JP2007292647A - Oscillation analyzing system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a technology capable of precisely analyzing the state of vibration energy of a structure with a small amount of holding data and calculation. <P>SOLUTION: The computer performs preprocesses including the processing for calculating the coefficient in the energy calculation formula, and processing for previously memorizing the coefficient calculated for each element, from the deformation of each element in the case of exciting the model of a plurality of elements and a rigidity matrix. After that the computer performs the processing for determining the phase to calculate the energy, the processing for calculating the strain energy of each element following to the energy calculation formula, and the processing for outputting the result of calculating result. <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 (see, for example, Patent Documents 1 to 3). 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. In particular, when a complicated three-dimensional structure such as a vehicle body is analyzed by a computer, a large-scale model with a million element order is used. It is also important to reduce the amount of retained data and increase the processing speed.
JP 2003-186117 A JP 2005-225348 A JP 2005-234040 A JP-A-11-271155

  The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a technique capable of accurately analyzing the state of vibration energy of a structure with a small amount of stored data and a small amount of calculation. There is to do.

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

A first aspect of the present invention is a vibration analysis system that analyzes a state of strain energy, and includes a displacement of each element when a model including a plurality of elements is excited at an angular frequency ω, and From the stiffness matrix, coefficient calculation means for calculating the coefficients C1, C2 and C3 in Equation 1, coefficient storage means for storing the coefficients C1, C2 and C3 calculated for each element, and a phase for calculating energy are determined. Phase determining means, energy calculating means for calculating the strain energy Es of each element from the determined phase ωt and previously stored coefficients C1, C2 and C3 according to Equation 1, and output means for outputting the energy calculation result And comprising.

  In the above configuration, since it is only necessary to hold the three values of the coefficients C1, C2, and C3 for each element, the amount of data to be held can be extremely small. In addition, since the distortion energy Es at an arbitrary phase can be obtained by simple and few calculations as shown in Equation 1 using the three coefficients C1, C2, and C3, the processing speed can be increased. Moreover, since the strain energy is calculated from the internal state quantity of the structure such as the displacement and stiffness matrix of each element, it can be obtained with high accuracy even in the energy state of a complicated three-dimensional structure such as a vehicle body. Furthermore, since the angular frequency ω, which is the excitation condition, can be freely selected, not only the natural mode of the model but also the vibration that is assumed to be actually applied to the model (for example, the engine vibration in the case of a vehicle body) It is possible to analyze the corresponding energy state.

A second aspect of the present invention is a vibration analysis system that analyzes the state of kinetic energy, and includes a displacement of each element when a model including a plurality of elements is vibrated at an angular frequency ω, and From the mass matrix, coefficient calculation means for calculating the coefficients C4, C5 and C6 in Equation 2, coefficient storage means for storing the coefficients C4, C5 and C6 calculated for each element, and a phase for calculating energy are determined. Phase determining means, energy calculating means for calculating the kinetic energy Ek of each element from the determined phase ωt and previously stored coefficients C4, C5 and C6 according to Equation 2, and output means for outputting the energy calculation result And comprising.

  In the above configuration, only the three values of the coefficients C4, C5, and C6 need be held for each element, so that the amount of data to be held can be extremely small. In addition, since the kinetic energy Ek in an arbitrary phase can be obtained by simple and few calculations as shown in Expression 2 using the three coefficients C4, C5, and C6, the processing speed can be increased. In addition, since the kinetic energy is calculated from the internal state quantity of the structure such as the displacement of each element and the mass matrix, it can be obtained with high accuracy even in the energy state of a complicated three-dimensional structure such as a vehicle body. Furthermore, since the angular frequency ω, which is the excitation condition, can be freely selected, not only the natural mode of the model but also the vibration that is assumed to be actually applied to the model (for example, the engine vibration in the case of a vehicle body) It is possible to analyze the corresponding energy state.

  The displacement of each element is preferably calculated by a finite element method. Of course, analysis methods other than the finite element method may be used.

  The model is preferably a model of a vehicle body.

  It is preferable that the phase determination unit determines a plurality of phases for which energy should be calculated from the specified number of divisions by allowing the user to specify the number of phase divisions. The user can specify an arbitrary number of divisions according to the purpose of vibration analysis. When energy distributions in a plurality of phases are calculated in accordance with the number of divisions, it is also preferable to display them in order. Thereby, the periodic change of energy distribution can be observed easily. The number of divisions may not be specified by the user, but the phase or time may be specified by the user.

  The output means preferably displays the magnitude of energy of each element on the model in a pseudo color display. As a result, originally invisible vibration energy can be visualized and the energy distribution and its periodic change can be intuitively grasped.

  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 as the third aspect of the present invention, the displacement of each element when the computer vibrates the model composed of a plurality of elements at the angular frequency ω, and the stiffness matrix of each element, The computer calculates energy after executing preprocessing including processing for calculating the coefficients C1, C2, and C3 in Equation 1 and processing for storing the coefficients C1, C2, and C3 calculated for each element in advance. Processing for determining the phase to be performed, processing for calculating the strain energy Es of each element from the determined phase ωt and the coefficients C1, C2 and C3 stored in advance according to Equation 1, and processing for outputting the energy calculation result And execute.

  Further, in the vibration analysis method as the fourth aspect of the present invention, from the displacement of each element when a computer vibrates a model composed of a plurality of elements at an angular frequency ω, and the mass matrix of each element, After performing preprocessing including processing for calculating coefficients C4, C5, and C6 in Equation 2 and processing for preliminarily storing the coefficients C4, C5, and C6 calculated for each element, the computer calculates energy Processing for determining the phase to be performed, processing for calculating the kinetic energy Ek of each element from the determined phase ωt and the coefficients C4, C5 and C6 stored in advance according to Equation 2, and processing for outputting the energy calculation result And execute.

  Further, the vibration analysis program as the fifth aspect of the present invention is based on the displacement of each element when a computer is vibrated at a angular frequency ω and a stiffness matrix of each element. Coefficient calculation means for calculating the coefficients C1, C2 and C3 in Equation 1, coefficient storage means for storing the coefficients C1, C2 and C3 calculated for each element, and phase determination means for determining the phase for calculating energy Energy calculating means for calculating the strain energy Es of each element from the determined phase ωt and the pre-stored coefficients C1, C2 and C3 according to Equation 1, and output means for outputting the energy calculation result, It is to function.

  Further, the vibration analysis program as the sixth aspect of the present invention is based on the displacement of each element when a computer is vibrated at a angular frequency ω and a mass matrix of each element. Coefficient calculation means for calculating the coefficients C4, C5 and C6 in Equation 2, coefficient storage means for storing the coefficients C4, C5 and C6 calculated for each element, and phase determination means for determining the phase for calculating energy Energy calculating means for calculating the kinetic energy Ek of each element from the determined phase ωt and the pre-stored coefficients C4, C5 and C6 according to Equation 2, and output means for outputting the energy calculation result, It is to function.

  According to the present invention, it is possible to accurately analyze the state of vibration energy of a structure with a small amount of retained data and a small amount of calculation.

  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 (kinetic energy and strain energy) in a three-dimensional structure such as a vehicle body, and visualizes the distribution and the change of each phase, thereby This is to support the investigation of the cause of occurrence and the planning of countermeasures.

<Method of calculating vibration energy>
Before describing the specific configuration of the vibration analysis system, the basic concept of the vibration energy 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, rigidity, mass) 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 is 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 position and an angular frequency is given to the FE model, a 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 strain energy and kinetic energy using the displacement, stiffness matrix, and mass matrix of each element obtained as a result of the finite element analysis.

(1) Strain energy For calculating the strain energy, the displacement of each element and the stiffness matrix are used. In addition, since it is necessary to use the displacement amount in the element coordinate system for the calculation of strain energy, if the result of finite element analysis is output in the global coordinate system, coordinate conversion from the global coordinate system to the element coordinate system Shall be given as appropriate.

Taking a plate element as an example, the plate element has four nodes, and each node has six degrees of freedom of movement in the x, y and z axis directions and rotation 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.

Incidentally, when the a-th component of the displacement u is denoted as u _a, 1 degree of freedom u _a is represented by the following formula.

The stiffness matrix K is represented by a matrix of n rows × n columns as follows. In the case of a plate element, n = 24 because there are four nodes and each node has six degrees of freedom.

The strain energy Es of the element can be obtained from the displacement u of the element and the stiffness matrix K as follows.

Substituting Equation 3 into Equation 4 and rearranging results in Equation 5 below. By using Equation 5, the strain energy Es of each element at an arbitrary phase ωt can be calculated, and the strain energy distribution of the entire model can be analyzed.

(2) Kinetic energy The kinetic energy is calculated by using the displacement (velocity) of each element and the mass matrix. Since kinetic energy must be calculated using the velocity in the element coordinate system, if the result of finite element analysis is output in the global coordinate system, coordinate conversion from the global coordinate system to the element coordinate system is performed. It shall be given as appropriate.

Taking the plate element as an example, the plate element has four nodes. Regarding kinetic energy, three degrees of freedom of movement in the x-, y-, and z-axis directions are considered for each node. Therefore, the displacement u of the plate element is represented by a vector composed of 12 components as in the following equation.

By limiting to the frequency range, the displacement can be converted into velocity by the following conversion.

The mass matrix M is represented by a matrix of n rows × n columns as follows. Node 4 for plate elements
In addition, since the degree of freedom of each node is 3, n = 12.

The kinetic energy Ek of the element can be obtained from the element displacement u and the mass matrix M as follows.

Substituting Equation 3 into Equation 6 and rearranging results in the following Equation 7. Using Equation 7, the kinetic energy Ek of each element at an arbitrary phase ωt can be calculated, and the kinetic energy distribution of the entire model can be analyzed.

(3) Reduction of retained data amount and calculation amount By using the above formulas 5 and 7, the vibration energy at an arbitrary phase can be obtained theoretically. However, it is not realistic to implement the calculations corresponding to these equations in the system as they are. This is because the amount of data to be retained and the amount of calculation required for energy calculation are enormous.

For example, in the case of a plate element, there are 576 (= 24 × 24) terms on the right side of Equation 5. In the energy calculation, since at least three values of “k _ij A _i A _j ”, “β _i ”, and “β _j ” must be known for each term, 1728 (= 576 × 3) data must be held. In a large-scale model such as a car body, the number of elements is about 1 million. If one data is held with double precision (64 bits), a data capacity of several tens of gigabytes is required.

  Therefore, in this embodiment, Equations 5 and 7 are modified and arranged as follows.

Applying the trigonometric product-sum formula and the addition theorem to one term on the right-hand side of Equation 5 and rearranging it, it becomes as follows.

Therefore, Expression 5 becomes Expression 8.

Similarly, by applying the trigonometric product-sum formula and the addition theorem to the right side of Equation 7, and organizing it, Equation 9 is obtained.

  Since the coefficients C1, C2, and C3 in Equation 8 and the coefficients C4, C5, and C6 in Equation 9 do not include time t (that is, do not depend on the phase), they must be calculated prior to the calculation of vibration energy. it can. If the coefficients C1 to C6 are calculated in advance as preprocessing and stored in the database, the vibration energy in an arbitrary phase can be calculated easily and quickly from the equations 8 and 9. Taking a plate element as an example, it can be seen that Equation 1 required as many as 1728 data, whereas Equation 8 requires only 3 data, and the amount of retained data can be greatly reduced to 1/576.

  Hereinafter, a configuration example of the vibration analysis system will be specifically described.

<System configuration>
FIG. 1 is a block diagram showing a functional configuration of the vibration analysis system.

The vibration analysis system includes a preprocessing unit 1 that performs preprocessing such as outline and coefficient calculation, and a postprocessing unit 2 that performs postprocessing such as calculation and output of vibration energy. The preprocessing unit 1 includes a coefficient calculation unit 10 and a characteristic database (DB) 11, and the postprocessing unit 2 includes a condition input unit 20, an energy calculation unit 21, and an output unit 22.

  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.

<Pretreatment>
FIG. 2 is a flowchart showing the flow of preprocessing.

  The coefficient calculation unit 10 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 and the stiffness matrix and mass matrix of each element when the FE model is vibrated at the angular frequency ω.

  Next, the coefficient calculation unit 10 converts the displacement of each element from the global coordinate system to the element coordinate system (step S11). However, if the displacement acquired in step S10 was originally in the element coordinate system, the coordinate conversion process in step S11 is unnecessary.

  Next, the coefficient calculation unit 10 obtains coefficients C1, C2 and C3 for calculating strain energy from the displacement and stiffness matrix for each element (see Equation 8), and kinetic energy from the displacement and mass matrix. Coefficients C4, C5, and C6 for calculation are obtained (see Equation 9) (step S12). And the coefficient calculation part 10 stores the coefficient C1-C6 calculated about each element in characteristic DB11 (step S13).

  In the present embodiment, the coefficient calculation unit 10 functions as the coefficient calculation unit of the present invention, and the characteristic DB 11 functions as the coefficient storage unit of the present invention.

  After the above pre-processing, post-processing such as calculation / output of vibration energy can be executed.

<Post-processing>
FIG. 3 is a flowchart showing the flow of post-processing.

  In step S <b> 20, the user can specify vibration energy analysis conditions using the condition input unit 20. Specifically, the user can specify the phase or the number of phase divisions as the analysis condition. Note that the phase may be designated by an angle (ωt) or may be designated by a time (t). When the number of phase divisions is designated, the condition input unit 20 determines a plurality of phases whose energy is to be calculated from the designated number of divisions. For example, if “4” is designated as the number of divisions, four phases of “0, π / 2, π, 3π / 2” are selected as phases.

  Next, the energy calculation unit 21 reads the coefficients C1 to C6 corresponding to the model to be analyzed from the characteristic DB 11 (step S21).

  Next, the energy calculating unit 21 calculates the strain energy Es of each element from the phase ωt determined in step S20 and the coefficients C1 to C3 obtained in step S21 according to the equation 8, and the phase ωt and the coefficients C4 to C6. Thus, the kinetic energy Ek of each element is calculated according to Equation 9 (step S22).

  Then, the output unit 22 outputs the calculation results of the strain energy Es and the kinetic energy Ek in step S22 to the display device (step S23).

  4 and 5 show display examples of calculation results. FIG. 4 shows an example of a cantilever and FIG. 5 shows an example of a vehicle body. In this display example, the energy magnitude of each element is displayed in a pseudo color superimposed on the FE model. In addition, the energy state of each phase is switched and displayed (animation display) at predetermined intervals. By viewing such a display, the user can intuitively grasp the vibration energy distribution, the change in each phase, and the like.

  In this embodiment, the condition input unit 20 functions as the phase determination unit of the present invention, the energy calculation unit 21 functions as the energy calculation unit of the present invention, and the output unit 22 functions as the output unit of the present invention. Yes.

  According to the configuration of the present embodiment described above, since it is only necessary to hold the coefficients C1 to C6 for each element, the amount of data to be held can be extremely small. In addition, using these coefficients, strain energy and kinetic energy at an arbitrary phase can be obtained with simple and few calculations such as Expression 8 and Expression 9, so that the processing speed can be increased. In addition, since energy is calculated from the internal state quantities of the structure such as the displacement, rigidity, and mass of each element, the energy state of a complicated three-dimensional structure such as a vehicle body can be obtained with high accuracy. Furthermore, since the angular frequency ω, which is the excitation condition, can be freely selected, not only the natural mode of the model but also the vibration that is assumed to be actually applied to the model (for example, the engine vibration in the case of a vehicle body) It is possible to analyze the corresponding energy state.

  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, both strain energy and kinetic energy are calculated, but a system configuration in which only one of them is calculated may be used. In the above embodiment, information such as displacement, rigidity, and mass of each element is acquired from the finite element analysis result. However, the information may be acquired from other structural analysis results, and if possible, measured values obtained by experiments may be used. May be.

FIG. 1 is a block diagram showing a functional configuration of the vibration analysis system. FIG. 2 is a flowchart showing the flow of preprocessing. FIG. 3 is a flowchart showing the flow of post-processing. FIG. 4 is a diagram illustrating a display example of the energy calculation result in the cantilever model. FIG. 5 is a diagram illustrating a display example of the energy calculation result in the vehicle body model.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Pre-processing part 10 Coefficient calculation part 11 Characteristic database 2 Post-processing part 20 Condition input part 21 Energy calculation part 22 Output part

Claims (11)

Coefficient calculation means for calculating the coefficients C1, C2 and C3 in Equation 1 from the displacement of each element when a model consisting of a plurality of elements is vibrated at an angular frequency ω and the stiffness matrix of each element;
Coefficient storage means for storing the coefficients C1, C2 and C3 calculated for each element;
Phase determining means for determining a phase for which energy is to be calculated;
Energy calculating means for calculating the strain energy Es of each element according to Equation 1 from the determined phase ωt and the pre-stored coefficients C1, C2 and C3;
Output means for outputting energy calculation results;
A vibration analysis system comprising:

Coefficient calculation means for calculating the coefficients C4, C5 and C6 in Equation 2 from the displacement of each element when a model consisting of a plurality of elements is vibrated at an angular frequency ω and the mass matrix of each element;
Coefficient storage means for storing the coefficients C4, C5 and C6 calculated for each element;
Phase determining means for determining a phase for which energy is to be calculated;
Energy calculating means for calculating the kinetic energy Ek of each element from the determined phase ωt and the coefficients C4, C5, and C6 stored in advance according to Equation 2,
Output means for outputting energy calculation results;
A vibration analysis system comprising:

  The vibration analysis system according to claim 1, wherein the displacement of each element is calculated by a finite element method.   The vibration analysis system according to claim 1, wherein the model is a model of a vehicle body.   5. The vibration according to claim 1, wherein the phase determination unit causes the user to specify the number of divisions of the phase, and determines a plurality of phases for calculating energy from the specified number of divisions. 6. Analysis system.   The vibration analysis system according to any one of claims 1 to 5, wherein the output means displays the magnitude of the energy of each element in a pseudo color on the model. Computer
A process of calculating coefficients C1, C2, and C3 in Equation 1 from the displacement of each element when a model composed of a plurality of elements is vibrated at an angular frequency ω, and the stiffness matrix of each element;
A process for preliminarily storing the coefficients C1, C2 and C3 calculated for each element;
After executing preprocessing including
Computer
A process for determining the phase for which energy is to be calculated;
A process of calculating the strain energy Es of each element according to Equation 1 from the determined phase ωt and the pre-stored coefficients C1, C2 and C3;
Processing to output energy calculation results;
The vibration analysis method characterized by performing.

Computer
A process of calculating coefficients C4, C5 and C6 in Equation 2 from the displacement of each element when a model composed of a plurality of elements is excited at an angular frequency ω, and the mass matrix of each element;
A process for preliminarily storing the coefficients C4, C5 and C6 calculated for each element;
After executing preprocessing including
Computer
A process for determining the phase for which energy is to be calculated;
A process of calculating the kinetic energy Ek of each element from the determined phase ωt and the coefficients C4, C5, and C6 stored in advance according to Equation 2,
Processing to output energy calculation results;
The vibration analysis method characterized by performing.

Computer
Coefficient calculation means for calculating the coefficients C1, C2 and C3 in Equation 1 from the displacement of each element when a model consisting of a plurality of elements is vibrated at an angular frequency ω and the stiffness matrix of each element;
Coefficient storage means for storing the coefficients C1, C2 and C3 calculated for each element;
Phase determining means for determining a phase for which energy is to be calculated;
Energy calculating means for calculating the strain energy Es of each element according to Equation 1 from the determined phase ωt and the pre-stored coefficients C1, C2 and C3;
Output means for outputting energy calculation results;
Vibration analysis program characterized by making it function.

Computer
Coefficient calculation means for calculating the coefficients C4, C5 and C6 in Equation 2 from the displacement of each element when a model consisting of a plurality of elements is vibrated at an angular frequency ω and the mass matrix of each element;
Coefficient storage means for storing the coefficients C4, C5 and C6 calculated for each element;
Phase determining means for determining a phase for which energy is to be calculated;
Energy calculating means for calculating the kinetic energy Ek of each element from the determined phase ωt and the coefficients C4, C5, and C6 stored in advance according to Equation 2,
Output means for outputting energy calculation results;
Vibration analysis program characterized by making it function.

  A computer-readable recording medium storing the vibration analysis program according to claim 9.