Analysis system, analysis method, and analysis program

Abstract

To analyze coupled vibration of an engine at a high speed and with stability.SOLUTION: An analysis system according to an example acquires external force acting on an analysis object that comprises a structure part having a stationary system and one or more rotary systems, and one or more bearing parts; acquires a stationary system characteristic matrix and a rotary system characteristic matrix; divides coupled vibration generated by the external force into a plurality of cells indicating combinations between vibration in a first angular frequency selected in the stationary system and vibration in each of a plurality of second angular frequencies associated with the first angular frequency in the rotary system; calculates a first constant number matrix indicating dynamic rigidity of the structure part and a second constant number matrix indicating dynamic rigidity of the bearing part for each of the plurality of cells on the basis of the characteristic matrix of the stationary system and the rotary system; generates a relational expression between the external force and the deviation in the analysis object on the basis of these constant number matrixes; and calculates the deviation in a predetermined position of the analysis object on the basis of the external force and the relational expression.SELECTED DRAWING: Figure 5

Description

[Technical field]

[0001] One aspect of the present disclosure relates to an analysis system, an analysis method, and an analysis program. [Background technology]

[0002] Conventionally, there are known methods for analyzing vibrations of an engine having both a stationary system and a rotating system. For example, Non-Patent Document 1 describes a tool for calculating the dynamics, vibration, and acoustics of a combustion engine, a transmission, and a complete ICE-based or electric drive unit. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] AVL LIST GmbH, "AVL EXCITETM", [online], Internet <URL:https: / / www.avl.com / en / simulation-solutions / software-offering / simulation-tools-z / avl-excite> Summary of the Invention [Problem to be solved by the invention]

[0004] In an engine having both the stationary and rotating systems described above, the stationary and rotating systems vibrate while interacting with each other, and the vibration (coupled vibration) is very complex. The conventional method realized by the above software, etc. is time domain analysis, but this method requires a long time to obtain results and there is a risk that the calculations will not converge. Therefore, a method for quickly and stably analyzing the coupled vibration of an engine is desired. [Means for solving the problem]

[0005] An analysis system according to an aspect of the present disclosure includes at least one processor, which acquires an external force acting on an analysis object including a structural part having a stationary system and one or more rotating systems, and one or more bearing parts supporting the one or more rotating systems in the stationary system, acquires a stationary system characteristic matrix indicating vibration characteristics of the stationary system and a rotating system characteristic matrix indicating vibration characteristics of the rotating system, divides a coupled vibration generated by the external force in the stationary system and the rotating system into a plurality of cells indicating a combination of a vibration at a first angular frequency selected in the stationary system and a vibration at each of a plurality of second angular frequencies associated with the first angular frequency in the rotating system, calculates a first constant matrix indicating a dynamic stiffness of the structural part and a second constant matrix indicating a dynamic stiffness of the bearing part for each of the plurality of cells based on the stationary system characteristic matrix and the rotating system characteristic matrix, generates a relational expression between the external force and a displacement in the analysis object based on the first constant matrix and the second constant matrix, and calculates a displacement at a predetermined position of the analysis object based on the external force and the relational expression.

[0006] An analysis method according to an aspect of the present disclosure is executed by an analysis device having at least one processor. The analysis method includes the steps of acquiring an external force acting on an analysis object having a structural part having a stationary system and one or more rotating systems, and one or more bearing parts supporting the one or more rotating systems in the stationary system, acquiring a stationary system characteristic matrix indicating vibration characteristics of the stationary system and a rotating system characteristic matrix indicating vibration characteristics of the rotating system, dividing a coupled vibration caused by the external force in the stationary system and the rotating system into a plurality of cells indicating a combination of a vibration at a first angular frequency selected in the stationary system and a vibration at each of a plurality of second angular frequencies associated with the first angular frequency in the rotating system, calculating a first constant matrix indicating a dynamic stiffness of the structural part and a second constant matrix indicating a dynamic stiffness of the bearing part for each of the plurality of cells based on the stationary system characteristic matrix and the rotating system characteristic matrix, generating a relational expression between the external force and a displacement in the analysis object based on the first constant matrix and the second constant matrix, and calculating the displacement at a predetermined position of the analysis object based on the external force and the relational expression.

[0007] An analysis program according to one aspect of the present disclosure causes a computer to execute the following steps: acquiring an external force acting on an analysis object having a structural part having a stationary system and one or more rotating systems, and one or more bearing parts that support the one or more rotating systems in the stationary system; acquiring a stationary system characteristic matrix indicating the vibration characteristics of the stationary system and a rotating system characteristic matrix indicating the vibration characteristics of the rotating system; dividing a coupled vibration generated by the external force in the stationary system and the rotating system into a plurality of cells indicating a combination of a vibration at a first angular frequency selected in the stationary system and a vibration at each of a plurality of second angular frequencies associated with the first angular frequency in the rotating system; calculating a first constant matrix indicating the dynamic rigidity of the structural part and a second constant matrix indicating the dynamic rigidity of the bearing parts for each of the plurality of cells based on the stationary system characteristic matrix and the rotating system characteristic matrix; generating a relational equation between the external force and a displacement in the analysis object based on the first constant matrix and the second constant matrix; and calculating a displacement at a predetermined position of the analysis object based on the external force and the relational equation.

[0008] In this aspect, the coupled vibration between the stationary system and the rotating system is decomposed into vibrations for each cell, and the dynamic stiffness of both the structural part and the bearing part is shown for each cell. In this way, by considering the coupled vibration between the stationary system and the rotating system as a collection of vibrations in each cell, it is possible to simplify the calculation of the displacement (vibration) in the object to be analyzed. As a result, it is possible to analyze the coupled vibration of the engine quickly and stably. Effect of the Invention

[0009] According to one aspect of the present disclosure, coupled vibration of an engine can be analyzed quickly and stably. [Brief description of the drawings]

[0010] [Figure 1] FIG. 2 is a diagram illustrating an example of an analysis target. [Diagram 2] FIG. 1 is a diagram illustrating an example of coupled vibration. [Diagram 3] FIG. 2 illustrates an example of a functional configuration of an analysis system. [Figure 4] FIG. 2 is a diagram illustrating an example of a hardware configuration of a computer that constitutes the analysis system. [Diagram 5] 13 is a flowchart illustrating an example of processing by the analysis system. [Figure 6] FIG. 2 is a diagram illustrating an example of a cell. [Figure 7] 13 is a flowchart showing an example of generation of a relational expression. [Figure 8] FIG. 2 is a diagram illustrating an example of a pod. [Figure 9] FIG. 13 is a diagram illustrating an example of a transformation matrix. [Figure 10] FIG. 13 is a diagram illustrating another example of a transformation matrix. [Figure 11] FIG. 2 is a diagram illustrating an example of a mode shape matrix. [Figure 12] FIG. 13 is a diagram showing another example of a mode shape matrix. [Figure 13] 13 is a flowchart showing another example of generating a relational expression. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the accompanying drawings. In the description of the drawings, the same or equivalent elements are designated by the same reference numerals, and duplicated explanations will be omitted.

[0012] [System Overview] The analysis system 10 according to one example is a system for analyzing vibrations of an analysis object. In one example, the analysis system 10 analyzes vibrations of an analysis object including a structural part having a stationary system and one or more rotating systems, and one or more bearing parts supporting the one or more rotating systems in the stationary system. In the present disclosure, the analysis object refers to an object whose vibrations are analyzed by the analysis system 10. The analysis object may be, for example, a reciprocating engine.

[0013] The configuration of the analysis object 1 according to this embodiment will be described with reference to FIG. 1. FIG. 1 is a diagram showing an example of the analysis object 1. The analysis object 1 includes a structural part 110, six bearing parts 120, four gears 130, and two gear meshing points 140. The structural part 110 includes a housing 111 and three rotating shafts 112a, 112b, and 112c. In the analysis object 1, the housing 111 is a stationary system, and the three rotating shafts 112a, 112b, and 112c are a rotating system. The bearing parts 120 support the three rotating shafts 112a, 112b, and 112c. In this embodiment, each of the rotating shafts 112a, 112b, and 112c is supported by two bearing parts 120. The four gears 130 are fixed to corresponding ones of the rotating shafts 112a, 112b, and 112c, and rotate together with the rotating shafts 112a, 112b, and 112c. In this embodiment, one gear 130 is fixed to one end of each of the rotating shafts 112a and 112c, and one gear 130 is fixed to both ends of the rotating shaft 112b. Two gear meshing points 140 are positions where the gears 130 mesh with each other.

[0014] In one example, the analysis system 10 analyzes the displacement (vibration) at a predetermined position of the analysis object 1 when an external force of a certain angular frequency acts on the analysis object 1. The external force refers to a force acting on the analysis object 1 from outside the analysis object 1. When the analysis object 1 is, for example, a reciprocating engine, examples of the external force include the thrust force of a piston and the load of a crank pin. In this disclosure, the displacement is a concept that includes at least one of displacement and velocity. Hereinafter, in order to distinguish from general displacement, the displacement that includes displacement and velocity may be referred to as a "complex form displacement". Therefore, in this disclosure, the analysis system 10 can analyze the complex form displacement at a predetermined position of the analysis object 1 when an external force of a certain angular frequency acts on the analysis object 1.

[0015] In one example, the analysis system 10 analyzes vibration at a predetermined position of the analysis object 1 when an external force acts on a position of the analysis object 1 where a transmission error may occur between the gears 130. The transmission error refers to a difference in the amount of rotation between the gears 130 meshing at the gear meshing point 140. Ideally, the amount of rotation between the gears 130 meshing at the gear meshing point 140 is equal, but a transmission error may occur due to, for example, a manufacturing error of the gears 130. In the present disclosure, analyzing vibration at a predetermined position of the analysis object 1 when an external force acts on a position where such a transmission error may occur is also referred to as vibration analysis of gear noise. From the above, it can be said that the analysis system 10 can be used for vibration analysis of gear noise.

[0016] When an external force acts on an engine having a stationary system and one or more rotating systems, such as the above-mentioned analysis target 1, the stationary system and the one or more rotating systems vibrate while interacting with each other. This type of vibration is called "coupled vibration."

[0017] For example, consider a case where an external force of a certain angular frequency acts on the analysis target 1. In this case, vibrations at the angular frequency of the external force and vibrations at an angular frequency shifted from the angular frequency of the external force by an integer multiple of the rotational angular velocity of the rotating system are sequentially excited in both the stationary system and the multiple rotating systems. Furthermore, the vibrations excited in the rotating system further excite vibrations at an angular frequency shifted by an integer multiple of the rotational angular velocity of the rotating system through the bearings in the rotating system. In this way, in the coupled vibration, vibrations with different angular frequencies are excited one after another by the applied external force, and these vibrations interact with each other while propagating between the stationary system and the rotating system.

[0018] The excitation of vibration in the coupled vibration will be described in more detail with reference to Fig. 2. Fig. 2 is a diagram showing a schematic example of the coupled vibration. The example shown in Fig. 2 shows a schematic example of the coupled vibration when an external force with an angular frequency ω0 acts on a stationary system in an analysis object in which the rotational angular velocity of one rotating system is Ω0.

[0019] As described above, when an external force of a certain angular frequency is applied to an object to be analyzed, vibrations at the angular frequency of the external force and vibrations at an angular frequency shifted from the angular frequency of the external force by an integer multiple of the rotational angular velocity of the rotating system are sequentially excited in both the stationary system and multiple rotating systems.

[0020] In the example shown in FIG. 2, the vibration with angular frequency ω0 acting on the stationary system is propagated to the rotating system via the bearings, and excites vibrations with angular frequencies ω0, ω0+Ω0, and ω0-Ω0 in the rotating system.

[0021] Next, the vibration at angular frequency ω0+Ω0 excited in the rotating system propagates through the bearing to the stationary system, and further excites, in the stationary system, vibrations at angular frequencies ω0+Ω0, ω0+2Ω0, and ω0. Furthermore, the vibration at angular frequency ω0+Ω0 excited in the rotating system further excites, in the rotating system, vibrations at angular frequencies ω0+3Ω0 and ω0-Ω0.

[0022] Similarly, the vibration at angular frequency ω0-Ω0 excited in the rotating system propagates to the stationary system via the bearing, and further excites, in the stationary system, vibrations at angular frequency ω0-Ω0, vibrations at angular frequency ω0, and vibrations at angular frequency ω0-2Ω0. Furthermore, the vibration at angular frequency ω0-Ω0 excited in the rotating system further excites, in the rotating system, vibrations at angular frequency ω0+Ω0 and vibrations at angular frequency ω0-3Ω0.

[0023] Each vibration excited in the stationary system propagates again to the rotating system via the bearings, and further excites a vibration in the rotating system whose angular frequency is shifted from the excited vibration by the rotation angular velocity Ω of the rotating system.

[0024] In this way, between the stationary system and the rotating system, a vibration is excited whose angular frequency is shifted by the rotational angular velocity Ω0 of the rotating system from the angular velocity ω0 of the applied external force. In the rotating system, a vibration whose angular frequency is shifted by 2Ω0 from the vibration excited in the rotating system is excited.

[0025] In the example shown in Fig. 2, the above-mentioned cycle of vibration propagation and excitation is performed while the angular frequency differs between the stationary system and the rotating system by the rotational angular velocity Ω0 of the rotating system. Moreover, the cycle is performed while the angular frequency differs between the rotating systems by 2Ω0, which is twice the rotational angular velocity Ω0 of the rotating system. Therefore, in the example shown in Fig. 2, the angular frequency of each vibration that occurs is expressed as ω0±x0Ω0, where x0 is an integer.

[0026] For the sake of convenience, the example shown in Fig. 2 has been described above with reference to a configuration in which the structural unit has a stationary system and one rotating system. However, it should be noted that even if the structural unit has a stationary system and two or more rotating systems, the details of the coupled vibration in that configuration can be understood in the same way as in the example shown in Fig. 2. For example, if the structural unit has a stationary system and three rotating systems, and the rotational angular velocity of each rotating system is Ω, 01 ,Ω 02 ,Ω 03 In this case, the angular frequency of each vibration is ω0±x0Ω. 01 ±y0Ω 02 ±z0Ω 03 Here, x0, y0, and z0 are integers. In the following explanation, ω0±x0Ω, which indicates the angular frequency of each vibration caused by the coupled vibration, is used. 01 ±y0Ω 02 ±z0Ω 03 In, the coefficient of the rotational angular velocity of each rotating system is called the order.

[0027] In the coupled vibration, the stationary system and the rotating system interact with each other, and vibrations with different angular frequencies are excited one after another. When the coupled vibration is analyzed using time domain analysis, it takes a long time to obtain the results, and there is a risk that the calculations will not converge. On the other hand, the analysis system 10 divides the coupled vibration caused by the external force acting on the analysis object into cells that indicate a combination of a vibration at a first angular frequency selected in the stationary system and a vibration at each of a plurality of second angular frequencies associated with the first angular frequency in the rotating system. In this way, the calculation of the vibration in the analysis object can be simplified by regarding the coupled vibration between the stationary system and the rotating system as a set of vibrations in each cell. As a result, the analysis system 10 can analyze the coupled vibration of the analysis object quickly and stably.

[0028] [System configuration] An example of the functional configuration of the analysis system 10 will be described with reference to Fig. 3. Fig. 3 is a diagram showing an example of the functional configuration of the analysis system 10. In the example, the analysis system 10 includes an acquisition unit 11, a division unit 12, a constant matrix calculation unit 13, a generation unit 14, a displacement calculation unit 15, and an output unit 16 as functional modules.

[0029] The acquisition unit 11 is a functional module that acquires an external force acting on the object to be analyzed and an analysis parameter that is a parameter used in the analysis of the coupled vibration. Furthermore, the acquisition unit 11 is also a functional module that acquires a stationary system characteristic matrix that indicates the vibration characteristics of a stationary system and a rotating system characteristic matrix that indicates the vibration characteristics of a rotating system. The division unit 12 is a functional module that divides the coupled vibration generated in the object to be analyzed by the acquired external force into a plurality of cells. The constant matrix calculation unit 13 is a functional module that calculates a first constant matrix that indicates the dynamic stiffness of a structural part and a second constant matrix that indicates the dynamic stiffness of a bearing part for each of the divided plurality of cells based on the acquired stationary system characteristic matrix and rotating system matrix. The generation unit 14 is a functional module that generates a relational expression between the external force and the displacement in the object to be analyzed based on the calculated first constant matrix and second constant matrix. The displacement calculation unit 15 is a functional module that calculates a displacement at a predetermined position of the object to be analyzed based on the acquired external force and the generated relational expression. The output unit 16 is a functional module that outputs a processing result.

[0030] 4 is a diagram showing an example of a general hardware configuration of a computer 100 constituting the analysis system 10. For example, the computer 100 includes a processor (e.g., a CPU) 101 that executes an operating system, application programs, etc., a main memory unit 102 composed of a ROM and a RAM, an auxiliary memory unit 103 composed of a storage device such as a hard disk or a flash memory, a communication control unit 104 composed of a network card or a wireless communication module, an input device 105 such as a keyboard or a mouse, and an output device 106 such as a monitor.

[0031] Each functional module of the analysis system 10 is realized by loading a predetermined program onto the processor 101 or the main memory unit 102 and having the processor 101 execute the program. In accordance with the program, the processor 101 operates the communication control unit 104, the input device 105, or the output device 106, and reads and writes data in the main memory unit 102 or the auxiliary memory unit 103. Data or a database required for processing is stored in the main memory unit 102 or the auxiliary memory unit 103.

[0032] The analysis system 10 is composed of at least one computer. When multiple computers are used, a single analysis system 10 is logically constructed by connecting these computers via a communication network such as the Internet or an intranet.

[0033] The analysis program for causing a computer or computer system to function as the analysis system 10 includes program codes for causing the computer or computer system to function as the acquisition unit 11, division unit 12, constant matrix calculation unit 13, generation unit 14, displacement calculation unit 15, and output unit 16. This analysis program may be provided after being non-temporarily recorded on a tangible recording medium such as a CD-ROM, a DVD-ROM, or a semiconductor memory. Alternatively, the analysis program may be provided via a communication network as a data signal superimposed on a carrier wave. The provided analysis program is stored in, for example, the auxiliary storage unit 103. The processor 101 reads out the analysis program from the auxiliary storage unit 103 and executes it to realize each of the above-mentioned functional modules.

[0034] [System Operation] An example of processing by the analysis system 10 and an analysis method according to the present embodiment will be described with reference to Fig. 5. Fig. 5 is a flow chart showing an example of processing by the analysis system.

[0035] In step S1, the acquisition unit 11 acquires an external force acting on the analysis object 1 and a position in the analysis object 1 for which a displacement is to be calculated. In one example, the acquisition unit 11 acquires an external force f EX P In one example, the acquisition unit 11 receives the external force and the position input by the user.

[0036] In step S2, the acquisition unit 11 acquires the analysis parameters. As described above, the analysis parameters are parameters used in the analysis of the coupled vibration, and include at least the rotational angular velocity of the rotation system, a stiffness parameter indicating the stiffness of the bearing, a damping parameter indicating the damping of the bearing, and the number of cell generations. The number of cell generations refers to a value indicating a criterion for determining how many cells the coupled vibration should be divided into, and is set in consideration of the convergence of the analysis by the analysis system 10. The relationship between the process of dividing the coupled vibration into a plurality of cells and the number of cell generations will be described later.

[0037] In one example, the acquisition unit 11 acquires, as the analysis parameters, the rotational angular velocities Ω1, Ω2, Ω3 of the rotating system (rotating shafts 112a, 112b, 112c), a stiffness parameter c1 indicating the stiffness of the bearing unit 120, a damping parameter k1 indicating the damping of the bearing unit 120, a stiffness parameter c2 indicating the stiffness of the gear meshing point 140, a damping parameter k2 indicating the damping of the gear meshing point 140, and the number of generations G of the cell. Here, the number of generations G is an integer equal to or greater than 0. In one example, the number of generations G is equal to or less than 3.

[0038] Each analysis parameter may be stored in, for example, a given storage unit. Each analysis parameter may be stored in a memory or database within the analysis system 10, or in a memory or database that is external to the analysis system 10. In this case, the acquisition unit 11 may acquire each analysis parameter from the storage unit. Alternatively, the acquisition unit 11 may accept analysis parameters input by a user.

[0039] In step S3, the acquisition unit 11 acquires a stationary system characteristic matrix, a rotational system characteristic matrix, and a transformation matrix.

[0040] In one example, the acquisition unit 11 acquires, as the stationary system characteristic matrix, a mass matrix M S , the damping matrix C S , stiffness matrix K S , and the mode shape matrix Φ SJ ,Φ SEX Here, the size of each matrix acquired as the stationary system characteristic matrix is ​​the same, and the size is set as the degree of freedom of the stationary system characteristic matrix.

[0041] Mass matrix M S is a matrix whose components are the mass of the housing 111 for each eigenmode. S is a matrix whose components are the damping of the housing 111 for each eigenmode. The stiffness matrix K S is a matrix whose components are the stiffness of the housing 111 for each eigenmode.

[0042] Mode Shape Matrix Φ SJ ,Φ SEX is a matrix whose components are complex-form displacements that occur at a given position of the analysis object 1 due to vibrations at frequencies corresponding to each eigenmode of the housing 111. The mode shape matrix Φ SJ is a matrix of the degrees of freedom of the bearing 120 in the housing 111, and the mode shape matrix Φ SEX is the matrix of degrees of freedom of the gear meshing points 140 in the housing 111.

[0043] As described above, the analysis system 10 can be used for vibration analysis of gear noise. In this case, no external force acts on the stationary system (casing 111). Therefore, when the analysis system 10 is used for vibration analysis of gear noise, the mode shape matrix Φ SEX Note that is the empty matrix.

[0044] In one example, the acquisition unit 11 acquires, as the rotation system characteristic matrix, a mass matrix m r1 ,m r2 ,m r3 , the damping matrix c r1 ,c r2 ,c r3 , stiffness matrix k r1 ,k r2 ,k r3 , and the mode shape matrix Φ r1J ,Φ r2J ,Φ r3J ,Φ r1EX ,Φ r2EX ,Φ r3EX ,Φ R1 ,Φ R2 ,Φ R3 Here, the size of each matrix acquired as the rotation system characteristic matrix is ​​the same, and the size is set as the degree of freedom of the rotation system characteristic matrix.

[0045] Mass matrix m r1 is a matrix whose components are the mass of the rotating shaft 112a for each eigenmode. r1 is a matrix whose components are the damping of the rotating shaft 112a for each eigenmode. r1 is a matrix whose components are the stiffness of the rotating shaft 112a for each eigenmode.

[0046] Mode Shape Matrix Φ r1J ,Φ r1EX ,Φ R1 is a matrix whose components are complex displacements generated at a given position of the analysis object 1 due to vibrations at frequencies corresponding to the respective eigenmodes of the rotating shaft 112a. r1J is a matrix of the degrees of freedom of the bearing 120 in the rotating shaft 112a. r1EX is the matrix of degrees of freedom of the gear meshing point 140 on the rotating shaft 112a. Mode shape matrix Φ R1 is the matrix of degrees of freedom of the gear meshing point 140 on the axis of rotation 112a.

[0047] For example, when the analysis system 10 is used for vibration analysis of gear noise, if an external force acts at a position where a transmission error occurs between the gears 130 fixed to the rotating shafts 112a and 112b, the mode shape matrix Φ r1EX and the mode shape matrix Φ R1 On the other hand, when the analysis system 10 is used for vibration analysis of gear noise, and an external force acts at a position where a transmission error occurs between the gears 130 fixed to the rotating shafts 112b and 112c, the mode shape matrix Φ r1EX is the empty matrix.

[0048] Alternatively, when the analysis system 10 is used for vibration analysis other than the vibration analysis of gear noise, and an external force acts on a position other than the gear meshing point 140 of the gear 130 fixed to the rotating shaft 112a and the rotating shaft 112b, the mode shape matrix Φ r1EX is a matrix of the degrees of freedom of the gear meshing point 140 at that position. On the other hand, when the analysis system 10 is used for vibration analysis other than the vibration analysis of gear noise, and no external force acts on the rotating shaft 112a, the mode shape matrix Φ r1EX is the empty matrix.

[0049] Mass matrix m r2 is a matrix whose components are the mass of the rotating shaft 112b for each eigenmode. r2 is a matrix whose components are the damping of the rotating shaft 112b for each eigenmode. r2 is a matrix whose components are the stiffness of the rotating shaft 112b for each eigenmode.

[0050] Mode Shape Matrix Φ r2J ,Φ r2EX ,Φ R2is a matrix whose components are complex displacements generated at a given position of the analysis object 1 due to vibrations at frequencies corresponding to the respective eigenmodes of the rotation axis 112b. r2J is a matrix of the degrees of freedom of the bearing 120 in the rotating shaft 112b. r2EX is the matrix of degrees of freedom of the gear meshing point 140 on the rotation axis 112b. Mode shape matrix Φ R2 is the matrix of degrees of freedom of the gear meshing point 140 at the axis of rotation 112b.

[0051] For example, when the analysis system 10 is used for vibration analysis of gear noise, the mode shape matrix Φ r2EX and the mode shape matrix Φ R2 is equal to

[0052] Alternatively, when the analysis system 10 is used for vibration analysis other than the vibration analysis of gear noise, and an external force acts on a position other than the gear meshing point 140 of one of the two gears 130 fixed to the rotating shaft 112b, the mode shape matrix Φ r2EX is a matrix of the degrees of freedom of the gear meshing point 140 at that position. On the other hand, when the analysis system 10 is used for vibration analysis other than the vibration analysis of gear noise, and no external force acts on the rotating shaft 112b, the mode shape matrix Φ r2EX is the empty matrix.

[0053] The mass matrix mr3 is a matrix whose components are the mass of the rotation axis 112c for each eigenmode. r3 is a matrix whose components are the damping of the rotating shaft 112c for each eigenmode. The stiffness matrix kr3 is a matrix whose components are the stiffness of the rotating shaft 112c for each eigenmode.

[0054] Mode Shape Matrix Φ r3J ,Φ r3EX ,Φ R3is a matrix whose components are complex displacements generated at a given position of the analysis object 1 due to vibrations at frequencies corresponding to the eigenmodes of the rotation axis 112c. r3J is a matrix of the degrees of freedom of the bearing 120 in the rotating shaft 112c. r3EX is the matrix of degrees of freedom of the gear meshing point 140 on the rotation axis 112c. R3 is the matrix of degrees of freedom of the gear meshing point 140 at the axis of rotation 112c.

[0055] For example, when the analysis system 10 is used for vibration analysis of gear noise, if an external force acts at a position where a transmission error occurs between the gears 130 fixed to the rotating shafts 112b and 112c, the mode shape matrix Φ r3EX and the mode shape matrix Φ R3 On the other hand, when the analysis system 10 is used for vibration analysis of gear noise, and an external force acts at a position where a transmission error occurs between the gears 130 fixed to the rotating shafts 112a and 112b, the mode shape matrix Φ r3EX is the empty matrix.

[0056] Alternatively, when the analysis system 10 is used for vibration analysis other than the vibration analysis of gear noise, and an external force acts on a position other than the gear meshing point 140 of the gear 130 fixed to the rotating shaft 112b and the rotating shaft 112c, the mode shape matrix Φ r3EX is a matrix of the degrees of freedom of the gear meshing point 140 at that position. On the other hand, when the analysis system 10 is used for vibration analysis other than the vibration analysis of gear noise, and no external force acts on the rotating shaft 112c, the mode shape matrix Φ r3EX is the empty matrix.

[0057] The method of dividing the mass, damping, stiffness, and displacement for each eigenmode in this way is also called modal analysis. In modal analysis, the above parameters are handled in a system different from the system in which general physical quantities are handled. In this disclosure, in order to distinguish between the two systems, the system in which general physical quantities are handled is also called the "physical domain," and the system in modal analysis is also called the "mode domain." Therefore, the mass matrix M S ,m r1 ,m r2 ,m r3 , the damping matrix C S ,c r1 ,c r2 ,c r3 , stiffness matrix K s ,k r1 ,k r2 ,k r3 , and the mode shape matrix Φ S ,Φ r1 ,Φ r2 ,Φ r3 It can be said that it is a matrix in the mode domain. In addition, the external force f EX P is expressed as a physical quantity, and can therefore be considered an external force in the physical domain.

[0058] In one example, the acquisition unit 11 uses a transformation matrix Φ WP We obtain the transformation matrix Φ WP is the displacement W in the mode region described later. P Let W be the displacement in the physical domain. P F is the matrix for converting to the transformation matrix Φ WP A different matrix is ​​set for each position of the analysis object 1. Therefore, the acquisition unit 11 sets the transformation matrix Φ WP Get the.

[0059] Each of the characteristic matrices and the transformation matrices may be stored in a given storage unit, for example. Each of the characteristic matrices and the transformation matrices may be stored in a memory or a database in the analysis system 10, or may be stored in a memory or a database that is external to the analysis system 10. In this case, the acquisition unit 11 may acquire each of the characteristic matrices and the transformation matrices from the storage unit. Alternatively, the acquisition unit 11 may accept the characteristic matrices and the transformation matrices input by the user.

[0060] In step S4, the dividing unit 12 divides the coupled vibration into a plurality of cells. In one example, the dividing unit 12 divides the coupled vibration into a plurality of cells by dividing ... EX P The coupled vibration generated by the above is divided into a plurality of cells C each representing a combination of a vibration at a first angular frequency selected in the housing 111 and a vibration at each of a plurality of second angular frequencies associated with the first angular frequency in the rotating shafts 112a, 112b, and 112c.

[0061] The cell C will be described in further detail with reference to Fig. 6. Fig. 6 is a diagram showing a schematic diagram of an example of a cell.

[0062] In the example shown in FIG. 6, the first angular frequency is the external force f EX P Consider the case where the angular frequency ω of the first angular frequency is selected. In this case, the vibration at the angular frequency ω selected as the first angular frequency propagates to the rotating shafts 112a, 112b, and 112c via the bearing portion 120. In the rotating shaft 112a, the vibration at the angular frequency ω excites vibration at the angular frequency ω, vibration at the angular frequency ω+Ω1, and vibration at the angular frequency ω-Ω1. In the rotating shaft 112b, the vibration at the angular frequency ω excites vibration at the angular frequency ω, vibration at the angular frequency ω+Ω2, and vibration at the angular frequency ω-Ω2. In the rotating shaft 112c, the vibration at the angular frequency ω excites vibration at the angular frequency ω, vibration at the angular frequency ω+Ω3, and vibration at the angular frequency ω-Ω3. These ten vibrations constitute one cell C.

[0063] From the above, it can be said that the multiple second angular frequencies associated with the first angular frequency are angular frequencies of vibrations directly excited by the vibration of the first angular frequency. In other words, it can be said that the cell C indicates a combination of vibration at the first angular frequency and vibrations directly excited by the vibration. Here, the "directly excited vibration" refers to vibrations excited without going through vibrations at angular frequencies other than the first angular frequency. The division unit 12 generates a cell C for each selected first angular frequency while changing the value of the selected first angular frequency, and divides the coupled vibration into multiple cells C.

[0064] As described above, in the coupled vibration, an external force acting on the analysis object excites, in both the stationary system and the rotating system, a vibration at the angular frequency of the external force and a vibration at an angular frequency shifted from the angular frequency of the external force by an integer multiple of the rotational angular velocity of the rotating system. Therefore, in the analysis object 1, whose structural part 110 has three rotation axes 112a, 112b, and 112c, the angular frequencies of the excited vibrations are expressed as ω±x0Ω1±y0Ω2±z0Ω3.

[0065] In one example, the dividing unit 12 selects a first angular frequency in the stationary system from the angular frequencies ω±x0Ω1±y0Ω2±z0Ω3. In this case, the dividing unit 12 selects the first angular frequency in the stationary system based on the generation number G of the cells acquired in step S2 and the angular frequencies ω±x0Ω1±y0Ω2±z0Ω3 of the vibrations excited by the external force acting on the analysis target 1, and divides the coupled vibration into a plurality of cells C.

[0066] In one example, the generation unit 14 selects a first angular frequency in a stationary system from among angular frequencies represented by a combination of orders x0, y0, and z0 that satisfy the following formula (1), and divides the coupled vibration into a plurality of cells C.

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[0067] That is, the generation unit 14 selects a first angular frequency from among the angular frequencies whose sum of the orders x0, y0, and z0 is equal to or less than the number of generations G, and divides the coupled vibration into a plurality of cells C. For example, when the number of generations G is "1", the seven first angular frequencies selected are "ω-Ω1", "ω-Ω2", "ω-Ω3", "ω", "ω+Ω1", "ω+Ω2", and "ω+Ω3".

[0068] In step S5, the constant matrix calculation unit 13 calculates a first constant matrix and a second constant matrix. The first constant matrix refers to a matrix indicating the dynamic stiffness of the structural part for each of the multiple cells C, and the second constant matrix refers to a matrix indicating the dynamic stiffness of the bearing part for each of the multiple cells C.

[0069] In one example, the constant matrix calculation unit 13 calculates a first constant matrix D indicating the dynamic stiffness of the structural unit 110 for each of the multiple cells C based on the stationary system matrix and the rotational system characteristic matrix. t (g i0 ) and a second constant matrix E indicating the dynamic stiffness of the bearing portion 120 JP Calculate the following:

[0070] First constant matrix D t (g i0 Here, an example of a method for calculating g i0 is a value that indicates the order of multiple cells C, for example, D t (1) indicates the first cell, and D t (5) indicates the fifth cell.

[0071] In one example, the order of the multiple cells C is determined by the magnitude of the first angular frequency in each cell C. In this case, for example, the order of the multiple cells C is determined in ascending order of the first angular frequency. When evaluating the magnitude of the first angular frequency, the magnitude of the first angular frequency itself may be directly evaluated, or an index indicating the magnitude of the first angular frequency itself may be calculated and then evaluated based on the index. In one example, the index is calculated by weighting the orders x0, y0, z0 of the first angular frequency expressed as ω±x0Ω1±y0Ω2±z0Ω3 by the rotational angular velocities Ω1, Ω2, Ω3 of the rotation axes 112a, 112b, 112c. By introducing such an index, the evaluation of the magnitude of the first angular frequency can be performed simply.

[0072] The constant matrix calculation unit 13 calculates a first constant matrix D t (g i0 ), first, the mass matrix M C ´ and the integration matrix E str and the remainder matrix M o_d ´ and are calculated.

[0073] Mass matrix M C The mass matrix M′ is a matrix that combines the mass matrices of both the stationary system (casing 111) and the rotating system (rotating shafts 112a, 112b, and 112c). C Each component of the mass matrix M′ includes at least a mass matrix of a stationary system and a mass matrix of a rotating system. C ´ is the mass matrix M of the housing 111 s and the mass matrix m of the rotation axes 112a, 112b, and 112c. r1 ,m r2 ,m r3 In this case, the mass matrix M C ' is expressed by the following equation (1). Mass matrix M C In ´, all elements other than the diagonal elements are zero.

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[0074] Integration Matrix E str is the damping matrix C of the stationary system (casing 111) S and stiffness matrix K S and the damping matrix C of the rotating system (rotating shafts 112a, 112b, 112c) r1 ,C r2 ,C r3 and stiffness matrix K r1 ,K r2 ,K r3 This is a matrix that integrates the above. str Each component of the stationary system integration matrix E s and the rotational system integration matrix E r1 ,E r2 ,E r3 The present invention includes at least the following:

[0075] Stationary system integration matrix E s is the damping matrix C of the housing 111 s and stiffness matrix K s For example, it is expressed by the following equation (3).

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[0076] Rotational system integration matrix E r1 is the damping matrix c of the rotating shaft 112a r1 and stiffness matrix k r1 For example, it is expressed by the following equation (4).

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[0077] Rotational system integration matrix E r2 is the damping matrix c of the rotating shaft 112b. r2 and stiffness matrix k r2 For example, it is expressed by the following equation (5).

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[0078] Rotational system integration matrix E r3 is the damping matrix c of the rotating shaft 112c r3 and stiffness matrix k r3 For example, it is expressed by the following equation (6).

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[0079] In one example, the integration matrix E str is the stationary system integration matrix E s and the rotational system integration matrix E r1 ,E r2 ,E r3 In this case, the integration matrix E str is expressed by the following equation (7). str In, all elements other than the diagonal elements are zero.

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[0080] Remainder matrix M o_d ´ is the first constant matrix D t (g i0 ) is introduced to simplify the remainder matrix M o_d By introducing ´, the first constant matrix D t (g i0 The reason why the remainder matrix M o_d Each component of the equation (1) includes at least the product of the rotational angular velocity of a rotating system and the mass matrix of the rotating system corresponding to the rotational angular velocity.

[0081] In one example, the remainder matrix M o_d ' is the rotational angular velocity Ω1 of the rotating shaft 112a and the mass matrix m r1, the rotational angular velocity Ω2 of the rotation shaft 112b, and the mass matrix m r2 , the rotational angular velocity Ω3 of the rotation axis 112c, and the mass matrix m r3 and the matrix placed on both ends of the diagonal. In this case, the remainder matrix M o_d ´ is expressed by the following equation (8). The remainder matrix M o_d In , all components other than those at both ends of the diagonal are zero.

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[0082] Next, the constant matrix calculation unit 13 calculates the eigenvalue λ i0 and the mass matrix M C ´ and the integration matrix E str , the imaginary unit j and the remainder matrix M o_d The first constant matrix D is calculated by solving the following equation (9) which is a product of ´ and a sum of . t (g i0 ) is calculated.

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[0083] Here, the first constant matrix D t (g i0 ) is calculated using the remainder matrix M o_d If we do not introduce ', we need to introduce a matrix that integrates the first and third terms on the right side of equation (9). The above matrix corresponds to the inertia term in the equation of motion for each of the multiple cells C. However, in the above matrix, the mass matrix M s and the mass matrix m r1 ,m r2 ,m r3 and must be placed on the diagonal. Therefore, in the above matrix, components corresponding to different angular frequencies exist in one matrix, which may make the equations complicated to handle.

[0084] On the other hand, the remainder matrix M o_d By introducing ´, the eigenvalue λ i0 The mass matrix M corresponding to s ,m r1 ,m r2 ,m r3 Then, we can extract only the eigenvalue λ i0 Mass matrix M corresponding to angular frequencies other than s ,m r1 ,m r2 ,m r3 is the remainder matrix M o_d This can be summarized as ´. i0 The part corresponding to and the other parts can be separated, and the first constant matrix D t (g i0 ) can be summarized succinctly.

[0085] Second constant matrix E JP An example of a method for calculating the second constant matrix E is described below. The constant matrix calculation unit 13 calculates the second constant matrix E for each of the multiple cells C based on the rotational angular velocities Ω1, Ω2, and Ω3, the stiffness parameters c1 and c2, and the damping parameters k1 and k2 among the analysis parameters. JP Calculate.

[0086] In one example, the constant matrix calculation unit 13 calculates the second constant matrix E JP First, the constant matrix calculation unit 13 calculates a dynamic stiffness matrix for each of the vibrations at the first angular frequency and a plurality of second angular frequencies constituting each cell C based on the rotational angular velocities Ω1, Ω2, Ω3, stiffness parameters c1, c2, and damping parameters k1, k2 among the analysis parameters. Next, the calculated dynamic stiffness matrix is ​​converted into a matrix arranged at the position of the corresponding angular frequency into a second constant matrix E. JP In this case, the second constant matrix E JP The relationship between the arrangement and the angular frequency within the space is defined, for example, as follows.

[0087] First, the constant matrix calculation unit 13 calculates the number of vibrations constituting the cell C by the second constant matrix E JP For example, in the example shown in FIG. 6, the number of vibrations constituting the cell C is "10". Therefore, in the above case, the constant matrix calculation unit 13 calculates the second constant matrix E JP Set as a matrix of 10 blocks by 10 blocks, where a block consists of one or more rows and one or more columns of the matrix. That is, the second constant matrix E JP It can be said that a matrix is ​​an integrated matrix of multiple blocks. In one example, such a block is also called a block matrix, and dividing a matrix into multiple blocks is also called block division.

[0088] Next, the constant matrix calculation unit 13 calculates the set second constant matrix E JP The block rows and block columns are regarded as the angular frequencies of the vibrations constituting cell C, and the calculated dynamic stiffness matrices are placed in the corresponding positions in the matrix. In the case of cell C shown in Fig. 6, the constant matrix calculation unit 13 regards the 1st block row to the 10th block row and the 1st block column to the 10th block column as the angular frequencies of the vibrations constituting cell C arranged in ascending order. That is, in cell C shown in Fig. 6, the 1st block row and the 1st block column correspond to the smallest angular frequency in cell C, and the 10th block row and the 10th block column correspond to the largest angular frequency in cell C.

[0089] Based on such a correspondence relationship, the constant matrix calculation unit 13 arranges the dynamic stiffness matrix for each vibration constituting the cell C in the corresponding block, thereby calculating the second constant matrix E JP Therefore, each dynamic stiffness matrix arranged in the corresponding block is calculated by the second constant matrix E JP It can also be said that the matrix is ​​a block matrix in

[0090] As mentioned above, the mass matrix M S ,m r1,m r2 ,m r3 , the damping matrix C S ,c r1 ,c r2 ,c r3 , and the stiffness matrix K s ,k r1 ,k r2 ,k r3 is a matrix in the mode domain. Therefore, the first constant matrix D calculated based on these matrices is t (g i0 ) and the second constant matrix E JP In other words, the constant matrix calculation unit 13 calculates a first constant matrix D t (g i0 ) and a second constant matrix E indicating the dynamic stiffness of the bearing portion 120 in the mode region. JP This can also be said to calculate the following.

[0091] In step S6, the generator 14 calculates the external force f EX P and the displacement W in the analysis object 1 P An example of this process will be described with reference to Fig. 7. Fig. 7 is a flow chart showing an example of generating the relational expression.

[0092] In step S6 shown in FIG. 7, the generation unit 14 calculates the external force f EX P and the displacement W in the analysis object 1 P The relational expression is generated by applying external force f EX P When an external force f acts on EX P In addition, the displacement generates a bearing force f J P The bearing force f J P In the process shown in FIG. 7, the generator 14 calculates the displacement of the object by applying an external force fex The first displacement u when J0 P and bearing force f JP The second displacement W when PJ By calculating both displacements and combining them, the external force f EX P and the displacement W in the analysis object 1 P Here, as described above, the displacement calculated by the analysis system 10 is a complex displacement. Therefore, the first displacement u J0 P The second displacement W PJ It should be noted that the above equations are also complex displacements. In the following, a method for calculating each matrix required for calculating both displacements and a method for generating the above relational expressions will be described in more detail.

[0093] In step S601, the generation unit 14 calculates a third constant matrix and a fourth constant matrix. The third constant matrix refers to a matrix indicating the dynamic stiffness of the structural part in all of the cells C, and the fourth constant matrix refers to a matrix indicating the dynamic stiffness of the bearing part in all of the cells C.

[0094] In one example, the generator 14 generates a first constant matrix D t (g i0 ) and the second constant matrix E JP Based on this, the third constant matrix D of the structure 110 in the entire plurality of cells C is ts and a fourth constant matrix E of the bearing portion 120 in the entire plurality of cells C. JPS Calculate.

[0095] Third constant matrix D ts An example of a method for calculating the first constant matrix D for each of the multiple cells C will be described. t (g i0 ) as the third constant matrix D ts In one example, the generation unit 14 calculates the first constant matrix D t (g i0) as diagonal elements, the third constant matrix D ts In this case, the third constant matrix D ts is expressed by the following equation (10). Here, the third constant matrix D ts In this case, all elements other than the diagonal elements are zero, and N indicates the number of cells C. That is, the third constant matrix D ts is the first constant matrix D of each cell C t (g i0 ) is arranged on the diagonal components in the same order as the number of cells C.

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[0096] Fourth constant matrix E JPS An example of a method for calculating the second constant matrix E for each of the multiple cells C will be described. JP The matrix with elements is the fourth constant matrix E JPS In one example, the generation unit 14 calculates the second constant matrix E JP The matrix with these elements arranged on the diagonal is called the fourth constant matrix E JPS In this case, the fourth constant matrix E JPS is expressed by the following equation (11). Here, the fourth constant matrix E JPS In, all elements other than the diagonal elements are zero.

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[0097] In step S602, the generation unit 14 extracts a pod P from each cell C. In one example, the generation unit 14 extracts a pod P from each cell C that indicates a combination of vibration at a selected first angular frequency in the stationary system (housing 111) and vibration at a second angular frequency equal to the first angular frequency among a plurality of second angular frequencies in the rotating system (rotating shafts 112a, 112b, 112c).

[0098] The pod P will be described in more detail with reference to Fig. 8. Fig. 8 is a diagram showing an example of a pod. Fig. 8 is a diagram showing a pod P extracted from the cell C (see Fig. 6) in which the angular frequency ω is selected as the first angular frequency.

[0099] As described above, when extracting the pod P from the cell C, a combination of vibration at the first angular frequency and vibration at a second angular frequency equal to the first angular frequency among a plurality of second angular frequencies is extracted. That is, vibration at the first angular frequency in both the housing 111 and the rotating shafts 112a, 112b, and 112c is extracted from each vibration excited by an external force acting on the analysis target 1. The pod P is composed of vibration at a single angular frequency (first angular frequency) and can be said to be the smallest unit of vibration in the coupled vibration.

[0100] In step S603, the generation unit 14 calculates a fifth constant matrix and a sixth constant matrix. The fifth constant matrix refers to a matrix indicating the dynamic stiffness of the structural parts in the entirety of the multiple pods P, and the sixth constant matrix refers to a matrix indicating the dynamic stiffness of the bearing parts in the entirety of the multiple pods P.

[0101] In one example, the generator 14 generates a third constant matrix D ts and the fourth constant matrix E JPS Based on this, a fifth constant matrix d representing the dynamic stiffness of the structural unit 110 in the entire pods P is calculated. ps and a sixth constant matrix E indicating the dynamic stiffness of the bearing portion 120 in the entirety of the plurality of pods P. JJS Calculate the following:

[0102] Fifth constant matrix d ps First, the generation unit 14 calculates the transformation matrix Q OR Calculate the transformation matrix Q OR is the third constant matrix D ts The fifth constant matrix d ps Therefore, the transformation matrix Q ORIt can be said that the matrix converts the dynamic stiffness of the structural unit 110 in the entirety of the multiple cells C into the dynamic stiffness of the structural unit 110 in the entirety of the multiple pods P.

[0103] The generation unit 14 generates a transformation matrix Q based on the size of the stationary system characteristic matrix and the size of the rotating system characteristic matrix acquired in step S3. OR In one example, the generation unit 14 calculates the fifth constant matrix d ps As mentioned above, the fifth constant matrix d ps is a matrix indicating the dynamic stiffness of the structural unit 110 in the entirety of the multiple pods P. Here, the third constant matrix D ts does not take into account the connections between the individual cells C. However, in actual coupled vibration, each of the divided multiple cells C does not exist as an independent vibration, but rather the multiple cells C exist while influencing each other. Similarly, in actual coupled vibration, each pod P extracted from the multiple cells C also exists while influencing each other. Therefore, when analyzing coupled vibration, it is necessary to perform calculations while taking into account such connections between each pod P. Therefore, the fifth constant matrix d ps In order to faithfully reflect the behavior of actual coupled vibration, the calculation is performed under the assumption that each of the multiple cells C is connected by a spring with infinite stiffness.

[0104] Therefore, the generation unit 14 generates a conversion matrix Q OR In this case, the generation unit 14 uses, for example, a unit matrix I and zero as components, and determines the arrangement of the unit matrix I based on the size of the stationary system characteristic matrix and the size of the rotating system characteristic matrix to calculate the transformation matrix Q OR Calculate.

[0105] In one example, the generation unit 14 adopts the number of degrees of freedom of the stationary system (housing 111) as the size of the stationary system characteristic matrix, and adopts the number of degrees of freedom of the rotating system (rotation axes 112a, 112b, 112c) as the size of the rotating system characteristic matrix. That is, the generation unit 14 calculates the transformation matrix Q based on the degrees of freedom of the housing 111 and the degrees of freedom of the rotation axes 112a, 112b, 112c. OR Determine the placement of the unit matrix I in the transformation matrix Q OR Transformation matrix Q OR In, all components other than the component in which the unit matrix I is placed are zero.

[0106] Next, the generation unit 14 calculates a third constant matrix D ts From the left, the transformation matrix Q OR Q is the transpose matrix of OR T Then multiply by the transformation matrix Q from the right. OR By multiplying by , the fifth constant matrix d ps As shown in equation (12), the fifth constant matrix d ps In this case, all elements except the diagonal elements are zero.

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[0107] The fifth constant matrix d shown in equation (12) ps The constant matrix d p (g i0 ) is expressed by the eigenvalue λ i0 and the mass matrix M S and the stationary system integration matrix E S and the eigenvalue λ for each of the rotation axes 112a, 112b, and 112c. i0 and the mass matrix (m r1 ,m r2 , or m r3 ) and the rotational system integration matrix (E r1 ,E r2 , or E r3) is arranged on the diagonal. p (g i0 ), all elements other than the diagonal are zero.

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[0108] The constant matrix d shown in equation (13) p (g i0 ) and the first constant matrix D t (g i0 ), the size of the constant matrix d p (g i0 ) is the size of the first constant matrix D t (g i0 ) is smaller than the size of the constant matrix d p (g i0 ) is the fifth constant matrix d ps The size of the first constant matrix D t (g i0 ) is placed on the diagonal of the third constant matrix D ts Therefore, the size of the third constant matrix D ts The fifth constant matrix d ps The size of the matrix can be reduced by converting it into

[0109] The transformation matrix Q reflects the above technical ideas. OR The fifth constant matrix d transformed by ps is calculated taking into consideration that multiple pods P affect each other. Therefore, the fifth constant matrix d ps It can be said that indicates the dynamic stiffness of the structure 110 in the entirety of the multiple pods P, which faithfully reflects the behavior of the actual coupled vibration.

[0110] Sixth constant matrix E JJS First, the generation unit 14 calculates the transformation matrix QOP Calculate the transformation matrix Q OP is the fourth constant matrix E JPS The sixth constant matrix E JJS Therefore, the transformation matrix Q OP It can also be said that the matrix converts the dynamic stiffness of the bearing portion 120 in the entirety of the multiple cells C into the dynamic stiffness of the bearing portion 120 in the entirety of the multiple pods P.

[0111] The generator 14 generates a transformation matrix Q OR Similar to the calculation of the above, the conversion matrix Q is calculated based on the size of the stationary system characteristic matrix and the size of the rotating system characteristic matrix obtained in step S3. OP In one example, the generation unit 14 calculates the transformation matrix Q OR The conversion matrix Q OP In this case, the generation unit 14 uses, for example, a unit matrix I and zero as components, and determines the arrangement of the unit matrix I based on the size of the stationary system characteristic matrix and the size of the rotating system characteristic matrix to calculate the transformation matrix Q OP Calculate.

[0112] In one example, the generation unit 14 adopts the number of degrees of freedom of the stationary system (housing 111) as the size of the stationary system characteristic matrix, and adopts the number of degrees of freedom of the rotating system (rotation axes 112a, 112b, 112c) as the size of the rotating system characteristic matrix. That is, the generation unit 14 calculates the transformation matrix Q based on the degrees of freedom of the housing 111 and the degrees of freedom of the rotation axes 112a, 112b, 112c. OP Determine the placement of the unit matrix I in the transformation matrix Q OP Transformation matrix Q OP In, all elements other than the diagonal elements are zero.

[0113] Next, the generation unit 14 calculates a fourth constant matrix E JPS For the transformation matrix Q OP Q is the transpose matrix of OPT Then multiply by the transformation matrix Q from the right. OP By multiplying by , the sixth constant matrix E JJS Calculate.

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[0114] Third constant matrix D ts and the fifth constant matrix d ps Similarly, the fourth constant matrix E JPS The size of the sixth constant matrix E JJS Therefore, the size of the fourth constant matrix E JPS The sixth constant matrix E JJS The size of the matrix can be reduced by converting it into

[0115] Fifth constant matrix d ps Similarly, the transformation matrix Q OP The sixth constant matrix E transformed by JJS In this calculation, the mutual influence of multiple pods P is taken into consideration. Therefore, the sixth constant matrix E calculated by equation (14) JJS It can be said that indicates the dynamic stiffness of the bearing portion 120 that faithfully reflects the actual coupled vibration.

[0116] In step S604, the generation unit 14 calculates the fifth constant matrix d ps and external force f EX P Based on the first displacement u J0 P In one example, the generator 14 calculates the external force f under the assumption that the damping and stiffness of the bearing 120 are zero. EX P The displacement when the force acts on the first displacement u J0 P That is, the generator 14 calculates the displacement when the bearing force is not taken into consideration as the first displacement u J0 P It can be calculated as:

[0117] The generator 14 calculates a first displacement u J0 P To calculate the mode shape matrix Φ J P ,Φ EX Calculate the mode shape matrix Φ J P is the mode shape matrix for the bearing 120. The mode shape matrix Φ EX refers to the mode shape matrix for the load point.

[0118] Mode Shape Matrix Φ J P An example of a method for calculating the mode shape matrix Φ SJ Based on the matrix Φ SJ In one example, the generator 14 calculates the mode shape matrix Φ SJ and an identity matrix I having a size corresponding to the relative displacement degree of freedom of the gear meshing point 140. ncs The matrix with the diagonal elements of SJ In this case, the matrix Φ SJ For example, the matrix Φ is expressed by the following equation (15). SJ In ´, all elements other than the diagonal elements are zero.

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[0119] Next, the generator 14 calculates a mode shape matrix Φ r1J ,Φ r2J ,Φ r3J Based on the matrix Φ r1J ',Φ r2J ',Φ r3J In one example, the generator 14 calculates the corresponding mode shape matrix Φ r1J ,Φ r2J ,Φ r3Jand the mode shape matrix Φ R1 ,Φ R2 ,Φ R3 The matrix containing and as components is called the matrix Φ r1J ',Φ r2J ',Φ r3J In this case, the matrix Φ r1J ',Φ r2J ',Φ r3J ' is expressed, for example, by the following equations (16), (17), and (18).

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[0120] Next, the generation unit 14 converts the calculated matrix Φ SJ ',Φ r1J ',Φ r2J ',Φ r3J The matrix with ´ placed on the diagonal is called the mode shape matrix Φ J P The mode shape matrix Φ is calculated as shown in Fig. 11. J P 1 is a diagram showing the mode shape matrix Φ J P In, all elements other than the diagonal elements are zero.

[0121] Mode Shape Matrix Φ EX An example of a method for calculating the mode shape matrix Φ SEX Based on the matrix Φ SEX In one example, the generator 14 calculates the mode shape matrix Φ SEX and an identity matrix I having a size corresponding to the relative displacement degree of freedom of the gear meshing point 140. ncs The matrix in which and are arranged as diagonal elements is called the matrix ΦSEX In this case, the matrix Φ SEX For example, the matrix Φ is expressed by the following equation (19). SEX In ´, all elements other than the diagonal elements are zero.

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[0122] Next, the generator 14 calculates the corresponding mode shape matrix Φ r1EX ,Φ r2EX ,Φ r3EX A matrix Φ with r1EX ',Φ r2EX ',Φ r3EX In one example, the generator 14 calculates the mode shape matrix Φ r1EX The matrix with the diagonal elements of r1EX The generator 14 calculates the mode shape matrix Φ r2EX The matrix with the diagonal elements arranged as the diagonal elements is called the matrix Φ r2EX The generator 14 calculates the mode shape matrix Φ r3EX The matrix with the diagonal elements of r3EX In this case, the matrix Φ r1EX ',Φ r2EX ',Φ r3EX ' is expressed by, for example, the following equations (20), (21), and (22). Matrix Φ r1EX ',Φ r2EX ',Φ r3EX In each of the ', the components other than the diagonal components are zero.

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[0123] Next, the generation unit 14 converts the calculated matrix Φ SEX ',Φ r1EX ',Φ r2EX ',Φ r3EX The matrix with ' arranged as diagonal elements is called the mode shape matrix Φ EX The mode shape matrix Φ is calculated as shown in Fig. 12. EX 1 is a diagram showing the mode shape matrix Φ EX In, all elements other than the diagonal elements are zero.

[0124] Next, the generator 14 generates a transfer matrix H PS Calculate the transfer matrix H PS is a transfer matrix between the input force and the displacement, and is a transfer matrix in the modal domain. In one example, the generation unit 14 generates a fifth constant matrix d ps The inverse matrix of the transfer matrix H PS It is calculated as follows.

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[0125] Next, the generation unit 14 calculates the external force f ex In one example, the generation unit 14 calculates the external force f EX P By converting it into the mode domain, the external force f ex For example, the generation unit 14 calculates an external force f EX P For the transformation matrix Q OR Transpose matrix Q OR T and the mode shape matrix Φ EX The transpose matrix Φ EX T By multiplying by f, the external force in the mode domain ex Calculate.

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[0126] Next, the generator 14 generates a transfer matrix H JJPS Calculate the transfer matrix H JJPS is the transfer matrix H PS Similarly, it refers to a transfer matrix between input forces and displacements, but the matrix is ​​a transfer matrix in the physical domain.

[0127] In one example, the generator 14 generates a transfer matrix H PS By converting to the physical domain, the transfer matrix H JJPS For example, the generation unit 14 calculates a transfer matrix H PS From the left, the mode shape matrix Φ JP and multiplying it by the mode shape matrix Φ JP The transpose matrix Φ JP T By multiplying by JJPS Calculate.

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[0128] Next, the generator 14 generates a first displacement u j0 P As mentioned above, the transfer matrix H PS is the transfer matrix between the input force and the displacement in the modal domain. Therefore, the external force f ex Let H be the transfer matrix PS By inputting the external force f ex Displacement due to external force f ex The first displacement u when J0 P Therefore, the generator 14 obtains the transfer matrix H PS External force fex By inputting the first displacement u j0 P Calculate.

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[0129] In step S605, the generation unit 14 calculates the fifth constant matrix d ps and the sixth constant matrix E JJS Based on the above, the bearing force f in the physical domain is JP In one example, the generator 14 calculates the first displacement u J0 P and the sixth constant matrix E JJS Based on the bearing force f JP In this case, the generator 14 calculates the bearing force f JP As described above, the first displacement u J0 P is the fifth constant matrix d PS The transfer matrix H is calculated as the inverse matrix of PS External force f ex Therefore, the first displacement u J0 P and the sixth constant matrix E JJS Even if the matrix is ​​based on the fifth constant matrix d PS and the sixth constant matrix E JJS Based on the bearing force f JP It can be said that the calculation is

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[0130] In equation (27), the first displacement u J0 P is the external force f ex Since this is the displacement when the force is applied, the first displacement u J0 P and the sixth constant matrix E JJS The product of this is the external force f ex The bearing force generated by the transfer matrix HJJPS is the external force f ex The displacement is also caused by the bearing force generated by the transfer matrix H JJPS and the sixth constant matrix E JJS The product of these two forces indicates the amount of change in the bearing force. Therefore, as shown in equation (27), the external force f EX P (External force f ex ) and the bearing force f that takes into account the displacement caused by the bearing force generated by the displacement JP can be calculated.

[0131] In step S606, the generation unit 14 calculates the fifth constant matrix d ps and bearing force f JP Based on the second displacement W PJ In one example, the generation unit 14 calculates a fifth constant matrix d ps The transfer matrix H calculated based on ps and bearing force f JP Based on the second displacement W PJ As mentioned above, the bearing force f JP is a quantity in the physical domain. Therefore, this bearing force f JP After converting to the modal domain, the bearing force in the modal domain is expressed as the transfer matrix H PS By inputting the bearing force f JP Displacement due to bearing force f JP The second displacement W when PJ As a result, the generator 14 obtains the bearing force f in the physical domain as shown in the following equation (28). JP From the left, the mode shape matrix Φ JP The matrix obtained by multiplying the transposed matrix of is called the transfer matrix H PS The second displacement W PJ Calculate.

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[0132] In step S607, the generation unit 14 calculates the external force f EX P and the displacement W in the analysis object 1 P In one example, the generation unit 14 generates a relational expression based on the first displacement u J0 P and the second displacement W calculated in step S605. PJ In one example, the generator 14 generates the above relational expression by combining the first displacement u J0 P and the second displacement W PJ By taking the sum of this and (29), the relational expression shown below in equation (29) is generated.

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[0133] Returning to FIG. 5, in step S7, the displacement calculation unit 15 calculates the displacement W P F In one example, the displacement calculation unit 15 first calculates the displacement W P Next, the displacement calculation unit 15 calculates the displacement W P By converting it into the physical domain, the displacement W P F That is, the displacement W P F It can also be said that the displacement in the physical domain. For example, the displacement calculation unit 15 calculates the displacement W in the mode domain as shown in the following equation (30): P For the transformation matrix Φ obtained in step S3 WP By multiplying by W, the displacement in the physical domain P F Calculate.

number

[0134] In step S8, the output unit 16 outputs the processing result. In one example, the output unit 16 outputs the displacement W calculated in step S7. P F Alternatively, the output unit 16 outputs the displacement W P F In addition to the first displacement u J0 P , the second displacement W PJ , displacement W P and bearing force f JP The output unit 16 outputs at least one of the displacements W and W as a processing result. P F Alternatively, the output unit 16 may store the displacement W P F Alternatively, the output unit 16 may output the displacement W P F may be transmitted.

[0135] Next, a modified example of the process of generating a relational equation will be described with reference to Fig. 13. Fig. 13 is a flowchart showing another example of the generation of a relational equation. In step S6 shown in Fig. 13, the generation unit 14 generates an equation of motion for each of the multiple cells C, and calculates a transfer matrix H C The generation unit 14 calculates the transfer matrix H C Let H be the transfer matrix H across multiple cells C. Ca and convert the transfer matrix H Ca Based on the external force f ex P and the displacement W in the analysis object 1. The method of generating the relational expression will be described in more detail below.

[0136] In step S611, the generation unit 14 generates an equation of motion for each of the multiple cells C. In one example, the generation unit 14 generates a matrix B and an integrated matrix E str and the second constant matrix E JP and the displacement matrix Wc (g i0 ) and the external force F, an equation of motion is generated for each of the cells C. Here, the external force F is an arbitrary external force set for the convenience of calculation, and the external force f acting on the analysis object 1 is EX P Note that this is different from

[0137] Matrix B represents the inertia term in the equation of motion of each cell C, and is expressed, for example, by the following equation (31). str represents the structural reaction term in the equation of motion of each cell C. The second constant matrix E JP represents the bearing force term in the equation of motion of each cell C. The displacement matrix W c (g i0 ) is the displacement (response) in each cell C, and its components are the displacements in vibrations at the angular frequencies contained in one cell. Here, g i0 As described above, is a value indicating the ordinal number of the cell among the multiple cells C.

number

[0138] When an equation of motion for each cell C is generated using the above-mentioned matrices, the equation of motion is expressed, for example, by the following equation (32).

number

[0139] In step S612, the generation unit 14 generates a transfer matrix for each of the multiple cells C. The generation unit 14 generates a transfer matrix for each of the multiple cells C by modifying the equation of motion expressed by equation (32), for example, as follows:

[0140] First, the generation unit 14 introduces a matrix B′ for transforming the equation expressed by the following equation (33), and combines the matrix B′ with the mass matrix M CUsing and, equation (32) is transformed into the following equation (34).

number

number

[0141] Next, the generation unit 14 calculates in the formula (34) J -B´-E str ) into the matrix E C ´, equation (34) is transformed into the following equation (35).

number

[0142] Next, the generation unit 14 adds (λ i0 M C ´-E C By multiplying it by the inverse matrix of (x,y), the right-hand side of equation (35) is rearranged, and equation (35) is transformed into the following equation (36).

number

[0143] From equation (36), the external force F and (λ i0 M C ´-E C The product of this with the inverse matrix of C (g i0 Therefore, (λ i0 M C ´-E C The inverse matrix of (λ ´) can be said to represent the transfer matrix for each cell C. Hereafter, as shown in the following equation (37), i0 M C ´-E C ´) is the inverse matrix of the transfer matrix H C (g i0 ) will be explained as follows.

number

[0144] In step S613, the generation unit 14 calculates the external force f EX P and the displacement W in the analysis object 1. In one example, the generation unit 14 first generates a relational expression for the transfer matrix H C (g i0 ) to generate an integrated matrix H, and the integrated matrix H is used as a transfer matrix H for the entire plurality of cells C. Ca Next, the generation unit 14 converts the converted transfer matrix H Ca Using the external force f EX P and the displacement W in the analysis object 1. The above process will be described in further detail below.

[0145] The generation unit 14 generates a transfer matrix H C (g i0 ) as the integrated matrix H. In one example, the generation unit 14 generates a transfer matrix H C (g i0 ) as diagonal elements is calculated as the integrated matrix H. In this case, the integrated matrix H is expressed by the following formula (38). Here, in the integrated matrix H, the cells other than the diagonal elements are zero, and N indicates the number of cells C. In other words, the integrated matrix H is calculated by dividing the transfer matrix H C It can also be said that this is a matrix in which the number of diagonal components is the same as the number of cells C.

number

[0146] Next, the generation unit 14 converts the integrated matrix H into a transfer matrix H Ca In one example, the generator 14 first converts the integrated matrix H into a transfer matrix HCa To convert to, the transformation matrix Q 0base Generate the transformation matrix Q 0base is the integration matrix H, which is the transfer matrix H Ca That is, the transformation matrix Q 0base is the transfer matrix H of each cell C C The integrated matrix H is arranged on the diagonal of the number of cells C, and the transfer matrix H Ca It can also be said that it is a matrix that transforms

[0147] The generation unit 14 uses the unit matrix I and zero as components, and determines the arrangement of the unit matrix I based on the size of the stationary system characteristic matrix, the size of the rotating system characteristic matrix, and the order of the multiple cells C, thereby generating the transformation matrix Q 0base Generate.

[0148] In one example, the number of degrees of freedom of the stationary system (housing 111) is used as the size of the stationary system characteristic matrix, and the number of degrees of freedom of the rotating system (rotation axes 112a, 112b, 112c) is used as the size of the rotating system characteristic matrix. That is, the generation unit 14 generates the transformation matrix Q based on the number of degrees of freedom of the housing 111, the number of degrees of freedom of the rotation axes 112a, 112b, 112c, and the order of the multiple cells C. 0base Determine the placement of the identity matrix I in

[0149] Next, the generation unit 14 generates the integrated matrix H and the transformation matrix Q 0base By matrix operation with, the integration matrix H is converted to the transfer matrix H Ca In one example, the integration matrix H is converted into the transfer function H Ca Convert to.

number

[0150] Next, the generation unit 14 calculates an external force f EX P The external force f in the mode areaEX In one example, the generator 14 converts the external force f EX P The external force f EX To convert to, first, the transformation matrix Φ EX_C Calculate the transformation matrix Φ EX_C is the external force f EX P The external force f EX This refers to a matrix for converting

[0151] Transformation matrix Φ EX_C An example of a method for calculating the matrix Φ SEX ',Φ r1EX ',Φ r2EX ',Φ r3EX The matrix with ' as its components is called the matrix Φ ex_c In one example, the generation unit 14 calculates the matrix Φ SEX ',Φ r1EX ',Φ r2EX ',Φ r3EX The matrix with ' arranged on the diagonal is called the matrix Φ ex_c In this case, the matrix Φ ex_c is expressed by the following equation (40), where the matrix Φ ex_c In, all elements other than the diagonal elements are zero.

number

[0152] Next, the generator 14 calculates the matrix Φ ex_c The matrix with elements is the transformation matrix Φ EX_C In one example, the generation unit 14 calculates the matrix Φ ex_c The matrix with the diagonal elements is called the transformation matrix Φ EX_C In this case, the transformation matrix Φ EX_C is expressed by the following equation (41). Here, the transformation matrix Φ EX_C In, all elements other than the diagonal elements are zero.

number

[0153] Next, the generation unit 14 calculates an external force f EX P From the left, the transformation matrix Φ EX_C The transpose matrix Φ EX_C T By multiplying by f EX Calculate.

number

[0154] Next, the generation unit 14 calculates the external force f EX P and the displacement W in the analysis object 1. In one example, the transfer matrix H Ca and external force f EX By multiplying with, we generate the relation shown in equation (43) below.

number

[0155] Here, matrix B expressed by equation (31) and integrated matrix E expressed by equation (7) str The sum of these is the first constant matrix D t (g i0 Therefore, the equation of motion for each of the cells C expressed by equation (32) is expressed as the first constant matrix D t (g i0 ) and the second constant matrix E JP That is, using the equation of motion expressed by equation (32), the external force f EX P In step S6 shown in FIG. 13, a relational expression between the displacement W in the analysis object 1 and the first constant matrix Dt(g i0 ) and the second constant matrix E JPBased on the external force f EX P and the displacement W in the analysis object 1.

[0156] Returning to FIG. 5, when step S6 shown in FIG. 13 is executed, in step S7, the displacement calculation unit 15 calculates the displacement W F In one example, the displacement calculation unit 15 first calculates the displacement W, which is the displacement in the mode domain, based on the formula (43). Next, the displacement calculation unit 15 converts the displacement W in the mode domain into a displacement in the physical domain to obtain the displacement W F That is, the displacement W F It can be said that W is a displacement in the physical domain. For example, the displacement calculation unit 15 calculates a transformation matrix Φ W By multiplying by W, the displacement in the physical domain F Calculate.

number

[0157] When step S6 shown in FIG. 13 is executed, the displacement W calculated in step S7 is F Alternatively, the output unit 16 calculates the displacement W F In addition, the output unit 16 outputs, as a processing result, at least one of the displacement W and the equation of motion for each of the plurality of cells C. The output unit 16 outputs the calculated displacement W F Alternatively, the output unit 16 may store the displacement W F Alternatively, the output unit 16 may output the displacement W F may be transmitted.

[0158] [Variations] Various examples of the present disclosure have been described in detail above. However, the present disclosure is not limited to the above examples. Various modifications of the present disclosure are possible without departing from the spirit and scope of the present disclosure.

[0159] The generation unit 14 may employ orders x, y, and z instead of the number of generations G when dividing the coupled vibration into a plurality of cells C. That is, the generation unit 14 may select a first angular frequency in the stationary system based on the orders x, y, and z and the angular frequencies ω±x0Ω1±y0Ω2±z0Ω3 of the vibrations excited by the external force acting on the analysis target 1, and divide the coupled vibration into a plurality of cells C. Here, the orders x, y, and z, like the number of generations G, also refer to values ​​indicating a criterion for determining how many cells the coupled vibration should be divided into, and are set for each rotational system.

[0160] For example, order x is the order set for rotation axis 112a, order y is the order set for rotation axis 112b, and order z is the order set for rotation axis 112c. Each of orders x, y, and z is an integer equal to or greater than 0. Orders x, y, and z may be different from each other, or at least two of these orders may be the same. In this case, in step S2, acquisition unit 11 may acquire orders x, y, and z.

[0161] When the orders x, y, and z are used to divide the coupled vibration into multiple cells C, the first angular vibration in the stationary system may be selected, for example, as follows. First, the division unit 12 sets the minimum value of the selection range for selecting the first angular frequency to ω-xΩ1-yΩ2-zΩ3 and the maximum value to ω+xΩ1+yΩ2+zΩ3. Next, the division unit 12 selects an angular frequency within the selection range as the first angular frequency in the stationary system, and divides the coupled vibration into multiple cells C. For example, when each of the orders x, y, and z is "1", the selected first angular frequencies are "ω-Ω1-Ω2-Ω3", "ω-Ω1-Ω2", "ω-Ω1-Ω2+Ω3", " ω-Ω1-Ω3”, “ω-Ω1”, “ω-Ω1+Ω3”, “ω-Ω1+Ω2-Ω3”, “ω-Ω1+Ω2”, “ω-Ω1+Ω2+Ω3”, “ω-Ω2-Ω3”, “ω-Ω2”, “ω-Ω2+Ω3”, “ω-Ω3”, “ω”, “ω+Ω3”, “ω+Ω2-Ω3”, “ω+Ω2”, “ω+Ω2+Ω3”, “ω+Ω1-Ω2-Ω3”, “ω+Ω1-Ω2”, “ω+Ω1-Ω2+Ω3”, “ω+Ω1-Ω3”, “ω+Ω1”, “ω+Ω1+Ω3”, “ω+Ω1+Ω2-Ω3”, “ω+Ω1+Ω2”, “ω+Ω1+Ω2+Ω3”.

[0162] The analysis method executed by at least one processor is not limited to the above examples. For example, some of the steps or processes described above may be omitted, or each step may be executed in a different order. Also, any two or more of the steps described above may be combined, or some of the steps may be modified or deleted. Alternatively, other steps may be executed in addition to each of the steps described above.

[0163] In this disclosure, the expression "at least one processor executes a first process, executes a second process, ... executes an nth process" or a corresponding expression indicates a concept including a case where the processor that executes the n processes from the first process to the nth process changes midway. In other words, this expression indicates a concept including both a case where all of the n processes are executed by the same processor and a case where the processor changes among the n processes according to an arbitrary policy.

[0164] [Note] As can be seen from the various examples above, the present disclosure includes the following aspects. <Item 1> At least one processor; the at least one processor: Acquire an external force acting on an analysis object including a structural part having a stationary system and one or more rotating systems, and one or more bearing parts supporting the one or more rotating systems in the stationary system; A stationary system characteristic matrix indicating vibration characteristics of the stationary system and a rotating system characteristic matrix indicating vibration characteristics of the rotating system are obtained; Dividing a coupled vibration generated by the external force in the stationary system and the rotating system into a plurality of cells each representing a combination of a vibration at a selected first angular frequency in the stationary system and a vibration at each of a plurality of second angular frequencies associated with the first angular frequency in the rotating system; calculating, for each of the plurality of cells, a first constant matrix indicating a dynamic stiffness of the structural portion and a second constant matrix indicating a dynamic stiffness of the bearing portion based on the stationary system characteristic matrix and the rotating system characteristic matrix; generating a relational expression between the external force and a displacement in the analysis object based on the first constant matrix and the second constant matrix; calculating the displacement at a predetermined position of the analysis object based on the external force and the relational expression; Analysis system. <Item 2> the at least one processor: calculating a third constant matrix indicating a dynamic stiffness of the structural portion in the entirety of the plurality of cells and a fourth constant matrix indicating a dynamic stiffness of the bearing portion in the entirety of the plurality of cells based on the first constant matrix and the second constant matrix; extracting, from each of the plurality of cells, a pod that indicates a combination of a vibration at the selected first angular frequency in the stationary system and a vibration at a second angular frequency equal to the first angular frequency among the plurality of second angular frequencies in the rotating system; calculating a fifth constant matrix indicating a dynamic stiffness of the structural part in the entirety of the plurality of pods and a sixth constant matrix indicating a dynamic stiffness of the bearing part in the entirety of the plurality of pods based on the third constant matrix and the fourth constant matrix; generating the relational expression based on the fifth constant matrix and the sixth constant matrix; Item 1. The analysis system according to item 1. <Item 3> the at least one processor: calculating a first displacement when the external force is applied based on the fifth constant matrix and the external force; calculating a bearing force, which is a reaction force according to the stiffness and damping of the bearing portion, generated by a displacement caused by the external force based on the fifth constant matrix and the sixth constant matrix; calculating a second displacement when the bearing force is applied based on the fifth constant matrix and the bearing force; generating the relational expression by combining the first displacement and the second displacement; Item 2. The analysis system according to item 2. <Item 4> the at least one processor: acquiring a number of cell generations, which is a value indicating a criterion for determining how many cells the coupled vibration should be divided into when dividing the coupled vibration into the plurality of cells; Dividing the coupled vibration into the plurality of cells based on the number of generations. The analysis system according to any one of items 1 to 3. <Item 5> 1. A method of analysis performed by an analysis system having at least one processor, comprising: acquiring an external force acting on an analysis object including a structural part having a stationary system and one or more rotating systems, and one or more bearing parts supporting the one or more rotating systems in the stationary system; acquiring a stationary system characteristic matrix indicating vibration characteristics of the stationary system and a rotating system characteristic matrix indicating vibration characteristics of the rotating system; Dividing a coupled vibration generated by the external force in the stationary system and the rotating system into a plurality of cells representing a combination of a vibration at a selected first angular frequency in the stationary system and a vibration at each of a plurality of second angular frequencies associated with the first angular frequency in the rotating system; calculating, for each of the plurality of cells, a first constant matrix indicating a dynamic stiffness of the structural portion and a second constant matrix indicating a dynamic stiffness of the bearing portion based on the stationary system characteristic matrix and the rotating system characteristic matrix; generating a relational expression between the external force and a displacement in the analysis object based on the first constant matrix and the second constant matrix; calculating the displacement at a predetermined position of the analysis object based on the external force and the relational expression; Analysis methods including: <Item 6> acquiring an external force acting on an analysis object including a structural part having a stationary system and one or more rotating systems, and one or more bearing parts supporting the one or more rotating systems in the stationary system; acquiring a stationary system characteristic matrix indicating vibration characteristics of the stationary system and a rotating system characteristic matrix indicating vibration characteristics of the rotating system; Dividing a coupled vibration generated by the external force in the stationary system and the rotating system into a plurality of cells representing a combination of a vibration at a selected first angular frequency in the stationary system and a vibration at each of a plurality of second angular frequencies associated with the first angular frequency in the rotating system; calculating, for each of the plurality of cells, a first constant matrix indicating a dynamic stiffness of the structural portion and a second constant matrix indicating a dynamic stiffness of the bearing portion based on the stationary system characteristic matrix and the rotating system characteristic matrix; generating a relational expression between the external force and a displacement in the analysis object based on the first constant matrix and the second constant matrix; calculating the displacement at a predetermined position of the analysis object based on the external force and the relational expression; An analysis program that causes a computer to execute the above.

[0165] According to items 1, 5, and 6, the coupled vibration between the stationary system and the rotating system is decomposed into vibrations for each cell, and the dynamic stiffness of both the structural part and the bearing part is shown for each cell. In this way, by considering the coupled vibration between the stationary system and the rotating system as a collection of vibrations in each cell, it is possible to simplify the calculation of the displacement (vibration) in the object to be analyzed. As a result, it is possible to analyze the coupled vibration of the engine quickly and stably.

[0166] As described above, the analysis system 10 can be used for the vibration analysis of gear noise. In the conventional vibration analysis of gear noise, the vibration analysis is performed by modeling a state in which the rotation of each rotating system (rotating shafts 112a to 112c) is ignored. Therefore, it cannot be said that the conventional vibration analysis of gear noise faithfully reflects the actual situation. Furthermore, in the conventional vibration analysis of gear noise, since the rotation of each rotating system is ignored, it is not possible to analyze vibrations at angular frequencies other than the angular frequency of the external force given as an input. On the other hand, in the analysis system 10, by using the rotation angular velocity of the rotating shafts 112a to 112c in the calculation, it is possible to consider the rotation of the rotating shafts 112a to 112c and analyze vibrations at each angular frequency selected as the first angular frequency and the multiple second angular frequencies. As a result, the analysis system 10 can perform an analysis that is in line with the actual situation. As described above, according to items 1, 5, and 6, even when performing vibration analysis of gear noise, an analysis that is more suited to actual conditions can be performed compared to conventional methods, and gear noise can be analyzed with even greater accuracy.

[0167] When the sizes of the third constant matrix and the fourth constant matrix are compared with the sizes of the fifth constant matrix and the sixth constant matrix, the sizes of the fifth constant matrix and the sixth constant matrix are smaller than the sizes of the third constant matrix and the fourth constant matrix. In item 2, a relational equation between an external force and an object to be analyzed is generated based on the fifth constant matrix and the sixth constant matrix, which are even smaller in size. Therefore, according to item 2, the relational equation can be generated even faster. In other words, according to item 2, the coupled vibration of an engine can be analyzed even faster.

[0168] In coupled vibration, a displacement occurs due to an applied external force, and a bearing force generated by this displacement further acts, causing the displacement to change. In item 3, the displacement when an external force is applied and the displacement when a bearing force is applied are combined in consideration of this change, thereby generating a relational equation between the external force and the object to be analyzed. Therefore, according to item 3, the coupled vibration of an engine can be analyzed with high accuracy.

[0169] In the coupled vibration, the cycle of vibration propagation and excitation is repeated countless times. On the other hand, the amplitude of the vibration becomes smaller as the vibration is at an angular frequency farther away from the angular frequency of the applied external force. Therefore, the amplitude of the vibration at an angular frequency sufficiently far away from the angular frequency of the applied external force is small enough to be ignored in the analysis of the coupled vibration, and ignoring such vibrations makes it possible to perform the analysis at a much higher speed. In item 4, by setting the number of cell generations, which is a value indicating a criterion for determining how many cells the coupled vibration should be divided into, the analysis can be performed without considering vibrations whose amplitude is small enough to be ignored. Therefore, according to item 4, the coupled vibration of the engine can be analyzed at a much higher speed. [Explanation of symbols]

[0170] 1...analysis object, 10...analysis system, 101...processor, 110...structural part, 120...bearing part, C...cell, P...pod.

Claims

1. At least one processor; the at least one processor: Acquire an external force acting on an analysis object including a structural unit having a stationary system and one or more rotating systems, and one or more bearing units supporting the one or more rotating systems in the stationary system; A stationary system characteristic matrix indicating vibration characteristics of the stationary system and a rotating system characteristic matrix indicating vibration characteristics of the rotating system are obtained; Dividing a coupled vibration generated by the external force in the stationary system and the rotating system into a plurality of cells each representing a combination of a vibration at a selected first angular frequency in the stationary system and a vibration at each of a plurality of second angular frequencies associated with the first angular frequency in the rotating system; calculating, for each of the plurality of cells, a first constant matrix indicating a dynamic stiffness of the structural portion and a second constant matrix indicating a dynamic stiffness of the bearing portion based on the stationary system characteristic matrix and the rotating system characteristic matrix; generating a relational expression between the external force and a displacement in the analysis object based on the first constant matrix and the second constant matrix; calculating the displacement at a predetermined position of the analysis object based on the external force and the relational expression; Analysis system.

2. the at least one processor: calculating a third constant matrix indicating a dynamic stiffness of the structural portion in the entirety of the plurality of cells and a fourth constant matrix indicating a dynamic stiffness of the bearing portion in the entirety of the plurality of cells based on the first constant matrix and the second constant matrix; extracting, from each of the plurality of cells, a pod that indicates a combination of a vibration at the selected first angular frequency in the stationary system and a vibration at a second angular frequency equal to the first angular frequency among the plurality of second angular frequencies in the rotating system; calculating a fifth constant matrix indicating a dynamic stiffness of the structural portion in the entirety of the plurality of pods and a sixth constant matrix indicating a dynamic stiffness of the bearing portion in the entirety of the plurality of pods based on the third constant matrix and the fourth constant matrix; generating the relational expression based on the fifth constant matrix and the sixth constant matrix; The analysis system according to claim 1 .

3. the at least one processor: calculating a first displacement when the external force is applied based on the fifth constant matrix and the external force; calculating a bearing force, which is a reaction force according to the stiffness and damping of the bearing portion, generated by a displacement caused by the external force based on the fifth constant matrix and the sixth constant matrix; calculating a second displacement when the bearing force is applied based on the fifth constant matrix and the bearing force; generating the relational expression by combining the first displacement and the second displacement; The analysis system according to claim 2 .

4. the at least one processor: acquiring a number of cell generations, which is a value indicating a criterion for determining how many cells the coupled vibration should be divided into when dividing the coupled vibration into the plurality of cells; Dividing the coupled vibration into the plurality of cells based on the number of generations. The analysis system according to any one of claims 1 to 3.

5. 1. A method of analysis performed by an analysis system having at least one processor, comprising: acquiring an external force acting on an analysis object including a structural part having a stationary system and one or more rotating systems, and one or more bearing parts supporting the one or more rotating systems in the stationary system; acquiring a stationary system characteristic matrix indicating vibration characteristics of the stationary system and a rotating system characteristic matrix indicating vibration characteristics of the rotating system; Dividing a coupled vibration generated in the stationary system and the rotating system by the external force into a plurality of cells representing a combination of a vibration at a selected first angular frequency in the stationary system and a vibration at each of a plurality of second angular frequencies associated with the first angular frequency in the rotating system; calculating, for each of the plurality of cells, a first constant matrix indicating a dynamic stiffness of the structural portion and a second constant matrix indicating a dynamic stiffness of the bearing portion based on the stationary system characteristic matrix and the rotating system characteristic matrix; generating a relational expression between the external force and a displacement in the analysis object based on the first constant matrix and the second constant matrix; calculating the displacement at a predetermined position of the analysis object based on the external force and the relational expression; Analysis methods including:

6. acquiring an external force acting on an analysis object including a structural part having a stationary system and one or more rotating systems, and one or more bearing parts supporting the one or more rotating systems in the stationary system; acquiring a stationary system characteristic matrix indicating vibration characteristics of the stationary system and a rotating system characteristic matrix indicating vibration characteristics of the rotating system; Dividing a coupled vibration generated in the stationary system and the rotating system by the external force into a plurality of cells representing a combination of a vibration at a selected first angular frequency in the stationary system and a vibration at each of a plurality of second angular frequencies associated with the first angular frequency in the rotating system; calculating, for each of the plurality of cells, a first constant matrix indicating a dynamic stiffness of the structural portion and a second constant matrix indicating a dynamic stiffness of the bearing portion based on the stationary system characteristic matrix and the rotating system characteristic matrix; generating a relational expression between the external force and a displacement in the analysis object based on the first constant matrix and the second constant matrix; calculating the displacement at a predetermined position of the analysis object based on the external force and the relational expression; An analysis program that causes a computer to execute the above.

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