Flexible matrix rapid calculation method for thrust bearing bush with elastic support

Abstract

The invention discloses a flexibility matrix rapid calculation method for a thrust bearing bush with an elastic support, which belongs to the technical field of sliding bearing design, and comprises the following steps: enabling an elastic support body at the back of the bearing bush to be equivalent to a discrete spring array, and coupling the discrete spring array with a finite element model of a bearing bush body; and thus, a simplified mechanical model for extracting the working surface flexibility matrix is constructed. The rigidity of the equivalent spring is determined based on the material performance and the geometric dimension of the supporting body and can be arranged in a partitioned mode to simulate actual deformation distribution. According to the method, entity mesh generation on a complex support body is avoided, so that the degree of freedom of a finite element model is remarkably reduced; on the basis, an overall flexibility matrix is efficiently obtained in a mode of extracting a system stiffness matrix and performing inversion, then a flexibility matrix subset of the working surface is accurately captured, and the numerical value difficulty of large-scale matrix inversion is effectively overcome. The method is high in calculation efficiency, simple and convenient in modeling, and particularly suitable for elastic fluid lubrication analysis of large-scale low-speed heavy-load thrust sliding bearings such as wind power spindles and the like.

Description

Technical Field

[0001] This invention relates to a calculation method in the field of sliding bearing design technology, and in particular to a rapid calculation method for the flexibility matrix of a wind turbine main shaft with elastic support thrust bearing. Background Technology

[0002] Wind turbine main shaft sliding bearings typically operate under low-speed, heavy-load conditions, with their thrust bearings bearing the enormous axial loads from the wind turbine and generator. To improve load distribution, reduce edge contact stress, and enhance self-aligning capability, industrial applications often incorporate elastic support structures (such as flexible gaskets) on the back of the thrust bearing. This structure allows for slight displacement of the bearing through elastic deformation, effectively avoiding stress concentration under eccentric or tilted conditions and improving the overall lubrication performance and operational reliability of the bearing.

[0003] When performing elastohydrodynamic lubrication analysis on thrust bearings with elastic supports, it is necessary to coupled the oil film pressure field and the structural deformation field. Currently, the deformation influence coefficient matrix method (i.e., the compliance matrix method) is a reliable means to handle this coupled problem. Its core lies in first obtaining the compliance matrix of the structural surface using the finite element method, and then rapidly converting the oil film pressure into surface deformation through matrix operations. Specifically, a complete finite element model including the bearing and the elastic support needs to be established. After meshing and setting boundary conditions, the overall stiffness matrix of the system is extracted, and its inverse is used to obtain the compliance matrix. However, when this traditional method is applied to thrust bearings with elastic supports, significant challenges arise: 1. Complex Modeling: For long thrust bearings used in applications such as wind turbine main shafts, the large number and complex layout of their back elastic support units make 3D modeling and assembly work cumbersome.

[0004] Second, the number of meshes is huge: In order to accurately capture the compression deformation behavior of the elastic support, a sufficient number of mesh elements need to be divided in the thickness direction, which leads to a sharp increase in the number of nodes in the overall model.

[0005] Third, the computational cost is high: the huge number of nodes results in a huge stiffness matrix, and inverting it faces severe numerical difficulties with long computation time and high memory requirements, and may even be difficult to solve.

[0006] Therefore, there is an urgent need in this field for an alternative calculation method that can accurately reflect the mechanical properties of elastic supports and has the advantages of simple modeling, low computational cost, and fast extraction of flexibility matrix. Summary of the Invention

[0007] To address the shortcomings of the aforementioned technologies, this invention proposes a rapid calculation method for the compliance matrix of a thrust bearing with elastic support, thereby solving the problems of complex modeling and low computational efficiency caused by the large number of meshes in traditional full-solid finite element models.

[0008] To achieve the above objectives, the present invention includes the following steps: Step 1: Construct the finite element model of the spring-supported bearing bush.

[0009] Finite element method software is used to create a three-dimensional solid mesh for the metal bearing body, while the elastic support on the back of the bearing is represented as an array of springs acting on the corresponding nodes, based on its actual support position and distribution. This spring array can be arranged according to the physical partitions of the support (for example, four spring clusters are set at the positions corresponding to four independent support units).

[0010] Step 2: Determine the equivalent spring stiffness

[0011] The stiffness coefficient of each equivalent spring is calculated based on the material elastic modulus, geometric thickness and the bearing area it represents of the elastic support, to ensure that the macroscopic mechanical behavior of the spring array (mainly axial compression and slight tilt) matches the characteristics of the real support.

[0012] Step 3: Extract the overall system compliance matrix

[0013] In the aforementioned "bearing-spring" coupled finite element model, the free ends of the spring array are set as fixed constraints to simulate actual support conditions, and a unit normal load is applied to the working surface of the bearing. Then, the overall system stiffness matrix K is exported using the matrix export function provided by the finite element software or a dedicated plugin, and the overall system flexibility matrix C is obtained by inverting K using an external program (C=K). -1 ).

[0014] Step 4: Process the compliance matrix and apply it to lubrication analysis

[0015] Based on the node number, the submatrix corresponding to the bearing working surface, namely the working surface compliance matrix Cs, is extracted from the overall system compliance matrix C. Cs is then substituted into the elastohydrodynamic lubrication control equation to quickly calculate the elastic deformation of the bearing working surface under arbitrary oil film pressure distribution, thereby enabling accurate lubrication performance analysis.

[0016] Furthermore, in step one above, the specific implementation of equating the elastic support on the back of the bearing bush to a spring array acting on the corresponding node on the back of the bearing bush is as follows: based on the actual physical partitions of the elastic support, each partition is equating to a spring cluster, and the spring array is composed of multiple spring clusters.

[0017] Furthermore, in this invention, the number of spring clusters is the same as the number of independent support units of the elastic support.

[0018] Furthermore, the specific method for calculating the stiffness coefficient of each spring in the spring array in step two above is as follows: using the formula... The calculation is performed, where k is the spring stiffness coefficient, in N / m; E is the elastic modulus of the elastic support, in Pa; and A is the bearing area of ​​the support represented by the spring, in m². 2 ; The thickness of the support is expressed in meters (m).

[0019] Furthermore, in step three above, the overall stiffness matrix K of the system is derived through finite element analysis using the matrix export function or a dedicated plugin provided by the finite element software.

[0020] Furthermore, in step three above, the steps of inverting K using an external program and extracting the working surface compliance matrix Cs were both completed using a self-written calculation program.

[0021] Furthermore, the present invention is specifically applicable to thrust sliding bearings subjected to axial loads.

[0022] The core of this invention lies in using a discrete spring array to equivalently replace the mechanical function of a solid elastic support.

[0023] Compared with the prior art, the present invention has the following advantages after adopting the above technical solutions: (1) Simplified modeling process: There is no need to perform three-dimensional solid meshing on the complex elastic support, which greatly reduces the preprocessing workload and model complexity. (2) Improved computational efficiency: Since the massive number of mesh nodes generated by the elastic support is avoided, the overall model degree of freedom is significantly reduced, which reduces the size of the system stiffness matrix, and its inversion operation to obtain the flexibility matrix is ​​faster and requires less computational resources. (3) Guarantee of thrust bearing accuracy: The method ensures the accuracy of deformation response in lubrication calculation by fixing the bottom of the spring array to accurately transmit the mechanical effect of the elastic support. This method is particularly suitable for thrust bearings with long dimensions and multi-support unit layout, and can guarantee computational accuracy under axial load.

[0024] This invention can be widely applied to the design optimization of large sliding bearings (such as thrust sliding bearings for wind turbine main shafts), simulation of elastic fluid lubrication coupling, and prediction of operating conditions. Attached Figure Description

[0025] Figure 1 This is a flowchart of an embodiment of the present invention; Figure 2 This is a schematic diagram of the bearing structure in an embodiment of the present invention; Figure 3 This is a schematic diagram of the finite element model of the "bearing bush-spring" in an embodiment of the present invention; Figure 4 This is a comparison of the elastic deformation results of the thrust bearing in the embodiments of the present invention. Detailed Implementation

[0026] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. These embodiments are based on the technical solutions of the present invention and provide detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments. Any process scheme that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art is within the scope of protection defined by the claims of the present invention. Example

[0027] Specific implementation examples Figures 1 to 4 As shown.

[0028] In this example, the thrust bearing of the wind turbine main shaft is a fan-shaped segmented bearing with a wrap angle of 60°, and its back is provided with 4 independent cylindrical resin-based flexible pads as a specific form of elastic support.

[0029] The implementation steps of this invention are as follows: S1. Constructing the finite element model of the spring-supported bearing bush.

[0030] Use general-purpose finite element software (such as Abaqus) to import or create a three-dimensional geometric model of the metal bearing body.

[0031] The bearing body is meshed into a three-dimensional solid mesh. The element type can be a tetrahedral element or other element suitable for contact and deformation analysis.

[0032] Key operation: Instead of solid modeling and meshing the four flexible bushings, discrete spring elements are created at the center of the contact area between the bearing shell and each bushing (or at multiple nodes distributed according to the actual support conditions). In this example, four spring clusters are created for the four bushings, and each spring cluster can contain one or more spring elements depending on the accuracy requirements.

[0033] One end of the spring unit is connected to the corresponding node on the back of the bearing bush, and the other end is set as a fixed constraint to simulate the case where the liner is installed on a rigid bearing housing.

[0034] S2. Determine the equivalent spring stiffness

[0035] The stiffness coefficient k of each equivalent spring, in N / m, is calculated using the following formula:

[0036] Where: E is the elastic modulus of the flexible padding material, in Pa; A is the bearing area of ​​the padding represented by the spring, in m². 2 ; The thickness of the padding is expressed in meters (m).

[0037] In this example, it is assumed that each pad has the same load-bearing area and is made of uniform material; therefore, the stiffness values ​​of the four spring clusters are the same. If the pad dimensions or materials differ, different stiffness values ​​can be calculated and assigned to them separately.

[0038] S3. Extract the overall system compliance matrix

[0039] In the aforementioned "bearing-spring" coupled finite element model, the free ends of the spring array are set as fixed constraints. Under this boundary condition, the load applied to the working surface of the bearing is transmitted to the spring array through the bearing body. The deformation of the spring directly determines the displacement response of the bearing node, thereby accurately simulating the mechanical behavior of the flexible bushing.

[0040] Apply a uniform unit normal pressure (e.g., 1 MPa) to the working surface of the bearing bush as the load condition.

[0041] Submit the assignment and perform finite element analysis. After the analysis is complete, use the matrix export function provided by the finite element software or a dedicated plugin to export the overall stiffness matrix K of the system as an external file.

[0042] Load the exported stiffness matrix file into a self-written external calculation program and perform the inversion operation. The overall system flexibility matrix C is obtained.

[0043] S4. Process the compliance matrix and apply it to lubrication analysis.

[0044] In the external calculation program, based on the preset node numbers of the bearing working surface, the overall system compliance matrix is ​​calculated. Extract the corresponding rows and columns to construct the bearing working surface compliance matrix specifically for lubrication calculations. .

[0045] The obtained working surface compliance matrix It is embedded as an input parameter into the elastohydrodynamic lubrication program.

[0046] In the EHL calculation iteration, for the oil film pressure distribution P (in Pa) obtained in each step, it is converted into an equivalent nodal force vector F (in N) based on its effective area, and then processed by matrix multiplication. The elastic deformation δ (in meters) of the working surface node of the bearing bush can be obtained quickly.

[0047] Deformation This is used to update the oil film thickness, which then participates in the next pressure iteration until the solution converges, ultimately obtaining accurate bearing lubrication performance parameters (such as pressure distribution, oil film thickness, friction power consumption, etc.).

[0048] To verify the superiority of this method, a thrust bearing with elastic support was modeled using both a traditional full solid model (simultaneously dividing the bearing shell and the bushing mesh) and the method of this invention, and the compliance matrix was extracted.

[0049] Model mesh count: The traditional model has 33,142 meshes, while the model of this invention has 18,860 meshes, a reduction of approximately 43%.

[0050] Matrix inversion time: The traditional method of stiffness matrix inversion takes about 4 hours on a high-end workstation (Intel Xeon Platinum8275CL CPU @ 3.00GHZ, 256 GB memory), while the method of this invention takes only about 30 minutes on a regular computer, improving computational efficiency by about 87.5%.

[0051] Accuracy Comparison: Under the same axial load (1 MPa uniform pressure), the bearing deformation calculated by the traditional method and the method of this invention are basically consistent, with a maximum deformation error of 3%. Figure 4 As shown, it meets the accuracy requirements of engineering design.

[0052] The above results demonstrate that the present invention achieves an order-of-magnitude improvement in modeling and computational efficiency while ensuring computational accuracy.

[0053] The above description of the embodiments of the present invention is descriptive and not limiting. Therefore, it should be noted that any modifications, substitutions, and improvements that do not depart from the spirit and scope of the present invention and the appended claims are within the scope of the present invention and should not be construed as exceeding the limitations of the above description and claims.

Claims

1. A method for rapid calculation of the compliance matrix for a thrust bearing with elastic support, characterized in that, Includes the following steps: Step 1: Construct the finite element model of the spring-supported bearing: Only the metal bearing body is meshed into a three-dimensional solid mesh, and the elastic support on the back of the bearing is equivalent to an array of springs acting on the corresponding nodes on the back of the bearing. Step 2, determine the equivalent spring stiffness: based on the material properties and geometric parameters of the elastic support, calculate the stiffness coefficient of each spring in the spring array; Step 3, extract the overall system compliance matrix: set the free ends of the spring array as fixed constraints on the finite element model; apply a unit normal pressure to the working surface of the bearing bush; derive the overall stiffness matrix K of the system through finite element analysis, and invert it using an external program to obtain the overall system compliance matrix C; Step 4: Process the compliance matrix and apply it to lubrication analysis: Extract the sub-matrix corresponding to the working surface of the thrust bearing from the overall compliance matrix C of the system according to the node number, that is, the working surface compliance matrix Cs; apply Cs to perform elastic fluid lubrication analysis of the thrust bearing.

2. The method for rapid calculation of the compliance matrix of a thrust bearing with elastic support according to claim 1, characterized in that... In step one, the specific implementation of equating the elastic support on the back of the bearing bush to a spring array acting on the corresponding node on the back of the bearing bush is as follows: based on the actual physical partitions of the elastic support, each partition is equating to a spring cluster, and the spring array is composed of multiple spring clusters.

3. The method for rapid calculation of the compliance matrix for a thrust bearing with elastic support according to claim 2, characterized in that... The number of spring clusters is the same as the number of independent support units of the elastic support.

4. The method for rapid calculation of the compliance matrix of a thrust bearing with elastic support according to claim 1, characterized in that... The specific method for calculating the stiffness coefficient of each spring in the spring array in step two is as follows: Using formula The calculation is performed, where k is the spring stiffness coefficient (N / m); E is the elastic modulus of the elastic support (Pa); and A is the bearing area of ​​the support represented by the spring (m²). 2 ; The thickness of the support is expressed in meters (m).

5. The method for rapid calculation of the compliance matrix of a thrust bearing with elastic support according to claim 1, characterized in that... In step three, the overall stiffness matrix K of the system is derived through finite element analysis using the matrix export function or a dedicated plugin provided by the finite element software.

6. The method for rapid calculation of the compliance matrix of a thrust bearing with elastic support according to claim 1, characterized in that... In step three, the steps of inverting K using an external program and extracting the working surface compliance matrix Cs were both completed using a self-written calculation program.

7. The method for rapid calculation of the compliance matrix of a thrust bearing with elastic support according to claim 1, characterized in that... This method is specifically applicable to thrust bearings subjected to axial loads.

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