JP2013077058A - Finite element method analysis method and strength analysis system of holder - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a finite element method analysis method and strength analysis system of a holder for automating a series of FEM(Finite Element Method) analysis processes by limiting a problem to centrifugal force/thermal expansion analysis.SOLUTION: The finite element method analysis method of a holder having a periodical symmetric structure includes the steps of: setting the minimum units configuring the periodical symmetric structure of the holder as an analysis model; and performing the element breakdown of the full analysis area of the analysis model by using a tetrahedral secondary element or hexahedral secondary element with a uniform size.

Description

  The present invention relates to a finite element method analysis method and a strength analysis system for a cage. In particular, the present invention targets a problem caused by centrifugal force or thermal expansion during rotation of a ball bearing cage, and performs a strength analysis based on a finite element method (FEM) and a finite element method analysis method and a strength analysis of the cage. About the system.

  When developing a cage, it is necessary to consider breaking under high-speed and high-temperature conditions and contact with other parts. Conventionally, these studies have been performed based on experiments. However, if a study by calculation is possible, the cost can be reduced and the strength can be estimated in a short time. In recent years, an environment in which FEM intensity analysis can be performed based on 3D CAD data is being prepared, and the application of calculation is also being considered in cage strength prediction. As a method for analyzing the strength of the cage by calculation, the finite element length used in the dynamic analysis model and the finite element length shorter than this finite element length are used to obtain the stress by FEM analysis. It has been proposed to output the ratio as a correction coefficient (see, for example, Patent Document 1).

JP 2008-1106040 A

  However, since the shape of the cage is complicated and the shape varies depending on the type of the cage, an analytical solution cannot be easily obtained. Further, even in the above-mentioned Patent Document 1 and the like, specific analysis assumptions and element division criteria are generally not clarified, and it is difficult to perform appropriate element division by general workers who do not have expertise in FEM. In addition, there is a problem that the analysis work is complicated and takes time.

  The present invention has been made in view of the above circumstances, and is limited to a centrifugal force / thermal expansion analysis that is a problem when the cage is adapted to high speed / high temperature, and a series of FEM analysis processes are automated. An object is to provide a finite element method analysis method and a strength analysis system.

The above object of the present invention can be achieved by the following constitution.
(1) A finite element analysis method for a cage having a periodically symmetric structure,
Setting a minimum unit constituting the periodic symmetric structure of the cage as an analysis model;
A finite element method analysis method for a cage, comprising a step of dividing an entire analysis region of the analysis model using a tetrahedral quadratic element or a hexahedral quadratic element of uniform size .
(2) designating an element division number of a line segment or a curve included in the shape data;
The method for analyzing the finite element method of a cage as described in (1) above, comprising the step of performing element division of the entire analysis region of the analysis model with an element size corresponding to the specified number of element divisions .
(3) designating the number of element divisions in the radial direction of the cage based on the radial dimension of the cage included in the shape data;
The method for analyzing the finite element method of a cage as described in (1) above, comprising the step of performing element division of the entire analysis region of the analysis model with an element size corresponding to the specified number of element divisions .
(4) The step of designating the number of element divisions of a line segment or curve included in the shape data includes:
A step of determining, by preliminary analysis, an influence curve that the number of line segments or curve element divisions included in the shape data has on an arbitrary finite element solution;
Obtaining a reference value of the number of element divisions that satisfies the approximation accuracy of a required solution based on the influence curve,
The cage finite element method analysis method according to (2), wherein the specified number of element divisions is equal to or greater than the reference value.
(5) The step of designating the number of element divisions in the radial direction of the cage based on the radial dimension of the cage included in the shape data,
A step of determining, by preliminary analysis, an influence curve that the number of element divisions in the radial direction in the shape data has on an arbitrary finite element solution;
Obtaining a reference value of the number of element divisions that satisfies the approximation accuracy of a required solution based on the influence curve,
The cage finite element method analysis method according to (3), wherein the specified number of element divisions is equal to or greater than the reference value.
(6) The finite element method analysis method for a cage as described in (4) or (5) above, wherein the approximate accuracy of the solution is determined by applying a maximum principal stress solution.
(7) A cage strength analysis system using the cage finite element method analysis method according to any one of (1) to (6) above,
An input unit for inputting shape data, physical property value data, and operating conditions of the cage, and an analysis execution command;
In response to the analysis execution command, the retainer is configured to automatically and continuously perform reading of the shape data and physical property value data, element division, setting of constraint conditions and boundary conditions, and matrix calculation. A control unit for analyzing the stress against centrifugal force and thermal expansion of
An intensity analysis system comprising: an output unit for outputting the analysis result.
(8) a physical property value library for storing physical property value data of the cage;
The strength analysis system according to (7), wherein the control unit reads physical property value data from the physical property value library in response to input or selection of a file name of the physical property value data included in the physical property value library. .
(9) A CAD shape file library of the cage is provided,
(7) or (8) above, wherein the control unit reads a shape file from the CAD shape file library in response to an input or selection of a file name of a shape file included in the CAD shape file library. Strength analysis system.

  According to the finite element method analysis method and strength analysis system for a cage according to the present invention, it is possible for a general worker to easily perform the strength prediction of the cage in a reproducible manner. As a result, the FEM intensity analysis enables the optimum design and problem investigation of the cage according to various conditions with the guarantee of the approximate accuracy of the solution.

1 is a schematic configuration diagram of a cage strength analysis system according to an embodiment of the present invention. It is a flowchart which shows the intensity | strength analysis process of this embodiment. It is a figure which shows an example of an input screen. It is a figure which shows the example of 1 input to the input screen of FIG. (A) is a figure which shows an example of the 3D CAD data of the crown type cage for ball bearings which can analyze intensity | strength by this embodiment, (b) is a figure which shows an example of the cyclic symmetry model which can be acquired from a shape file library And it is the V section enlarged view of (a). (A) is a figure which shows the element division | segmentation model of FIG.5 (b), (b) is the VI section enlarged view of (a). It is a figure which shows the influence which the number of element divisions has on the approximation accuracy and calculation time of a finite element solution. It is a figure which shows the stress distribution output example of an analysis result.

  Hereinafter, an embodiment of a cage finite element method analysis method and a strength analysis system according to the present invention will be described in detail with reference to the drawings.

  The cage finite element method analysis method and strength analysis system according to this embodiment analyze stress distribution and displacement distribution due to centrifugal force and thermal expansion during rotation for a series of ball bearing cages from small to large. Is to do.

  As shown in FIG. 1, in the retainer strength analysis system 10 according to the present embodiment, a CPU 12 that functions as a control unit includes a keyboard 11 that functions as an input unit, a display 19 that functions as an output unit, and storage. The hard disk 14 functioning as a unit and the memory 13 are connected. The hard disk 14 stores an operating system (OS) 15, an intensity analysis program 16, and a database 17. The database 17 stores a physical property value library 21 and a shape file library 22.

  Hereinafter, the processing operation of the intensity analysis program 16 will be described with reference to FIG. The strength analysis program 16 of the present invention performs the processing in cooperation with the operating system 15. However, part or all of the processing may be performed by the intensity analysis program 16 alone.

  First, the CPU 12 displays an input screen 29 for prompting input of analysis conditions on the display 19 (step S1). FIG. 3 is a diagram illustrating an example of the input screen 29 displayed on the display 19. As shown in FIG. 3, the input screen 29 displays a cage rotation speed input box 31, a temperature input box 32, and an ambient temperature input box 33 for inputting operating conditions. The input screen 29 also includes a cage material name input box 34 for inputting physical property values, a material name selection button 34S for selecting a material name from the physical property value library 21, and an elastic modulus input box 35. A Poisson's ratio input box 36, a density input box 37, and a linear expansion coefficient input box 38 are displayed. The input screen 29 includes a 3D CAD file name designation box 39 for inputting a file name of shape data, a file name selection button 39S for selecting a file name from the shape file library 22, and a thickness of the cage. A thickness input box 41 and an analysis execution button 42 are displayed.

  On such an input screen 29, the operator inputs or selects operating conditions, physical property values, and shape data. The physical property values are input to the cage material name input box 34, the elastic modulus input box 35, the Poisson's ratio input box 36, the density input box 37, and the linear expansion coefficient input box 38. The operator inputs the material name and each physical property value. This can be done manually. Each physical property value can be automatically input by selecting a material name from the list of the physical property value library 21 displayed when the operator presses the material name selection button 34S. The automatically entered physical property values can be manually edited. The shape data can be input by selecting the 3D CAD file, and the operator can select a file name from the list of the shape file library 22 displayed by pressing the file name selection button 39S. . It is also possible for the operator to manually enter a file name in the 3D CAD file name designation box 39.

FIG. 4 shows an input example to the input screen 29 displayed on the display 19. In this example, a SUJ2 material (high carbon chromium bearing steel) ball bearing crown-shaped cage is operated at a cage rotation speed of 10000 min ⁻¹ and a cage estimated temperature of 100 ° C. Other conditions are also entered. Then, the CPU 12 determines whether there is all input data, whether the data formats match, and whether there is an analysis execution command (step S2).

  If it is determined in step S2 that all input data is present or the data format is the same and there is an analysis execution command, the CPU 12 determines that the specified 3D CAD file name “CAGE1. ***” The corresponding 3D shape data is acquired from the shape file library 22 (step S3), and the physical property value data is acquired from the physical property value library 21 (step S4).

  Each 3D shape data in FIG. 5B stored in the shape file library 22 corresponds to the file name “CAGE1. ***”, and the existing shape of the crown bearing cage 100 for the ball bearing in FIG. 5A. It is created in advance based on the 3D CAD data. The ball bearing crown-shaped cage 100 includes an outer diameter surface 106, an inner diameter surface 108, a plurality of grooves 103 that are arranged at substantially equal intervals in the circumferential direction and hold a ball (not shown) in a freely rolling manner, A pair of claw portions 107 are provided at both ends in the circumferential direction 103.

  In general, a cage for a ball bearing has a periodically symmetrical structure in which 1 / (number of rolling elements × 2) of the entire cage is a minimum unit, and the whole is formed by repeating this unit shape. The crown-shaped cage 100 also has a period in which the claw portions 107 and 107 adjacent to each other in the circumferential direction have a single unit shape (period symmetric model) from the circumferential middle portion to the groove bottom portion 105 (V portion in FIG. 5A). It has a symmetrical structure. And, when operating at high speed rotation and high temperature without contact, due to centrifugal force and thermal expansion, a deformed state having the same periodic symmetry is obtained. In the present embodiment, a periodically symmetric model 200 as shown in FIG. 5B extracted from the 3D CAD data in FIG. 5A is stored in advance in the shape file library 22 as 3D shape data for FEM analysis. Yes. By using such a periodic symmetry model 200, the number of nodes required for the FEM analysis is reduced, and the calculation time can be greatly shortened. When creating a shape model for FEM analysis, the detailed shape may be simplified as necessary.

  Next, the CPU 12 acquires various physical property value data from the physical property value library 21 based on the material name selected by the operator from the physical property value library 21 displayed by pressing the material name selection button 34S. In addition, CPU12 can also acquire material name and each physical-property value data based on the sliding input data by an operator (step S4). Next, the CPU 12 reads various analysis conditions input on the input screen 29. Then, the CPU 12 performs element division based on the cyclically symmetric 3D shape acquired in step S3 (step S5). The element division performed in step S5 is a process in which know-how of finite element method analysis is required and standardization and automation of analysis work is difficult.

  In the present invention, by limiting the subject to the centrifugal force / thermal expansion problem of the ball bearing cage, it is possible to formulate the element division condition and to automate the element division work. The element division model 300 shown in FIG. 6A reduces the target FEM analysis area to the cyclic symmetry model of FIG. 5B, and divides the entire analysis area with uniform element division accuracy. As the type, a tetrahedral secondary element is used. The condition relating to the accuracy of element division is that the number of radial divisions of the radial edge 102 of the groove bottom 105 is set to the reference value N. The reference value N regarding the accuracy of the element division is a value determined in advance by verifying the accuracy of the solution for the entire ball bearing retainer to be analyzed.

  FIG. 7 is a diagram showing the influence of the number of divisions of the radial edge 102 of the groove bottom 105 on the approximation accuracy and calculation time of the maximum principal stress solution. In the figure, the solid line indicates the influence of the number of divisions of the radial edge 102 on the numerical error (influence curve), and the alternate long and short dash line indicates the calculation time. The reference value N is a minimum value of the number of divisions for the numerical error of the maximum principal stress solution to be equal to or less than a specified allowable value, and is an application reference value for the number of radial divisions in the groove bottom cross section 101. In determining the approximate accuracy of the solution, a relative error with respect to the maximum principal stress solution in the detailed division model is applied.

  More specifically, as shown in FIG. 7, the reference value N is based on the relationship between the number of radial edge divisions obtained by the verification analysis, the approximation accuracy of the maximum principal stress solution, and the allowable value of the numerical error. The required minimum number of divisions. The required accuracy of the solution can be determined according to quantitative prediction, qualitative prediction, trend grasp, etc., and depending on the required accuracy and calculation time of the solution, the radial edge 102 A reference value N for the number of divisions is determined. It has been confirmed that the relationship between the number of radial edge divisions and the approximate accuracy of the solution shown in FIG. 7 can be obtained almost in the same manner for various ball bearing cages ranging from small to large. .

  When dividing the element, it is also effective to use the radial thickness t of the cage input to the input screen 29 in addition to the above-described conditions based on the radial edge 102 of the groove bottom 105. The radial thickness t of the cage shown in FIG. 6B is slightly shorter than the curved length of the radial edge 102 of the groove bottom 105, but the difference between the two is large in a normal cage. By using the radial thickness of the cage, (input value of the radial thickness of the cage / reference value N) is automatically calculated at the time of element division, and automatically as the size of one side of the element Entered. Thereby, especially when the length of the curved radial edge 102 is unclear, the convenience of the finite element method analysis method and the strength analysis system can be further improved.

  The CPU 12 determines whether or not the element division has been executed correctly, that is, whether or not the element division has been executed so that the radial division number becomes the reference value N (step S6). When it is determined that the element division is correctly performed, the CPU 12 automatically sets the constraint condition and the boundary condition (step S7). In the case of centrifugal thermal expansion analysis assuming cyclic symmetry, since these are well-known setting methods, details are omitted. Next, the CPU 12 automatically performs matrix calculation (step S8). In addition, the analysis standard in each process including element division is determined in advance based on verification analysis of a series of ball bearing cages from small to large.

  The outline and effects of the finite element method analysis method and strength analysis system for a cage according to the present invention are as follows.

Performing FEM analysis requires specialized knowledge to appropriately determine the size and distribution of elements, aspect ratio, element type, etc., and it may be difficult for general workers to perform FEM analysis. . In addition, when the number of element divisions is too large, the calculation time becomes enormous, and thus there is a problem that the practical use becomes difficult. In addition, when element division is performed using primary elements that are generally used in commercially available FEM software, if the bending deformation is large, such as the centrifugal force / thermal expansion deformation of the crown cage, the calculation time There is a problem that the solution is difficult to stabilize as the value increases. As this factor, there is the locking of the primary element which is a problem in the FEM structural analysis. (Reference: Kenjiro Terada “Common sense of finite element method (Solid / Structure)”) 3.2.2 Elemental expression in deformation problems, [Online] (Internet <URL: http: //www.jsce. or.jp/committee/amc/compmech/pdftext/terada.pdf>)
Therefore, in the present invention, the object is limited to the centrifugal force / thermal expansion analysis of the cage, and the conditions regarding the element division are defined as follows.
Model shape: Periodically symmetric structure [1 / (number of rolling elements × 2)]
Element division: Dividing the entire analysis area with a uniform size Applied element: Secondary element In addition, an influence curve indicating the influence of the number of radial divisions on the approximation accuracy of the FEM solution (finite element solution) ( Based on the accuracy of the required solution based on FIG. 7), the number of radial divisions is determined as a reference value N, and element division is performed by the strength analysis system. The parameter used for determining the accuracy of the FEM solution includes a maximum principal stress solution.

  By using such a finite element method analysis method and strength analysis system for the strength prediction of the cage, the element division work process that requires FEM expertise and know-how is omitted, and careless mistakes can be avoided even by general workers. Without fear, the FEM intensity analysis result can be obtained in a short time. Further, by performing element division using elements of a uniform size, an increase in the approximation error of the solution due to distortion of the element shape, which is likely to occur when a general worker performs fine element division locally, is prevented. Further, it has been analytically verified that the stability of the maximum principal stress solution, the approximation accuracy, and the calculation time are greatly improved by performing the division by the secondary element. According to the performance of CAD CPUs that are generally used at present, the FEM can be reached within 1 to 2 minutes for normal ball bearing crown resin cages and within 5 minutes for special ball bearing cages. The analysis can be terminated.

  Furthermore, there is no difference in solution among workers due to differences in element division, and any worker can obtain the same FEM strength analysis result, so it can be used as a general cage design tool. can do. For example, it can be used as a cage strength analysis system for long-term projects, or as a FEM analysis tool shared within the group in the short term. Can be tied.

  After the calculation is completed, various strength studies can be performed using the post-processor function. For example, the CPU 12 outputs and displays stress distribution, displacement distribution, and the like on the display 19 using the post-processor function (step S9). FIG. 8 is an example of an analysis result displayed on the display 19 and is a diagram showing a stress distribution model 400. In the figure, the stress distribution indicated by shading means that the darker the portion, the greater the stress, and the thinner the portion, the smaller the stress. The stress increases near the intersection of the groove bottom 105 and the inner diameter surface 108. I understand that. Further, the CPU 12 extracts the maximum principal stress and the maximum displacement, and outputs and displays them on the display 19 (step S10). In addition, the CPU 12 can output and display analysis results such as strain distribution, Mises stress, radial maximum displacement, principal strain, and the like on the display 19.

  As described above, according to the finite element method analysis method and the strength analysis system of the present invention, it is possible for a general worker to easily predict the strength of the cage in a reproducible manner. As a result, it is possible to perform optimum design and problem investigation of the cage according to various conditions under the guarantee of solution approximation by FEM intensity analysis.

  In addition, this invention is not limited to embodiment mentioned above, A change, improvement, etc. are possible suitably. For example, in the embodiment described above, the analysis is performed for the ball bearing crown-shaped cage 100, but the present invention is not limited to this. Applying the present invention to centrifugal force thermal expansion analysis for ball bearing cages in general and roller bearing cages in general, and analysis that separately considers the influence of contact force between rolling elements and cages, It is also possible to estimate deformation and stress increase. Further, instead of the tetrahedral secondary element, the division may be performed by the hexahedral secondary element. Further, the number of element divisions may be a value equal to or greater than the reference value N.

  In the present embodiment, the analysis result or the like is displayed on the display 19 provided as a display unit, but other output formats such as paper output by a printer or the like may be used. In this embodiment, the strength analysis program 16 and the database 17 are realized by a single device. However, these are stored in a server or the like, and each terminal device accesses the server, whereby the strength analysis of the present invention is performed. A system may be realized.

10 Strength analysis system 11 Keyboard 12 CPU
14 Hard disk 16 Strength analysis program 17 Database 19 Display 21 Property value library 22 Shape file library

Claims (9)

A finite element method analysis method for a cage having a periodically symmetric structure,
Setting a minimum unit constituting the periodic symmetric structure of the cage as an analysis model;
A finite element method analysis method for a cage, comprising a step of dividing an entire analysis region of the analysis model using a tetrahedral quadratic element or a hexahedral quadratic element of uniform size . Designating the number of element divisions of a line segment or a curve included in the shape data;
2. The finite element method analysis method for a cage according to claim 1, further comprising a step of performing element division of the entire analysis region of the analysis model with an element size corresponding to the specified number of element divisions. Designating the number of element divisions in the radial direction of the cage based on the radial dimension of the cage included in the shape data;
2. The finite element method analysis method for a cage according to claim 1, further comprising a step of performing element division of the entire analysis region of the analysis model with an element size corresponding to the specified number of element divisions. Specifying the number of line segments or curve elements included in the shape data,
A step of determining, by preliminary analysis, an influence curve that the number of line segments or curve element divisions included in the shape data has on an arbitrary finite element solution;
Obtaining a reference value of the number of element divisions that satisfies the approximation accuracy of a required solution based on the influence curve,
3. The finite element method analysis method for a cage according to claim 2, wherein the specified number of element divisions is a necessary condition that the specified number of element divisions is not less than the reference value. Designating the number of element divisions in the radial direction of the cage based on the radial dimension of the cage included in the shape data,
A step of determining, by preliminary analysis, an influence curve that the number of element divisions in the radial direction in the shape data has on an arbitrary finite element solution;
Obtaining a reference value of the number of element divisions that satisfies the approximation accuracy of a required solution based on the influence curve,
The finite element method analysis method for a cage according to claim 3, wherein the specified number of element divisions is a necessary condition that the specified number of element divisions is equal to or greater than the reference value.   6. The finite element method analysis method for a cage according to claim 4 or 5, wherein the approximate accuracy of the solution is determined by applying a maximum principal stress solution. A cage strength analysis system using the cage finite element method analysis method according to any one of claims 1 to 6,
An input unit for inputting shape data, physical property value data, and operating conditions of the cage, and an analysis execution command;
In response to the analysis execution command, the retainer is configured to automatically and continuously perform reading of the shape data and physical property value data, element division, setting of constraint conditions and boundary conditions, and matrix calculation. A control unit for analyzing the stress against centrifugal force and thermal expansion of
An intensity analysis system comprising: an output unit for outputting the analysis result. A physical property value library for storing physical property data of the cage;
8. The intensity analysis system according to claim 7, wherein the control unit reads physical property value data from the physical property value library in response to an input or selection of a file name of physical property value data included in the physical property value library. A CAD shape file library of the cage;
9. The intensity analysis according to claim 7, wherein the control unit reads a shape file from the CAD shape file library in response to an input or selection of a file name of a shape file included in the CAD shape file library. system.

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