Equivalent linear stiffness processing method for rolling bearing

Abstract

The invention discloses a rolling bearing equivalent linear stiffness processing method, which comprises the following steps of: firstly, inputting shaft and bearing design parameters, setting an iteration error control quantity epsilon and an iteration step number n, dividing system nodes and calculating a shaft element stiffness matrix; then applying an axial load Fa, radial load components Fx and Fy and torque load components M theta x and M theta y, setting boundary constraints, determining a right end item of an equation, and giving a bearing load initial value Qb old; bearing displacement delta id and an equivalent stiffness matrix K are iteratively calculated through an N-R method, and the iteration formula is Xc, i = Xc, i-1-Ac-1B; coupling the equivalent stiffness matrixes of the shaft and the bearing to form an integral stiffness matrix Ktotal; finally, system deformation is calculated through delta = Q / Ktotal, bearing node displacement is obtained, nonlinear stress is calculated, iteration errors are judged, the node displacement, an equivalent stiffness matrix and bearing stress are output when the iteration errors are met, it is ensured that deformation and loads are coordinated, and the result is accurate and reliable.

Description

Technical Field

[0001] The invention relates to a method for processing equivalent linear stiffness of a rolling bearing. Background Art

[0002] Rolling bearings are mass-produced, highly standardized, and serialized industrial products. Aside from specialized bearings for special purposes or specific hosts that require special design, rolling bearings are generally able to adapt to the requirements of most operating conditions, making them one of the most widely used basic mechanical components. In modern mechanical simulation analysis, the finite element method is often used to analyze rotor systems. However, when applying the finite element method to analyze the coupling between bearings and shafts, the finite element matrix is linear, while the bearings are nonlinear. This makes it difficult to process the bearings when analyzing rotor systems. Directly coupling the nonlinear stiffness of the bearings to the shaft only ensures deformation coordination between the bearing nodes and the shaft nodes, which will lead to load incoordination between the bearing nodes and the shaft nodes, which is problematic. If the bearing stiffness is coupled to the shaft as a constant, ignoring the nonlinearity of the bearing, the calculated results are also unreliable. Summary of the Invention

[0003] In view of the shortcomings of the existing technology, the present invention provides a method for processing the equivalent linear stiffness of rolling bearings, which can effectively ensure the deformation coordination and load coordination of bearing nodes and shaft nodes, making the calculation results accurate and reliable and in line with actual application conditions.

[0004] To achieve the above object, the present invention provides a method for processing the equivalent linear stiffness of a rolling bearing, comprising the following steps: Step 1: Input parameters, input the design parameters of the shaft and bearing, set the iterative error control value ε and the number of iteration steps n, divide the system nodes, and calculate the stiffness matrix of the shaft unit; Step 2: Load setting, apply system load, including axial load F a , radial load component F x , radial load component F y , moment load component M θx , moment load component M θy Function, set boundary constraints, determine the right-hand side of the equation; give the initial value of the bearing load Q b old ; Step 3: NR method iterative calculation, calculate the bearing displacement by NR method δ id and the equivalent stiffness matrix K , the iteration formula is: X c,i =X c,i-1 -A c -1 B, where Xc is the equivalent stiffness calculation point; Step 4, coupling the system stiffness matrix, coupling the stiffness matrix of the shaft and the equivalent stiffness matrix of the bearing K to form the overall system stiffness matrix K total ; Step 5, solve for the system deformation through δ = Q / K total to calculate the system deformation δ and obtain the bearing node displacement δ b ; From δ b, calculate the non - linear force on the bearing Q b old , judge the iteration error: ∣ δ - δ old ∣≤ ε ; If not satisfied, update the iteration step k = k +1 and repeat the calculation; If satisfied, then converge, and output the displacements of the shaft and bearing nodes, the equivalent stiffness matrix of the bearing K t and the bearing force Q b .

[0005] The beneficial effects of such a setting are as follows: With such a setting, the types of rolling bearings here include but are not limited to deep groove ball bearings, angular contact ball bearings, tapered roller bearings, cylindrical roller bearings, needle roller bearings, four - point contact ball bearings, double - row deep groove ball bearings, double - row angular contact ball bearings, double - row tapered roller bearings, double - row cylindrical roller bearings, self - aligning ball bearings, self - aligning roller bearings, thrust ball bearings, thrust roller bearings. The static load conditions refer to including but not limited to axial load, radial load, moment load, and the static mechanical conditions of maintaining a balanced state when rotating at a constant speed or in a stationary state. The five - degree - of - freedom non - linear stiffness refers to the 5×5 stiffness matrix when the bearing is in balance under the action of axial load F a , radial load component F x , radial load component F y , moment load component M θx , moment load component M θy . If the radial load component F x and the radial load component F y , the radial component Fr can be obtained by force synthesis. If the moment load component M θx and the moment load component M θy , the moment load M θ, At this time, the stiffness matrix when the bearing is balanced is expressed as a 3×3 stiffness matrix. Nonlinear stiffness means that the stiffness matrix of the bearing is a function related to the bearing structure and the bearing working condition load, and it changes nonlinearly with the working condition load. The equivalent linear stiffness processing method refers to the equivalent processing of the five-degree-of-freedom nonlinear stiffness of the rolling bearing using the stiffness matrix of linear stiffness. This method is applicable to and not limited to all scenarios where linearization processing of rolling bearings is required, such as the finite element method, etc. Description of the Drawings

[0006] Figure 1 It is a schematic diagram of nonlinear stiffness and linear stiffness; Figure 2 It is the algorithm flowchart of the embodiment of the present invention. Detailed Implementation Manner

[0007] An embodiment of the equivalent linear stiffness processing method for the rolling bearing of the present invention is as follows: (1) Where represents the equivalent stiffness matrix, represents the bearing node deformation, represents the bearing nonlinear load.

[0008] ,

[0009] Expanding the bearing equivalent linear load and nonlinear load balance equation (1) gives: (2) Using the N-R method to solve the equivalent stiffness calculation point X for formula (2) c,

[0010] According to X c Calculate K c =K(X c ) ,

[0011]

[0012] The above example is only one preferred specific example of the present invention. Common changes and substitutions made by those skilled in the art within the scope of the technical solution of the present invention are all included in the protection scope of the present invention.

Claims

1. A method for processing the equivalent linear stiffness of a rolling bearing, characterized in that: including the following steps, Step 1, input parameters, the design parameters of the input shaft and bearing, set the iterative error control amount ε and the number of iterative steps n, divide the system nodes, and calculate the stiffness matrix of the shaft element; Step 2: Load setting, apply system load, including axial load F a , radial load component F x , radial load component F y , moment load component M θx , moment load component M θy Function, set boundary constraints, determine the right-hand side of the equation; give the initial value of the bearing load Q b old ; Step 3: Iterative calculation by the Newton-Raphson method to calculate the bearing displacement δ id and the equivalent stiffness matrix K , and the iterative formula is: X c,i = X c,i-1 - A c -1 B, where Xc is the equivalent stiffness calculation point; Step 4, coupling the system stiffness matrices, coupling the stiffness matrix of the shaft with the equivalent stiffness matrix of the bearing K to form the overall system stiffness matrix K total ; Step 5, solve for δ = Q / K total Calculate the system deformation δ to obtain the bearing node displacement δ b ; From δ b calculate the non-linear bearing force Q b old , judge the iteration error: ∣ δ - δ old ∣ ≤ ε ; If not satisfied, update the number of iterations k = k +1 and repeat the calculation; if it meets the requirements, it converges, and the displacement of the output shaft and bearing nodes, and the bearing equivalent stiffness matrix K t and bearing forces Q b .

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