Radial spherical plain bearing rated static load calculation method and system
By analyzing the geometric relationship of radial plane contact deformation in radial spherical bearings, expressions characterizing the limiting contact angle and radius are established. Combined with numerical iteration methods, the problems of slow calculation speed and inaccurate results in the existing technology are solved, and fast and accurate calculation of rated static load is achieved.
Patent Information
- Application Number
- CN202511200001.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-26
- Publication Date
- 2025-12-09
AI Technical Summary
In the existing technology, the calculation method for the rated static load of radial spherical plain bearings has the problems of large computational resource requirements and long time consumption. Moreover, the calculation results of empirical formulas differ greatly from the actual load-bearing capacity, and do not fully reflect the influence of bearing size and material properties on load-bearing capacity.
By analyzing the geometric relationship of radial plane contact deformation in radial spherical bearings, expressions characterizing the limiting contact angle and limiting contact radius are established. Combining bearing structural parameters and material properties, the rated static load is calculated using a numerical iteration method.
It enables rapid and accurate calculation of rated static load, more comprehensively reflects the influence of bearing size and material properties on load-bearing capacity, and the calculation results are close to reality and suitable for engineering applications.
Smart Images
Figure CN121093508A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of radial spherical plain bearing technology, and in particular to a method and system for calculating the rated static load of radial spherical plain bearings. Background Technology
[0002] The rated static load of a radial spherical plain bearing refers to the maximum load capacity that the bearing can withstand in a static state. The rated static load is one of the important parameters for bearing users and manufacturers when selecting and designing radial spherical plain bearings. Currently, the main methods for calculating the rated static load of radial spherical plain bearings are finite element simulation and empirical formulas. The empirical formula is the finite projected area of the radial spherical plain bearing multiplied by the load modulus, as shown below:
[0003] C s =f s Cd k ;
[0004] In the formula, C s For the rated static load, f s Where C is the load modulus, C is the width of the outer ring of the radial spherical plain bearing, and d is the load modulus. k The diameter of the ball bearing is the diameter of the radial spherical plain bearing.
[0005] The finite element method (FEM) requires significant computational resources and is time-consuming. It also necessitates precise modeling of the radial joint bearing structure, lacks universality, and is time-consuming to solve. For existing empirical formulas, its static load modulus f... s The value is too small, and the calculated rated static load differs significantly from the actual bearing capacity of the radial spherical plain bearing. Furthermore, the formula does not fully reflect the influence of bearing size parameters and material properties on the rated static load of the radial spherical plain bearing. Summary of the Invention
[0006] Based on the shortcomings of the existing technology, the present invention provides a method and system for calculating the rated static load of radial spherical plain bearings, which solves the problems of large computational resource requirements, long solution time, and large discrepancy between the rated static load calculated by the existing empirical formula and the actual bearing capacity of the radial spherical plain bearing.
[0007] The present invention adopts the following technical solution:
[0008] In a first aspect, the present invention provides a method for calculating the rated static load of a radial spherical plain bearing, comprising the following steps:
[0009] The contact deformation geometry on the radial plane of the radial spherical plain bearing is analyzed. Based on the analysis results, a first expression for characterizing the limiting contact angle and a second expression for characterizing the limiting contact radius are obtained. The limiting contact angle is the angle formed by the line connecting the limiting contact position and the center of the outer ring, and the limiting contact radius is the distance between the limiting contact position and the center line of the outer ring. The limiting contact position is the position where the inner ring has zero penetration displacement under allowable stress. The penetration displacement is the inner ring displacement of the radial spherical plain bearing under allowable stress.
[0010] Obtain the outer ring radius, bearing clearance, equivalent elastic modulus, initial maximum penetration displacement, and allowable stress value of the radial spherical plain bearing to be calculated; where the penetration displacement is the inner ring displacement of the radial spherical plain bearing to be calculated after loading.
[0011] Input the bearing clearance value and initial maximum permeation displacement of the radial spherical plain bearing to be calculated into the first expression to obtain the limiting contact angle of the radial spherical plain bearing to be calculated; input the limiting contact angle and outer ring radius of the radial spherical plain bearing to be calculated into the second expression to obtain the limiting contact radius of the radial spherical plain bearing to be calculated; obtain the current maximum permeation displacement of the radial spherical plain bearing to be calculated based on the limiting contact radius, equivalent elastic modulus and allowable stress value of the radial spherical plain bearing to be calculated.
[0012] Obtain the relative error between the current maximum permeation displacement and the initial maximum permeation displacement of the radial spherical plain bearing to be calculated. If the relative error is less than the allowable iteration error, obtain the corresponding rated static load based on the current maximum permeation displacement of the radial spherical plain bearing to be calculated.
[0013] Preferably, the first expression is as follows:
[0014]
[0015] In the formula, θ max Δr is the limit contact angle, Δr is the bearing clearance value, and δ is the maximum penetration displacement.
[0016] Preferably, the second expression is as follows:
[0017]
[0018] In the formula, r max R1 is the limit contact radius, and R2 is the inner circle radius.
[0019] Preferably, the maximum permeation displacement is as follows:
[0020]
[0021] In the formula, k1 and k2 are the equivalent elastic modulus, B is the integral influence coefficient, P0 is the allowable stress value, μ1 and μ2 are the Poisson's ratios of the inner and outer ring materials of the radial spherical bearing, E1 and E2 are the elastic modulus of the inner and outer ring materials, and n is the pressure distribution index.
[0022] Preferably, the rated static load is as follows:
[0023]
[0024] In the formula, C s The rated static load is given, u is the pressure concentration effect factor, C is the width of the outer ring of the radial spherical plain bearing, and d is the static load rating. k Let I be the inner ring diameter of the radial spherical bearing, and I be the integral parameter.
[0025] Preferably, if the relative error is greater than the allowable iteration error, the current maximum permeation displacement is used as the initial maximum permeation displacement to calculate and iterate the limiting contact angle, the limiting contact radius, and the current maximum permeation displacement until the relative error is greater than the allowable iteration error.
[0026] In a second aspect, the present invention provides a system for calculating the rated static load of a radial spherical plain bearing, comprising:
[0027] The analysis module is used to analyze the contact deformation geometry on the radial plane of the radial spherical plain bearing. Based on the analysis results, a first expression for characterizing the limiting contact angle and a second expression for characterizing the limiting contact radius are obtained. The limiting contact angle is the angle formed by the line connecting the limiting contact position and the center of the outer ring, and the limiting contact radius is the distance between the limiting contact position and the center line of the outer ring. The limiting contact position is the position where the inner ring has zero penetration displacement under allowable stress. The penetration displacement is the inner ring displacement of the radial spherical plain bearing under allowable stress.
[0028] The acquisition module is used to acquire the outer ring radius, bearing clearance value, equivalent elastic modulus, initial maximum penetration displacement, and allowable stress value of the radial spherical plain bearing to be calculated; wherein the penetration displacement is the inner ring displacement of the radial spherical plain bearing to be calculated after being loaded;
[0029] The calculation module is used to input the bearing clearance value and initial maximum permeation displacement of the radial spherical plain bearing to be calculated into the first expression to obtain the limiting contact angle of the radial spherical plain bearing to be calculated; input the limiting contact angle and outer ring radius of the radial spherical plain bearing to be calculated into the second expression to obtain the limiting contact radius of the radial spherical plain bearing to be calculated; and obtain the current maximum permeation displacement of the radial spherical plain bearing to be calculated based on the limiting contact radius, equivalent elastic modulus and allowable stress value of the radial spherical plain bearing to be calculated.
[0030] The comparison module is used to obtain the relative error between the current maximum permeation displacement and the initial maximum permeation displacement of the radial spherical plain bearing to be calculated. If the relative error is less than the allowable iteration error, the corresponding rated static load is obtained based on the current maximum permeation displacement of the radial spherical plain bearing to be calculated.
[0031] Compared with the prior art, the above-mentioned at least one technical solution adopted by the present invention can achieve the following beneficial effects:
[0032] This invention first analyzes the contact deformation geometry on the radial plane of a radial spherical plain bearing. Based on the analysis results, a first expression characterizing the limiting contact angle and a second expression characterizing the limiting contact radius are obtained. Then, the outer ring radius, bearing clearance, equivalent elastic modulus, initial maximum penetration displacement, and allowable stress value of the radial spherical plain bearing to be calculated are input into the first and second expressions to obtain the corresponding limiting contact angle and limiting contact radius. Based on the limiting contact radius, equivalent elastic modulus, and allowable stress value, the maximum penetration displacement of the radial spherical plain bearing to be calculated is obtained, and the rated static load value is obtained based on the maximum penetration displacement. This invention only requires inputting the bearing structural parameters and material parameters to obtain the rated static load value, which is faster than the finite element simulation method. Compared with existing empirical formulas, the calculation results are more accurate and more comprehensively reflect the influence of the radial spherical plain bearing's size and material properties on its load-bearing capacity. The calculation results are closer to the actual size and fit engineering applications, making the theoretical calculation of the rated static load of radial spherical plain bearings more complete. Attached Figure Description
[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0034] Figure 1 This is a schematic diagram of the radial joint bearing of the present invention;
[0035] Figure 2 This is a schematic diagram of the radial plane contact of the radial joint bearing of the present invention;
[0036] Figure 3 This is a radial plane pressure distribution diagram of the present invention;
[0037] Figure 4 This is a flowchart of a method for calculating the rated static load of a radial spherical bearing according to the present invention;
[0038] Figure 5This is a schematic diagram comparing the rated static load results of different radial spherical bearing size series of the present invention with existing standard results;
[0039] Figure 6 This invention relates to a device for testing the rated static load of radial joint bearings. Detailed Implementation
[0040] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0041] Reference Figure 4 This invention provides a method for calculating the rated static load of a radial spherical plain bearing, comprising the following steps:
[0042] S1: Reference Figure 1 The contact deformation geometry on the radial plane of the radial spherical bearing is analyzed, and based on the analysis results, a first expression for characterizing the limiting contact angle and a second expression for characterizing the limiting contact radius are obtained.
[0043] The structure of a radial spherical bearing mainly consists of an inner ring and an outer ring. Its sliding contact surface is an inner spherical surface and an outer spherical surface, which can rotate and swing at any angle during movement.
[0044] like Figure 2 This is a schematic diagram of the contact on the radial plane of a radial spherical bearing. Analysis of the geometric relationships yields:
[0045]
[0046] In the formula, θ is the contact angle, Δp is the difference in radii between the inner and outer rings of the bearing, δ is the maximum penetration displacement, R2 is the inner ring radius of the bearing, R1 is the outer ring radius of the bearing, and δ(θ) is the penetration displacement at other positions in the contact area. The penetration displacement is the inner ring displacement of the radial spherical plain bearing after loading.
[0047] Solving equation (1) above yields the permeation displacement δ(θ):
[0048]
[0049] For bearing clearance and slight leakage, we have (Δp+δ). 2 sin 2 θ << R1 2 The permeation displacement δ(θ) can be transformed into:
[0050] δ(θ)=(Δp+δ)cosθ-Δp (3);
[0051] The bearing clearance is defined as Δr = 2Δp, combined with δ(θ) max Substituting 0 into equation (3) above, we get:
[0052]
[0053] In the formula, Δr is the bearing clearance value, and θ max This is the limit contact angle.
[0054] Then the limiting contact radius r max for:
[0055]
[0056] S2: Obtain the outer ring radius, bearing clearance, equivalent elastic modulus, initial maximum penetration displacement, and allowable stress value of the radial spherical plain bearing to be calculated; where the penetration displacement is the inner ring displacement of the radial spherical plain bearing under load. The initial maximum penetration displacement is set manually.
[0057] S3: Input the bearing clearance value and initial maximum permeation displacement of the radial spherical plain bearing to be calculated into the first expression to obtain the limiting contact angle of the radial spherical plain bearing to be calculated; input the limiting contact angle and outer ring radius of the radial spherical plain bearing to be calculated into the second expression to obtain the limiting contact radius of the radial spherical plain bearing to be calculated; obtain the current maximum permeation displacement of the radial spherical plain bearing to be calculated based on the limiting contact radius, equivalent elastic modulus and allowable stress value of the radial spherical plain bearing to be calculated.
[0058] The maximum permeation displacement δ can be calculated using the following formula:
[0059]
[0060] In the formula: k1 and k2 are the equivalent elastic modulus, B is the integral influence coefficient, P0 is the allowable stress, μ1 and μ2 are the Poisson's ratios of the inner and outer ring materials of the radial spherical plain bearing, respectively; E1 and E2 are the elastic modulus of the inner and outer ring materials of the radial spherical plain bearing, respectively; n is the pressure distribution index; the remaining parameters are the same as above. Equation (6) can be calculated using a numerical iteration method to obtain the permeation displacement δ under the allowable contact pressure P0 of the specified radial spherical plain bearing material.
[0061] The contact pressure distribution on the radial plane of a radial spherical bearing is related to the contact area formation angle. The pressure distribution under the radial plane is as follows: Figure 3 As shown, it can be expressed by the following formula:
[0062]
[0063] In the formula, P(θ) represents the pressure distribution on the radial plane of the centripetal spherical bearing.
[0064] The rated static load of the radial spherical bearing can be obtained from the calculated maximum permeation displacement δ.
[0065]
[0066] In the formula, C s The rated static load is given by u, which is the pressure concentration effect factor, with a value of 0.9; C is the width of the outer ring of the radial spherical plain bearing, and d is the value of d. k Let I be the inner ring diameter of the radial spherical bearing, and I be the integral parameter.
[0067] S4: The rated static load calculation uses a simple numerical iteration method. An initial penetration displacement δ0 and allowable iteration error are set. Matlab software is used for programming to calculate the penetration amount under the allowable stress of the radial spherical plain bearing. Then, the rated static load value of the radial spherical plain bearing can be calculated based on the penetration displacement. The calculation process for the rated static load of the radial spherical plain bearing is as follows: Figure 4 .
[0068] Obtain the relative error between the current maximum permeation displacement and the initial maximum permeation displacement of the radial spherical plain bearing to be calculated. If the relative error is less than the allowable iteration error, obtain the corresponding rated static load based on the current maximum permeation displacement of the radial spherical plain bearing to be calculated.
[0069] If the relative error is greater than the allowable iteration error, the current maximum permeation displacement is used as the initial maximum permeation displacement to calculate and iterate the limiting contact angle, limiting contact radius, and current maximum permeation displacement until the relative error is greater than the allowable iteration error.
[0070] Figure 5 To compare the rated static load results of different radial spherical plain bearing series calculated using the new model with existing standard results, from... Figure 5 It can be seen that the calculation results of the new model are closer to the finite element elastoplastic simulation results than the calculation results of the old standard, proving the accuracy of the new model.
[0071] This invention also provides a test model for testing the rated static load of radial spherical plain bearings to verify the accuracy of the rated static load value, such as... Figure 6 As shown. The procedure involves mounting the bearing on the experimental setup, applying a preload of 4% to 6% of the rated static load value, maintaining this load for 15 seconds, and recording the micrometer reading. Then, the load is gradually increased to the rated static load value, maintained for 1 minute, and finally, the load value is gradually decreased back to the preload. If the micrometer reading matches the initial reading, the static load value is accurate; otherwise, it is inaccurate.
[0072] This invention proposes a new method for calculating the rated static load of radial spherical plain bearings, which is faster and more accurate than currently known calculation methods.
[0073] The rated static load calculation method of this invention better reflects the influence of the size and material properties of radial joint bearings on the bearing load capacity.
[0074] The rated static load testing device in this invention is used to determine whether the static load calculation results of radial joint bearings are accurate.
[0075] Based on the same concept, the present invention also provides a system for calculating the rated static load of a radial spherical bearing, including an analysis module, an acquisition module, a calculation module and a comparison module.
[0076] The analysis module is used to analyze the contact deformation geometry on the radial plane of the radial spherical plain bearing. Based on the analysis results, a first expression for characterizing the limiting contact angle and a second expression for characterizing the limiting contact radius are obtained. The limiting contact angle is the angle formed by the line connecting the limiting contact position and the center of the outer ring, and the limiting contact radius is the distance between the limiting contact position and the center line of the outer ring. The limiting contact position is the position where the inner ring has zero penetration displacement under allowable stress. The penetration displacement is the inner ring displacement of the radial spherical plain bearing under allowable stress.
[0077] The acquisition module is used to acquire the outer ring radius, bearing clearance value, equivalent elastic modulus, initial maximum permeation displacement, and allowable stress value of the radial spherical plain bearing to be calculated; where the permeation displacement is the inner ring displacement of the radial spherical plain bearing to be calculated after being loaded.
[0078] The calculation module is used to input the bearing clearance value and initial maximum permeation displacement of the radial spherical plain bearing to be calculated into the first expression to obtain the limiting contact angle of the radial spherical plain bearing to be calculated; input the limiting contact angle and outer ring radius of the radial spherical plain bearing to be calculated into the second expression to obtain the limiting contact radius of the radial spherical plain bearing to be calculated; and obtain the current maximum permeation displacement of the radial spherical plain bearing to be calculated based on the limiting contact radius, equivalent elastic modulus and allowable stress value of the radial spherical plain bearing to be calculated.
[0079] The comparison module is used to obtain the relative error between the current maximum permeation displacement and the initial maximum permeation displacement of the radial spherical plain bearing to be calculated. If the relative error is less than the allowable iteration error, the corresponding rated static load is obtained based on the current maximum permeation displacement of the radial spherical plain bearing to be calculated.
[0080] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.
[0081] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.
Claims
1. A method for calculating the rated static load of a radial spherical plain bearing, characterized in that, Includes the following steps: The contact deformation geometry on the radial plane of the radial spherical plain bearing is analyzed. Based on the analysis results, a first expression for characterizing the limiting contact angle and a second expression for characterizing the limiting contact radius are obtained. The limiting contact angle is the angle formed by the line connecting the limiting contact position and the center of the outer ring, and the limiting contact radius is the distance between the limiting contact position and the center line of the outer ring. The limiting contact position is the position where the inner ring has zero penetration displacement under allowable stress. The penetration displacement is the inner ring displacement of the radial spherical plain bearing under allowable stress. Obtain the outer ring radius, bearing clearance, equivalent elastic modulus, initial maximum permeation displacement, and allowable stress value of the radial spherical bearing to be calculated; Input the bearing clearance value and initial maximum permeation displacement of the radial spherical plain bearing to be calculated into the first expression to obtain the limiting contact angle of the radial spherical plain bearing to be calculated. Input the limiting contact angle and outer ring radius of the radial spherical plain bearing to be calculated into the second expression to obtain the limiting contact radius of the radial spherical plain bearing to be calculated. The current maximum permeation displacement of the radial spherical plain bearing to be calculated is obtained based on its limiting contact radius, equivalent elastic modulus, and allowable stress value. Obtain the relative error between the current maximum permeation displacement and the initial maximum permeation displacement of the radial spherical plain bearing to be calculated. If the relative error is less than the allowable iteration error, obtain the corresponding rated static load based on the current maximum permeation displacement of the radial spherical plain bearing to be calculated.
2. The method for calculating the rated static load of a radial spherical plain bearing as described in claim 1, characterized in that, The first expression is as follows: In the formula, θ max Δr is the limit contact angle, Δr is the bearing clearance value, and δ is the maximum penetration displacement.
3. The method for calculating the rated static load of a radial spherical plain bearing as described in claim 2, characterized in that, The second expression is as follows: In the formula, r max R1 is the limit contact radius, and R2 is the inner circle radius.
4. The method for calculating the rated static load of a radial spherical plain bearing as described in claim 3, characterized in that, The maximum permeation displacement is as follows: In the formula, k1 and k2 are the equivalent elastic modulus, B is the integral influence coefficient, P0 is the allowable stress value, μ1 and μ2 are the Poisson's ratios of the inner and outer ring materials of the radial spherical bearing, E1 and E2 are the elastic modulus of the inner and outer ring materials, and n is the pressure distribution index.
5. The method for calculating the rated static load of a radial spherical plain bearing as described in claim 4, characterized in that, The specific rated static load is as follows: In the formula, C s The rated static load is given, u is the pressure concentration effect factor, C is the width of the outer ring of the radial spherical plain bearing, and d is the static load rating. k Let I be the inner ring diameter of the radial spherical bearing, and I be the integral parameter.
6. The method for calculating the rated static load of a radial spherical plain bearing as described in claim 1, characterized in that, If the relative error is greater than the allowable iteration error, the current maximum permeation displacement is used as the initial maximum permeation displacement to calculate and iterate the limiting contact angle, limiting contact radius, and current maximum permeation displacement until the relative error is greater than the allowable iteration error.
7. A system for calculating the rated static load of a radial spherical plain bearing, characterized in that, include: The analysis module is used to analyze the contact deformation geometry on the radial plane of the radial spherical plain bearing. Based on the analysis results, a first expression for characterizing the limiting contact angle and a second expression for characterizing the limiting contact radius are obtained. The limiting contact angle is the angle formed by the line connecting the limiting contact position and the center of the outer ring, and the limiting contact radius is the distance between the limiting contact position and the center line of the outer ring. The limiting contact position is the position where the inner ring has zero penetration displacement under allowable stress. The penetration displacement is the inner ring displacement of the radial spherical plain bearing under allowable stress. The acquisition module is used to acquire the outer ring radius, bearing clearance value, equivalent elastic modulus, initial maximum penetration displacement, and allowable stress value of the radial spherical plain bearing to be calculated; wherein the penetration displacement is the inner ring displacement of the radial spherical plain bearing to be calculated after being loaded; The calculation module is used to input the bearing clearance value and the initial maximum permeation displacement of the radial spherical plain bearing to be calculated into the first expression to obtain the limit contact angle of the radial spherical plain bearing to be calculated. Input the limiting contact angle and outer ring radius of the radial spherical plain bearing to be calculated into the second expression to obtain the limiting contact radius of the radial spherical plain bearing to be calculated. The current maximum permeation displacement of the radial spherical plain bearing to be calculated is obtained based on its limiting contact radius, equivalent elastic modulus, and allowable stress value. The comparison module is used to obtain the relative error between the current maximum permeation displacement and the initial maximum permeation displacement of the radial spherical plain bearing to be calculated. If the relative error is less than the allowable iteration error, the corresponding rated static load is obtained based on the current maximum permeation displacement of the radial spherical plain bearing to be calculated.