JP2007298324A - Vibration analysis system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide technique capable of precisely estimating transfer of vibration energy in a complex structure and visualizing its transfer state. <P>SOLUTION: For each of a plurality of elements constituting a model, a computer executes processing for calculating transfer vector expressing the vibration energy transmitted in the element and processing for displaying the calculated transfer vector for each element with the model. In the processing for calculating the transfer vector, the computer calculates the transfer vector from displacement of each element and internal force acting on each element. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a technique for supporting analysis of a vibration phenomenon of a structure.

  In vehicle development, reduction of body vibration and noise is one of the important issues. However, since the vibration phenomenon is invisible, it is difficult to accurately grasp the cause of the phenomenon. Accordingly, there has been a demand for the emergence of a system that analyzes and visualizes vibration energy (kinetic energy, strain energy) distribution, phase-by-phase change, transmission path, and the like in a three-dimensional structure with high accuracy by a computer.

  Patent Document 1 proposes a system for measuring actual vibration and estimating in what vibration mode the object to be measured vibrates. However, it is possible to estimate with high accuracy if it is a relatively simple structure. However, if the object to be measured is a complicated three-dimensional structure, it is possible to accurately estimate how vibration is transmitted. It was difficult to do.

Moreover, there is a vibration intensity as one of studies for identifying a transmission path of vibration energy in a structure (see Non-Patent Documents 1 and 2). However, the conventional vibration intensity only measures the surface vibration (out-of-plane vibration) of a two-dimensional structure such as a flat plate by experiment and calculates the energy transmission path. Application to three-dimensional structures is difficult.
Japanese Patent Laid-Open No. 11-148858 JP 2000-55776 A JP 2000-120768 A JP-A-6-274184 Naoya Kojima, “Measurement of transient vibration energy flow in passenger car skins using intensity method”, JSME Spring Conference Preprint, 2000, Vol. 31, no. 2, P.I. 23-27 Nakagawa, Y., “Analysis of Dissipated Energy by Vibration Intensity”, Transactions of the Japan Society of Mechanical Engineers (C), 1995, 61, 589, p. 3482-3488

  The present invention has been made in view of the above circumstances, and the object of the present invention is a technique capable of accurately estimating the transmission of vibration energy in a complex structure and visualizing the state of the transmission. It is to provide.

  In order to achieve the above object, the present invention employs the following configuration.

  According to a first aspect of the present invention, for each of a plurality of elements constituting a model, a transfer vector calculating means for calculating a transfer vector representing vibration energy transmitted through the element, and the transfer vector calculated for each element together with the model And an output means for displaying. Here, the transmission vector calculation means calculates the transmission vector from the displacement of each element and the internal force acting on each element.

In the above configuration, the model of the structure to be analyzed is composed of a plurality of elements, and the transmission vector is obtained from the displacement and internal force for each element. It is possible to accurately estimate the vibration energy transmission path in the interior. By displaying the transmission vector thus obtained together with the model, it is possible to visualize how vibration energy is transmitted, and it is possible to support the identification of the cause of vibration and the planning of countermeasures.

  The transmission vector calculation means calculates the power of each mass point from the displacement of the mass point and the internal force acting on the mass point for the two mass points on the element, and calculates the difference in power between the two mass points of the transmission vector. The component in the direction connecting the two mass points is preferable. For example, if the transfer vector is considered in the xy plane of the element coordinate system, the x-direction component of the transfer vector is calculated by focusing on two mass points aligned in the x-axis direction, and the two mass points aligned in the y-axis direction are focused. Thus, the y direction component of the transmission vector may be calculated.

  The inventors of the present invention assume that “vibration energy is transmitted from a larger work to a smaller work in order to maintain an energy balance state”, and under this assumption, the transmission vector is defined as a difference in power between two points. Defined. As a result, the transfer vector can be calculated with high accuracy by a relatively simple calculation. The work rate is the work per unit time, and can be calculated by multiplying the internal force by the speed (time derivative of displacement). The difference in work rate is the difference in work between two points when considered in one cycle in a system with no attenuation (or a system with extremely small attenuation). This is because it becomes 0 (or almost 0), and energy transfer between two points cannot be accurately captured.

  The internal force may include at least one of an axial force, a shearing force, a transverse shearing force, a bending moment and a torsional moment, and more preferably all of an axial force, a shearing force, a transverse shearing force, a bending moment and a torsional moment. It is good to include. Considering many types of internal forces, the accuracy is further improved.

  The transmission vector calculation means preferably obtains the displacement of each element and the internal force acting on each element from the calculation result of the finite element method. Of course, analysis methods other than the finite element method may be used. As the calculation result of the finite element method, since the displacement of each node of the element is usually obtained, the transfer vector calculation means may calculate the displacement of each mass point from the displacement of each node.

  The model is preferably a model of a vehicle body.

  Preferably, the output means displays the transmission vector in a pseudo color according to the size. As a result, not only the energy transmission direction but also information corresponding to the magnitude of vibration energy can be visualized.

  The present invention can be understood as a vibration analysis system having at least a part of the above means. Further, the present invention can also be understood as a vibration analysis method including at least a part of the above processing, a vibration analysis program for realizing the method, or a computer-readable recording medium storing the vibration analysis program. it can. Each of the above means and processes can be combined with each other as much as possible to constitute the present invention.

  For example, in the vibration analysis method according to the second aspect of the present invention, the computer calculates, for each of a plurality of elements constituting the model, a process of calculating a transfer vector representing vibration energy transmitted through the element, and each element. In the vibration analysis method for executing the process of displaying the transmitted vector together with the model, the computer calculates the transmission vector from the displacement of each element and the internal force acting on each element in the process of calculating the transmitted vector. Is to be calculated.

  In addition, the vibration analysis program as the third aspect of the present invention includes a transmission vector calculation means for calculating a transfer vector representing vibration energy transmitted through an element for each of a plurality of elements constituting the model, and each element A vibration analysis program that functions as an output unit that displays the transmission vector calculated for the model together with the model, wherein the transmission vector calculation unit calculates the transmission vector from the displacement of each element and the internal force acting on each element. Is calculated.

  According to the present invention, transmission of vibration energy in a complicated structure can be accurately estimated, and the state of the transmission can be visualized.

  Exemplary embodiments of the present invention will be described in detail below with reference to the drawings.

  The vibration analysis system according to the embodiment of the present invention analyzes the state of vibration energy in a three-dimensional structure such as a vehicle body and visualizes the transmission path of the vibration energy, thereby investigating the cause of vibration and planning countermeasures. It is for support.

<Transmission vector calculation method>
Before describing the specific configuration of the vibration analysis system, the basic concept of the transfer vector calculation method in this embodiment will be described.

  In order to analyze vibration energy in a three-dimensional structure with high accuracy, it is desirable to use state quantities (displacement) and internal forces (axial force, shear force, moment) inside the structure. However, it is extremely difficult to measure such internal state quantities and internal forces by experiments. Therefore, in this embodiment, the internal state quantity and the internal force are calculated by structural analysis by a computer.

As a structural analysis method, a finite element method (FEM) is used. In the finite element method, a three-dimensional structure is represented by an FE model composed of a large number of elements (plate elements, beam elements, etc.). For example, in the case of a vehicle body, an FE model composed of about one million elements is used. When an excitation condition such as an excitation point or an angular frequency is given to the FE model, an internal force acting on each element, a displacement of a node of each element, and the like are calculated. Each element of the FE model also has volume and material information, and a stiffness matrix and a mass matrix for each element are calculated from the information.

  The vibration analysis system calculates a transfer vector representing vibration energy transmitted through the element by using the displacement of the node of each element and the internal force acting on each element obtained as a result of the finite element analysis. As the internal force, axial force, shear force, lateral shear force, bending moment and torsion moment are taken into consideration.

Hereinafter, as illustrated in FIG. 1, a transmission vector calculation method will be described using a plate element having an xy plane that is rectangular and has a thickness in the z-axis direction as an example. The plate element has four nodes P1 to P4, and each node has six degrees of freedom of movement in the x, y, and z axis directions and rotation (angular displacement) around the x, y, and z axes. Therefore, the displacement u of the plate element is represented by a vector composed of 24 components as in the following equation. Note that x, y, and z here are element coordinate systems. If the result of finite element analysis is obtained in the global coordinate system, it is necessary to perform coordinate conversion from global coordinates to element coordinates.

The velocity of the node can be obtained as follows by differentiating the displacement with time.

  Here, two side surfaces facing in the x-axis direction are referred to as plane A and plane B, respectively, an axial force Fx on the x-axis, a lateral shearing force Fxy, a shearing force Vx on the x-axis, a bending moment My around the x-axis, and It is assumed that the torsional moment Mxy acts on points (mass points) PA and PB that are the centers of gravity of the surfaces A and B, respectively. Similarly, the two side surfaces facing in the y-axis direction are plane C and plane D, respectively, the axial force Fy in the y-axis, the transverse shear force Fxy, the shear force Vy in the y-axis, the bending moment Mx around the y-axis, and It is assumed that the torsional moment Mxy acts on the points (mass points) PC and PD which are the centers of gravity of the surfaces C and D, respectively.

The speed of the point PA is obtained as follows by linearly interpolating the speeds of the nodes P1 and P3.

  Similarly, the speed of the point PB is obtained from the speeds of the nodes P2 and P4, the speed of the point PC is obtained from the speeds of the nodes P1 and P2, and the speed of the point PD is obtained from the speeds of the nodes P3 and P4.

(1) Axial Force FIG. 2 schematically shows the transmission direction of vibration energy when the axial force Fx on the x-axis acts. When the axial force Fx acts on the points PA and PB as shown in the figure, the vibration energy is considered to be transmitted in the x-axis direction (direction connecting the points PA and PB). The magnitude of vibration energy transmitted per unit time can be defined as the difference in power due to the axial force Fx between the point PA and the point PB, and specifically can be expressed by the following equation. .

(2) Lateral Shear Force FIG. 3 schematically shows the transmission direction of vibration energy when the transverse shear force Fxy is applied. When the transverse shear force Fxy acts on the points PA and PB as shown in the figure, the vibration energy is considered to be transmitted in the x-axis direction. The magnitude of vibration energy transmitted per unit time can be defined as the difference in power due to the transverse shear force Fxy between the point PA and the point PB. Specifically, it can be expressed by the following equation. it can.

(3) Shear Force FIG. 4 schematically shows the transmission direction of vibration energy when the x-axis shear force Vx is applied. When the shear force Vx acts on the points PA and PB as shown in the figure, the vibration energy is considered to be transmitted in the x-axis direction. The magnitude of vibration energy transmitted per unit time can be defined as the difference in power due to the shearing force Vx between the point PA and the point PB, and specifically can be expressed by the following equation. .

(4) Bending Moment FIG. 5 schematically shows the transmission direction of vibration energy when the bending moment My around the x axis acts. When the bending moment My acts on the points PA and PB as shown in the figure, the vibration energy is considered to be transmitted in the x-axis direction. The magnitude of vibration energy transmitted per unit time can be defined as the difference in power due to the bending moment My between the point PA and the point PB, and specifically can be expressed by the following equation. .

(5) Torsional moment FIG. 6 schematically shows the transmission direction of vibration energy when the torsional moment Mxy acts. When the torsional moment Mxy acts on the points PA and PB as shown in the figure, the vibration energy is considered to be transmitted in the x-axis direction. The magnitude of vibration energy transmitted per unit time can be defined as the difference in power due to the torsional moment Mxy between the point PA and the point PB, and specifically can be expressed by the following equation. .

From the above, the x-axis direction component VIx of the transmission vector can be expressed by Equation 4.

Similarly, the y-axis direction component VIy of the transmission vector can be expressed by Equation 5.

Although the description has been given here taking the plate element shown in FIG. 1 as an example, the transmission vector is calculated using the above equations 4 and 5 if the mass points PA to PD are appropriately set for elements of other shapes. can do.

  Next, a configuration example of the vibration analysis system using the above formulas 4 and 5 will be specifically described.

<System configuration>
FIG. 7 is a block diagram illustrating a functional configuration of the vibration analysis system.

  The vibration analysis system includes a transmission vector calculation unit 1 that calculates a transmission vector, a characteristic value database 2 that stores a calculation result, and an output unit 3 that outputs the calculation result.

  This vibration analysis system typically includes a general-purpose computer including an arithmetic processing unit (CPU), a main storage device (memory), an auxiliary storage device (hard disk, etc.), a display device, and an input device (mouse, keyboard, etc.). And a program that runs on this computer. The functional elements shown in FIG. 1 are realized by an arithmetic processing unit executing a program and controlling hardware resources such as a main storage device, an auxiliary storage device, a display device, and an input device as necessary. . However, a part of these functional elements may be replaced with a dedicated chip. Moreover, it is not necessary for all of these functional elements to be executed by a single computer, and a plurality of computers may cooperate to constitute a vibration analysis system.

<Process flow>
FIG. 8 is a flowchart showing the flow of processing.

  The transfer vector calculation unit 1 acquires the result of the finite element analysis via a storage device or a network (step S10). The information acquired here includes at least the displacement of each element when the FE model is vibrated at a predetermined angular frequency ω and the internal force acting on each element (axial force, shear force, lateral shear force, bending moment, Torsional moment).

  Next, the transmission vector calculation unit 1 calculates the velocity of the node from the displacement of the node of each element (step S11). Conversion from displacement to speed may be performed by time differentiation (see Equation 2).

  Next, the transmission vector calculation unit 1 calculates the speed at the action points PA to PD of the internal force from the speed of the node (step S12). The speed at the point of action can be calculated by linearly interpolating the speed of the node (see Equation 3).

  Next, the transfer vector calculation unit 1 converts the speed of the action point calculated in step S12 from the global coordinate system to the element coordinate system (step S13). However, if the displacement acquired in step S10 was originally in the element coordinate system, the coordinate conversion process here is unnecessary. It should be noted that the same result can be obtained regardless of the order of steps S11 to S13.

  Next, the transfer vector calculation unit 1 calculates the transfer vector of each element according to Expression 4 and Expression 5 from the internal force of each element acquired in Step S10 and the speed of each action point of each element calculated in Step S13. (Step S14). The calculation results are sequentially stored in the characteristic value database 2.

  And the output part 3 reads the transmission vector of each element from the characteristic value database 2, and outputs them to a display apparatus with a model (step S15).

9 and 10 show display examples of calculation results. FIG. 9 shows an example of a cantilever and FIG. 10 shows an example of a vehicle body. In this display example, the transmission vector of each element is displayed superimposed on the FE model. In addition, an excitation point is also displayed on the FE model. By viewing such a display, it is possible to intuitively and easily grasp what path the vibration generated at the excitation point is transmitted to each part of the structure. Further, each transmission vector is displayed in a pseudo color according to its size, so that information corresponding to the magnitude of vibration energy can be intuitively grasped.

  Assume that the analysis result of FIG. 10 is obtained when the vibration sound of the roof panel is a problem. Looking at the display of FIG. 10, it can be seen that vibration energy in the engine compartment is transmitted to the roof panel via the front pillar and vibrates a part of the roof panel. As a result, it is possible to easily guess the mechanism by which the vibration noise of the roof panel is generated. If such consideration is obtained, it will be understood that it is only necessary to reinforce somewhere in the transmission path from the engine compartment to the roof panel or to attach damping materials as countermeasures, and it becomes easy to take appropriate countermeasures. . In addition, since the transmission path and transmission mechanism have been clarified, for example, the location of countermeasures and the contents of countermeasures such as reinforcement of the joint part in the engine compartment, change of the shape of the front pillar, and thickening of the roof panel. Since the degree of freedom increases, there is also an advantage that it is only necessary to take measures that are the easiest to cope with (design change).

  According to the configuration of the present embodiment described above, the model of the structure to be analyzed is composed of a plurality of elements, and the transfer vector is obtained from the displacement and internal force for each element, so calculation (computer simulation) Thus, it is possible to accurately estimate the vibration energy transmission path inside a complex structure (particularly a three-dimensional structure). By displaying the transmission vector thus obtained together with the model, it is possible to visualize how vibration energy is transmitted, and it is possible to support the identification of the cause of vibration and the planning of countermeasures.

  The above embodiment is merely an example of the present invention. The scope of the present invention is not limited to the above embodiment, and various modifications can be made within the scope of the technical idea.

  For example, in the above embodiment, axial force, shearing force, lateral shearing force, bending moment, and torsional moment are considered as the internal force acting on the element, but it is known that a specific internal force is dominant. In this case, only the specific internal force may be used for calculating the transmission vector. In the above embodiment, information such as the displacement and internal force of each element is acquired from the finite element analysis result. However, it may be acquired from other structural analysis results, and if possible, use experimentally measured values. Also good.

FIG. 1 is a diagram for explaining plate elements and internal forces acting thereon. FIG. 2 is a diagram schematically showing the transmission direction of vibration energy when the axial force Fx is applied. FIG. 3 is a diagram schematically showing the transmission direction of vibration energy when the transverse shear force Fxy is applied. FIG. 4 is a diagram schematically showing the transmission direction of vibration energy when the shearing force Vx is applied. FIG. 5 is a diagram schematically showing the transmission direction of vibration energy when the bending moment My is applied. FIG. 6 is a diagram schematically showing the transmission direction of vibration energy when the torsional moment Mxy is applied. FIG. 7 is a block diagram illustrating a functional configuration of the vibration analysis system. FIG. 8 is a flowchart showing the flow of processing of the vibration analysis system. FIG. 9 is a diagram illustrating a display example of a transfer vector calculation result in the cantilever model. FIG. 10 is a diagram illustrating a display example of a transmission vector calculation result in the vehicle body model.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Transfer vector calculation part 2 Characteristic value database 3 Output part

Claims (9)

For each of a plurality of elements constituting the model, a transfer vector calculating means for calculating a transfer vector representing vibration energy transmitted in the element;
Output means for displaying the transmission vector calculated for each element together with the model, and
The transmission vector calculating means calculates the transmission vector from the displacement of each element and the internal force acting on each element.   The transmission vector calculation means calculates the power of each mass point from the displacement of the mass point and the internal force acting on the mass point for the two mass points on the element, and calculates the difference in power between the two mass points of the transmission vector. The vibration analysis system according to claim 1, wherein the vibration analysis system is a component in a direction connecting two mass points.   The vibration analysis system according to claim 1, wherein the internal force includes at least one of an axial force, a shearing force, a transverse shearing force, a bending moment, and a torsional moment.   The vibration analysis system according to any one of claims 1 to 3, wherein the transfer vector calculation means obtains displacement of each element and internal force acting on each element from a calculation result of a finite element method.   The vibration analysis system according to claim 1, wherein the model is a model of a vehicle body.   The vibration analysis system according to claim 1, wherein the output unit displays the transmission vector in a pseudo color according to the size of the transmission vector. Computer
For each of a plurality of elements constituting the model, a process for calculating a transfer vector representing vibration energy transmitted in the element;
In a vibration analysis method for executing a process of displaying a transmission vector calculated for each element together with the model,
A vibration analysis method, wherein the computer calculates the transmission vector from a displacement of each element and an internal force acting on each element in the process of calculating the transmission vector. Computer
For each of a plurality of elements constituting the model, a transfer vector calculating means for calculating a transfer vector representing vibration energy transmitted in the element;
A vibration analysis program that functions as an output unit that displays a transmission vector calculated for each element together with the model,
The transmission vector calculation means calculates the transmission vector from the displacement of each element and the internal force acting on each element.   A computer-readable recording medium storing the vibration analysis program according to claim 8.

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