JP4440015B2 - Hitting sound prediction method - Google Patents

Description

  The present invention relates to a hitting sound prediction method for predicting hitting sound generated when a ball is hit with a hitting tool such as a golf club by computer analysis.

  In the development of golf clubs, increasing the flight distance and directionality of the golf ball to be hit is an important factor required for the club, but the hitting sound generated when hitting the ball with the golf club is also Since it greatly affects the feeling given to the golfer, whether or not the hitting sound is good is one of the examination items for designing the golf club.

  However, in order to check the hitting sound, a golf club prototype is manufactured and actually tested, and then experimentally performed (JP 2003-250934 A, JP 10-267744 A) or CAD. There is no other way than to create an FEM model on the computer from the data, calculate the natural frequency of the golf club head by eigenvalue analysis, and predict which frequency of sound is likely to become a typical hitting sound. Is the current situation.

However, if the golf ball prototype was created and the hitting sound was confirmed as in the former case, there is a problem that it takes time and cost for development. In the latter case, even if it is possible to predict which frequency sound will sound, what value the sound pressure level of each peak frequency is likely to have, what order natural frequency is a typical peak As for whether it is likely to become, it depends on the experience of the developer, and the accuracy is insufficient.
Furthermore, the frequency characteristics of the force applied to the golf club head at the time of actual hitting and the position where the head is vibrated influences the vibration of the head and the hitting sound also changes, but these effects are not taken into account at present. Therefore, the hitting sound cannot be accurately predicted.
JP 2003-250934 A JP-A-10-267744

  The present invention has been made in view of the above problems, and an object of the present invention is to provide a method capable of predicting a hitting sound more accurately on a computer without actually making a prototype of a golf club or the like.

（Ｐは音圧、ｋ＝ω／Ｃ０、ωは微少定常振動する時の媒質中における角振動数、Ｃ０は音速を表している。） In order to solve the above problems, the present invention provides:
The vibration generated in the hitting tool is applied by adding the excitation force generated in the hitting part at the time of hitting the ball to the calculation model on the computer in advance for the hitting sound generated when hitting the ball by the hitting part of the hitting tool. A method for predicting a hitting sound on a computer by predicting,
The computer,
An analysis unit that calculates modal parameters of a calculation model divided into finite elements by eigenvalue analysis, calculates an excitation force applied to the calculation model by collision analysis, and calculates an attenuation value to be applied to the calculation model by experimental modal analysis When,
A calculation unit that calculates a frequency characteristic of a sound pressure to be reproduced from the modal parameter, the excitation force, and the attenuation value to perform acoustic analysis;
An output unit that reproduces and outputs a hitting sound at the time of hitting a ball with a frequency characteristic of sound pressure acquired from the calculation unit,
The instruction of the operator, on the computer, with calculation model divided the hitting portion finite element is created, material property value to each and these divided elements are input, and ball contact on the calculation model The area is divided into multiple areas,
The analysis unit of the computer calculates modal parameters including the natural frequency and natural vibration mode of the calculation model by eigenvalue analysis, and obtains the excitation force applied to the hitting unit at the time of hitting the ball by collision analysis. Using the reaction force of each node, the reaction force of each node in the plurality of regions is added, and then subjected to Fourier transform and converted to the frequency region, and the excitation force in the frequency region is calculated on the calculation model in the region. Enter the node corresponding to the center position,
In operation of the computer, the acoustic analysis, the modal parameters, based on the exciting force and the damping values to obtain a vibration result of the striking portion generated during ball striking, as a boundary condition in front Kifu dynamic results, under There is provided a hitting sound prediction method characterized by obtaining a frequency characteristic of sound pressure generated at the time of hitting by calculating using the wave equation.

(P is the sound pressure, k = ω / C0, ω is the angular frequency in the medium when a slight steady vibration occurs, and C0 represents the speed of sound.)

Specifically, the hitting tool is a golf club, and a head as a hitting part is formed from a polygonal element using an element division method selected from a finite element method, a finite difference method, a finite volume method, and a boundary element method. The calculation model is created, material physical values including elastic modulus and specific gravity of the head are input to the nodes of the element, and the modal parameters of the head are calculated by eigenvalue analysis,
An excitation force applied to the head when hitting a golf ball obtained in advance is input to the node.

  According to the hitting sound prediction method, a modal parameter is obtained by eigenvalue analysis for a calculation model of a golf club head to be designed, and an effect generated in the club at the time of hitting the ball, which is previously obtained from the calculation model based on the modal parameter By inputting the vibration force, it is possible to obtain the vibration state at the time of hitting the head that is the design object. If the vibration situation of the calculation model is known, the frequency characteristics of the sound pressure, that is, the sound pressure level of each peak frequency, can be obtained by solving the wave equation using it as a boundary condition, and the hitting sound is reproduced on the computer. Can be heard.

The mode attenuation value of the modal parameter is calculated by using the attenuation value obtained by the experimental modal analysis and substituting the attenuation value into the wave equation. The obtained attenuation value is used because the attenuation value to be substituted cannot be calculated by calculation in the process of solving the wave equation. Use attenuation values. In this way, by using the fact that there is no significant difference in the attenuation value if the heads have substantially the same volume, the attenuation value can be obtained without creating a head that is a design target.

The excitation force at the time of hitting the ball to be input to the calculation model is separately analyzed in advance by the computer analysis unit and the ball to analyze the collision between the calculation model and the computer calculation unit to determine the contact reaction force generated at the node, The time history data of the contact reaction force is converted into the frequency domain by Fourier transform.
In this way, by determining the frequency characteristics of the excitation force according to the actual situation, the influence of the frequency characteristics of the force applied to the golf club head upon actual hitting on the head vibration can be considered . By increasing the accuracy of the hitting sound at the time of hitting the ball reproduced by the output unit, it is possible to predict the hitting sound with high accuracy.

There are the following three patterns of input to the nodes of the excitation force calculation model.
(1) When excitation force is input to one node at the center of the face surface of the head When the collision analysis is executed, time history data of contact reaction force of all nodes on the contact surface is output. All of these are averaged and the time history data averaged and averaged are converted into a frequency domain by Fourier transform and input to one node in the center of the face.
(2) When the excitation force is input to a plurality of nodes on the face surface The face surface is divided into a plurality of regions in advance, and addition averaging and Fourier transformation are performed in the region, and the node corresponding to the center position of the region Enter the excitation force in.
(3) The time history data of the nodal reaction force at all the nodes existing on the face surface is directly Fourier transformed, and the information is used as a boundary condition.

Wherein with one of the three patterns from (1) (2) we can predict approximate to actual hitting sound, (3) from the viewpoint of too much computing time on a computer, the present invention, as described above have adopted the method of (2).
Therefore, on the calculation model, for example, it is preferable that the ball contact area is an area divided into five groups or more, and the excitation force is input as a different excitation force for each group.

As described above, in the present invention, the computer operator inputs the material physical property values to the nodes of the calculation model divided into finite elements, and the natural frequency of the modal parameters is calculated from the eigenvalue analysis in the analysis unit of the computer. determined vibration mode, also determine the attenuation values of the modal parameters by the calculation unit from the experimental modal analysis in the analysis unit obtains the excitation force by the arithmetic unit from the crash analysis in the analysis unit, resulting natural frequency, vibration mode, A computer operator inputs the attenuation value and the excitation force to the acoustic analysis software, performs acoustic analysis on the computer using the acoustic software, and generates a hitting sound from the output unit of the computer .

The calculation model is preferably a continuum element.
When this continuum element is used, details can be expressed more than when the shell element is used. Therefore, if the element is divided sufficiently small, the calculation accuracy can be improved.
Moreover, when a secondary element is used among continuum elements, calculation can be performed with high accuracy.

Furthermore, in order to increase the accuracy of the hitting sound to be generated, it is preferable that the sound reflectance inside the calculation model is set to 10% or more and 98% or less and substituted into the wave equation for calculation.
For example, when the calculation is performed with the sound reflectance being 100%, the resonance sound generated inside the head affects the hitting sound that can be heard outside, resulting in a sound different from the actual hitting sound. Therefore, by setting the sound reflectance to 10% to 98% according to the actual material of the golf club, it is possible to obtain a hitting sound close to the actual hitting sound.

Further, in order to increase the accuracy of the generated hitting sound, the hitting sound is generated from the frequency characteristics of the sound pressure, and the generated hitting sound is generated from the wind noise before impact and / or the golf ball at impact. By synthesizing the sound, it is possible to reproduce not only the sound generated from the golf club head but also the sound of the golf club shaft during the swing and the sound generated from the ball itself, Evaluation can be performed under conditions close to actual hitting sound.

  As is clear from the above description, according to the present invention, a modal parameter is obtained by eigenvalue analysis for a golf club head calculation model, and the excitation force at the time of hitting the ball is input to the calculation model based on the modal parameter. By doing so, it is possible to calculate the head vibration situation at the time of hitting. By solving the wave equation using this vibration result as a boundary condition, the frequency characteristic of the sound pressure is obtained, and the hitting sound can be reproduced and heard on a computer.

Embodiments of the present invention will be described with reference to the drawings.
As shown in the flowchart of FIG. 1, the modal parameters (natural frequency and vibration mode shape) of the calculation model obtained by the eigenvalue analysis (S1) and the excitation force applied to the calculation model obtained by the collision analysis (S2) And the acoustic model analysis (S7) using the attenuation values of the calculation model obtained from the experimental modal analysis (S3) as inputs, respectively, so that the hitting sound at the time of hitting the ball can be reproduced on the computer.
As shown in FIG. 1, the computer includes an analysis unit that performs eigenvalue analysis, collision analysis, and experimental modal analysis. Further, the modal parameters of the calculation model obtained by the eigenvalue analysis, the excitation force applied to the calculation model obtained by the collision analysis, and the attenuation value of the calculation model obtained by the experimental modal analysis are calculated, and these A calculation unit including an acoustic analysis unit that calculates the frequency of the sound pressure based on the vibration of the hitting sound reproduced from the calculation value is provided. Further, an output unit is provided that reproduces and outputs a hitting sound at the time of hitting the ball based on the frequency obtained by the acoustic analysis.
Below, to the minute theory for each step.

`` Eigenvalue analysis ''
First, as shown in FIG. 2, using a commercially available preprocessor (HyperMesh or the like) on a computer , the computer operator calculates a calculation model 10 in which a golf club head to be examined for hitting sound is divided into finite elements 11. Create
In addition, when using a continuum element, the length of one side of each element 11 is preferably as small as possible. However, when a tetrahedral secondary element is used, the length of one side of the element 11 is about 3 mm. Accuracy is obtained.
Modal parameters (by using eigenvalue analysis software such as ABAQUS (manufactured by ABAQUS INC.), MARC (manufactured by MSC SOFT), IDEAS (manufactured by EDS PLM Solutions), etc. The natural frequency and the mode shape are calculated (S4).

  In this embodiment, IDEAS is used, and the elastic modulus and specific gravity are input as material property values, and the upper limit of the vibration frequency is analyzed up to 20 kHz. The reason why 20 kHz is set is that the human audible range is up to 20 kHz, but relative comparison of the hitting sound is possible even if the upper limit is set to about 12 kHz.

"Collision analysis"
The contact reaction force of the golf club head at the time of hitting the ball is calculated using collision analysis software such as ls-dyna (LSTC) or PAM-CRASH (ESI). In this embodiment, ls-dyna is used, and the face surface of the calculation model 10 described above collides with the golf ball model at an initial speed of 40 m / s on the computer. Thereby, the time history data of the reaction force of all the nodes 12 in the contact area of the calculation model 10 with the ball is output.
At this time, after the contact area of the face surface with the ball is divided into a plurality of groups (areas) G1 to G5 as shown in FIG. 4, the reaction forces of the nodes in the groups G1 to G5 are added and averaged. By applying the Fourier transform to the frequency domain as shown in FIG. 3, the excitation force to be applied to the nodes for each of the groups G1 to G5 is calculated in the acoustic analysis in the subsequent process (S5).
When outputting the time history data of the nodal reaction force in the collision analysis, it is necessary to pay attention to the time increment (sampling frequency). That is, when calculating up to 20 kHz by acoustic analysis, the time history data of the nodal reaction force is output at a sampling frequency of about 2.2 times or more.

"Experimental Modal Analysis"
Since the attenuation value input in acoustic analysis cannot be obtained by calculation, it is obtained by experiment. The most ideal is to conduct an experimental modal analysis of the actual golf club head and obtain the attenuation value at each resonance frequency. However, with this method, the attenuation value cannot be obtained if there is no actual object. Therefore, an experimental modal analysis is performed with a head having approximately the same volume as that of the calculation model 10 in which the hitting sound is to be investigated among the existing real heads, and an average value of attenuation values at each resonance frequency up to 10 kHz is obtained (S6).
In the experimental modal analysis, the transfer function of the theoretical model is applied to the transfer function obtained by measurement, and the attenuation value is obtained by curve fitting. The curve fitting method includes an SDOF method, an MDOF method, etc. In this embodiment, a poly-reference method of the MDOF method is used, and a transfer function obtained by experiment and a theoretical formula obtained by curve fitting are used. After comparing with the transfer function and confirming that the curve fit is correct, the attenuation value is used.

"Acoustic analysis"
Analyzes the frequency characteristics of the hitting sound when hitting the ball using the acoustic analysis software of SYSNOISE (manufactured by LMS International) and RAYON (manufactured by ESI). In this embodiment, RAYON is used, the natural frequency and mode shape obtained by eigenvalue analysis, the attenuation value obtained by experimental modal analysis are input, and the excitation force obtained by collision analysis is input to the face of the golf club head calculation model. Enter the node of the face.
The calculation model for acoustic analysis may be shared with the calculation model 10 for eigenvalue analysis. However, the degree of fineness of element division for obtaining sufficient accuracy when performing eigenvalue analysis is generally the same as that for acoustic analysis. Since there are many cases that are finer than the analysis, it is preferable to finely divide the calculation model 10 at the time of eigenvalue analysis.

In the collision analysis, all the nodal reaction forces included in each of the five groups G1 to G5 shown in FIG. 4 are added to obtain an excitation force, and the excitation force is applied to the face of the calculation model in the acoustic analysis. Is added to the representative node closest to the center of each of the groups G1 to G5.
The sound pressure is calculated by solving the wave equation by the boundary element method using the vibration result of the calculation model by the input of the excitation force as the boundary condition.

ここで、Ｐは音圧、ｋ＝ω／Ｃ_０、ωは微少定常振動する時の媒質中における角振動数、Ｃ_０は音速を表している。 The wave equation (Helmholtz) governing the sound pressure in space in the acoustic problem is shown in Equation 1.

Here, P is a sound pressure, k = ω / C ₀ , ω is an angular frequency in the medium when a minute steady vibration occurs, and C ₀ is a sound velocity.

ここで、ｑ＝−ｉωρν、ρは媒質の密度、νは節点の粒子速度を表している。Γは波動方程式が適用される領域Ωを仮定するもので、ｎは境界の法線ベクトルを表す。Γ＝Γ₁＋Γ₂である。
なお、この加振力の入力による計算モデルの振動結果を境界条件とする際には、境界を構成している節点の粒子速度νが入力条件となる。また、音響媒質の密度ρは１．２ｋｇ／ｍ³として計算する。 The boundary conditions in the acoustic problem are expressed by the following formulas 2 and 3.

Here, q = −iωρν, ρ represents the density of the medium, and ν represents the particle velocity at the node. Γ assumes a region Ω to which the wave equation is applied, and n represents a normal vector of the boundary. Γ = Γ ₁ + Γ ₂ .
In addition, when the vibration result of the calculation model by inputting this excitation force is used as the boundary condition, the particle velocity ν of the nodes constituting the boundary is the input condition. Further, the density ρ of the acoustic medium is calculated as 1.2 kg / m ³ .

ここで、Ｐ*（ｘ、ｙ）は２階まで微分可能な関数である。 When the wave equation of the acoustic problem described above is converted into an integral equation in order to solve by the boundary element method, it is expressed as Equation 4.

Here, P * (x, y) is a function that can be differentiated up to the second order.

ここで、Ｚ＝Ｐ／νで音反射率を表し、Γ_Zは音響インピーダンスの既知の境界、Γ_νはそれ以外の境界である。 Therefore, the sound pressure in the region is expressed by Equation 6.

Here, Z = P / ν represents the sound reflectance, Γ _Z is a known boundary of acoustic impedance, and Γ _ν is the other boundary.

  By performing the above processing with the acoustic analysis software RAYON, the frequency characteristics of the sound pressure at the observation point are calculated. At this time, since the human audible range is up to 20 kHz, the upper limit is preferably analyzed up to 20 kHz.

Next, the sound pressure of this output result can be reproduced and heard as an actual hitting sound on a computer by performing inverse Fourier transform using the commercially available software such as Matlab (MathWorks) and converting it into the time domain. . At this time, in addition to the head hitting sound, the wind hitting sound of the golf club shaft at the time of swing and the sound generated from the ball itself are synthesized, and the hitting sound is reproduced at the output unit of the computer, so that the hitting ball at the time of actual hitting Sound close to the sound can be reproduced. Note that sound synthesis can be performed by software such as Matlab.

  In this embodiment, as an input method to the excitation force calculation model, the contact area with the ball on the face surface of the head is grouped. However, as a modified example, the following method is used. Also good.

As a first modification, there is a method of applying an excitation force to one node at the center of the face surface. Specifically, when collision analysis is performed, the time history data of the nodal reaction force at all nodes in the contact area is output, but the time history information obtained by averaging all of them is Fourier transformed to the frequency domain and calculated. Enter the representative node closest to the center of the face of the model.
As a second modification, the time history data of the contact reaction force at all the nodes existing on the face surface is directly Fourier transformed into the frequency domain, and the information is directly input to each node of the acoustic analysis calculation model.

Hereinafter, based on Table 1, an Example and a comparative example are demonstrated.

Example 1
In the first embodiment, when the excitation force is input to the calculation model in the acoustic analysis, as described above, the excitation force is distributed to the nodes in each region divided into the five groups G1 to G5 shown in FIG. Is entered. Further, as described above, the excitation force obtained from the collision analysis result was used. The sound reflectance was 90%, the attenuation value was 0.3%, and the calculation model was a tetrahedral quadratic element. FIG. 5 is a graph showing the relationship between the time and frequency of the hitting sound of Example 1. In addition to the hitting sound of the head, the wind noise of the golf club shaft during the swing and the sound generated from the ball itself are shown. It is synthesized.

(Example 2)
In Example 2, when the excitation force was input to the calculation model in the acoustic analysis, the same excitation force was input to all the nodes of the contact area with the ball on the face surface of the club. Other conditions are the same as in the first embodiment.

(Comparative Example 1)
In the first comparative example, when the excitation force is input to the calculation model in the acoustic analysis, the contact reaction force of all the nodes is added to obtain the excitation force as in the first modification described above. The excitation force was input on behalf of one node located at the center of the contact area with the ball. Other conditions are the same as in the first embodiment.

(Comparative Example 2)
In Comparative Example 2, a rectangular wave (pulse width 1 ms, 1N) was applied as the excitation force. Other conditions are the same as in the first embodiment.

(Comparative Example 3)
In Comparative Example 3, the setting of the sound reflectance during acoustic analysis was set to 100%. Other conditions are the same as in the first embodiment.

(Comparative Example 4)
In Comparative Example 4, the attenuation value setting for acoustic analysis was set to 0.1%. Other conditions are the same as in the first embodiment.

(Comparative Example 5)
In Comparative Example 5, the setting of the sound reflectance at the time of acoustic analysis was set to 0%. Other conditions are the same as in the first embodiment.

(Comparative Example 6)
In Comparative Example 6, the calculation model for acoustic analysis was divided into elements with tetrahedral primary elements. Other conditions are the same as in the first embodiment.

(Comparative Example 7)
In Comparative Example 7, the calculation model for acoustic analysis was divided into elements using shell elements. Other conditions are the same as in the first embodiment.

(Discussion)
When the hitting sound of the acoustic analysis result for each of the above-described examples and comparative examples was reproduced on a computer, as shown in Table 1, the actual hits for Example 1 and Example 2 were compared to Comparative Examples 1-7. It was confirmed that a sound similar to the sound of the time was reproduced.

  The hitting sound prediction method of the present invention is particularly suitable for predicting the hitting sound generated when hitting a golf ball with a golf club, but is not limited to the hitting sound of golf, for example, hitting the ball with a bat in baseball Used for sports when doing. Furthermore, the present invention is not limited to hitting with a hitting tool of sports equipment, and can be used for predicting sounds generated when hitting, such as hitting sound generated when hitting a wall or floor with a hitting tool such as a hammer. It is.

It is drawing which shows the flowchart of this invention. It is a perspective view of a calculation model. It is a graph which shows the frequency characteristic of an exciting force. It is drawing which shows the node which inputs an exciting force. It is a graph which shows the relationship between the time of the hitting sound after a synthesis | combination, and a frequency.

Explanation of symbols

10 calculation model 11 element 12 nodes G1 to G5 group

Claims (5)

The vibration generated in the hitting tool is applied by adding the excitation force generated in the hitting part at the time of hitting the ball to the calculation model on the computer in advance for the hitting sound generated when hitting the ball by the hitting part of the hitting tool. A method for predicting a hitting sound on a computer by predicting,
The computer,
An analysis unit that calculates modal parameters of a calculation model divided into finite elements by eigenvalue analysis, calculates an excitation force applied to the calculation model by collision analysis, and calculates an attenuation value to be applied to the calculation model by experimental modal analysis When,
A calculation unit that calculates a frequency characteristic of a sound pressure to be reproduced from the modal parameter, the excitation force, and the attenuation value to perform acoustic analysis;
An output unit that reproduces and outputs a hitting sound at the time of hitting a ball with a frequency characteristic of sound pressure acquired from the calculation unit,
The instruction of the operator, on the computer, with calculation model divided the hitting portion finite element is created, material property value to each and these divided elements are input, and ball contact on the calculation model The area is divided into multiple areas,
The analysis unit of the computer calculates modal parameters including the natural frequency and natural vibration mode of the calculation model by eigenvalue analysis, and obtains the excitation force applied to the hitting unit at the time of hitting the ball by collision analysis. Using the reaction force of each node, the reaction force of each node in the plurality of regions is added, and then subjected to Fourier transform and converted to the frequency region, and the excitation force in the frequency region is calculated on the calculation model in the region. Enter the node corresponding to the center position,
In operation of the computer, the acoustic analysis, the modal parameters, based on the exciting force and the damping values to obtain a vibration result of the striking portion generated during ball striking, as a boundary condition in front Kifu dynamic results, under A hitting sound prediction method characterized by obtaining a frequency characteristic of sound pressure generated at the time of hitting by calculating the wave equation.

(P is the sound pressure, k = ω / C0, ω is the angular frequency in the medium when a slight steady vibration occurs, and C0 represents the speed of sound.)   2. The hitting sound prediction method according to claim 1, wherein the mode attenuation value of the modal parameter is calculated by substituting the attenuation value into the wave equation by the calculation unit using an attenuation value obtained by an experimental modal analysis. The hitting sound prediction method according to claim 1 or 2, wherein the calculation unit performs calculation by substituting into the wave equation with a sound reflectance inside the calculation model of 10% to 98% . The hitting sound prediction method according to any one of claims 1 to 3, wherein the calculation model includes continuum elements . The output unit generates a hitting sound from the frequency characteristics of the sound pressure, and the generated hitting sound is synthesized with a wind noise before impact and / or a sound generated from a golf ball at impact. The hitting sound prediction method according to any one of claims 1 to 4.

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