Determination method, program and calculation device

Abstract

To suppress a workload involved in determination while reducing an error in a determination method for characteristics of a rotary machine including a rolling bearing.SOLUTION: A determination method for characteristics of a rotary machine includes steps of: calculating a first spring constant between a rolling element and a first bearing ring; calculating a second spring constant between the rolling element and a second bearing ring; calculating a third spring constant of a first finite element model; calculating a fourth spring constant of a second finite element model; calculating a spring constant of a third finite element model on the basis of the first spring constant to fourth spring constant; and determining the characteristics of a rotary machine by using the calculated spring constant of the third finite element model.SELECTED DRAWING: Figure 8

Description

[Technical field]

[0001] The present disclosure relates to a determination method, a program, and a computing device. [Background technology]

[0002] Patent Document 1 (JP 2019-45472 A) discloses a device that monitors the state of a rotating machine and detects abnormalities. Anomalies that occur in rotating machines include abnormalities caused by sound vibrations. There are cases where the occurrence of abnormalities caused by sound vibrations is suppressed by using the natural frequency of an object that is the target of abnormality judgment.

[0003] A rotating machine can be modeled using the finite element method (FEM) at the design stage. By performing eigenvalue analysis on a finite element model that mimics a rotating machine, the natural frequency of the actual rotating machine can be predicted at the design stage. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2019-45472 A Summary of the Invention [Problem to be solved by the invention]

[0005] As a method for creating a finite element model of a rolling bearing, there is a method for creating a simplified finite element model by approximating the rolling element to a single spring element. However, the spring constant of the simplified finite element model obtained by approximation may have an error between the spring constant of the actual rolling element. If an error occurs in the spring constant of the rolling element, an error will also occur in the spring constant of the entire rotating machine, and an error may also occur in the natural frequency of the entire rotating machine obtained by eigenvalue analysis. The spring constant of the entire rotating machine can be used to determine characteristics of the rotating machine other than the natural frequency. For example, the stiffness, stress, and displacement of the rotating machine are also calculated based on the spring constant of the rotating machine.

[0006] If a finite element model of the rolling element is created as an accurate model divided into a fine mesh, it is possible to create a model that expresses the spring constant of the actual rolling element; however, the workload of creating an accurate model of the rolling element that repeatedly makes nonlinear contact with the outer and inner rings is large, and the calculation load is also large.

[0007] The present disclosure has been made to solve such problems, and its purpose is to reduce errors that occur in the characteristics of a rotating machine determined based on a spring constant in a method for determining the characteristics of a rotating machine including a rolling bearing using the finite element method, while also reducing the workload involved in determining the characteristics of the rotating machine. [Means for solving the problem]

[0008] The determination method disclosed herein is a determination method for determining characteristics of a rotating machine having a bearing by using a finite element model. In the determination method, the bearing includes a rolling element, a first raceway, and a second raceway. The first raceway is modeled as a first finite element model. The second raceway is modeled as a second finite element model. The rolling element is modeled as a third finite element model. The third finite element model is a one-dimensional elastic finite element model that connects a first point included in a first contact area that is an area on a first raceway surface of the first raceway and contacts the rolling element, and a second point included in a second contact area that is an area on a second raceway surface of the second raceway and contacts the rolling element. A first rigid element having a linear shape passing through the first point is arranged on the first contact area in the first finite element model. A second rigid element having a linear shape passing through the second point is arranged on the second contact area in the second finite element model. The determination method includes the steps of calculating a first spring constant between the rolling element and the first raceway using Hertz theory, calculating a second spring constant between the rolling element and the second raceway using Hertz theory, calculating a third spring constant of the first finite element model in a first contact area where the first rigid element is arranged, calculating a fourth spring constant of the second finite element model in a second contact area where the second rigid element is arranged, calculating a spring constant of the third finite element model based on the first spring constant, the second spring constant, the third spring constant and the fourth spring constant, and determining at least one of the stiffness, stress, displacement and natural frequency of the rotating machine using the calculated spring constant of the third finite element model.

[0009] The program in the present disclosure is a program for causing a computer to execute a determination of characteristics of a rotating machine having a bearing using a finite element model. The bearing includes a rolling element, a first raceway, and a second raceway. The first raceway is modeled as a first finite element model. The second raceway is modeled as a second finite element model. The rolling element is modeled as a third finite element model. The third finite element model is a one-dimensional elastic finite element model that connects a first point included in a first contact area that is an area on a first raceway surface of the first raceway and contacts the rolling element, and a second point included in a second contact area that is an area on a second raceway surface of the second raceway and contacts the rolling element. A first rigid element having a linear shape passing through the first point is arranged on the first contact area in the first finite element model. A second rigid element having a linear shape passing through the second point is arranged on the second contact area in the second finite element model. The program causes the computer to execute the steps of: calculating a first spring constant between the rolling element and the first raceway using Hertz theory; calculating a second spring constant between the rolling element and the second raceway using Hertz theory; calculating a third spring constant of the first finite element model in a first contact area where the first rigid element is arranged; calculating a fourth spring constant of the second finite element model in a second contact area where the second rigid element is arranged; calculating a spring constant of the third finite element model based on the first spring constant, the second spring constant, the third spring constant and the fourth spring constant; calculating a spring constant of the bearing using the calculated spring constant of the third finite element model; and determining at least one of the stiffness, stress, displacement and natural frequency of the rotating machine using the calculated spring constant of the bearing.

[0010] The computing device in the present disclosure is a computing device that determines the characteristics of a rotating machine having a bearing by using a finite element model. The computing device includes a computing circuit and a storage device. The bearing includes a rolling element, a first raceway, and a second raceway. The storage device stores a first finite element model that models the first raceway, a second finite element model that models the second raceway, and a third finite element model that models the rolling element. The third finite element model is a one-dimensional elastic finite element model that connects a first point included in a first contact area that is an area on a first raceway surface of the first raceway and contacts the rolling element, and a second point included in a second contact area that is an area on a second raceway surface of the second raceway and contacts the rolling element. The storage device further stores a first rigid element that is arranged on the first contact area in the first finite element model and has a linear shape that passes through the first point, and a second rigid element that is arranged on the second contact area in the second finite element model and has a linear shape that passes through the second point. The calculation circuit calculates a first spring constant between the rolling element and the first raceway using Hertz theory, calculates a second spring constant between the rolling element and the second raceway using Hertz theory, calculates a third spring constant of the first finite element model in a first contact area where the first rigid element is arranged, calculates a fourth spring constant of the second finite element model in a second contact area where the second rigid element is arranged, calculates a spring constant of the third finite element model based on the first spring constant, the second spring constant, the third spring constant and the fourth spring constant, and determines at least one of the stiffness, stress, displacement and natural frequency of the rotating machine using the calculated spring constant of the third finite element model. Effect of the Invention

[0011] According to the determination method of the present disclosure, by performing a simple modeling of the rolling bearing taking into account the errors generated by the finite element method, it is possible to create a model in which the errors in the spring constant are reduced while reducing the workload.Therefore, it is possible to reduce the errors that occur in the characteristics of the rotating machine determined based on the spring constant while also reducing the workload involved in determining the characteristics of the rotating machine. [Brief description of the drawings]

[0012] [Figure 1]1 is a cross-sectional view of a rotary machine according to an embodiment of the present invention. [Diagram 2] FIG. 2 is a diagram for explaining modeling of a rolling bearing in the present embodiment. [Diagram 3] FIG. 4 is a diagram for explaining a contact region between an inner ring and a rolling element in a finite element model. [Figure 4] FIG. 2 is a diagram for explaining a contact region between an outer ring and a rolling element in a finite element model. [Diagram 5] 11 is a diagram for explaining a method for determining a spring constant of a model. FIG. [Figure 6] FIG. 13 is a diagram for explaining calculation of a spring constant on the surface of a model simulating an inner ring. [Figure 7] 13A and 13B are diagrams for explaining calculation of a spring constant on the surface of a model simulating an outer ring. [Figure 8] 5 is a flowchart showing a processing procedure for determining a spring constant of a rolling element model in the present embodiment. [Figure 9] FIG. 4 is a cross-sectional view of a rolling bearing according to a first modified example. [Figure 10] FIG. 13 is a diagram for explaining calculation of a spring constant on a surface of a model simulating an inner ring in Modification 1. [Figure 11] 13 is a diagram for explaining calculation of a spring constant on the surface of a model simulating an outer ring in Modification 1. FIG. [Figure 12] FIG. 11 is a cross-sectional view of a rolling bearing according to Modification 2. [Figure 13] FIG. 11 is a cross-sectional view of a rolling bearing according to a third modified example. [Figure 14] FIG. 13 is a cross-sectional view of a rolling bearing according to a fourth modified example. [Figure 15] 13 is a diagram showing a model of an inner race and a model of an outer race of Modification 4. FIG. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0013] Hereinafter, the present embodiment will be described in detail with reference to the drawings. In the drawings, the same or corresponding parts are designated by the same reference characters and their description will not be repeated.

[0014] [Embodiment Mode] Hereinafter, embodiments of the present disclosure will be described with reference to the drawings. In the following drawings, the same or corresponding parts are designated by the same reference numerals, and the description thereof will not be repeated.

[0015] <Configuration of Rotating Machine 100> The configuration of a rotating machine 100 that is the subject of a determination method according to the present embodiment will be described with reference to Fig. 1. Fig. 1 is a cross-sectional view of the rotating machine 100 according to the present embodiment. Although Fig. 1 illustrates a pump as the rotating machine 100, the rotating machine 100 may be other machines such as industrial equipment, robots, and home appliances.

[0016] As shown in FIG. 1, a rotating machine 100 has a rolling bearing 10. The rolling bearing 10 in FIG. 1 is a radial ball bearing. A shaft 5 is rotatably supported by the rolling bearing 10. Hereinafter, a rotation axis direction Ax1 of the shaft 5 is referred to as a "Y-axis direction". A direction perpendicular to the Y-axis direction is referred to as a "Z-axis direction". A direction perpendicular to the Z-axis direction and the Y-axis direction is referred to as an "X-axis direction". The rotating machine 100 in FIG. 1 is placed on an XY plane.

[0017] In this embodiment, the characteristics of the rotating machine 100 are determined using the arithmetic device 200. The characteristics of the rotating machine 100 include, for example, the rigidity, stress, displacement, and natural frequency of the rotating machine 100. The displacement of the rotating machine 100 means the displacement when a predetermined load is applied to the rotating machine 100. The rigidity and stress of the rotating machine 100 are calculated based on the Young's modulus. The arithmetic device 200 has an arithmetic circuit 201 and a storage device 202. The arithmetic circuit 201 is configured with, for example, a central processing unit (CPU), a field programmable gate array (FPGA), a graphics processing unit (GPU), or a multi processing unit (MPU).

[0018] The storage device 202 provides a storage area for temporarily storing program code, work memory, etc., when the arithmetic circuit 201 executes an arbitrary program. The storage device 202 is composed of a volatile memory such as a dynamic random access memory (DRAM) or a static random access memory (SRAM), a read only memory (ROM) or a flash memory, and a non-volatile memory such as a hard disk drive (HDD) or a solid state disk (SSD).

[0019] 1 illustrates an example of determining the natural vibration value for the vibration mode in the XY directions of the rotating machine 100. The vibration mode in the XY directions is a vibration mode in which the amount of elastic deformation of the shaft 5 is smaller than that in the vibration modes in other directions.

[0020] The rotating machine 100 is modeled using the finite element method (FEM). The finite element method is a simulation in which an object is divided into a finite number of meshes and a numerical analysis is performed. The arithmetic device 200 executes a program that provides a simulation using the finite element method.

[0021] Hereinafter, a model created by the finite element method may be referred to as a "finite element model." Increasing the number of meshes constituting the finite element model allows creation of a more detailed model that is closer to the actual object, but the amount of work required to create the model increases, and the calculation time also increases. In this embodiment, an example will be described in which a simple model is created for the rolling element 15 of the rolling bearing 10 included in the rotating machine 100, without creating a detailed model.

[0022] In this embodiment, an eigenvalue analysis is performed on the finite element model of the rotating machine 100. The eigenvalue analysis is an analytical method for determining the natural frequency of an actual object based on the spring constant and mass. By setting the spring constant and mass of the rotating machine 100, the eigenvalue analysis is performed in a program that provides a simulation using the finite element method. Since the rotating machine 100 includes the rolling bearing 10, it is necessary to set the spring constant and mass of the finite element model of the rolling bearing 10.

[0023] <Modeling in the finite element method> FIG. 2 is a diagram for explaining modeling of the rolling bearing 10 in this embodiment. FIG. 2(A) shows an actual rolling bearing 10 that is not modeled. The rolling bearing 10 includes an outer ring 12, an inner ring 11, and a rolling element 15. The rolling element 15 is any one of a plurality of rolling elements included in the rolling bearing 10. Although FIG. 1 shows an example in which the rolling bearing 10 has a total of eight rolling elements, in some aspects the rolling bearing 10 may have other numbers of rolling elements, such as 16, 24, or 32. The inner ring 11 is an example of a "first raceway" in this disclosure. The outer ring 12 is an example of a "second raceway" in this disclosure.

[0024] FIG. 2(B) shows a model 10M that imitates the rolling bearing 10. The model 10M is a model created using a finite element model. The outer ring 12 is modeled as a model 12M. The inner ring 11 is modeled as a model 11M. The model 11M is an example of a "first finite element model" in the present disclosure. The model 12M is an example of a "second finite element model" in the present disclosure.

[0025] In the first embodiment, the rolling element 15 is modeled as a model 15M. The model 15M is a model that imitates a single spring that has no mass. The model 15M is an element that is made of a linear elastic body that has no volume and is called a bush element or a beam element.

[0026] That is, in this embodiment, the rolling element 15 is simply modeled by a finite element model of a one-dimensional elastic body. As a result, in this embodiment, it is not necessary to precisely model the rolling element 15 as a sphere, and the workload required for modeling can be reduced. Note that model 15M is an example of a "third finite element model" in this disclosure.

[0027] In the simulation, the models 11M, 12M, and 15M are all set as elastic bodies, so that when the models 11M, 12M, and 15M come into contact with other models, such as shafts, the models 11M, 12M, and 15M do not restrict the movements of the other models in the simulation.

[0028] 2, when rolling element 15 is simply modeled as model 15M, it is necessary to set a spring constant for model 15M. The spring constant of rolling element 15 can be calculated from Hertz theory based on the outer diameter and mass of the actual rolling bearing 10. If the spring constant of rolling element 15 calculated from Hertz theory is set as the spring constant of model 15M and an eigenvalue analysis of the rotating machine is performed, an error may occur in the natural frequency of rotating machine 100.

[0029] The inventors of the present disclosure have found that an error in the natural frequency of the rotating machine 100 that occurs when the spring constant of the rolling element 15 calculated by the Hertz theory is set as the spring constant of the model 15M is based on the spring constants generated on the outer ring surface and the inner ring surface in the finite element model. Below, a method for setting the spring constant of the model 15M in a simulation after removing the influence of the spring constants generated on the outer ring surface and the inner ring surface will be described.

[0030] FIG. 3 is a diagram for explaining the contact area Ar1 between the inner ring 11 and the rolling element 15 in the finite element model. FIG. 3(A) shows a perspective view of the model 10M. The model 11M in FIG. 3 shows the inner ring raceway surface Sf1 and the contact area Ar1. The inner ring raceway surface Sf1 is an area where the rolling element 15 can contact the inner ring 11. The contact area Ar1 indicates an area on the inner ring raceway surface Sf1 where the rolling element 15 contacts the inner ring 11 when the rotation of the rolling bearing 10 is fixed. As shown in FIG. 3, the contact area Ar1 has an elliptical shape with the minor radius direction along the X-axis direction.

[0031] 3 also shows an outer ring raceway surface Sf2 and a contact area Ar2, similar to model 11M. The outer ring raceway surface Sf2 is an area where the rolling elements 15 can come into contact with the outer ring 12. The contact area Ar2 indicates an area on the outer ring raceway surface Sf2 where the rolling elements 15 come into contact with the outer ring 12 when the rotation of the rolling bearing 10 is fixed. The contact area Ar2 has an elliptical shape with its minor radius along the X-axis direction.

[0032] FIG. 3B shows an enlarged view of the contact area Ar1 and the end of the model 15M on the negative side of the Z axis. The end of the model 15M is connected to a node P1 that is the center of the elliptical contact area Ar1. The node P1 is an example of a "first point" in the present disclosure. In this embodiment, three linear models RL1 to RL3 are arranged in the contact area Ar1. The models RL1 to RL3 are models called rigid links and are defined as rigid bodies. That is, the models RL1 to RL3 do not deform even when subjected to an external force in the simulation. Each of the models RL1 to RL3 passes through the node P1.

[0033] Fig. 4 is a diagram for explaining the contact area Ar2 between the outer ring 12 and the rolling element 15 in the finite element model. Fig. 4(A) shows a perspective view of the model 10M, similar to Fig. 3(A). Fig. 4 shows the outer ring raceway surface Sf2 and the contact area Ar2.

[0034] FIG. 4B shows an enlarged view of the contact area Ar2 and the end of the model 15M on the square side of the Z axis. The end of the model 15M is connected to the node P2 of the elliptical contact area Ar2. That is, the model 15M connects the node P1 and the node P2 in FIG. 3. The node P2 is an example of the "second point" in the present disclosure. In this embodiment, three models RL4 to RL6 called rigid links are arranged in the contact area Ar2. Each of the models RL4 to RL6 has a linear shape passing through the node P2 and is defined as a rigid body. The models RL4 to RL6 do not deform even when subjected to an external force in the simulation, similar to the models RL1 to RL3. The finite element models shown in FIGS. 3 and 4 are stored in the storage device 202.

[0035] <How to determine the spring constant of Model 15M> Fig. 5 is a diagram for explaining a method for determining the spring constant of model 15M. The left side of Fig. 5 shows a diagram for explaining an example of calculating the spring constant of an actual rolling element 15 by Hertz theory. Meanwhile, the right side of Fig. 5 shows a diagram showing an example of calculating the spring constant of model 15M in a simulation.

[0036] As described above, by using the Hertz theory, the actual spring constant of the rolling element 15 can be calculated. As shown in Fig. 5, the actual spring constant of the rolling element 15 is obtained as a combination of the spring constant Kh1 between the rolling element 15 and the inner ring 11 and the spring constant Kh2 between the rolling element 15 and the outer ring 12. Therefore, the spring constant of the rolling element 15 calculated by the Hertz theory is expressed by the following formula (1).

[0037]

number

[0038] In Hertz theory, rolling element 15 and the contact areas Ar1, Ar2 of inner ring 11 and outer ring 12 are treated as rigid bodies. Meanwhile, as described above, model 11M of inner ring 11 and model 12M of outer ring 12 are defined as elastic bodies in a simulation using the finite element method, and therefore each of inner ring raceway surface Sf1 of model 11M and outer ring raceway surface Sf2 of model 12M deforms due to contact with model 15M. That is, in the simulation, a spring constant Km1 is generated due to the deformation of inner ring raceway surface Sf1 of model 11M, and a spring constant Km2 is generated due to the deformation of outer ring raceway surface Sf2 of model 12M.

[0039] In the simulation, it is necessary to set the spring constant Kb of model 15M. However, the spring constant Kb of model 15M is a combination of the spring constants Km1 and Km2 of the inner ring raceway surface Sf1 and the outer ring raceway surface Sf2. In other words, as shown in Fig. 5, the combination of the spring constants of model 15 in the simulation of the finite element model is expressed by the following formula (1).

[0040]

number

[0041] Therefore, when applying the spring constant of the actual rolling element 15 calculated according to the Hertz theory to the spring constant Kb of the model 15M, it is necessary to remove the spring constants Km1 and Km2 from the spring constant of the actual rolling element 15 calculated according to the Hertz theory.

[0042] That is, as shown in FIG. 5, the spring constant Kb set in the simulation is expressed by the following formula (3).

[0043]

number

[0044] In this way, the value of the spring constant considering the inner ring raceway surface Sf1 and the outer ring raceway surface Sf2 generated in the simulation can be set as the spring constant Kb of the model 15M. As a result, in this embodiment, the rolling element 15 included in the rolling bearing 10 is modeled by approximating it to a single spring element, thereby reducing the workload required for modeling and suppressing errors caused by the spring constants Km1 and Km2. Therefore, while reducing errors in the natural frequency of the rotating machine 100 obtained by eigenvalue analysis, the workload required for determining the natural frequency of the rotating machine 100 can also be suppressed. The spring constant Kh1 is an example of the "first spring constant" in the present disclosure. The spring constant Kh2 is an example of the "second spring constant" in the present disclosure. The spring constant Km1 is an example of the "third spring constant" in the present disclosure. The spring constant Km2 is an example of the "fourth spring constant" in the present disclosure.

[0045] <How to calculate spring constants Km1 and Km2> Fig. 6 is a diagram for explaining calculation of the spring constant Km1 at the inner ring raceway surface Sf1 of a model 11M simulating the inner ring 11. Fig. 6 shows a diagram of the contact area Ar1 and the node P1 viewed from the positive side of the Z axis.

[0046] In this embodiment, the amount of deformation of the inner ring raceway surface Sf1 when a load is applied to the model 10M from the normal direction of the contact area Ar1 is calculated. The normal direction of the contact area Ar1 is the Z-axis direction. The calculation device 200 calculates the amount of deformation of the inner ring raceway surface Sf1 by comparing the contact area Ar1 with the reference area Rg1.

[0047] In the simulation, when a load is applied, the contact area Ar1 of the inner ring raceway surface Sf1 sinks toward the negative side of the Z axis. That is, the position of the contact area Ar1 in the Z axis direction differs from the position of the area around the contact area Ar1 on the inner ring raceway surface Sf1 in the Z axis direction. If the difference is large, the sinking of the load is large, so the rigidity of the model 11M is low, i.e., the spring constant Km1 is large. On the other hand, if the difference is small, the sinking of the load is small, so the rigidity of the model 11M is high, i.e., the spring constant Km1 is small.

[0048] Due to the sinking of the contact area Ar1, the surrounding area of ​​the contact area Ar1 also sinks. The closer the area of ​​the inner ring raceway surface Sf1 is to the contact area Ar1, the deeper it sinks because it is pulled by the contact area Ar1, and the greater the amount of deformation in the negative direction of the Z axis. On the other hand, the farther the area is from the contact area Ar1, the less affected by the sinking of the contact area Ar1, and the smaller the amount of deformation in the negative direction of the Z axis.

[0049] Therefore, when calculating the spring constant Km1, if the position of the reference area Rg1 to be compared with the contact area Ar1 is not appropriately determined, the calculated spring constant Km1 will be inappropriately small or large. Figure 6 explains the appropriate position of the reference area Rg1 determined by experiments.

[0050] As shown in FIG. 6, the reference area Rg1 is a shaded area surrounding the contact area Ar1. More specifically, the reference area Rg1 is an area outside the inner ellipse Ic1 on the inner ring raceway surface Sf1 and inside the outer ellipse Oc1. As described above, the contact area Ar1 has an elliptical shape centered on node P1. The major axis of the contact area Ar1 is distance L0. The minor axis of the contact area Ar1 is distance M0.

[0051] The inner ellipse Ic1, the outer ellipse Oc1, and the elliptical shape of the contact area Ar1 share the same node P1. In other words, the center points of the inner ellipse Ic1, the outer ellipse Oc1, and the elliptical shape of the contact area Ar1 overlap when viewed from the positive side of the Z axis. The semi-major axis of the inner ellipse Ic1 is distance L1. The inner radius of the inner ellipse Ic1 is distance M1. The semi-major axis of the outer ellipse Oc1 is distance L2. The inner radius of the outer ellipse Oc1 is distance M2.

[0052] Distance M1 is 4 times longer than distance M0. Distance M2 is 8 times longer than distance M0. Distance L1 is 1.5 times longer than distance L0. Distance L2 is 4 times longer than distance L0.

[0053] In this manner, in this embodiment, the spring constant Km1 is calculated based on the difference between the points in the contact area Ar1 and the points in the reference area Rg1 on the positive side of the Z axis, so that the spring constant Km1 does not become inappropriately large or small.

[0054] As described in Fig. 3, models RL1 to RL3, which are rigid links, are arranged in the contact area Ar1. Therefore, the load is applied uniformly to the contact area Ar1 of the inner ring raceway surface Sf1. In other words, the positions of all points in the contact area Ar1 of the inner ring raceway surface Sf1 are the same in the Z-axis direction.

[0055] The reference region Rg1 may be within the region indicated by diagonal lines in FIG. 6. That is, the outer ellipse Oc1 may be smaller than the ellipse shown in FIG. 6, and the inner ellipse Ic1 may be larger than the ellipse shown in FIG. 6. That is, if the distance M2 is longer than the distance M1 and the distance L2 is longer than the distance L1, the distance M1 may be longer than four times the distance M0, the distance M2 may be shorter than eight times the distance M0, the distance L1 may be longer than 1.5 times the distance L0, and the distance L2 may be shorter than four times the distance L0. The inner ellipse Ic1 is an example of the "first ellipse" in the present disclosure. The outer ellipse Oc1 is an example of the "second ellipse" in the present disclosure.

[0056] FIG. 7 is a diagram for explaining calculation of the spring constant Km2 in the outer ring raceway surface Sf2 of the model 12M simulating the outer ring 12. The spring constant Km2 is also calculated for the outer ring raceway surface Sf2, similar to the inner ring raceway surface Sf1. That is, a reference area Rg2 is also set for the model 12M, as shown in FIG. 7. The reference area Rg2 is the area indicated by the diagonal lines between the outer ellipse Oc2 and the inner ellipse Ic2. The relationship in size between the contact area Ar2 and the reference area Rg2 is the same as the relationship between the contact area Ar1 and the reference area Rg1.

[0057] As in FIG. 6, in FIG. 7, when the major axis of the contact area Ar2 is the distance L0 and the minor axis of the contact area Ar2 is the distance M0, the major axis of the inner ellipse Ic2 is the distance L1, the inner radius of the inner ellipse Ic2 is the distance M1, the major axis of the outer ellipse Oc2 is the distance L2, and the inner radius of the outer ellipse Oc2 is the distance M2. In this case, as in FIG. 6, the distance M1 in FIG. 7 is four times as long as the distance M0. The distance M2 is eight times as long as the distance M0. The distance L1 is 1.5 times as long as the distance L0. The distance L2 is four times as long as the distance L0. This prevents the spring constant Km2 from becoming unnecessarily large or small. The inner ellipse Ic2 is an example of the "third ellipse" in this disclosure. The outer ellipse Oc2 is an example of the "fourth ellipse" in this disclosure.

[0058] Similar to the reference region Rg1, the reference region Rg2 may be within the region indicated by diagonal lines in Fig. 7. That is, the outer ellipse Oc2 may be smaller than the ellipse shown in Fig. 7, and the inner ellipse Ic2 may be larger than the ellipse shown in Fig. 7. That is, if the distance M2 is longer than the distance M1 and the distance L2 is longer than the distance L1, the distance M1 may be longer than four times the length of the distance M0, the distance M2 may be shorter than eight times the length of the distance M0, the distance L1 may be longer than 1.5 times the length of the distance L0, and the distance L2 may be shorter than four times the length of the distance L0.

[0059] <Processing Procedure> Fig. 8 is a flowchart showing a process for determining the spring constant Kb of the model 15M of the rolling element 15 in this embodiment. The flowchart in Fig. 8 is stored as a program in the storage device 202. The arithmetic circuit 201 of the arithmetic device 200 executes the program.

[0060] The arithmetic circuit 201 calculates the spring constant Kh1 of the rolling element 15 in the contact area Ar1 by using the Hertz theory (step S11). Specifically, the arithmetic circuit 201 calculates the spring constant Kh1 of the rolling element 15 based on data indicating the outer diameter and mass of the rolling element 15 input by the designer. The arithmetic circuit 201 calculates the spring constant Kh2 of the rolling element 15 in the contact area Ar2 by using the Hertz theory (step S12).

[0061] The arithmetic circuit 201 calculates the spring constant Km1 of the model 11M in the contact area Ar1 (step S13). Specifically, the arithmetic circuit 201 applies a load to the model 10M in a simulation to obtain the amount of displacement described in FIG. 6. The amount of displacement described in FIG. 6 is the distance between a point in the reference area Rg1 in the Z-axis direction and a point in the contact area Ar1. The arithmetic circuit 201 calculates the spring constant Km1 based on the amount of displacement. The storage device 202 stores a database indicating the relationship between the magnitude of the load, the amount of displacement, and the spring constant Km1. The arithmetic circuit 201 calculates the spring constant Km2 of the model 12M in the contact area Ar2 (step S14).

[0062] The arithmetic circuit 201 calculates the spring constant Kb of the model 15M based on the spring constant Kh1 calculated in step S11, the spring constant Kh2 calculated in step S12, the spring constant Km1 calculated in step S13, and the spring constant Km2 calculated in step S14 (step S15). Specifically, the arithmetic circuit 201 derives Kb using the formula described in FIG.

[0063] The arithmetic circuit 201 calculates the natural frequency of the rotating machine 100 using the spring constant Kb calculated in step S15 (step S16). Specifically, the arithmetic device 200 calculates the spring constant of the entire rotating machine 100 from the spring constant of the entire rolling bearing 10 including the spring constant Kb and the spring constant of the components other than the rolling bearing 10 included in the rotating machine 100. The spring constants of the components other than the rolling bearing 10 included in the rotating machine 100 are input to the arithmetic device 200 by the designer. Similarly, the mass of the entire rotating machine 100 is input to the arithmetic device 200 by the designer. The arithmetic device 200 calculates the natural frequency of the rotating machine 100 from the spring constant and mass of the entire rotating machine 100 based on eigenvalue analysis.

[0064] In this manner, in the present embodiment, the spring constant Kb of the model 15M obtained by approximating the rolling element 15 is determined in consideration of the spring constants Km1 and Km2 resulting from the use of the finite element method. As a result, in the present embodiment, the rolling element 15 included in the rolling bearing 10 is modeled by approximating it to a single spring element, thereby reducing the workload required for modeling the rolling bearing 10 and reducing errors. That is, in the present embodiment, the workload required for determining the natural frequency of the rotating machine 100 can be suppressed while reducing errors in the determined natural frequency. The arithmetic device 200 may also obtain the Young's modulus from the spring constant of the entire rotating machine 100 to obtain the stiffness and stress of the entire rotating machine 100. Furthermore, the arithmetic device 200 may obtain the displacement amount of the rotating machine 100 when a predetermined load is applied to the rotating machine 100 based on the determined stiffness and stress of the entire rotating machine 100. As a result, in this embodiment, it is possible to reduce errors that occur in the characteristics of the rotating machine 100 that are determined based on the spring constant, while suppressing the workload involved in determining the characteristics of the rotating machine 100.

[0065] <Variation 1> In the present embodiment, an example has been described in which the rolling bearing 10 is a radial ball bearing. In Modification 1, a radial roller bearing will be applied.

[0066] 9 is a diagram showing a cross-sectional view of rolling bearing 10A in Modification 1. The configuration in Modification 1 is the same as the configuration in this embodiment, except that rolling bearing 10A is a radial roller bearing rather than a radial ball bearing. In Modification 1, the description of the configuration that overlaps with this embodiment will not be repeated.

[0067] 9 shows a rolling bearing 10A that is a radial roller bearing having a rotation axis Ax2. The rolling bearing 10A includes an outer ring 12A, an inner ring 11A, and a rolling element 15A. The inner ring 11A is an example of a "first raceway ring" in the present disclosure. The outer ring 12A is an example of a "second raceway ring" in the present disclosure. In the first modification, the calculation device 200 also determines the spring constant of a model that approximates the rolling element 15A, taking into account the spring constants Km1 and Km2.

[0068] Fig. 10 is a diagram for explaining calculation of the spring constant Km1 at the inner ring raceway surface Sf1 of model 11M simulating inner ring 11 in modified example 1. Fig. 10 shows the contact area Ar1 and node P1 as viewed from the positive side of the Z axis. In modified example 1, rolling bearing 10A is a radial roller bearing, so contact area Ar1 has a rectangular shape. Therefore, reference area Rg3 in modified example 1 also has a rectangular shape. Reference area Rg3 is the area between outer rectangle Os3 and inner rectangle Is3.

[0069] In variant 1, the length of the long side of contact area Ar1 is distance I0. The length of the short side of contact area Ar1 is distance W0. The length of the long side of inner rectangle Is3 is distance I1. The length of the short side of inner rectangle Is3 is distance W1. The length of the long side of outer rectangle Os3 is distance I2. The length of the short side of outer rectangle Os3 is distance W2.

[0070] Distance I1 is 1.1 times as long as distance I0. Distance I2 is twice as long as distance I0. Distance W1 is four times as long as distance W0. Distance W2 is eight times as long as distance W0.

[0071] In this manner, even in the first modification, the spring constant Km1 is calculated based on the difference between the points in the rectangular contact area Ar1 and the points in the rectangular reference area Rg3 on the positive side of the Z axis. As a result, even in the first modification, the spring constant Km1 does not become unnecessarily large or small. Note that the inner rectangle Is3 is an example of a "first rectangle" in this disclosure. The outer rectangle Os3 is an example of a "second rectangle" in this disclosure.

[0072] Similar to the reference region Rg1, the reference region Rg3 may be within the region indicated by diagonal lines in Fig. 10. That is, the outer rectangle Os3 may be smaller than the rectangle indicated in Fig. 10, and the inner rectangle Is3 may be larger than the rectangle indicated in Fig. 10. That is, in Fig. 10, if the distance W2 is longer than the distance W1 and the distance I2 is longer than the distance I1, the distance W1 may be longer than four times the distance W0, the distance W2 may be shorter than eight times the distance W0, the distance I1 may be longer than 1.1 times the distance I0, and the distance I2 may be shorter than twice the distance I0.

[0073] FIG. 11 is a diagram for explaining calculation of the spring constant Km2 at the outer ring raceway surface Sf2 of a model 12M simulating the outer ring 12 in Modification 1. A reference area Rg4 is also set in FIG. 11. The reference area Rg4 is an area indicated by diagonal lines between an outer rectangle Os4 and an inner rectangle Is4. In Modification 1, the size of the contact area Ar2 is the same as that of the contact area Ar1 in Modification 1. That is, the length of the long side of the contact area Ar2 is the distance I0. The length of the short side of the contact area Ar2 is the distance W0.

[0074] 10, the length of the short side of the inner rectangle Is4 is the distance I1. The length of the long side of the inner rectangle Is4 is the distance W1. The length of the short side of the outer rectangle Os4 is the distance I2. The length of the long side of the outer rectangle Os4 is the distance W2.

[0075] Also in FIG. 7, similarly to FIG. 6, distance I1 is 1.1 times as long as distance I0. Distance I2 is twice as long as distance I0. Distance W1 is four times as long as distance W0. Distance W2 is eight times as long as distance W0. This prevents the spring constant Km2 from becoming unnecessarily large or small. Note that inner rectangle Is4 is an example of a "third rectangle" in this disclosure. Outer rectangle Os4 is an example of a "fourth rectangle" in this disclosure.

[0076] Similar to the reference region Rg1, the reference region Rg4 may be within the region indicated by diagonal lines in Fig. 11. That is, the outer rectangle Os4 may be smaller than the rectangle indicated in Fig. 11, and the inner rectangle Is4 may be larger than the rectangle indicated in Fig. 11. That is, in Fig. 11, if the distance W2 is longer than the distance W1 and the distance I2 is longer than the distance I1, the distance W1 may be longer than four times the distance W0, the distance W2 may be shorter than eight times the distance W0, the distance I1 may be longer than 1.1 times the distance I0, and the distance I2 may be shorter than twice the distance I0.

[0077] In this way, in the first modification using radial roller bearing 10A, similarly to the present embodiment, by modeling rolling elements 15 included in rolling bearing 10A by approximating them to a single spring element, the workload required for modeling can be reduced and errors due to spring constants Km1 and Km2 can be reduced. That is, in the first modification, the workload required for determining the natural frequency of rotating machine 100 can be reduced while reducing errors in the determined natural frequency of rotating machine 100.

[0078] <Variation 2> In the present embodiment, an example in which the rolling bearing 10 is a radial ball bearing has been described. In Modification 2, an example in which a thrust bearing is applied will be described. FIG. 12 is a diagram showing a cross-sectional view of rolling bearing 10B in Modification 2. The configuration in Modification 2 is the same as the configuration in the present embodiment, except that the type of rolling bearing 10B is a thrust bearing rather than a radial ball bearing. In Modification 2, the description of the configuration that overlaps with the present embodiment will not be repeated.

[0079] 12 shows a rolling bearing 10B that is a thrust bearing having a rotation axis Ax3. The rolling bearing 10B includes an outer ring 12B, an inner ring 11B, and a rolling element 15B. The inner ring 11B is an example of a "first raceway ring" in the present disclosure. The outer ring 12B is an example of a "second raceway ring" in the present disclosure. In the second modification, the calculation device 200 also determines the spring constant of a model that approximates the rolling element 15B, taking into account the spring constants Km1 and Km2.

[0080] In this way, in the second modification in which a thrust bearing is applied, similarly to the present embodiment, by modeling the rolling element 15B included in the rolling bearing 10B by approximating it to a single spring element, the workload required for modeling can be reduced and errors due to the spring constants Km1 and Km2 can be reduced. That is, in the second modification as well, the workload required for determining the natural frequency of the rotating machine 100 can be reduced while reducing errors in the determined natural frequency of the rotating machine 100.

[0081] <Variation 3> In the present embodiment, an example in which the rolling bearing 10 is a radial ball bearing has been described. In Modification 3, an example in which an angular ball bearing is applied will be described. FIG. 13 is a diagram showing a cross-sectional view of a rolling bearing 10C in Modification 3. The configuration in Modification 3 is the same as that in the present embodiment, except that the type of rolling bearing 10B is an angular ball bearing rather than a radial ball bearing. In Modification 3, the description of the configuration that overlaps with the present embodiment will not be repeated.

[0082] 13 shows rolling bearing 10C, which is an angular ball bearing. Rolling bearing 10C includes outer ring 12C, inner ring 11C, and rolling element 15C. In addition, inner ring 11C is an example of a "first raceway ring" in the present disclosure. Outer ring 12C is an example of a "second raceway ring" in the present disclosure. In Modification 3 as well, calculation device 200 determines the spring constant of a model that approximates rolling element 15C, taking into account spring constants Km1 and Km2.

[0083] In Fig. 13, model 15M, which is a model of rolling element 15C, is shown superimposed on rolling element 15C. Furthermore, in Fig. 13, a node P1 connecting model 11M, which is a model of inner ring 11C, to model 15M, and a node P2 connecting model 12M, which is a model of outer ring 12C, to model 15M are shown.

[0084] In this way, in the third modification using an angular ball bearing, similarly to the present embodiment, by modeling rolling element 15C included in rolling bearing 10C by approximating it to a single spring element, the workload required for modeling can be reduced and errors due to spring constants Km1 and Km2 can be reduced. That is, in the third modification, the workload required for determining the natural frequency of rotating machine 100 can be reduced while reducing errors in the determined natural frequency of rotating machine 100.

[0085] <Variation 4> In Modification 3, an example in which an angular ball bearing is used has been described. In Modification 4, an example in which an angular ball bearing is used and nodes P1 and P2 are disposed at positions different from those in Modification 3 will be described.

[0086] 14 is a diagram showing a cross-sectional view of a rolling bearing 10D in Modification 4. In Modification 4, the description of the configuration that overlaps with Modification 3 will not be repeated. In Modification 4, inner ring 11D is an example of a "first raceway ring" in the present disclosure. Outer ring 12D is an example of a "second raceway ring" in the present disclosure.

[0087] In Fig. 14, model 15M, which is a model of rolling element 15D in Modification 4, is shown superimposed on rolling element 15D. As shown in Fig. 14, in Modification 4, node P1 is not located on the inner ring raceway surface. Similarly, node P2 is not located on the outer ring raceway surface. Node P1 and node P2 are located at the center of the groove curvature radius of each raceway. As a result, the line connecting node P1 and node P2 coincides with the line connecting the contact positions of the inner and outer rings, making it unnecessary to calculate the contact position.

[0088] Fig. 15 is a diagram showing a model of an inner ring 11D and a model of an outer ring 12D in a model 10D of the fourth modification. As shown in Fig. 15, a node P1 is supported by a model RL7 which is a rigid link having a triangular shape. The model RL7 is disposed between the outer ring 12D and the node P1. A node P2 is supported by a model RL8 which is a rigid link having a triangular shape. The model RL8 is disposed between the inner ring 11D and the node P2.

[0089] Returning to Fig. 14, model 15M, which is a one-dimensional elastic body that models rolling element 15D, is placed between node P1 and node P2. This makes it possible to determine the natural frequency without calculating the contact position between the ball and the raceway.

[0090] In this way, even in the fourth modification in which the nodes P1 and P2 are not disposed on the raceway surface, by modeling the rolling element 15D included in the rolling bearing 10D by approximating it to a single spring element, as in the present embodiment, it is possible to reduce the workload required for modeling and also to reduce errors due to the spring constants Km1 and Km2. That is, even in the fourth modification, it is possible to reduce errors in the determined natural frequency of the rotating machine 100 while suppressing the workload required for determining the natural frequency of the rotating machine 100.

[0091] <Summary> The method for determining the characteristics of a rotating machine described above has the following features.

[0092] (Item 1) A method for evaluating characteristics of a rotating machine having a bearing by using a finite element model. The bearing includes rolling elements, a first raceway, and a second raceway, the first raceway being modeled as a first finite element model, the second raceway being modeled as a second finite element model, and the rolling elements being modeled as a third finite element model, the third finite element model being a one-dimensional elastic finite element model connecting a first point included in a first contact area that is an area on a first raceway surface of the first raceway and that contacts the rolling elements, and a second point included in a second contact area that is an area on a second raceway surface of the second raceway and that contacts the rolling elements, a first rigid element having a linear shape passing through the first point is disposed on the first contact area in the first finite element model, and a second rigid element having a linear shape passing through the second point is disposed on the second contact area in the second finite element model. The determination method includes the steps of calculating a first spring constant between the rolling element and the first raceway using Hertz theory, calculating a second spring constant between the rolling element and the second raceway using Hertz theory, calculating a third spring constant of the first finite element model in a first contact area where the first rigid element is arranged, calculating a fourth spring constant of the second finite element model in a second contact area where the second rigid element is arranged, calculating a spring constant of the third finite element model based on the first spring constant, the second spring constant, the third spring constant and the fourth spring constant, and determining at least one of the stiffness, stress, displacement and natural frequency of the rotating machine using the calculated spring constant of the third finite element model.

[0093] (Clause 2) In the determination method in clause 1, the step of calculating a third spring constant includes a step of calculating the third spring constant based on a change in distance between the first contact area and a first reference area on a first orbital surface different from the first contact area when a load is applied to the first finite element model in a normal direction of the first contact area.

[0094] (Item 3) In the determination method according to item 2, the rolling elements are balls, the first contact area has an elliptical shape when viewed from a normal direction to the first raceway surface, the first reference area is an area outside a first ellipse on the first raceway surface and inside a second ellipse on the first raceway surface, center points of the first contact area, the first ellipse, and the second ellipse overlap when viewed from a normal direction to the first raceway surface, the minor axis of the second ellipse is longer than the minor axis of the first ellipse, the major axis of the second ellipse is longer than the major axis of the first ellipse, the minor axis of the first ellipse is more than four times the minor axis of the first contact area, the minor axis of the second ellipse is less than eight times the minor axis of the first contact area, the major axis of the first ellipse is more than 1.5 times the major axis of the first contact area, and the major axis of the second ellipse is less than four times the major axis of the first contact area.

[0095] (Item 4) In the determination method of item 2, the rolling elements are rollers, the first contact area has a rectangular shape when viewed from the normal direction to the first raceway surface, the first reference area is an area outside a first rectangle on the first contact area and inside a second rectangle on the first contact area, center points of the first contact area, the first rectangle, and the second rectangle overlap when viewed from the normal direction to the first raceway surface, the length of the short side of the second rectangle is longer than the length of the short side of the first rectangle, the length of the long side of the second rectangle is longer than the length of the long side of the first rectangle, the length of the short side of the first rectangle is longer than four times the length of the short side of the first contact area, the length of the short side of the second rectangle is shorter than eight times the length of the short side of the first contact area, the length of the long side of the first rectangle is longer than 1.1 times the length of the long side of the first contact area, and the length of the long side of the second rectangle is shorter than two times the length of the long side of the first contact area.

[0096] (Clause 5) In the determination method of clauses 1 to 4, the step of calculating the fourth spring constant includes a step of calculating the fourth spring constant based on the change in distance between the second contact area and a second reference area on a second orbital surface different from the second contact area when a load is applied to the second finite element model in the normal direction of the second contact area.

[0097] (Item 6) In the determination method of item 5, the rolling elements are balls, the second contact area has an elliptical shape when viewed from a normal direction to the second raceway surface, the second reference area is an area outside a third ellipse on the second raceway surface and inside a fourth ellipse on the second raceway surface, the center points of the second contact area, the third ellipse, and the fourth ellipse are arranged at positions where they overlap when viewed from the normal direction to the second raceway surface, the minor axis of the fourth ellipse is longer than the minor axis of the third ellipse, the major axis of the fourth ellipse is longer than the major axis of the third ellipse, the minor axis of the third ellipse is longer than four times the minor axis of the second contact area, the minor axis of the fourth ellipse is shorter than eight times the minor axis of the second contact area, the major axis of the third ellipse is longer than 1.5 times the major axis of the second contact area, and the major axis of the fourth ellipse is shorter than four times the major axis of the second contact area.

[0098] (Item 7) In the determination method in Item 5, the rolling elements are rollers, the second contact area has a rectangular shape when viewed from the normal direction to the second raceway surface, the second reference area is an area outside a third rectangle on the second contact area and inside a fourth rectangle on the second contact area, the center points of the second contact area, the third rectangle, and the fourth rectangle are arranged at positions where they overlap when viewed from the normal direction to the second raceway surface, the length of the short side of the fourth rectangle is longer than the length of the short side of the third rectangle, the length of the long side of the fourth rectangle is longer than the length of the long side of the third rectangle, the length of the short side of the third rectangle is longer than four times the length of the short side of the second contact area, the length of the short side of the fourth rectangle is shorter than eight times the length of the short side of the second contact area, the length of the long side of the third rectangle is longer than 1.1 times the length of the long side of the second contact area, and the length of the long side of the fourth rectangle is shorter than twice the length of the long side of the second contact area.

[0099] (Clause 8) In any of the determination methods from Clause 1 to Clause 7, if the first spring constant is Kh1, the second spring constant is Kh2, the third spring constant is Km1, the fourth spring constant is Km2, and the spring constant of the third finite element model is Kb, then in the step of calculating the spring constant of the third finite element model,

[0100]

number

[0101] The spring constant of the third finite element model is calculated using the relational expression.

[0102] (Item 9) A program for causing a computer to execute judgment of characteristics of a rotating machine having a bearing using a finite element model. The bearing includes rolling elements, a first raceway and a second raceway, the first raceway being modeled as a first finite element model, the second raceway being modeled as a second finite element model, and the rolling elements being modeled as a third finite element model, the third finite element model being a one-dimensional elastic finite element model connecting a first point included in a first contact area that is an area on a first raceway surface of the first raceway and that contacts the rolling elements, and a second point included in a second contact area that is an area on a second raceway surface of the second raceway and that contacts the rolling elements, a first rigid element having a linear shape passing through the first point is arranged on the first contact area in the first finite element model, and a second rigid element having a linear shape passing through the second point is arranged on the second contact area in the second finite element model. The program causes the computer to execute the steps of: calculating a first spring constant between the rolling element and the first raceway using Hertz theory; calculating a second spring constant between the rolling element and the second raceway using Hertz theory; calculating a third spring constant of the first finite element model in a first contact area where the first rigid element is arranged; calculating a fourth spring constant of the second finite element model in a second contact area where the second rigid element is arranged; calculating a spring constant of the third finite element model based on the first spring constant, the second spring constant, the third spring constant and the fourth spring constant; calculating a spring constant of the bearing using the calculated spring constant of the third finite element model; and determining at least one of the stiffness, stress, displacement and natural frequency of the rotating machine using the calculated spring constant of the bearing.

[0103] (Item 10) A computing device that uses a finite element model to determine characteristics of a rotating machine having a bearing. The computing device includes an arithmetic circuit and a storage device. The bearing includes a rolling element, a first raceway, and a second raceway. The storage device stores a first finite element model that models the first raceway, a second finite element model that models the second raceway, and a third finite element model that models the rolling element. The third finite element model is a one-dimensional elastic finite element model that connects a first point included in a first contact area that is an area on a first raceway surface of the first raceway and contacts the rolling element, and a second point included in a second contact area that is an area on a second raceway surface of the second raceway and contacts the rolling element. The storage device further stores a first rigid element that is arranged on the first contact area in the first finite element model and has a linear shape that passes through the first point, and a second rigid element that is arranged on the second contact area in the second finite element model and has a linear shape that passes through the second point. The calculation circuit calculates a first spring constant between the rolling element and the first raceway using Hertz theory, calculates a second spring constant between the rolling element and the second raceway using Hertz theory, calculates a third spring constant of the first finite element model in a first contact area where the first rigid element is arranged, calculates a fourth spring constant of the second finite element model in a second contact area where the second rigid element is arranged, calculates a spring constant of the third finite element model based on the first spring constant, the second spring constant, the third spring constant and the fourth spring constant, and determines at least one of the stiffness, stress, displacement and natural frequency of the rotating machine using the calculated spring constant of the third finite element model.

[0104] The embodiments disclosed herein should be considered to be illustrative and not restrictive in all respects. The scope of the present invention is defined by the claims, not the above description, and is intended to include all modifications within the meaning and scope of the claims. [Explanation of symbols]

[0105] 5 shaft, 10, 10A-10D rolling bearing, 10M, 11M, 12M, 15M, RL1-RL8 model, 11, 11A-11D inner ring, 12, 12A-12D outer ring, 100, 1000 rotating machine, 200 calculation device, 201 calculation circuit, 202 storage device, 15, 15A-15D rolling element, Ar1, Ar2 contact area, Ax1 rotation axis direction, I0-I2, L0-L2, M0-M2, W0-W2 distance, Ic1, Ic2 inner ellipse, Is3, Is4 inner rectangle, Oc1, Oc2 outer ellipse, Os3, Os4 outer rectangle, Kb, Kh1, Kh2, Km1, Km2 spring constant, P1, P2 nodes, Rg1-Rg4 Reference area, Sf1 inner raceway surface, Sf2 outer raceway surface.

Claims

1. 1. A method for determining a characteristic of a rotating machine having a bearing by using a finite element model, comprising the steps of: The bearing includes a rolling element, a first raceway, and a second raceway, the first race is modeled as a first finite element model; the second race is modeled as a second finite element model; The rolling element is modeled as a third finite element model; The third finite element model is a first point included in a first contact area that is an area on a first raceway surface of the first raceway and that comes into contact with the rolling element; a second point included in a second contact area that is in contact with the rolling element and is on a second raceway surface of the second race; a first rigid element having a linear shape passing through the first point is disposed on the first contact region in the first finite element model; a second rigid element having a linear shape passing through the second point is disposed on the second contact region in the second finite element model; The determination method includes: calculating a first spring constant between the rolling element and the first race using Hertz theory; calculating a second spring constant between the rolling element and the second race using Hertz theory; calculating a third spring constant of the first finite element model in the first contact region where the first rigid element is disposed; calculating a fourth spring constant of the second finite element model in the second contact region where the second rigid element is disposed; calculating a spring constant of the third finite element model based on the first spring constant, the second spring constant, the third spring constant, and the fourth spring constant; and determining at least one of a stiffness, a stress, a displacement, and a natural frequency of the rotating machine using the calculated spring constant of the third finite element model.

2. The step of calculating the third spring constant includes:

2. The method according to claim 1, further comprising a step of calculating the third spring constant based on a change in distance between the first contact area and a first reference area on the first orbital surface different from the first contact area when a load is applied to the first finite element model in a normal direction of the first contact area.

3. The rolling elements are balls, the first contact region has an elliptical shape when viewed from a normal direction of the first track plane, the first reference region is a region outside a first ellipse on the first orbital plane and inside a second ellipse on the first orbital plane, a center point of each of the first contact area, the first ellipse, and the second ellipse overlap with each other when viewed from a normal direction of the first orbital plane, The second ellipse has a shorter radius than the first ellipse, The semimajor axis of the second ellipse is longer than the semimajor axis of the first ellipse, the minor axis of the first ellipse is greater than four times the minor axis of the first contact area; the second ellipse has a minor axis that is shorter than eight times the minor axis of the first contact area; the semimajor axis of the first ellipse is greater than 1.5 times the semimajor axis of the first contact area; The method of claim 2 , wherein the semimajor axis of the second ellipse is shorter than four times the semimajor axis of the first contact area.

4. The rolling elements are rollers, the first contact region has a rectangular shape when viewed from a normal direction of the first track surface, the first reference area is an area outside a first rectangle on the first contact area and inside a second rectangle on the first contact area, a center point of each of the first contact area, the first rectangle, and the second rectangle overlap when viewed from a normal direction of the first orbital plane, The length of a short side of the second rectangle is longer than the length of a short side of the first rectangle, The length of a long side of the second rectangle is longer than the length of a long side of the first rectangle, a length of a short side of the first rectangle is greater than four times a length of a short side of the first contact area; a length of a short side of the second rectangle is shorter than eight times the length of a short side of the first contact area; The length of a long side of the first rectangle is longer than 1.1 times the length of a long side of the first contact area, The method according to claim 2 , wherein a length of a longer side of the second rectangle is shorter than twice a length of a longer side of the first contact area.

5. The step of calculating the fourth spring constant includes:

2. The method according to claim 1, further comprising a step of calculating the fourth spring constant based on a change in distance between the second contact area and a second reference area on the second orbital surface different from the second contact area when a load is applied to the second finite element model in a normal direction of the second contact area.

6. The rolling elements are balls, the second contact region has an elliptical shape when viewed from a normal direction of the second raceway plane, the second reference region is a region that is outside a third ellipse on the second orbital plane and inside a fourth ellipse on the second orbital plane, the second contact area, the third ellipse, and the fourth ellipse have center points that overlap each other when viewed from a normal direction of the second orbital plane, The minor axis of the fourth ellipse is longer than the minor axis of the third ellipse, The semimajor axis of the fourth ellipse is longer than the semimajor axis of the third ellipse, The third ellipse has a minor axis that is greater than four times the minor axis of the second contact area; the fourth ellipse has a minor axis that is shorter than eight times the minor axis of the second contact area; The semimajor axis of the third ellipse is greater than 1.5 times the semimajor axis of the second contact area; The method according to claim 5 , wherein the semimajor axis of the fourth ellipse is shorter than four times the semimajor axis of the second contact area.

7. The rolling elements are rollers, the second contact region has a rectangular shape when viewed from a normal direction of the second track surface, the second reference area is an area outside a third rectangle on the second contact area and inside a fourth rectangle on the second contact area, the second contact area, the third rectangle, and the fourth rectangle have center points that overlap when viewed from a normal direction of the second orbital plane, The length of a short side of the fourth rectangle is longer than the length of a short side of the third rectangle, The length of the long side of the fourth rectangle is longer than the length of the long side of the third rectangle, The length of the short side of the third rectangle is greater than four times the length of the short side of the second contact area, a length of a short side of the fourth rectangle is shorter than eight times the length of a short side of the second contact area; The length of the long side of the third rectangle is longer than 1.1 times the length of the long side of the second contact area, The method according to claim 5 , wherein a length of a longer side of the fourth rectangle is shorter than twice the length of a longer side of the second contact area.

8. The first spring constant is Kh1, The second spring constant is Kh2, The third spring constant is Km1, The fourth spring constant is Km2, If the spring constant of the third finite element model is Kb, then In the step of calculating a spring constant of the third finite element model, [0030] The method according to any one of claims 1 to 7, further comprising the step of calculating a spring constant of the third finite element model using the following relational expression:

9. A program for causing a computer to execute determination of characteristics of a rotating machine having a bearing using a finite element model, the program comprising: The bearing includes a rolling element, a first raceway, and a second raceway, the first race is modeled as a first finite element model; the second race is modeled as a second finite element model; The rolling element is modeled as a third finite element model; The third finite element model is a first point included in a first contact area that is an area on a first raceway surface of the first raceway and that comes into contact with the rolling element; a second point included in a second contact area that is in contact with the rolling element and is on a second raceway surface of the second race; a first rigid element having a linear shape passing through the first point is disposed on the first contact region in the first finite element model; a second rigid element having a linear shape passing through the second point is disposed on the second contact region in the second finite element model; The computer includes: calculating a first spring constant between the rolling element and the first race using Hertz theory; calculating a second spring constant between the rolling element and the second race using Hertz theory; calculating a third spring constant of the first finite element model in the first contact region where the first rigid element is disposed; calculating a fourth spring constant of the second finite element model in the second contact region where the second rigid element is disposed; calculating a spring constant of the third finite element model based on the first spring constant, the second spring constant, the third spring constant, and the fourth spring constant; calculating a spring constant of the bearing using the calculated spring constant of the third finite element model; and determining at least one of stiffness, stress, displacement, and natural frequency of the rotating machine using the calculated spring constant of the bearing.

10. 1. A computing device for determining a characteristic of a rotating machine having a bearing using a finite element model, comprising: An arithmetic circuit; a storage device; The bearing includes a rolling element, a first raceway, and a second raceway, The storage device includes: a first finite element model that models the first bearing ring; a second finite element model that models the second bearing ring; a third finite element model that models the rolling element; The third finite element model is a first point included in a first contact area that is an area on a first raceway surface of the first raceway and that comes into contact with the rolling element; a second point included in a second contact area that is in contact with the rolling element and is on a second raceway surface of the second race; The storage device includes: a first rigid element having a linear shape that is disposed on the first contact area in the first finite element model and passes through the first point; a second rigid body element having a linear shape that is disposed on the second contact area in the second finite element model and passes through the second point; The arithmetic circuit includes: Calculating a first spring constant between the rolling element and the first raceway using Hertz theory; Calculating a second spring constant between the rolling element and the second raceway using Hertz theory; Calculating a third spring constant of the first finite element model in the first contact region where the first rigid element is disposed; Calculating a fourth spring constant of the second finite element model in the second contact region where the second rigid element is disposed; calculating a spring constant of the third finite element model based on the first spring constant, the second spring constant, the third spring constant, and the fourth spring constant; A computing device that uses the calculated spring constant of the third finite element model to determine at least one of a stiffness, a stress, a displacement, and a natural frequency of the rotating machine.

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