the experimental data, the friction torque is corrected to obtain the corrected friction torque, which can be expressed by the following formula: M=aM f +b (10) In equation (10) above, both a and b can be correction coefficients determined based on experimental data. For example, a set of theoretical values ​​M can be combined. f The corresponding measured value M is used to perform a linear regression to determine the slope a and intercept b as correction coefficients.

[0069] In this way, the theoretically calculated friction torque is corrected using actual experimental data, eliminating systematic deviations caused by model simplification, processing errors, and material dispersion. This improves the consistency between the calculated and experimental results, ensuring that the optimized design can be implemented in engineering and avoiding a disconnect between theory and practice.

[0070] S105. With the goal of minimizing the frictional torque, the design parameters in the optimization model are determined through iterative optimization using a genetic algorithm.

[0071] Optionally, the frictional torque can be the theoretical frictional torque determined by equation (9) above, and the final frictional torque can be obtained after being corrected by equation (10) above.

[0072] According to the methods in steps S101-S105 above, this application first simulates the initial inner ring deformation parameters of the inner ring displacement and tilt in step S102, and then iteratively corrects them until the inner ring is in force equilibrium, determining the load conditions of each slice of each rolling element and the whole bearing. Then, in step S103, the load of the rolling element is decomposed according to the contact surface. Furthermore, in step S104, the friction torque is solved based on the load and friction coefficient of each contact surface. With the goal of minimizing the friction torque, the design parameters in the optimization model are iteratively optimized using a genetic algorithm to determine the optimized design parameters under the premise of satisfying boundary constraints such as rated dynamic load and processing feasibility. In this way, the stress and deformation state of the bearing under actual load is accurately reproduced, making the load distribution obtained after iterative convergence more accurate and closer to the actual working conditions, ensuring reliable results. At the same time, with the goal of minimizing frictional torque, combined with genetic algorithms and bearing calculation theory, multiple design parameters can be optimized in a coordinated manner to achieve global optimization. This breaks through the limitations of traditional methods that rely solely on improving precision to reduce friction, and achieves a significant reduction in frictional torque without increasing processing costs.

[0073] Based on the above embodiments, this application adopts the above method to optimize the friction torque using a 32212 tapered roller bearing as an example. The configured parameters include outer diameter D=110mm, inner diameter d=60mm, total width T=29.75mm, contact angle α=15°6′34″, and diameter and width series of 22. The genetic algorithm is configured as follows: population size n=100; number of iterations G=50; initial crossover probability PC=0.8; initial mutation probability PM=0.7.

[0074] The following table compares the parameters of the 32212 tapered roller bearing before and after optimization:

[0075] Furthermore, the improvement in friction torque before and after optimization is as follows: Figure 4The diagram shows a comparison of frictional torque before and after optimization under the condition of varying bearing axial load and constant rotational speed. Figure 5 The diagram shows a comparison of frictional torque before and after optimization under the condition of constant bearing axial load and changing rotational speed. The frictional torque is significantly reduced compared to before optimization.

[0076] Based on the above embodiments, see Figure 6 The diagram shows a structural schematic of a friction torque optimization device. This application also provides a friction torque optimization device, comprising: Construction unit 601 is used to construct an optimization model of the bearing based on the initial quantity, design variables, and boundary constraints of the bearing; the boundary constraints are configured based on the rated dynamic load and machining constraints. Processing unit 602 is used to determine the overall deformation of each rolling element in the bearing based on the optimization model and inner ring deformation parameters; calculate the deformation and force of each slice of each rolling element using the slicing method to determine the total load of the rolling element and the inner ring force parameters; iterate the inner ring deformation parameters until the inner ring force balance is determined based on the inner ring force parameters to meet the accuracy requirements; the inner ring deformation parameters include displacement and tilt angle; The decomposition unit 603 is used to determine the contact load of the rolling element on each contact surface in contact with the rolling element based on the total load of each rolling element corresponding to the converged inner ring deformation parameters. The calculation unit 604 is used to determine the friction torque by combining the load and friction coefficient of each contact surface of each rolling element; The optimization unit 605 is used to determine the design parameters in the optimization model by iterative optimization through a genetic algorithm with the goal of minimizing the frictional torque.

[0077] Based on the above-mentioned device, this application accurately reproduces the stress and deformation state of the bearing under actual load, making the load distribution obtained after iterative convergence more accurate and closer to the actual working conditions, ensuring reliable results. At the same time, with the minimum friction torque as the target, combined with genetic algorithm and bearing calculation theory, multiple design parameters can be optimized in a coordinated manner to achieve global optimization, breaking through the limitations of traditional methods that rely solely on improving accuracy to reduce friction, and achieving a significant reduction in friction torque without increasing processing costs.

[0078] In one possible implementation, the bearing is a tapered roller bearing; the boundary constraints include: the rated dynamic load being greater than the rated dynamic load before optimization; the ratio of the width of the bearing's large flange to the width of the inner ring being greater than a first value; the ratio of the width of the bearing's small flange to the width of the inner ring being greater than a second value; the length difference between the large end and raceway of the rolling element and the length difference between the small end and raceway of the rolling element being greater than zero; the roller head clearance being the maximum of 0.57 and a third value, where the third value is the product of 0.057 and the diameter of the large end of the rolling element; the effective wall thickness of the inner ring being greater than the product of the difference between the bearing's outer diameter and inner diameter and 0.07; the absolute value of the difference between the effective wall thickness of the inner ring and the effective wall thickness of the outer ring being less than the product of the difference between the bearing's outer diameter and inner diameter and 0.02; and the width of the cage beam being greater than the product of a fourth value and the thickness of the cage plate.

[0079] In one possible implementation, the inner ring deformation parameters include the inner ring radial displacement, the inner ring axial displacement, and the inner ring tilt angle; The processing unit 602 uses the following formula to calculate the overall deformation of each rolling element in the bearing: ; Where, δ j Let δr be the overall deformation of the j-th rolling element, δa be the radial displacement of the inner ring, θ be the tilt angle of the inner ring, dm be the mean diameter of the rolling element, and α be the bearing contact angle. j Let be the circumference angle of the j-th rolling element.

[0080] In one possible implementation, the processing unit 602 is specifically used to divide each rolling element into multiple slices along the length direction; calculate the deformation of each slice of the rolling element based on the overall deformation of the rolling element and the rolling element shaping curve; solve the force balance equation and deformation compatibility equation of each rolling element to obtain the force on each slice, and sum the slice forces of the rolling element to obtain the total load of the rolling element.

[0081] In one possible implementation, the processing unit 602 is specifically configured to determine the radial force included in the inner ring force parameters based on the sum of the radial components of the forces exerted by all the rolling elements of the bearing on the inner ring; determine the axial force included in the inner ring force parameters based on the sum of the axial components of the forces exerted by all the rolling elements of the bearing on the inner ring; and determine the torque included in the inner ring force parameters based on the sum of the total load torque of each rolling element and the additional torque caused by the forces exerted on the slices included in each rolling element.

[0082] In one possible implementation, the device further includes an analysis unit for determining the minimum film thickness ratio of each rolling element to each contact surface; and for solving the friction coefficient of each contact surface in contact with the rolling element by means of a piecewise function of the friction coefficient based on the minimum film thickness ratio of each rolling element to each contact surface.

[0083] In one possible implementation, the calculation unit 604 is specifically used to calculate the frictional torque as follows: when the inner ring of the bearing rotates, the frictional torque is the sum of the torque generated by the friction between all the rolling elements of the bearing and the outer ring, and the torque generated by the sliding friction between all the rolling elements and the large flange of the inner ring; when the outer ring of the bearing rotates, the frictional torque is the sum of the torque generated by the friction between all the rolling elements of the bearing and the inner ring, and the torque generated by the sliding friction between all the rolling elements and the large flange of the inner ring.

[0084] In one possible implementation, the calculation unit 604 is further configured to correct the friction torque based on a correction coefficient determined from experimental data, thereby obtaining the corrected friction torque.

[0085] This application also provides corresponding electronic devices and computer storage media for implementing the solutions provided in this application.

[0086] The device includes a memory and a processor. The memory stores instructions or code, and the processor executes the instructions or code to enable the device to perform a friction torque optimization method according to any embodiment of this application.

[0087] The computer storage medium stores code, and when the code is run, the device running the code implements a friction torque optimization method according to any embodiment of this application.

[0088] In the embodiments of this application, the terms "first" and "second" (if they exist) are used only as name identifiers and do not represent the order of first and second.

[0089] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that all or part of the steps in the methods of the above embodiments can be implemented by means of software plus a general-purpose hardware platform. Based on this understanding, the technical solution of this application can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as a read-only memory (ROM) / RAM, magnetic disk, optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, a server, or a network communication device such as a router) to execute the methods described in various embodiments or some parts of the embodiments of this application.

[0090] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on its differences from other embodiments. In particular, the apparatus embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0091] The above description is merely an exemplary implementation of this application and is not intended to limit the scope of protection of this application.

Claims

1. A method for optimizing friction torque, characterized in that, The method includes: An optimization model for the bearing is constructed based on its initial quantity, design variables, and boundary constraints; the boundary constraints are configured according to the rated dynamic load and machining constraints. Based on the optimization model and inner ring deformation parameters, the overall deformation of each rolling element in the bearing is determined; the deformation and force of each slice of each rolling element are calculated by the slicing method to determine the total load of the rolling element and the inner ring force parameters; the inner ring deformation parameters are iterated until the inner ring force balance is determined based on the inner ring force parameters to meet the accuracy requirements; the inner ring deformation parameters include displacement and tilt angle. Based on the total load of each rolling element corresponding to the converged inner ring deformation parameters, determine the contact load of each contact surface of the rolling element in contact with the contact surface. The friction torque is determined by combining the load and friction coefficient of each contact surface of each rolling element; With the goal of minimizing the frictional torque, the design parameters in the optimization model are determined through iterative optimization using a genetic algorithm.

2. The method according to claim 1, characterized in that, The bearing is a tapered roller bearing; The boundary constraints include: the rated dynamic load being greater than the rated dynamic load before optimization; the ratio of the width of the bearing large flange to the width of the inner ring being greater than a first value; the ratio of the width of the bearing small flange to the width of the inner ring being greater than a second value; the length difference between the large end and the raceway of the rolling element and the length difference between the small end and the raceway of the rolling element being greater than zero; the roller big end clearance being the maximum value between 0.57 and a third value, where the third value is the product of 0.057 and the diameter of the large end of the rolling element; the effective wall thickness of the inner ring being greater than the product of the difference between the bearing outer diameter and the inner diameter and 0.07; the absolute value of the difference between the effective wall thickness of the inner ring and the effective wall thickness of the outer ring being less than the product of the difference between the bearing outer diameter and the bearing inner diameter and 0.02; and the width of the cage beam being greater than the product of a fourth value and the thickness of the cage plate.

3. The method according to claim 1, characterized in that, The inner ring deformation parameters include the inner ring radial displacement, the inner ring axial displacement, and the inner ring tilt angle; The formulas for calculating the overall deformation of each rolling element include: ； Where, δ j Let δr be the overall deformation of the j-th rolling element, δa be the radial displacement of the inner ring, θ be the tilt angle of the inner ring, dm be the mean diameter of the rolling element, and α be the bearing contact angle. j Let be the circumference angle of the j-th rolling element.

4. The method according to claim 3, characterized in that, The step of calculating the deformation and stress of each slice of each rolling element using the slice method, and determining the total load on the rolling element, includes: Each rolling element is divided into multiple slices along its length; Based on the overall deformation of the rolling element and the rolling element shaping curve, the deformation of each slice of the rolling element is calculated. By simultaneously solving the force balance equations and deformation compatibility equations of each rolling element, the force on each slice is obtained, and the total load of the rolling element is obtained by summing the forces on the slices included in the rolling element.

5. The method according to claim 4, characterized in that, The inner ring force parameters include radial force, axial force, and moment; determining the inner ring force parameters includes: The radial force included in the inner ring force parameters is determined based on the sum of the radial components of the forces exerted by all rolling elements on the inner ring of the bearing. The axial force included in the force parameters of the inner ring is determined based on the sum of the axial component forces of all rolling elements of the bearing on the inner ring. The torque included in the inner ring force parameters is determined based on the sum of the total load torque of all rolling elements in the bearing and the additional torque caused by the force on the slices included in each rolling element.

6. The method according to claim 5, characterized in that, Before determining the frictional torque by combining the load and friction coefficient of each rolling element at each corresponding contact surface, the method further includes: Determine the minimum film thickness ratio of each rolling element to each contact surface; Based on the minimum film thickness ratio of each rolling element to each contact surface, the friction coefficient of each contact surface in contact with the rolling element is solved by a piecewise function of the friction coefficient.

7. The method according to claim 5, characterized in that, The method of determining the frictional torque by combining the load and friction coefficient of each rolling element with the corresponding contact surface also includes: When the inner ring of the bearing rotates, the frictional torque is the sum of the torque generated by the friction between all the rolling elements of the bearing and the outer ring, and the torque generated by the sliding friction between all the rolling elements and the large flange of the inner ring. When the outer ring of a bearing rotates, the frictional torque is the sum of the torque generated by the friction between all the rolling elements and the inner ring, and the torque generated by the sliding friction between all the rolling elements and the large flange of the inner ring.

8. The method according to claim 7, characterized in that, After determining the frictional torque by combining the load and friction coefficient of each rolling element at each corresponding contact surface, the method further includes: Based on the correction coefficient determined by the experimental data, the friction torque is corrected to obtain the corrected friction torque.

9. A friction torque optimization device, characterized in that, The device includes: A construction unit is used to construct an optimization model of the bearing based on the bearing's initial quantity, design variables, and boundary constraints; the boundary constraints are configured based on the rated dynamic load and machining constraints. The processing unit is used to determine the overall deformation of each rolling element in the bearing based on the optimization model and the inner ring deformation parameters; calculate the deformation and force of each slice of each rolling element using the slicing method to determine the total load of the rolling element and the inner ring force parameters; iterate the inner ring deformation parameters until the inner ring force balance is determined based on the inner ring force parameters to meet the accuracy requirements; the inner ring deformation parameters include displacement and tilt angle; The decomposition unit is used to determine the contact load of the rolling element on each contact surface in contact with the rolling element based on the total load of each rolling element corresponding to the converged inner ring deformation parameters. The calculation unit is used to determine the friction torque by combining the load and friction coefficient of each contact surface of each rolling element; An optimization unit is used to determine the design parameters in the optimization model by iterative optimization using a genetic algorithm, with the goal of minimizing the frictional torque.

10. An electronic device, characterized in that, The device includes a memory and a processor, the memory being used to store instructions or code, and the processor being used to execute the instructions or code to cause the device to perform a friction torque optimization method according to any one of claims 1-8.

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