A simplified model and calculation method for wheel tread contact stress

Abstract

The application discloses a simplified model of wheel tread contact stress, which comprises a wheel pair on a track, and a brake shoe which is in contact with a wheel tread when braking; the brake shoe is regarded as a cantilever beam with a rectangular section in the lateral direction, one end of which is fixed to a brake lever system, and a working surface bears contact load; the contact pressure between the wheel and the brake shoe is linearly distributed along the working surface, and can be decomposed into normal pressure stress and bending stress; the normal pressure stress is generated by braking force, and the bending stress is caused by the overturning moment generated by the lateral force; when the brake shoe and the wheel are not worn and the normal pressure stress generated by the braking force is uniformly distributed on the wheel shoe, the overturning moment generated by the wheel rail lateral force is borne by two parallel paths. The simplified model of wheel tread contact stress and the calculation method provided by the application are efficient, greatly reduce the calculation complexity compared with the finite element method, and can complete the calculation and evaluation of the contact stress between the wheel shoes within several minutes.

Description

Technical Field

[0001] This invention belongs to the technical field of rail transit vehicle equipment, specifically relating to a simplified model and calculation method for wheel bearing contact stress. Background Technology

[0002] Braking of heavy-haul trains relies on the friction generated by the brake shoes pressing tightly against the wheel tread. The distribution of contact stress in the brake shoes directly determines their wear rate, tendency to develop hot cracks, and fatigue life. Accurately calculating this stress is crucial for the selection of brake shoe materials and structural design.

[0003] Currently, engineering mainly relies on two methods: one is finite element simulation based on Hertzian contact theory, which has high accuracy but large computational load and is mostly used for final verification; the other is an extremely simplified material mechanics formula, which only considers the brake shoe pressure divided by the area (σ = F / A). Although this method is fast, it ignores the negative impact of the huge wheel-rail lateral force generated by the train in actual operation due to track irregularities, curves, etc. on the brake shoe.

[0004] The closest existing approach is the "compressive stress calculation model based on the assumption of uniformly distributed load," which simplifies the brake shoe as a compressed block. It assumes that the contact pressure between the brake shoe and the wheel tread is uniformly distributed under the pressure of the brake cylinder. The calculation formula is: σ = F / A, where F is the braking force and A is the nominal contact area. This approach is commonly found in basic materials mechanics textbooks and early brake shoe design manuals, and is a classic engineering estimation method. The drawback of this approach is that its physical model is overly idealized; it completely ignores the bending effect of the brake shoe as a cantilever structure when subjected to lateral forces, such as the lateral force applied to the brake shoe when the wheel passes through a curve. In practical applications, it has been found that brake shoe failure often begins at the edges, which is the result of the superposition of tensile / compressive bending stress and the foundation compressive stress, a phenomenon that existing models cannot explain or predict.

[0005] However, existing methods for calculating wheel bearing pressure have the following drawbacks:

[0006] (1) The contradiction between calculation accuracy and efficiency: Existing methods for calculating wheel bearing contact stress mainly rely on finite element analysis. Although this method has high accuracy, it is complex to model, has high calculation costs, and is time-consuming, which cannot meet the needs of rapid evaluation and parameter optimization in the early stage of engineering.

[0007] (2) Ignoring complex load coupling: Traditional simplified algorithms usually only consider the brake shoe pressure, that is, the uniformly distributed compressive stress generated by the braking force, while ignoring the influence of the lateral force generated by the wheel-rail interaction and the overturning moment it causes on the stress distribution of the brake shoe. This simplification leads to a large deviation between the calculation results and the actual working conditions, and it is impossible to accurately assess the stress concentration and fatigue risk at the edge of the brake shoe. Summary of the Invention

[0008] The purpose of this invention is to solve the above problems and provide a simplified model and calculation method for brake shoe contact stress that, by constructing reasonable mechanical assumptions and stiffness distribution mechanisms, introduces the complex lateral force of wheel and rail into the calculation model, accurately and quickly calculates the total contact stress of the brake shoe working surface, and balances calculation efficiency and physical reality.

[0009] To solve the above-mentioned technical problems, the technical solution of the present invention is: a simplified model of brake shoe contact stress, including a wheelset located on the track, the wheelset being composed of two wheels connected by an axle, and the brake shoe contacting the wheel tread during braking; the brake shoe is regarded as a cantilever beam with a rectangular cross-section in the transverse direction, one end of which is fixed to the brake rod system, and the working surface bears the contact load; the contact pressure between the wheel and the brake shoe is linearly distributed along the working surface and can be decomposed into: normal compressive stress and bending stress, the normal compressive stress being generated by the braking force, and the bending stress being caused by the overturning moment generated by the transverse force; when neither the brake shoe nor the wheel is worn, and the normal compressive stress generated by the braking force is uniformly distributed on the brake shoe, the overturning moment generated by the wheel-rail transverse force is borne by two parallel paths.

[0010] This invention also discloses a calculation method for a simplified model of wheel bearing contact stress, comprising the following steps:

[0011] S1. Obtain basic parameters through measurement or simulation: F b A, F y h, E, and geometric dimensions, where the geometric dimensions include the axle diameter D and the brake shoe cross-sectional width w. b and height h b E represents the material properties; A represents the contact area of ​​the bearing shell.

[0012] S2, Calculate the total overturning force M y ;

[0013] S3, Estimating stiffness k a and k b And combined with the correction coefficient k p Calculate the effective torque M b ;

[0014] S4, combined with correction coefficient Calculate the compressive stress σ in the foundation p And calculate the effective bending stress σ b ;

[0015] S5. The total stress σ is obtained by superposition.

[0016] S6, Output wheel bearing contact stress distribution diagram.

[0017] Furthermore, the total overturning force M in S2 yThe calculation process is as follows: Wheel-rail lateral force F y The overturning moment acting on the center of the wheel is:

[0018] ; (1)

[0019] Where F y ρ is the lateral force between the wheel and rail, in N; h is the vertical lever arm from the point of application of the lateral force to the center of the wheel, in m.

[0020] Furthermore, among the basic parameters in S1, the braking force F b The uniform compressive stress generated when the bearings are in contact is:

[0021] ; (2)

[0022] F b Braking force, measured in N. This represents the actual contact area between the brake shoe and the wheel tread, in m². The contact non-uniformity coefficient, It can be calculated using the following formula:

[0023] ; (3)

[0024] Where e is the eccentricity between the point of application of the braking force and the center of the contact surface; The characteristic length of the contact surface is equal to the width of the brake shoe in the transverse direction; It is a dimensionless empirical correction coefficient used to characterize the "influence of eccentricity on the uneven distribution of contact pressure". Its value ranges from 0 to 0.5, and 0.3 is preferred based on simulation experience.

[0025] Furthermore, step S3 also includes the following sub-steps:

[0026] S31, equivalent lateral stiffness of the brake shoe;

[0027] As a cantilever beam, the lateral bending stiffness of the brake shoe is:

[0028] ; (4)

[0029] in This represents the elastic modulus of the brake shoe material, expressed in Pa. The effective cantilever length of the brake shoe is in meters and can be taken as the distance from the brake shoe support point to the center of the contact surface. Let be the moment of inertia of the brake shoe cross-section about the neutral axis, in meters (m). 4 ;in It can be calculated using the following formula:

[0030] ; (5)

[0031] in The width of the brake shoe cross-section, The height of the cross section;

[0032] S32, equivalent lateral stiffness of the axle;

[0033] The axle is considered as a simply supported beam, and its lateral bending stiffness is:

[0034] ; (6)

[0035] in This represents the elastic modulus of the axle material, expressed in Pa. The moment of inertia of the axle cross section is expressed in meters (m). 4 ; The span between the bearing support points at both ends of the axle, in meters; where It can be calculated using the following formula:

[0036] ; (7)

[0037] Where D is the wheel diameter. Since the axle diameter D is relatively large compared to the brake shoe size, therefore... Usually much larger ;

[0038] S33, Effective torque distribution;

[0039] Total overturning moment The path to the brake shoe is distributed according to the principle of parallel stiffness connection:

[0040] ; (8)

[0041] This refers to the effective torque that actually acts on the brake shoe system, causing it to bend and deform.

[0042] Furthermore, the bending stress in S4 is calculated as follows:

[0043] brake shoes under effective torque Under the action of the force, the bending stress generated at its edge is:

[0044] ; (9)

[0045] in This is the distance from the neutral axis of the brake shoe cross-section to its outermost edge, in meters (m). The moment of inertia of the brake shoe cross section is expressed in meters (m). 4 .

[0046] Furthermore, the material of the brake shoe may undergo plastic deformation under high pressure, therefore a plasticity correction factor is introduced. This is used to reduce bending stress, with a typical value range of 0.6 to 1.0, and can be calculated using the following formula:

[0047] ; (10)

[0048] in The relative stress level is defined as the elastic bending stress. With material yield strength The ratio, that is:

[0049] ; (11)

[0050] in The calculation formula is:

[0051] ;(12)

[0052] in The section modulus for the bending resistance of the brake shoe.

[0053] Furthermore, the total stress in S5 is the total contact stress, which is synthesized as follows:

[0054] The total stress on any edge of the working surface of the brake shoe is the algebraic sum of the compressive stress and the bending stress:

[0055] ; (13)

[0056] The sign depends on whether the calculation location is a compressive stress zone or a tensile stress zone.

[0057] The beneficial effects of this invention are:

[0058] 1. The simplified model and calculation method for contact stress between wheel bearings provided by this invention are highly efficient. Compared with the finite element method, it significantly reduces the computational complexity and can complete the calculation and evaluation of contact stress between wheel bearings within minutes. It is suitable for rapid design and iteration in the early stages of engineering.

[0059] 2. This invention is accurate, taking into account the overturning moment generated by the lateral force and its distribution on multiple paths, making the calculation results closer to the real physical process, and the stress assessment accuracy is significantly higher than that of the traditional simplified algorithm.

[0060] 3. This invention has physical clarity, clarifying the competitive relationship between the "brake shoe path" and the "axle path" of the torque, providing theoretical guidance for structural optimization design, such as changing the brake shoe stiffness or support method. Attached Figure Description

[0061] Figure 1 This is a flowchart of a calculation method for a simplified model of wheel bearing contact stress according to the present invention;

[0062] Figure 2 This is a schematic diagram of the torque distribution in a simplified model of wheel bearing contact stress according to the present invention;

[0063] Figure 3 This is a diagram of the wheel bearing contact stress during emergency braking according to the present invention;

[0064] Figure 4 This is a schematic diagram illustrating the verification results of a simplified model of wheel bearing contact stress according to the present invention. Detailed Implementation

[0065] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0066] like Figures 1 to 4 As shown, this invention provides a simplified model of brake shoe contact stress, including a wheelset located on a track. The wheelset consists of two wheels connected by an axle, and the brake shoe contacts the wheel tread during braking. The brake shoe is considered laterally as a cantilever beam with a rectangular cross-section, one end of which is fixed to the brake lever system, and its working surface bears the contact load. The contact pressure between the wheel and the brake shoe is linearly distributed along the working surface and can be decomposed into normal compressive stress and bending stress. The normal compressive stress is generated by the braking force, and the bending stress is caused by the overturning moment generated by the lateral force. When neither the brake shoe nor the wheel is worn, and the normal compressive stress generated by the braking force is uniformly distributed on the brake shoe, the overturning moment generated by the wheel-rail lateral force is borne by two parallel paths.

[0067] This invention provides a simplified calculation method for the contact stress of wheel bearings, comprising the following steps:

[0068] S1. Obtain basic parameters through measurement or simulation: F b A F y h, E, and geometric dimensions, where the geometric dimensions include the axle diameter D and the brake shoe cross-sectional width w. b and height h b Where E is a material property, This represents the actual contact area of ​​the bearing shell. If the bearing shells are in complete contact, then... A represents the contact area of ​​the wheel bearing.

[0069] S2, Calculate the total overturning force M y .

[0070] The total overturning force M in step S2 y The calculation process is as follows: Wheel-rail lateral force F y The overturning moment acting on the center of the wheel is:

[0071] ; (1)

[0072] Where F y ρ is the lateral force between the wheel and rail, in N; h is the vertical lever arm from the point of application of the lateral force to the center of the wheel, in m.

[0073] In the basic parameters of step S1 of this invention, the braking force F b The uniform compressive stress generated when the bearings are in contact is:

[0074] ; (2)

[0075] F b Braking force, measured in N. This represents the actual contact area between the brake shoe and the wheel tread, in m². The contact non-uniformity coefficient, It can be calculated using the following formula:

[0076] ; (3)

[0077] Where e is the eccentricity between the point of application of the braking force and the center of the contact surface; The characteristic length of the contact surface is equal to the width of the brake shoe in the transverse direction; It is a dimensionless empirical correction coefficient used to characterize the "influence of eccentricity on the uneven distribution of contact pressure", with a value range of 0 to 0.5, preferably 0.3.

[0078] The above calculations are based on the calculation of basic compressive stress.

[0079] S3, Estimating stiffness k a and k b And combined with the correction coefficient k p Calculate the effective torque M b .

[0080] Step S3 also includes the following sub-steps:

[0081] S31, equivalent lateral stiffness of the brake shoe.

[0082] As a cantilever beam, the lateral bending stiffness of the brake shoe is:

[0083] ; (4)

[0084] in This represents the elastic modulus of the brake shoe material, expressed in Pa. The effective cantilever length of the brake shoe is in meters and can be taken as the distance from the brake shoe support point to the center of the contact surface. Let be the moment of inertia of the brake shoe cross-section about the neutral axis, in meters (m).4 ;in It can be calculated using the following formula:

[0085] ; (5)

[0086] in The width of the brake shoe cross-section, This represents the cross-sectional height.

[0087] S32, equivalent lateral stiffness of the axle.

[0088] The axle is considered as a simply supported beam, and its lateral bending stiffness is:

[0089] ; (6)

[0090] in This represents the elastic modulus of the axle material, expressed in Pa. The moment of inertia of the axle cross section is expressed in meters (m). 4 ; The span between the bearing support points at both ends of the axle, in meters; where It can be calculated using the following formula:

[0091] ; (7)

[0092] Where D is the wheel diameter. Since the axle diameter D is relatively large compared to the brake shoe size, therefore... Usually much larger .

[0093] S33, Effective Torque Distribution.

[0094] Total overturning moment The path to the brake shoe is distributed according to the principle of parallel stiffness connection:

[0095] ; (8)

[0096] This refers to the effective torque that actually acts on the brake shoe system, causing it to bend and deform.

[0097] S4, combined with correction coefficient Calculate the compressive stress σ in the foundation p And calculate the effective bending stress σ b .

[0098] The bending stress calculation in step S4 is as follows:

[0099] brake shoes under effective torque Under the action of the force, the bending stress generated at its edge is:

[0100] ; (9)

[0101] in This is the distance from the neutral axis of the brake shoe cross-section to its outermost edge, in meters (m). The moment of inertia of the brake shoe cross section is expressed in meters (m). 4 .

[0102] Since the brake shoe material may undergo plastic deformation under high pressure, a plasticity correction factor is introduced. This is used to reduce bending stress, with a typical value range of 0.6 to 1.0, and can be calculated using the following formula:

[0103] ; (10)

[0104] in The relative stress level is defined as the elastic bending stress. With material yield strength The ratio, that is:

[0105] ; (11)

[0106] in The calculation formula is:

[0107] ;(12)

[0108] in The section modulus for the bending resistance of the brake shoe.

[0109] S5, the total stress σ is obtained by superposition.

[0110] The total stress in step S5 is the total contact stress, which is synthesized as follows:

[0111] The total stress on any edge of the working surface of the brake shoe is the algebraic sum of the compressive stress and the bending stress:

[0112] ; (13)

[0113] The sign depends on whether the calculation location is a compressive stress zone or a tensile stress zone. In this embodiment, the tensile stress is signified negatively, meaning that the bending stress is opposite to the brake shoe pressure, while the compressive stress is signified positively.

[0114] S6, Output wheel bearing contact stress distribution diagram.

[0115] Plot a line graph with the lateral position of the wheel as the x-axis and the total stress value as the y-axis.

[0116] This invention is applicable to tread braking structures in both straight and curved driving conditions, and can be used with common materials such as synthetic brake shoes and cast iron brake shoes. When brake shoes experience severe uneven wear, significant changes in contact area, or complex brake shoe support methods, the assumption of uniform compressive stress distribution between the brake shoes will no longer apply, and corrections must be made using finite element analysis or experiments: by conducting experiments (pressure-sensitive paper, thin-film sensors) or finite element calculations, the compressive stress distribution diagram of the working surface of the brake shoe (or wheel) under wear conditions is obtained, and then the bending stress calculation method of this invention is used to calculate the total stress at the contact point of the brake shoes.

[0117] Figure 3 The diagram shows the stress distribution of the wheel bearing contact during emergency braking. The calculated braking force is 25.5 kN, the average compressive stress is 0.89 MPa, and the maximum contact stress is 0.914 MPa, located at the edge of the wheel bearing contact. Figure 4 To verify the reliability of the model, the results of numerical calculations and finite element method (FEM) calculations were compared under the same working conditions. The FEM results were taken from the literature "Study on the Wear of Metro Wheel Treads under Different Braking Conditions". Figure 4 As shown, the calculation results of this method are in good agreement with the finite element results.

[0118] This invention discloses a simplified model for wheel bearing contact stress, which calculates the overturning moment generated by the lateral force between the wheel and rail based on the equivalent stiffness ratio of the brake shoe system and the axle system. It clarifies that the "brake shoe path" and "axle path" resisting the lateral moment are in parallel, and the effective moment M... b The force is determined by the ratio of the stiffness of the two components, rather than acting entirely on the brake shoes.

[0119] The simplified model for wheel bearing contact stress disclosed in this invention includes a four-step method for determining wheel bearing contact stress: "calculating foundation compressive stress, calculating stiffness and distributing moment, calculating effective bending stress, and superimposing total stress." This method systematically incorporates the complex lateral force interaction between the wheel and rail into a closed analytical solution framework.

[0120] This invention has low computational cost and is suitable for engineering applications: It retains the fast calculation characteristics of analytical formulas, without the need for complex mesh generation and iterative calculations, making it very suitable for embedding into the front-end tools of vehicle dynamics software or braking system design to achieve large-scale parameter scanning and optimization.

[0121] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A simplified model of contact stress in wheel bearings, characterized in that: The system includes wheelsets located on the track, consisting of two wheels connected by an axle. Brake shoes contact the wheel tread during braking. The brake shoes are considered as cantilever beams with a rectangular cross-section in the lateral direction, with one end fixed to the brake lever system. The working surface bears the contact load. The contact pressure between the wheel and the brake shoe is linearly distributed along the working surface and can be decomposed into normal compressive stress and bending stress. The normal compressive stress is generated by the braking force, and the bending stress is caused by the overturning moment generated by the lateral force. When neither the brake shoe nor the wheel is worn, and the normal compressive stress generated by the braking force is evenly distributed on the wheel shoe, the overturning moment generated by the lateral force of the wheel and rail is borne by two parallel paths.

2. A calculation method based on the simplified model of wheel bearing contact stress according to claim 1, characterized in that, Includes the following steps: S1. Obtain basic parameters through measurement or simulation: F b A, F y h, E, and geometric dimensions, where the geometric dimensions include the axle diameter D and the brake shoe cross-sectional width w. b and height h b E represents the material properties; A represents the contact area of ​​the bearing shell. S2, Calculate the total overturning force M y ; S3, Estimate stiffness k a and k b And combined with the correction coefficient k p Calculate the effective torque M b ; S4, combined with correction coefficient Calculate the compressive stress σ in the foundation p And calculate the effective bending stress σ b ; S5. The total stress σ is obtained by superposition. S6, Output wheel bearing contact stress distribution diagram.

3. The calculation method for a simplified model of wheel bearing contact stress according to claim 2, characterized in that, The total overturning force M in S2 y The calculation process is as follows: Wheel-rail lateral force F y The overturning moment acting on the center of the wheel is: ； （1） Where F y ρ is the lateral force between the wheel and rail, in N; h is the vertical lever arm from the point of application of the lateral force to the center of the wheel, in m.

4. The calculation method for a simplified model of wheel bearing contact stress according to claim 2, characterized in that, Among the basic parameters in S1, the braking force F b The uniform compressive stress generated when the bearings are in contact is: ； （2） F b Braking force, measured in N. This represents the actual contact area between the brake shoe and the wheel tread, in m². The contact non-uniformity coefficient, It can be calculated using the following formula: ； （3） Where e is the eccentricity between the point of application of the braking force and the center of the contact surface; The characteristic length of the contact surface is equal to the width of the brake shoe in the transverse direction; It is a dimensionless empirical correction coefficient used to characterize the "influence of eccentricity on the uneven distribution of contact pressure". Its value ranges from 0 to 0.5, and 0.3 is preferred based on simulation experience.

5. The calculation method for a simplified model of wheel bearing contact stress according to claim 2, characterized in that, S3 further includes the following sub-steps: S31, equivalent lateral stiffness of the brake shoe; As a cantilever beam, the lateral bending stiffness of the brake shoe is: ； （4） in This represents the elastic modulus of the brake shoe material, expressed in Pa. The effective cantilever length of the brake shoe is in meters and can be taken as the distance from the brake shoe support point to the center of the contact surface. Let be the moment of inertia of the brake shoe cross-section about the neutral axis, in meters (m). 4 ;in It can be calculated using the following formula: ； （5） in The width of the brake shoe cross-section, The height of the cross section; S32, equivalent lateral stiffness of the axle; The axle is considered as a simply supported beam, and its lateral bending stiffness is: ； （6） in This represents the elastic modulus of the axle material, expressed in Pa. The moment of inertia of the axle cross section is expressed in meters (m). 4 ; The span between the bearing support points at both ends of the axle, in meters; in It can be calculated using the following formula: ； （7） Where D is the wheel diameter. Since the axle diameter D is relatively large compared to the brake shoe size, therefore... Usually much larger ; S33, Effective torque distribution; Total overturning moment The path to the brake shoe is allocated according to the principle of parallel stiffness connection: ； （8） This refers to the effective torque that actually acts on the brake shoe system, causing it to bend and deform.

6. The calculation method for a simplified model of wheel bearing contact stress according to claim 2, characterized in that, The bending stress in S4 is calculated as follows: brake shoes under effective torque Under the action of the force, the bending stress generated at its edge is: ； （9） in This is the distance from the neutral axis of the brake shoe cross-section to its outermost edge, in meters (m). The moment of inertia of the brake shoe cross section is expressed in meters (m). 4 .

7. The calculation method for a simplified model of wheel bearing contact stress according to claim 6, characterized in that, The material of the brake shoe may undergo plastic deformation under high pressure, therefore a plasticity correction factor is introduced. This is used to reduce bending stress, with a typical value range of 0.6 to 1.0, and can be calculated using the following formula: ； （10） in The relative stress level is defined as the elastic bending stress. With material yield strength The ratio, that is: ； （11） in The calculation formula is: ； （12） in The section modulus for the bending resistance of the brake shoe.

8. The calculation method for a simplified model of wheel bearing contact stress according to claim 2, characterized in that, The total stress in S5 is the total contact stress, which is synthesized as follows: The total stress on any edge of the working surface of the brake shoe is the algebraic sum of the compressive stress and the bending stress: ； （13） The sign depends on whether the calculation location is a compressive stress zone or a tensile stress zone.

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