Analytical Calculation Method for Bending Stress in the Bolt Locking Area of ​​Wheel Rim Spreader

Abstract

This invention discloses an analytical calculation method for bending stress in the bolt locking area of ​​a wheel rim spoke, comprising the following steps: Step S1, calculate the arc length under force according to the following formula; Step S2, calculate the effective distributed force according to the following formula; Step S3, calculate the bending stress at the bolt hole edge according to the following formula; Step S4, compare the bending stress calculated in the above steps with the allowable stress or fatigue limit of the material. When it is less than the corresponding allowable stress or fatigue limit of the material, the strength requirement is met. This invention has advantages such as theoretical completeness, calculation efficiency, accurate results, and broad application prospects.

Description

Technical Field

[0001] This invention belongs to the field of bending stress analysis technology, specifically relating to an analytical calculation method for bending stress in the bolt locking area of ​​a wheel rim. Background Technology

[0002] In tire assembly design, the bolt hole area connecting the wheel rim spokes and the hub is a high-risk area for fatigue failure. Stress verification typically relies on finite element analysis (FEM), but FEM modeling is time-consuming, computationally expensive, and requires specialized software and personnel. It's difficult to quickly respond to multi-scheme comparisons during the conceptual design phase. For example, tire manufacturers may not know how to verify rim mechanics, and rim manufacturers may not know the actual deformation area of ​​the rear rim caused by tire deformation. In practice, a secondary modeling analysis should be performed based on the stress distribution in the tire-rim contact area under load, using the tire's pressure on the rim as the boundary condition for rim mechanics analysis.

[0003] For rim spoke strength verification, existing technologies include relatively mature simulation analysis methods. However, current empirical formulas are often overly simplistic and fail to accurately reflect the impact of tire contact characteristics on rim stress. This results in either excessively thick rims, increasing vehicle weight, or excessively thin rims, posing safety hazards. These newer methods typically simplify the spokes as a structure with uniform stress across the entire circumference. Based on the total bending moment and bolt hole distribution, the nominal bending stress at the critical section is calculated, and the required thickness is determined using the material's yield strength. This method effectively addresses the static strength issue of the spokes and prevents overall plastic deformation.

[0004] However, actual wheel failure statistics show that fatigue cracking at the bolt hole edge is the main failure mode, rooted in local stress concentration. This fatigue problem differs significantly from static strength problems in its mechanical nature: fatigue failure depends on local peak stress, rather than the nominal stress of the cross section; the load is not uniformly distributed across the entire circumference, but concentrated within a finite arc segment corresponding to the tire contact patch; parameters such as tire contact pressure distribution and subsidence directly affect local stress, but existing static strength analysis methods do not incorporate these parameters.

[0005] Currently, the assessment of fatigue stress at the edge of bolt holes mainly relies on finite element analysis or empirical correction factors, and there is a lack of an analytical method that can quickly and accurately estimate the local peak stress. After initially determining the plate thickness, designers still need to repeatedly iterate through finite element analysis to meet fatigue requirements, which is inefficient. Summary of the Invention

[0006] This invention aims to provide an analytical calculation method for bending stress in the bolt locking area of ​​the wheel rim spokes. Based on the tire's basic parameters, it can quickly and accurately estimate the bending stress at the edge of the bolt holes and in the center of the spokes, solving the problems of long finite element modeling cycles, high calculation costs, and the lack of fatigue stress assessment for the bolt hole edges and center of the spokes.

[0007] Therefore, the technical solution adopted by this invention is: an analytical calculation method for bending stress in the bolt locking area of ​​a wheel rim, comprising the following steps:

[0008] Step S1: Calculate the arc length under force according to the following formula. ;

[0009] ;

[0010] ;

[0011] ;

[0012] in, The diameter of the tire. δ is the rim engagement diameter, and δ is the tire sinking amount; This refers to the angle of force applied to the circumferential surface of the wheel rim.

[0013] Step S2: Calculate the effective distributed force according to the following formula. ;

[0014] ;

[0015] ;

[0016] ; ;

[0017] in, Where LC is the lumped coefficient, M is the grounding length, and M is the total bending moment. The equivalent concentrated force of the bead seat, The total distributed force per unit arc length;

[0018] Step S3: Calculate the bending stress at the edge of the bolt hole. When, follow the formula below;

[0019] ;

[0020] ;

[0021] ;

[0022] Where t is the thickness of the sheet. DPCD is the diameter lever arm, where DPCD is the pitch circle diameter of the bolt hole. The bending moment at the root of a cantilever beam per unit width;

[0023] Step S4: Compare the bending stress calculated in the above steps with the allowable stress or fatigue limit of the material. When the bending stress is less than the corresponding allowable stress or fatigue limit of the material, the strength requirement is met.

[0024] As a preferred embodiment of the above scheme, in step S2, the total bending moment M is calculated according to the following formula. ;

[0025] Where μ is the coefficient of friction, R is the tire static load radius, d is the offset, F is the rated load, and S is the reinforcement coefficient.

[0026] More preferably, in step S3, when calculating the stress in the region from the root of the sheet metal to the bolt hole... When, follow the formula below:

[0027] ;

[0028] in, , r(x) is the radius coordinate.

[0029] Because the stress distribution can be linearly interpolated along the radial direction, the stress at any position inside the bolt hole can be calculated using linear interpolation.

[0030] More preferably, in step S1, the circumferential force angle of the wheel rim is... This refers to the range of angles within which the tire sidewall undergoes significant deformation due to the tire's sinking δ, covering the main area of ​​the rim that bears the load.

[0031] More preferably, in step S2, the concentration factor C is the ratio of the ground contact length LC to the tire circumference. The proportion reflects the degree of concentration of grounding pressure in the circumferential direction.

[0032] The present invention also employs a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above method.

[0033] The beneficial effects of this invention are:

[0034] (1) Compared with the long cycle and high computational cost of finite element modeling, this application introduces the tire sinkage δ and ground contact length LC to analyze the stress of the rim spokes, establishes a direct correlation between the tire ground contact characteristics and the local stress of the rim, determines the circumferential stress angle θ of the rim based on the diffusion effect, determines the stress area of ​​the rim, considers the tire sidewall deformation, and by introducing the diffusion effect, makes the calculation results closer to the actual load distribution, thereby improving the accuracy of stress estimation, providing a clear physical picture, and using a concentration factor. The circumferential concentration effect of quantified grounding pressure conforms to the actual load distribution law.

[0035] (2) The lever arm is determined based on the theory of bending symmetry deformation, which overcomes the deficiency of traditional methods in that the value of the lever arm lacks physical basis. When the lever arm is taken as the diameter difference At that time, it directly corresponds to the distance between the resultant force centers of the tension and compression zones. This distance determines the actual lever arm length in the cantilever beam model, and the peak stress at the bolt hole edge is directly calculated. .

[0036] (3) All parameters required for this invention are standard inputs for wheel design; the total bending moment M is calculated according to GB / T 5909 standard and standard test data can be directly used; the rim diameter Bolt hole distribution circle diameter DPCD and plate thickness t are design geometric parameters; tire diameter The subsidence δ and grounding length LC can be easily obtained through static pressure testing or finite element simulation, without the need to build complex finite element models. Parameter acquisition costs are low, and the system has wide engineering applicability. Only simple algebraic calculations are required to estimate the peak stress at the bolt hole edge, without iterative calculations or specialized software support. A single calculation can be completed within minutes, supporting rapid comparison of multiple schemes; it provides direct basis for initial thickness selection in the conceptual design stage, significantly improving design efficiency.

[0037] (4) The peak bending stress at the edge of the bolt hole is directly output. This position is the high-incidence part of wheel fatigue failure. The calculation result can be directly compared with the material fatigue limit. When the bending stress is less than the allowable stress or fatigue limit of the corresponding material, the strength requirement is met. Fatigue safety can be quickly judged. This provides a brand-new engineering tool for wheel fatigue design of tire assembly, and provides reliable initial input for subsequent finite element analysis and bench test, reducing the number of iterations.

[0038] In summary, this invention has advantages such as theoretical completeness, computational efficiency, result accuracy, and broad application prospects. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the wheel structure corresponding to the present invention.

[0040] Figure 2 for Figure 1AA sectional view.

[0041] Figure 3 This is a geometric diagram showing the relationship between tire sinking and ground contact length in this invention.

[0042] Figure 4 This is a force analysis diagram of a cantilever beam model for a wheel rim spoke.

[0043] Figure 5 This is a verification diagram of the finite element simulation results. Detailed Implementation

[0044] The present invention will be further described below with reference to the embodiments and accompanying drawings:

[0045] Combination Figure 1 — Figure 5 As shown, an analytical calculation method for bending stress in the bolt locking area of ​​a wheel rim spoke is presented, with the following specific implementation steps:

[0046] Step S1: Calculate the arc length under force according to the following formula. ;

[0047] ;

[0048] ;

[0049] ;

[0050] in, The diameter of the tire. δ is the rim engagement diameter, and δ is the tire sinking amount; This is the angle of force applied to the circumferential direction of the wheel rim.

[0051] In step S1, the circumferential force angle of the wheel rim It represents the range of angles at which the tire sidewall undergoes significant deformation due to the tire's sinking δ, and it covers the main area of ​​the rim that bears the load.

[0052] Step S2: Calculate the effective distributed force according to the following formula. ;

[0053] ;

[0054] ;

[0055] ;

[0056] ;

[0057] in, Where LC is the lumped coefficient, M is the grounding length, and M is the total bending moment. The equivalent concentrated force of the bead seat, The total distributed force per unit arc length.

[0058] Where μ is the coefficient of friction, R is the tire static load radius, d is the offset, F is the rated load, and S is the reinforcement coefficient.

[0059] In step S2, the total bending moment M is calculated according to the following formula. ;

[0060] In step S2, the concentration factor C is the ratio of the ground contact length LC to the tire circumference. The proportion reflects the degree of concentration of grounding pressure in the circumferential direction.

[0061] Step S3: Calculate the bending stress at the bolt hole edge using the following formula. ;

[0062] ;

[0063] ;

[0064]

[0065] Wherein, DPCD is the pitch circle diameter of the bolt hole. The lever arm is the diameter. t represents the bending moment at the root of the cantilever beam per unit width, and t represents the thickness of the slab.

[0066] In step S3, when calculating the stress in the area from the root of the sheet to the bolt hole... When, follow the formula below:

[0067] ;

[0068] in, , r(x) is the radius coordinate.

[0069] Because the stress distribution can be linearly interpolated along the radial direction, the stress at any position inside the bolt hole can be calculated using linear interpolation.

[0070] Step S4: Calculate the results from the above steps. Compared with the allowable stress or fatigue limit of the material, when The strength requirement is met when the stress is less than the allowable stress or fatigue limit of the corresponding material.

[0071] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0072] Example 1

[0073] The parameters for commercial vehicle wheels are as follows:

[0074] Total bending moment ;

[0075] Rim engagement diameter ;

[0076] Bolt hole pitch circle diameter ;

[0077] Plate thickness ;

[0078] Tire diameter ;

[0079] Tire deflection ;

[0080] grounding length .

[0081] The calculation was performed according to the steps above:

[0082] Tire section height ;

[0083] Circumferential force angle of wheel rim ;

[0084] Circumferential arc length ;

[0085] Concentration factor ;

[0086] equivalent concentrated force of the bead seat ;

[0087] Total distributed force per unit arc length ;

[0088] Effective distributed force

[0089] Diameter lever arm ;

[0090] unit width bending moment ;

[0091] Bolt hole edge stress .

[0092] like Figure 5 The maximum stress value shown in the finite element simulation results is 98 MPa to 110 MPa, and the stress at the edge of the bolt hole is 101.0 MPa. The error between the finite element simulation results and the actual stress value is within 10%, which verifies the accuracy of the present invention.

[0093] like Figure 3 As shown, according to The calculated circumferential force arc length is 307 mm, which is arc length CD in the figure. Meanwhile, according to the geometric projection method, the corresponding rim arc length of angle θc is 169.8 mm, which is arc length HI in the figure, covering the main area of ​​the rim bearing the load. The circumferential force arc length calculated based on the diffusion effect is 371 mm, which is arc length FG in the figure, and the diffusion area is 370m~411m.

[0094] After verification by bending finite element simulation, the area with significant actual stress on the rim covers approximately 340mm to 412mm, with an average of 376mm, thus verifying the correctness of the diffusion effect.

Claims

1. An analytical calculation method for bending stress in the bolt-locking area of ​​a wheel rim spoke, characterized in that, Includes the following steps: Step S1: Calculate the arc length under force according to the following formula. ; ； ； ； in, The diameter of the tire. δ is the rim engagement diameter, and δ is the tire sinking amount; This refers to the angle of force applied to the circumferential surface of the wheel rim. Step S2: Calculate the effective distributed force according to the following formula. ; ； ； ； ； in, Where LC is the lumped coefficient, M is the grounding length, and M is the total bending moment. The equivalent concentrated force of the bead seat, The total distributed force per unit arc length; Step S3: Calculate the bending stress at the edge of the bolt hole. When, follow the formula below; ； ； ； in, DPCD is the diameter lever arm, where DPCD is the pitch circle diameter of the bolt hole. t represents the bending moment at the root of the cantilever beam per unit width, and t represents the thickness of the plate. Step S4: Compare the bending stress calculated in the above steps with the allowable stress or fatigue limit of the material. When the bending stress is less than the corresponding allowable stress or fatigue limit of the material, the strength requirement is met.

2. The analytical calculation method for bending stress in the bolt locking area of ​​a wheel rim spoke as described in claim 1, characterized in that: In step S2, the total bending moment M is calculated according to the following formula. ； Where μ is the coefficient of friction, R is the tire static load radius, d is the offset, F is the rated load, and S is the reinforcement coefficient.

3. The analytical calculation method for bending stress in the bolt locking area of ​​a wheel rim spoke as described in claim 1, characterized in that: In step S3, when calculating the stress from the root of the sheet metal to the bolt hole area... When, follow the formula below: ； in, , r(x) is the radius coordinate.

4. The analytical calculation method for bending stress in the bolt locking area of ​​a wheel rim spoke as described in claim 1, characterized in that: In step S1, the circumferential force angle of the wheel rim is... It represents the range of angles at which the tire sidewall undergoes significant deformation due to the tire's sinking δ, and it covers the main area of ​​the rim that bears the load.

5. The analytical calculation method for bending stress in the bolt locking area of ​​a wheel rim as described in claim 1, characterized in that: In step S2, the concentration factor C is the ratio of the ground contact length LC to the tire circumference. The proportion reflects the degree of concentration of grounding pressure in the circumferential direction.

6. A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method according to any one of claims 1-5.

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