Vibration analysis method and vibration analysis program

Abstract

To provide a vibration analyzing method for precisely analyzing vibration of a focused portion of an object subjected to analysis.SOLUTION: In a vibration analyzing method, the following processes are executed. For a discretization model for an object subjected to vibration analysis, focused node points representing node points of an element that forms a focused portion are identified. A characteristic value and a characteristic vibration vector of each node point are calculated by executing characteristic-value analysis on the discretization model. The characteristic vibration vector of the focused node point is extracted from the characteristic vibration vector of each node point. One or a plurality of vibration modes that forms the vibration of the focused portion, and a partial mode contribution rate representing the degree of contribution to the vibration of the focused portion by each vibration mode are calculated on the basis of the characteristic vibration vector of the focused node point.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention mainly relates to a vibration analysis method for analyzing vibrations occurring in an object by using a numerical simulation. [Background technology]

[0002] Patent Document 1 discloses a vibration analysis device that analyzes vibrations using the finite element method. The vibration analysis device calculates the vibration mode of an object by performing eigenvalue analysis on an input finite element model. Furthermore, the vibration analysis device divides the finite element model into regions and calculates the vibration mode for the nodes included in each region. The vibration mode calculated for each region is used to calculate the degree of interlocking that indicates the degree of interlocking vibration between the regions. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2008-307271 A Summary of the Invention [Problem to be solved by the invention]

[0004] Patent Document 1 discloses calculating the vibration mode of the entire object and the vibration mode in area units, but does not disclose a method for analyzing the vibration occurring in each area in more detail.

[0005] The present invention has been made in consideration of the above circumstances, and a main object of the present invention is to provide a vibration analysis method for analyzing in detail the vibration of a target portion of an object. [Means for solving the problem]

[0006] The problem to be solved by the present invention has been described above. Next, the means for solving this problem and the effects thereof will be described.

[0007] According to a first aspect of the present invention, there is provided a vibration analysis method including the following processes. That is, a node of interest indicating a node of an element constituting a part of interest is identified for a discretized model of an object to be subjected to vibration analysis. An eigenvalue and an eigenvibration vector of each node are calculated by performing an eigenvalue analysis on the discretized model. An eigenvibration vector of the node of interest is extracted from the calculated eigenvibration vectors of each node. Based on the extracted eigenvibration vector of the node of interest, one or more vibration modes constituting the vibration of the part of interest and a partial mode contribution rate indicating the degree to which each vibration mode contributes to the vibration of the part of interest are calculated.

[0008] According to a second aspect of the present invention, there is provided a vibration analysis program as follows. That is, this vibration analysis program causes an information processing device to execute a process including a specification step, an analysis step, an extraction step, and a calculation step. In the specification step, a node of interest indicating a node of an element constituting a portion of interest is specified for a discretized model of an object to be subjected to vibration analysis. In the analysis step, an eigenvalue analysis by the finite element method is performed on the discretized model to calculate an eigenvector of each node. In the extraction step, an eigenvector of the node of interest is extracted from the eigenvectors of each node calculated in the analysis step. In the calculation step, one or more vibration modes constituting the vibration of the portion of interest and a partial mode contribution rate indicating the degree to which each vibration mode contributes to the vibration of the portion of interest are calculated based on the eigenvector of the node of interest extracted in the extraction step.

[0009] By referring to the partial mode contribution rate of the target part, it is possible to confirm the type of vibration occurring in the target part and the degree to which each vibration contributes to the vibration of the target part. Therefore, it is possible to grasp the vibration of the target part in more detail compared to a method of performing vibration analysis on the entire target object. Effect of the Invention

[0010] According to the present invention, it is possible to provide a vibration analysis method for analyzing in detail the vibration of a target portion of an object. [Brief description of the drawings]

[0011] [Figure 1] 2 is a schematic diagram of a vibration analysis method according to the present embodiment; [Diagram 2] 3 is a flowchart of a vibration analysis method. [Diagram 3] FIG. 4 is a diagram conceptually showing a modal contribution rate and a partial modal contribution rate. [Figure 4] FIG. 4 is a diagram conceptually showing a partial mode contribution rate. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] Next, an embodiment of the present invention will be described with reference to the drawings. First, an outline of a vibration analysis method according to the present embodiment will be described with reference to FIG.

[0013] In this embodiment, the vibration of the object is analyzed using a numerical simulation. As the numerical simulation, for example, the finite element method, the finite volume method, the boundary element method, etc. can be used, but in this embodiment, the case where the finite element method is used will be described. Note that the finite element method is a method of dividing the object into a plurality of elements, performing a calculation for each element, and accumulating the results to calculate information about the object. Since the finite element method is well known, a detailed description will be omitted.

[0014] Methods of vibration analysis using the finite element method include eigenvalue analysis and frequency response analysis. Eigenvalue analysis is a method of analyzing the vibration of an object based on the mass distribution and stiffness distribution of the object. Frequency response analysis is a method of analyzing the vibration of an object based on the mass distribution and stiffness distribution of the object, as well as the damping distribution of the object and an external force acting on the object. Since the vibration analysis method of this embodiment is an eigenvalue analysis, it is not necessary to input damping and external force.

[0015] In this embodiment, the object of vibration analysis is a vehicle, specifically a motorcycle. Note that the object is not limited to a motorcycle, and may be another vehicle, a ship, or an aircraft. The object is not limited to a vehicle, and may be a building, industrial machine, or the like.

[0016] In this embodiment, the vibration analysis is used to determine the direction of a design proposal in the early stage of vehicle design, for example, before a prototype is manufactured. For example, the vibration analysis is used to verify vibrations that may occur in a certain design proposal, or to search for a structure to reduce vibrations that may become a problem. In this embodiment, as shown in FIG. 1, vibration analysis is performed on two three-dimensional models A and B having different frame shapes, and vibrations that may occur in the three-dimensional models A and B are compared. The three-dimensional model is CAD data that indicates the three-dimensional shape of an object, and further includes information indicating the distribution of mass and rigidity of the object. The vibration analysis method of this embodiment is not limited to the early stage of design, and may be used to search for improvement plans after a prototype is manufactured.

[0017] The vibration analysis method is performed by an analysis device 1. The analysis device 1 is an information processing device, and includes a calculation device such as a CPU, and a storage device such as an HDD or SSD. The calculation device reads and executes programs stored in the storage device, allowing the analysis device 1 to perform various calculations. The programs stored in the storage device include a vibration analysis program for performing the vibration analysis method.

[0018] The analysis device 1 performs a vibration analysis method using, for example, the finite element method on the input three-dimensional models A and B to calculate the partial mode contribution rate (the detailed calculation method will be described later). The partial mode contribution rate is information that associates the vibration modes of natural vibrations that may occur in a target part of the object with their contribution rates. The contribution rate is the rate at which each vibration mode contributes to the vibration of the target part (degree of contribution).

[0019] As shown in Fig. 1, in this embodiment, the partial mode contribution rate is calculated by using the motorcycle seat as a target part. In Fig. 1, the partial mode contribution rate is shown in a graph format. The horizontal axis of the graph represents the vibration frequency, and the vertical axis of the graph represents the contribution rate. By performing a vibration analysis method, a plurality of vibration modes that may occur in the target part are calculated. Each vibration mode is plotted using a symbol according to the vibration direction, at a horizontal axis position according to the vibration frequency and at a vertical axis position according to the contribution rate.

[0020] Furthermore, in the graph of FIG. 1, a predetermined vibration frequency range is set as the evaluation range. The evaluation range is the frequency range of vibrations generated in a motorcycle (for example, vibrations caused by the engine). In order to reduce the effects of resonance, it is undesirable for vibration modes with high contribution rates to be in the evaluation range. As shown by the dotted line in FIG. 1, in three-dimensional model A, vibration modes with high contribution rates exist in the evaluation range, whereas in three-dimensional model B, these types of vibration modes do not exist (or their contribution rates are low). Therefore, it can be assumed that by making the frame shape like three-dimensional model B, the vibrations generated in the seat will be reduced.

[0021] The comparison between the partial mode contribution rate of the three-dimensional model A and the partial mode contribution rate of the three-dimensional model B may be performed by the designer or by the analysis device 1. For example, when the designer performs the comparison, the analysis device 1 outputs a graph showing the mode contribution rates of the three-dimensional models A and B to a display. When the analysis device 1 performs the comparison, the analysis device 1 identifies a vibration mode whose contribution rate exceeds a threshold value within the evaluation range and exists in one partial mode contribution rate but does not exist in the other partial mode contribution rate. Note that the method of comparing the partial mode contribution rates is one example, and the comparison may be performed by a different method. Alternatively, the process of performing the comparison may be omitted. In this case, it is possible to identify a vibration mode that may occur in a focused portion of one design proposal.

[0022] Next, a method for calculating the partial mode contribution rate and the effects thereof will be specifically described with reference to FIG. 2 to FIG.

[0023] First, the analysis device 1 generates a discretized model of an object based on an input 3D model (S101). Specifically, the analysis device 1 divides the 3D model into elements of a predetermined 3D shape based on information specified by a designer or the like. The shape of each element is, for example, a tetrahedron, but may be a different shape. Furthermore, the analysis device 1 sets nodes at the boundaries between the elements. The nodes are set, for example, at the end points of the elements, but may also be set at other locations (for example, the midpoints of the element sides). Furthermore, the elements and the nodes are associated with each other, and for example, by selecting an element, it is possible to identify the nodes located at the boundaries of the selected element.

[0024] In this embodiment, the analysis device 1 generates a discretized model, but an externally generated discretized model may be input to the analysis device 1. In addition, the analysis method is not limited to the finite element method, and a known analysis method may be used, and the analysis device 1 generates a discretized model according to the analysis method.

[0025] Next, the analysis device 1 groups the nodes of the portion of interest (S102, identification step). Specifically, the analysis device 1 identifies elements included in an area designated by a designer or the like using an operation device such as a mouse, and identifies nodes associated with the elements. The analysis device 1 adds information indicating that the identified nodes are nodes of the portion of interest to the identified nodes (more specifically, identification information for identifying settings). This makes it possible to read out the nodes of the portion of interest in a later process. In the following description, the nodes of the portion of interest are referred to as nodes of interest.

[0026] Note that the node of interest may be identified by a method different from that of this embodiment. For example, when the three-dimensional model is grouped by part or assembly, a designer or the like may specify a part or assembly, and the analysis device 1 may specify the node of an element that constitutes the specified part or assembly.

[0027] Next, the analysis device 1 performs eigenvalue analysis on the discretized model of the object to calculate the natural frequency and natural vibration vector (S103, analysis step). Since eigenvalue analysis is a well-known technique, it will be explained briefly. As described above, eigenvalue analysis does not require the input of an external force, and calculates the natural frequency (eigenvalue) and natural vibration vector (eigenvector, mode vector) from the mass distribution and stiffness distribution of the object.

[0028] Specifically, the natural frequency and the natural vibration vector are calculated by solving the equation (1) in FIG. 2, that is, the eigenvalue equation. As described above, the three-dimensional model input to the analysis device 1 includes information indicating the distribution of the mass and the distribution of the stiffness of the object. The analysis device 1 calculates the stiffness matrix and the mass matrix based on this information. The stiffness matrix is ​​used to evaluate the stiffness of each element, and the mass matrix is ​​used to evaluate the mass of each element. Note that instead of the method in which the analysis device 1 calculates the stiffness matrix and the mass matrix, a method in which the stiffness matrix and the mass matrix calculated externally are input to the analysis device 1 may be used. By applying the stiffness matrix and the mass matrix to the eigenvalue equation, multiple sets of natural frequencies and natural vibration vectors that satisfy the eigenvalue equation are calculated. Note that in the following description, a matrix representation of multiple natural vibration vectors is referred to as a mode matrix.

[0029] Next, the analysis device 1 extracts the mass matrix and mode matrix of the part of interest (S104, extraction step). The mass matrix of the part of interest is a mass matrix in which only the elements constituting the part of interest of the entire object are extracted and described, and is hereinafter referred to as a partial mass matrix. In other words, the partial mass matrix is ​​calculated based on the mass matrix and information that identifies the part of interest. The mode matrix of the part of interest is a mode matrix in which only the elements constituting the part of interest of the entire object are extracted and described, and is hereinafter referred to as a partial mode matrix. In other words, the partial mode matrix is ​​calculated based on the mode matrix and information that identifies the part of interest.

[0030] Next, the analysis device 1 calculates the partial modal contribution rate (S105, calculation step). The calculation method of the partial modal contribution rate is based on the calculation method of the modal contribution rate. Therefore, the calculation method of the modal contribution rate will be described first, and then the calculation method of the partial modal contribution rate will be described.

[0031] The modal contribution ratio is calculated using formula (2) shown in Fig. 3. The left side of formula (2) indicates the modal contribution ratio, and the right side of formula (2) is the product of the transpose of the modal matrix, the mass matrix, and the transformation matrix. Since the process of calculating the modal contribution ratio (stimulation coefficient) using formula (2) is a publicly known technique, a detailed explanation of the method of deriving formula (2) will be omitted. The modal contribution ratio is information that associates the vibration modes of the natural vibration with the proportion (contribution degree) that each vibration mode contributes to the vibration of the entire object.

[0032] In Figure 3, seven vibration modes are shown using the vibration of a tuning fork as an example. To make the explanation easier to understand, the vibration of a tuning fork is used in Figure 3, but in reality, a similar process is performed on an object such as a motorcycle. The overall vibration of the tuning fork, which is the object, is generated by a combination of seven vibration modes. The values ​​such as 32% written under the vibration mode are the modal contribution rates.

[0033] The modal contribution rate evaluates the vibration of the entire object. The 3rd, 4th, and 7th modes in Figure 3 are vibration modes in which the two rod-shaped parts of the tuning fork are in opposite phase, so the vibration of the two rod-shaped parts cancels out, making the vibration of the tuning fork smaller when viewed as a whole. As a result, even if vibrations of the 3rd, 4th, and 7th modes are occurring, the modal contribution rates of these vibration modes will be low. In other words, the vibration of the object cannot be accurately estimated.

[0034] Next, the partial mode contribution rate will be described. The partial mode contribution rate is calculated using formula (3) shown in FIG. 4. Formula (3) is obtained by changing the mass matrix of formula (2) to a partial mass matrix, changing the mode matrix to a partial mode matrix, and changing the transformation matrix to a partial transformation matrix. The transformation matrix is ​​a matrix for allocating the product of the mode matrix and the mass matrix to each directional component. Generally, a unit matrix or a nodal transformation matrix that moves the coordinate system to a reference point is used. In detail, it is a matrix that indicates the distance from the reference point of the element of the focused part to the whole object. By carrying out the above changes, the partial mode contribution rate, which is the mode contribution rate of the focused part, can be calculated.

[0035] As shown in Figure 4, the partial modal contribution rate indicates the modal contribution rate in the vibration of a target part, not in the vibration of the entire object. In this example, one rod-shaped part of the tuning fork is the target part. Therefore, the vibration of the other rod-shaped part does not cancel each other out, so appropriate modal contribution rates can be calculated even in the 3rd mode, 4th mode, and 7th mode, where the two rod-shaped parts of the tuning fork are in opposite phase.

[0036] Furthermore, since vibrations occurring in a target area can be properly detected, vibrations occurring in areas where it is desired to suppress vibrations can be properly evaluated, for example, areas where it is desired to suppress vibrations include areas that people touch in the case of a vehicle (such as the seat and handlebars in the case of a motorcycle), and areas where parts that are vulnerable to vibrations are located in the case of industrial machinery.

[0037] Furthermore, the partial mode contribution ratio can take positive and negative values. For example, when the vibration indicated by the partial mode contribution ratio first starts to vibrate on the positive side of the coordinate system, the partial mode contribution ratio takes a positive value. On the other hand, when the vibration indicated by the partial mode contribution ratio first starts to vibrate on the negative side of the coordinate system, the partial mode contribution ratio takes a negative value. Therefore, for example, when comparing partial mode contribution ratios, it is preferable to use the absolute value of the partial mode contribution ratio.

[0038] If the contribution rate of each vibration mode in the target portion can be described, the partial mode contribution rate may be calculated using an equation other than equation (3).

[0039] Next, the analysis device 1 calculates the partial effective mass (S106). The partial effective mass is a value obtained by squaring the partial modal contribution rate. Since the partial effective mass is always a positive value, the process of comparing the partial effective masses is easy. Note that when only the comparison is performed using the absolute values ​​of the partial modal contribution rates, the process of calculating the partial effective mass can be omitted.

[0040] As described above, the vibration analysis method of this embodiment includes the following processes. That is, a node of interest indicating a node of an element constituting a part of interest is identified for a discretized model of an object to be subjected to vibration analysis. An eigenvalue and an eigenvibration vector of each node are calculated by performing an eigenvalue analysis on the discretized model. An eigenvibration vector of the node of interest is extracted from the calculated eigenvibration vectors of each node. Based on the extracted eigenvibration vector of the node of interest, one or more vibration modes constituting the vibration of the part of interest and a partial mode contribution rate indicating the degree to which each vibration mode contributes to the vibration of the part of interest are calculated.

[0041] By referring to the partial mode contribution rate of the target part, it is possible to confirm the type of vibration occurring in the target part and the degree to which each vibration contributes to the vibration of the target part. Therefore, it is possible to grasp the vibration of the target part in more detail compared to a method of performing vibration analysis on the entire target object.

[0042] In the vibration analysis method of this embodiment, when calculating an eigenvector, a mass matrix of the entire object and a mode matrix describing the eigenvector of the entire object are calculated. When extracting the eigenvector, a partial mass matrix obtained by extracting values ​​related to a node of interest from the mass matrix and a partial mode matrix obtained by extracting values ​​related to the node of interest from the mode matrix are calculated. The calculated partial mode contribution rate is described including the partial mass matrix and the partial mode matrix.

[0043] This makes it possible to calculate the partial modal contribution rate by utilizing a conventional method for calculating the modal contribution rate.

[0044] In the vibration analysis method of this embodiment, a node of interest is identified, an eigenvibration vector is calculated, the eigenvibration vector is extracted, and a partial mode contribution rate is calculated for a portion of interest in a three-dimensional model A (first discretized model) and a portion of interest in a three-dimensional model B (second discretized model) which is a modified version of the three-dimensional model A. After that, the partial mode contribution rate of the portion of interest in the first discretized model is compared with the partial mode contribution rate of the portion of interest in the second discretized model.

[0045] This makes it possible to evaluate the vibration modes resulting from differences in the shapes and structures of 3D models A and B.

[0046] In the vibration analysis method of the present embodiment, a value obtained by squaring a partial mode contribution rate (partial effective mass) is calculated.

[0047] Since partial effective masses are always positive values, it is easy to compare them with each other. In addition, since the unit of partial effective mass is mass, it is easy to understand the calculated numerical value intuitively.

[0048] Although the preferred embodiment of the present invention has been described above, the above configuration can be modified, for example, as follows.

[0049] The flowcharts shown in the above embodiment are merely examples, and some processes may be omitted, some processes may be changed, or new processes may be added. For example, steps S101 and S103 may be performed in advance to store the analysis results of the eigenvalue analysis of the entire object. This method is effective when there are multiple target parts. This is because the analysis results of the eigenvalue analysis of the object are necessary regardless of the part identified as the target part. In other words, if the analysis results of the entire object are stored in advance, the partial mode contribution rate can be calculated by simply performing steps S102, S104, and S105.

[0050] In the above embodiment, the vibration analysis method is executed by the analysis device 1 which is one piece of hardware, but the vibration analysis method may be executed by a plurality of pieces of hardware connected via a network.

[0051] The functions of the elements disclosed herein can be performed using circuits or processing circuits, including general purpose processors, special purpose processors, integrated circuits, Application Specific Integrated Circuits (ASICs), conventional circuits, and / or combinations thereof, configured or programmed to perform the disclosed functions. Processors are considered processing circuits or circuits because they include transistors and other circuits. In this disclosure, a circuit, unit, or means is hardware that performs the recited functions or hardware that is programmed to perform the recited functions. The hardware may be hardware disclosed herein or other known hardware that is programmed or configured to perform the recited functions. Where the hardware is a processor, which is considered a type of circuit, the circuit, means, or unit is a combination of hardware and software, and the software is used to configure the hardware and / or the processor. [Explanation of symbols]

[0052] 1 Analysis device

Claims

1. Identifying nodes of interest that indicate the nodes of elements that constitute the part of interest for a discretized model of the object to be subjected to vibration analysis; Calculating eigenvalues ​​and natural vibration vectors of each node by performing eigenvalue analysis on the discretized model; Extracting the natural vibration vector of the target node from the natural vibration vectors of each node calculated, calculating one or more vibration modes constituting the vibration of the portion of interest and a partial mode contribution rate indicating a degree to which each of the vibration modes contributes to the vibration of the portion of interest based on the extracted natural vibration vector of the node of interest; A vibration analysis method comprising:

2. 2. The vibration analysis method according to claim 1, When calculating the natural vibration vector, a mass matrix of the entire object and a mode matrix describing the natural vibration vector of the entire object are calculated; When extracting the natural vibration vector, a partial mass matrix is ​​calculated by extracting values ​​related to the node of interest from the mass matrix, and a partial mode matrix is ​​calculated by extracting values ​​related to the node of interest from the mode matrix, 4. A vibration analysis method, comprising: a vibration analysis unit for calculating the partial mode contribution ratio, the partial mode contribution ratio being described by including the partial mass matrix and the partial mode matrix.

3. 3. The vibration analysis method according to claim 1, further comprising: After performing the identification of the node of interest, the calculation of the eigenvector, the extraction of the eigenvector, and the calculation of the partial mode contribution rate for the portion of interest of the first discretized model and the portion of interest of a second discretized model obtained by changing a part of the first discretized model, A vibration analysis method comprising: comparing a partial mode contribution rate of the portion of interest of the first discretized model with a partial mode contribution rate of the portion of interest of the second discretized model.

4. A vibration analysis method according to any one of claims 1 to 3, comprising: A vibration analysis method comprising the steps of: calculating a value obtained by squaring the partial mode contribution rate;

5. A vibration analysis method according to any one of claims 1 to 3, comprising:

13. A vibration analysis method, comprising the steps of:

6. An identifying step of identifying a node of interest indicating a node of an element constituting a portion of interest for a discretized model of an object to be subjected to vibration analysis; an analysis step of calculating an eigenvalue vector of each node by performing an eigenvalue analysis on the discretized model; an extraction step of extracting an eigenfrequency vector of the target node from the eigenfrequency vectors of each node calculated in the analysis step; a calculation step of calculating one or more vibration modes constituting the vibration of the portion of interest and a partial mode contribution rate indicating a degree to which each vibration mode contributes to the vibration of the portion of interest, based on the natural vibration vector of the node of interest extracted in the extraction step; A vibration analysis program for causing an information processing device to execute a process including the steps of:

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