A method for calculating the service life of an elliptical raceway rolling bearing

Abstract

This invention relates to the field of rolling bearing design and life assessment technology, specifically a method for calculating the life of an elliptical raceway bearing, comprising the following steps: S100, measured multi-point profile: obtaining a set of discrete points i of the measured profile of the raceway surface of the elliptical deformed raceway of the bearing to be assessed; S200, least squares fitting to an ideal ellipse: performing ellipse fitting on the discrete point set i to obtain an ideal ellipse, and determining the length of the major axis 2a and the length of the minor axis 2b of the ideal ellipse; S300, extraction of three points: extracting one endpoint A of the minor axis and two endpoints C1 and C2 of the major axis on the ideal ellipse; This transforms the complex geometric deformation problem into a change in the standard parameter of the bearing's internal clearance, thereby realizing the quantitative calculation of the life of the elliptical raceway bearing.

Description

Technical Field

[0001] This invention relates to the field of rolling bearing design and life assessment technology, specifically a method for calculating the life of an elliptical ring rolling bearing. Background Technology

[0002] Rolling bearings are core components of mechanical equipment, and accurate prediction of their fatigue life is crucial for the safe operation and maintenance of the equipment. Currently, the industry generally adopts bearing life calculation methods based on standards such as ISO 281 and ISO / TS 16281. One of the core assumptions of these standards is that the bearing raceways are ideally circular, without considering shape errors that occur during actual machining, assembly, or service. However, in the manufacturing process of large self-aligning roller bearings, wind turbine bearings, and special precision bearings, elliptical deformation of the raceways is inevitable due to limitations in grooving, heat treatment, or grinding processes. This ellipticity leads to a significant change in the load distribution within the bearing: in the direction of the minor axis of the ellipse, the radius of curvature of the raceway increases, the number of bearing elements decreases, and local contact stress increases, thereby shortening the actual service life of the bearing. Existing life calculation methods cannot quantify the impact of this elliptical deformation, resulting in life predictions that are overly optimistic and pose a potential threat to the reliability of the main equipment. Summary of the Invention

[0003] In view of the shortcomings of the prior art, the present invention provides a method for calculating the life of elliptical ring rolling bearings, which solves the problem that the existing standard does not take into account the elliptical deformation of the ring, resulting in an overestimation of the actual usable life and failing to guide the design of machining tolerances and the selection of bearings.

[0004] To achieve the above objectives, the present invention provides a method for calculating the life of an elliptical ring rolling bearing, comprising the following steps: S100, Measured Multi-Point Profile: Obtain the set of discrete points i of the measured profile of the raceway surface of the elliptical deformed ring of the bearing to be evaluated; S200, Least squares method fitting to an ideal ellipse: Perform ellipse fitting on the discrete point set i to obtain an ideal ellipse, and determine the length of the major axis 2a and the length of the minor axis 2b of the ideal ellipse; S300. Extract three points: Extract one endpoint A of the minor axis and two endpoints C1 and C2 of the major axis on the ideal ellipse. S400, Three points define a circle, calculate the diameter: Based on the non-collinear endpoints A, C1 and C2 in the previous step, there exists a unique circumcircle, and the diameter De of this circle can be calculated using geometric formulas; S500, Calculate the equivalent increase in clearance Δu: Obtain the original design raceway diameter D0 of the raceway, and calculate the equivalent increase in clearance Δu = D e -D0; S600, Equivalent Original Clearance Calculation: Obtain the original design radial clearance u of the bearing, and calculate the equivalent original clearance u. e =u + Δu; S700, Calculate the actual working clearance: based on the equivalent original clearance u e Taking into account assembly interference, operating temperature and preload factors, calculate the actual working clearance of the bearing; S800. Calculate the life using bearing life simulation software combined with load spectrum: Based on the actual working clearance, use bearing life simulation software, input a load spectrum including load magnitude, rotational speed and load time ratio, and calculate the corrected fatigue life of the elliptical deformed ring bearing.

[0005] Further, in step S100, for the raceway surface of the machined inner or outer ring of the bearing, ≥36 measurement points are uniformly selected along the circumferential direction of the ring, and the radial contour coordinate data of the raceway surface are collected point by point to obtain the discrete point set i.

[0006] Furthermore, in step 200, the ideal ellipse fitting employs the least squares method to minimize the sum of the squared distances from all discrete points to the fitted ellipse.

[0007] Furthermore, in step 200, the ellipticity is also calculated, wherein the ellipticity = |ab| / D0.

[0008] Further, in step 400, a coordinate system is established with the center of the ellipse as the origin and the major axis as the x-axis. The coordinates of point A are (0, -b), and the coordinates of points C1 and C2 are (-a, 0) and (a, 0) respectively. The diameter D of the circumcircle... e Calculate using the following formula: D e = (a² + b²) / b.

[0009] Furthermore, in step S500, the original design raceway diameter D0 refers to the raceway bottom diameter for the outer ring and the raceway surface diameter for the inner ring.

[0010] Furthermore, in step S700, the actual working clearance is calculated according to the method considering the effects of fit and temperature in the national standard GB / T 4604.

[0011] Further, in step S800, the bearing life simulation software is Romax software, and the corrected fatigue life is L. 10r life.

[0012] The core of this invention lies in: equating complex elliptical geometric deformations to an increase in clearance, and through the transformation of "elliptical feature points → circumcircle diameter → equivalent clearance increase," enabling existing mature lifetime calculation theories and software to directly handle shape error problems. Equivalent original clearance ue The introduction of this method allows all subsequent standard calculations based on clearance (such as working clearance and lifetime) to reflect the adverse effects of ellipticity without changing the model.

[0013] The beneficial effects of the present invention are: (1) A quantitative relationship between elliptical deformation and radial clearance is established, with clear physical meaning, which solves the problem that the standard life formula cannot be directly applied to non-circular rings.

[0014] (2) The method is based on existing mature measurement methods and life simulation software. It can be implemented by data fitting and simple geometric calculation. It has strong engineering applicability and does not require the redevelopment of complex software.

[0015] (3) It can effectively correct the overestimation of the life of deformable bearings in existing standards. Examples show that the corrected life is significantly lower than the calculation result of ISO / TS 16281, providing safe and direct data support for the design of main machine reliability and machining tolerance. Attached Figure Description

[0016] Figure 1 This is an overall flowchart of the present invention; Figure 2 This is a schematic diagram of the measured discrete contour points and the fitted ideal ellipse of the present invention; Figure 3 This is a schematic diagram illustrating the calculation principle of the three-point circle determination and the equivalent increase in clearance in this invention. Figure 4 This is a schematic diagram of the bearing life calculation model based on Romax according to the present invention; Figure 5 This is a comparison chart of the lifetime calculation method of this invention and the ISO / TS 16281 standard; Detailed Implementation

[0017] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0018] like Figure 1-5 As shown, one embodiment of the present invention provides a method for calculating the life of an elliptical ring rolling bearing, comprising the following steps: S100, Measured Multi-Point Profile: Obtain the set of discrete points i of the measured profile of the raceway surface of the elliptical deformed ring of the bearing to be evaluated; S200, Least squares method to fit to ideal ellipse: Perform ellipse fitting on discrete point set i to obtain ideal ellipse, and determine the length of the major axis 2a and the length of the minor axis 2b of ideal ellipse; S300, Extract three points: Extract one endpoint A of the minor axis and two endpoints C1 and C2 of the major axis on the ideal ellipse; S400. Three points define a circle; calculate the diameter: Based on the non-collinear endpoints A, C1, and C2 from the previous step, there exists a unique circumcircle with a diameter D. e It can be calculated using geometric formulas; S500, Calculate the equivalent increase in clearance Δu: Obtain the original design raceway diameter D0 of the raceway, and calculate the equivalent increase in clearance Δu = D e -D0; S600, Equivalent Original Clearance Calculation: Obtain the original design radial clearance u of the bearing, and calculate the equivalent original clearance u. e =u + Δu; The original design radial clearance is derived from the national standard formula.

[0019] S700, Calculate the actual working clearance: based on the equivalent original clearance u e Taking into account assembly interference, operating temperature and preload factors, calculate the actual working clearance of the bearing; S800: The bearing life is calculated using bearing life simulation software combined with load spectrum: Based on the actual working clearance, the bearing life simulation software is used to input a load spectrum containing load magnitude, speed and load time ratio, and the corrected fatigue life of the elliptical deformed ring bearing is calculated.

[0020] In one embodiment, in step S100, for the raceway surface of the machined inner or outer ring of the bearing, ≥36 measurement points are uniformly selected along the circumferential direction of the ring, and the radial contour coordinate data of the raceway surface are collected point by point to obtain a discrete point set i.

[0021] It should be noted that this step, based on the discrete contour point set collected in the previous step, uses the least squares ellipse fitting algorithm for numerical calculation. This algorithm obtains a unique ideal ellipse mathematical model by minimizing the sum of squared distances from all discrete points to the fitted ellipse, and then accurately extracts key geometric parameters such as the major axis length 2a, minor axis length 2b, ellipse center coordinates, and ellipticity (ellipticity = |ab| / D0, where D0 is the original design raceway diameter).

[0022] In one embodiment, in step 200, the ideal ellipse fitting employs the least squares method to minimize the sum of the squared distances from all discrete points to the fitted ellipse.

[0023] In one embodiment, step 200 also calculates the ellipticity, where ellipticity = |ab| / D0.

[0024] It should be noted that this step, based on the discrete contour point set collected in the previous step, uses the least squares ellipse fitting algorithm for numerical calculation. This algorithm obtains a unique ideal ellipse mathematical model by minimizing the sum of squared distances from all discrete points to the fitted ellipse, and then accurately extracts key geometric parameters such as the major axis length 2a, minor axis length 2b, ellipse center coordinates, and ellipticity (ellipticity = |ab| / D0, where D0 is the original design raceway diameter).

[0025] In one embodiment, in step 400, a coordinate system is established with the center of the ellipse as the origin and the major axis as the x-axis. The coordinates of point A are (0, -b), and the coordinates of points C1 and C2 are (-a, 0) and (a, 0) respectively. The diameter D of the circumcircle... e Calculate using the following formula: D e = (a² + b²) / b.

[0026] In one embodiment, in step S500, the original design raceway diameter D0 refers to the raceway bottom diameter for the outer ring and the raceway surface diameter for the inner ring.

[0027] In one embodiment, in step S700, the actual working clearance is calculated according to the method considering the effects of fit and temperature in the national standard GB / T 4604.

[0028] In one embodiment, in step S800, the bearing life simulation software is Romax software, and the corrected fatigue life is L. 10r life.

[0029] Further preferred, taking a certain FS-EA87 self-aligning roller bearing as an example, its outer ring is elliptical due to machining, and the original design radial clearance u = 0.09 mm.

[0030] Step S100: Use a roundness tester to uniformly collect 72 measuring points along the circumference of the outer raceway to obtain a discrete coordinate point set that reflects the actual contour.

[0031] Step S200: The point set is processed using the least squares ellipse fitting algorithm to obtain the ideal ellipse parameters: major axis 2a = 336.085 mm, minor axis 2b = 335.915 mm. The ellipticity is calculated as (ab) / D0 ≈ 0.025%. The ellipse is illustrated as follows: Figure 2 .

[0032] Step S300: As Figure 3 As shown, extract the major axis endpoints C1 and C2 and the minor axis endpoint A on the ideal ellipse.

[0033] Step S400: As Figure 3As shown, establish a coordinate system with the center of the ellipse as the origin, with coordinates C1(-168.0425, 0), C2(168.0425, 0), and A(0, -167.9575). The three points determine a unique circumcircle, with its diameter defined by D. e = (a² + b²) / b Calculation: a=168.0425, b=167.9575, D e =(168.0425²+167.9575²) / 167.9575≈336.172mm.

[0034] Step S500: The original design raceway diameter of the bearing outer ring is D0 = 336.087 mm. Calculate the equivalent increase in clearance Δu = D. e -D0 = 0.085 mm.

[0035] Step S600: Calculate the equivalent original clearance u e =u+Δu=0.09+0.085=0.175mm.

[0036] Step S700: Considering the actual assembly interference to reduce the clearance by 0.02mm, and the working temperature rise of 60℃ to reduce the clearance by 0.015mm, without additional preload, the final bearing actual working clearance is negative clearance or a small positive clearance. Substitute the specific values ​​into the corresponding formula.

[0037] Step S800: In Romax software, create a shaft system model containing this bearing, input the actual working clearance, and apply... Figure 4 The load spectrum shown is (radial load 50kN, axial load 10kN, speed 1500r / min, with each condition accounting for 100% cumulatively). The corrected bearing L is calculated. 10r Lifespan is 6.32 × 10⁻⁶ 5 Hour.

[0038] In contrast, ignoring elliptic deformation, the lifespan calculated using the traditional ISO / TS 16281 standard under the same operating conditions is 9.85 × 10⁻⁶. 5 Hours, such as Figure 5 The differences between the two are significant, demonstrating that this invention effectively corrects the problem of overestimating lifespan, and the calculated lifespan is closer to reality.

[0039] The advantage of this invention is that by utilizing existing mature bearing life calculation theories and software, and through the "ellipse-clearance" equivalent transformation method, the life of elliptical ring bearings can be quickly and accurately evaluated, providing a direct basis for bearing machining tolerance design and main machine selection.

[0040] In the above-mentioned method for calculating the life of an elliptical ring rolling bearing: Innovation Point 1: Fitting of Elliptical Ring Contour Data and Determination of Ideal Ellipse Parameters.

[0041] By performing multi-point radial measurements on the machined bearing rings, discrete data of the actual profile were obtained. Numerical fitting methods, such as the least squares method, were used to fit the discrete points to an ideal ellipse, thereby determining the major axis length, minor axis length, and ellipticity of this ellipse. This method provides accurate geometric characteristic parameters for subsequent clearance equivalent conversion.

[0042] Innovation Point 2: A quantitative calculation model for the equivalent increase in clearance based on elliptical feature points.

[0043] Three feature points are extracted from the fitted ideal ellipse: the endpoints of the minor axis and the two endpoints of the major axis. A fitted circle is determined by these three points, and the diameter of this circle is calculated. The difference between this diameter and the diameter of the ideal raceway (standard circle) under the original design conditions is defined as the equivalent increase in clearance Δu. Its physical meaning is that ellipse deformation leads to an increase in the local raceway curvature radius, which is equivalent to the radial clearance of the bearing being "enlarged" in that direction, thus weakening the bearing's load-bearing capacity.

[0044] Innovation Point 3: A bearing life simulation evaluation method that considers equivalent original clearance and actual working conditions.

[0045] Add the equivalent increase in clearance Δu obtained from innovation point two to the original design clearance u to obtain the equivalent original clearance u. e = (u + Δu). Based on this, considering factors such as assembly tightness, temperature, and preload, the actual working clearance of the bearing is calculated. Then, a bearing life analysis model is established using Romax software, and a load spectrum (including load magnitude, speed, percentage, and other operating conditions) is applied to calculate the L of the elliptical ring bearing. 10r Lifespan. This method overcomes the limitation of existing standards that cannot consider ring deformation, and realizes a quantitative and engineering-based assessment of the lifespan of machined elliptical ring bearings.

[0046] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0047] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0048] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0049] In this invention, unless otherwise explicitly specified and limited, "above" or "below" a second feature can mean that the first and second features are in direct contact, or that they are in indirect contact through an intermediate medium. Furthermore, "above," "over," and "on top" of a second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" a second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature. It should be noted that when an element is referred to as "fixed to" or "set on" another element, it can be directly on the other element or there may be an intermediate element present. When an element is considered to be "connected" to another element, it can be directly connected to the other element or there may be an intermediate element present. The terms "vertical," "horizontal," "above," "below," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible embodiments.

Claims

1. A method for calculating the life of an elliptical ring rolling bearing, characterized in that: Includes the following steps, S100, Measured Multi-Point Profile: Obtain the set of discrete points i of the measured profile of the raceway surface of the elliptical deformed ring of the bearing to be evaluated; S200, Least squares method fitting to an ideal ellipse: Perform ellipse fitting on the discrete point set i to obtain an ideal ellipse, and determine the length of the major axis 2a and the length of the minor axis 2b of the ideal ellipse; S300. Extract three points: Extract one endpoint A of the minor axis and two endpoints C1 and C2 of the major axis on the ideal ellipse. S400. Three points define a circle; calculate the diameter: Based on the non-collinear endpoints A, C1, and C2 from the previous step, there exists a unique circumcircle with a diameter D. e It can be calculated using geometric formulas; S500, Calculate the equivalent increase in clearance Δu: Obtain the original design raceway diameter D0 of the raceway, and calculate the equivalent increase in clearance Δu = D e -D0; S600, Equivalent Original Clearance Calculation: Obtain the original design radial clearance u of the bearing, and calculate the equivalent original clearance u. e =u + Δu; S700, Calculate the actual working clearance: based on the equivalent original clearance u e Taking into account assembly interference, operating temperature and preload factors, calculate the actual working clearance of the bearing; S800. Calculate the life using bearing life simulation software combined with load spectrum: Based on the actual working clearance, use bearing life simulation software, input a load spectrum including load magnitude, rotational speed and load time ratio, and calculate the corrected fatigue life of the elliptical deformed ring bearing.

2. The method for calculating the life of an elliptical ring rolling bearing according to claim 1, characterized in that: In step S100, for the raceway surface of the machined inner or outer ring of the bearing, ≥36 measurement points are uniformly selected along the circumference of the ring, and the radial contour coordinate data of the raceway surface are collected point by point to obtain the discrete point set i.

3. The method for calculating the life of an elliptical ring rolling bearing according to claim 1, characterized in that: In step 200, the ideal ellipse fitting uses the least squares method to minimize the sum of the squared distances from all discrete points to the fitted ellipse.

4. The method for calculating the life of an elliptical ring rolling bearing according to claim 1, characterized in that: In step 200, the ellipticity is also calculated, where ellipticity = |ab| / D0.

5. The method for calculating the life of an elliptical ring rolling bearing according to claim 1, characterized in that: In step 400, a coordinate system is established with the center of the ellipse as the origin and the major axis as the x-axis. The coordinates of point A are (0, -b), and the coordinates of points C1 and C2 are (-a, 0) and (a, 0) respectively. The diameter D of the circumcircle... e Calculate using the following formula: D e = (a² + b²) / b.

6. The method for calculating the life of an elliptical ring rolling bearing according to claim 1, characterized in that: In step S500, the original design raceway diameter D0 refers to the bottom diameter of the raceway for the outer ring and the surface diameter of the raceway for the inner ring.

7. The method for calculating the life of an elliptical ring rolling bearing according to claim 1, characterized in that: In step S700, the actual working clearance is calculated according to the method considering the effects of fit and temperature in the national standard GB / T 4604.

8. A method for calculating the life of an elliptical ring rolling bearing according to any one of claims 1-7, characterized in that: In step S800, the bearing life simulation software is Romax software, and the corrected fatigue life is L. 10r life.

Images