JP2003139668A - Simulation method for predicting performance of product composed of viscoelastic material - Google Patents

Abstract

PROBLEM TO BE SOLVED: To predict the performance of a product composed of a viscoelastic material exhibiting nonlinear physical properties accurately by simulation under actual use conditions. SOLUTION: Under measurement conditions of a product composed of a viscoelastic material assuming actual use conditions, values of strain, strain rate, and stress occurring in the viscoelastic material are measured every moment, time record data of viscous resistance of the viscoelastic material is derived from the time record data of strain, strain rate and stress and a viscoelastic model taking account of the viscosity of the viscoelastic material for a state loaded with strain and a state free from strain or a restored state. That product is set as a product model being analyzed and a relation of strain, strain rate and viscous resistance is inputted to the product model and then the stress and strain of a differential component are calculated using differential main strain and strain rate converted from the entire coordinate system into the main strain and strain rate coordinate system thus simulating the performance while taking account of the difference of viscous resistance under a state loaded with strain and a state free from strain or a restored state even for the same value of strain.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a simulation method for predicting the performance of a product made of a viscoelastic material, and more particularly to a simulation method for accurately predicting the performance of a product made of a viscoelastic material by simulation. is there.

[0002]

Viscoelastic materials represented by polymer materials such as rubber and elastomer have been widely applied to various products such as tires, various balls used in sports competitions, and rolls used in printing machines.

With respect to various industrial products such as the above viscoelastic materials and metallic materials, product development using simulation is being carried out in various fields in order to save the cost and time for trial manufacture. For example, in order to predict the resilience performance of a golf ball, a simulation method of an actual impact test has been proposed.

Conventionally, in the case of performing the above-mentioned simulation, the constituent materials of the ball generally measured by a viscoelasticity spectrometer for measuring the rigidity and viscosity of the material, a tensile tester for measuring the longitudinal elastic modulus (Young's modulus), and the like. The physical properties of are used as input values to the simulation.
In particular, the viscoelasticity spectrum meter measures the physical property values of a test piece to which a dynamic strain is applied, and is therefore useful for simulating a product made of a viscoelastic material.

[0005]

However, a large amount of deformation cannot be given to the test piece by the measurement with the above-mentioned viscoelasticity spectrum meter, a tensile tester for measuring the longitudinal elastic modulus, etc. The maximum strain rate applied to the test piece made of is from 0.001 / s to 1.
It is as small as 0 / s and the maximum compressive strain is 0.00.
The value is as small as 01 to 0.02.

On the other hand, a product made of a viscoelastic material may undergo large deformation at high speed due to the influence of external force when it is actually used. For example, in the material forming the golf ball, the maximum strain rate is 500 / s to 5000 / s when actually hit.
s, and the maximum compressive strain is mainly 0.05 to 0.
It is about 50, which is a very large value.

Thus, the viscoelasticity spectrum meter,
In the measurement with a tensile tester that measures the longitudinal elastic modulus, etc., it is not possible to measure the physical property value of the viscoelastic material under the same high speed and large deformation conditions as the above-mentioned actual use conditions. , The maximum strain rate and the maximum compressive strain are very different. Therefore, there is a problem in that it is not possible to perform an accurate simulation in consideration of the physical properties of the viscoelastic material in the conventional simulation in which the physical property values of the material obtained by a viscoelastic spectrum meter, a tensile tester, etc. are input.

That is, it is known that the deformation behavior of a viscoelastic material subjected to an impact load is significantly influenced by the amount of deformation or the deformation speed, unlike the case of receiving a static load. In particular, a polymer material typified by rubber or elastomer causes a very high-speed deformation of 10,000 minutes or a few thousandths of a second due to an impact load, and the amount of deformation also becomes a very large value of several tens of percent. There are many viscoelastic materials with such high-speed and large-deformation behavior, and highly accurate simulations are required for efficient product development. Specifically, in products such as golf balls that are subject to impact during use, the dynamic behavior under high-speed and large-deformation conditions and material properties affect the performance of the product. Simulation is essential for product development.

Further, as the viscoelastic material, there is a material in which physical values such as a loss coefficient change according to the magnitude of strain and strain rate when an external force such as an impact load is applied. That is, since the viscoelastic material has a wide range of deformation speed and size, the physical property values are not linearly linear depending on the deformation speed and size.
There is a property with a strong nonlinear change. Specifically, as the material deforms due to external force and the strain increases, S
-The loop area of the S (strain-stress) curve increases,
The physical properties such as loss factor are the deformation state of the material (deformation speed,
It changes with the size) and shows non-linearity. Many viscoelastic materials have strong non-linearity, and highly accurate simulation is required for products using such viscoelastic materials.

However, there has been no method capable of accurately expressing a physical property showing the non-linearity of a viscoelastic material, for example, a phenomenon in which the loss coefficient strongly changes non-linearly depending on the speed and size of deformation of the material. Conventionally, simulations have been performed on products such as golf balls made of a viscoelastic material assuming that the physical properties of the viscoelastic material hardly change. As a result, there is a problem that the performance of a product made of viscoelastic material in actual use cannot be accurately predicted by simulation, and in reality, the performance of the product must be evaluated by making a prototype. There is a problem that there is no.

The present invention has been made in view of the above problems, and it is an object of the present invention to accurately predict the performance of a product made of a viscoelastic material whose material properties are non-linear under actual use conditions by simulation. I am trying.

[0012]

In order to solve the above-mentioned problems, the present invention provides a strain, a strain rate, and a stress generated in the viscoelastic material under measurement conditions assuming a practical use state of a product made of the viscoelastic material. Of the strain, strain rate, time history data of the stress, and a viscoelastic model considering the viscosity of the viscoelastic material, from the strain loading state and the strain unloading or restoration state. The time history data of the viscous resistance of the viscoelastic material is derived by dividing into time and time, a product made of the viscoelastic material is set as a product model to be analyzed, and the product model is divided into a large number of elements. , The strain, the strain rate, the relationship of the viscous resistance is input, and an analysis is performed by the finite element method in consideration of the difference in the viscous resistance between the strain-loaded state and the strain-unloaded or restored state. Viscous bullet In predicting the performance of a product model of material to decompose the strain and strain rate of the global coordinate system generated for each of the elements to the deviation component and volume component,
Strain and strain rate of the deviation component is converted from the overall coordinate system to the main strain coordinate system and the main strain rate coordinate system, using the converted deviation main strain and deviation main strain rate,
For each coordinate axis of the main strain coordinate system and the main strain velocity coordinate system, even if the strain is the same value, different viscous resistance is determined when the strain is loaded and when the strain is unloaded or restored. We provide a simulation method for predicting the performance of products made of viscoelastic materials.

As described above, the strain and strain rate measured under actual use conditions are decomposed into a volume component and a deviation component, and converted into a principal strain coordinate system and a principal strain rate coordinate system. Even if the strain has the same value for each axis of the main strain coordinate system and the main strain velocity coordinate system using the velocity, different viscous resistances are determined when the strain is loaded and when the strain is unloaded or restored. However, the viscous resistance is made variable for each element for each of the three axial components. Therefore, whether the deformed state of the material is the loaded state or the unloaded state, it is possible to perform an accurate analysis corresponding to the actual situation, and it is possible to perform an accurate analysis in the three-dimensional direction, The performance prediction accuracy of simulation can be improved.

That is, the deformed state of the viscoelastic material is the "loaded state" in which the applied strain increases in the compression direction.
And the "restoration state" in which the amount of compression gradually decreases, and the relationship between strain and strain rate differs depending on that state. Therefore, as described above, considering the two strain states of the viscoelastic material, that is, the load state and the unloading (or restoring) state, the strain and strain rate are different under load and unloading. It is possible to accurately grasp the actual state of deformation of the material by determining the viscous resistance using the relationship of, and deriving different viscous resistance values under the strain loading and unloading conditions even when the strain has the same value. it can. Therefore, it is possible to accurately represent the phenomenon that the material changes depending on the deformation speed, size, etc., and it is possible to further improve the accuracy of the simulation.

Further, by calculating the magnitude (norm) of the main strain for each of the above-mentioned elements and comparing it with the norm of the previous step at the time of simulation, when the norm increases, the load and norm decrease. If it is present, it is preferably judged as unloading, and the strain load and the unloading state are preferably judged. For example, if the main strain in one direction alone shows various changes in load and unloading with a minute change, by setting the size in multiple directions in this way, the load and unload will be changed to some extent. Since the unloading does not change, the stability of calculation can be improved.

In the present invention, ε in the global coordinate system_x, Ε_y, Ε
_z, Ε_xy, Ε_yz, Ε_zxDistortion that occurs for each element
And consider viscoelastic characteristics in the deviation component of strain rate
In order to obtain the deviation of the above strain and strain rate from the volume component,
Into a main strain coordinate system and a main strain velocity coordinate system.
Using the principal strain and principal strain rate of the converted deviation component
Distortion for each axis of the main strain coordinate system and the main strain velocity coordinate system
Load condition and strain unloading or restoring condition
Determine different viscous resistances and apply the viscous resistance to each axis for each element.
The three components in the direction are variable. Therefore, three-dimensional
Accurate directional analysis considering viscoelasticity of viscoelastic materials
Can improve the accuracy of the simulation
be able to. Here, the volume component is ε_v= (Ε_x+
ε_y+ Ε_z), The deviation component is ε
_xy’＝ ε_xy/ 2, ε_yz’＝ ε_yz/ 2, ε_zx’
= Ε_{z x}/ 2, ε_x’＝ ε_x−ε_v/ 3, ε_y’＝ ε_y
−ε_v/ 3, ε_z’＝ ε_z−ε _vThe component represented by / 3
Point to. Note that the shear component is halved because of the physical
This is because the strain is converted. Convert only deviation component
The viscoelastic component of the volume component is very small,
Also, the reason why it is not possible to obtain it by actual measurement under the present circumstances
by. That is, there is almost no viscoelastic component of the volume component.
Then, it is judged only by the deviation component, and the conversion is based on the measurement
Since there are only directional results, ε_xy, Ε_yz, Ε_zxSuccess
Convert so that min = 0, and ε₁, Ε_Two, Ε_Three(Main horn
Only the three components) are used, and the measured results are used.
The global coordinate system is the initial shape, that is, the shape of the model.
The main strain coordinate system and the main strain coordinate system
Strain rate coordinate system is the shear of strain and strain rate.
When the component is converted so that it becomes 0, the whole coordinate system has the same angle.
Refers to the coordinate system converted in degrees.

Strain (strain rate) generated for each element
Is a six-component material, but the material properties measured under the conditions of high-speed large-deformation are uniaxial material properties, so consideration of the material properties in the shear direction is insufficient. Therefore, the strain 6 component generated for each element is converted into the main strain coordinate system, and the strain 3 component in the main axis direction is obtained. That is, when the strain in the shearing direction is set to 0, the six components (ε _x ,
ε _y , ε _z , ε _xy , ε _yz , ε _zx ) are strain (main strain coordinate system, ε ₁ , ε ₂ , ε ₃ ) 3 components in the principal axis direction. Thereby, the material property of the viscoelastic material can be evaluated from the measurement result without considering the shear direction.

Specifically, the strain and strain rate of the entire coordinate system generated for each element are decomposed into a deviation component and a volume component, and viscoelasticity is considered as the deviation component. Six components of strain and strain velocity deviations that have been decomposed are converted from the global coordinate system to the main strain coordinate system and the main strain velocity coordinate system, and the main strain coordinate system and the main strain velocity coordinate system deviate the main strain and the deviation main strain velocity system. Each of the three components is used. Thus, the viscous resistance can be determined for each axis in the main strain coordinate system and the main strain velocity coordinate system.

Further, the stress and strain of the deviation component are calculated in consideration of viscoelasticity from the above-mentioned viscous resistance, and the stress and strain of the deviation component are reconverted into the original general coordinate system to calculate the stress and strain of the volume component. And the stress and strain of each element are calculated from the stress and strain of the deviation component. In this way, by calculating the stress and strain for each element, the stress and strain can be calculated every moment.

Specifically, from the following equations 1 and 2, the deviation main strain and the deviation main strain velocity are used, and the viscosity is different for each coordinate axis when the strain is loaded and when the strain is unloaded or restored. The resistance is determined, and the stress and strain of the deviation component considering the viscoelasticity are calculated from the viscous resistance. (Formula 1) Here, E _i : deviation main strain of the i-th element, n: analysis time step, β _i : β of the i-th element (where β = E
_{t / η, E t = E} short -E lo ng, η: viscosity resistance), gamma _i: refers to deviation main strain rate of i-th element.
(Formula 2) Here, σ _i : i-th element stress, F _i : stiffness coefficient, G
_short : short-term shear coefficient, G _long : long-term shear coefficient. After calculating β in Formulas 1 and 2 and the coefficient F of rigidity from the experimental data, the 6 components of the deviation of strain are updated by Formula 1, and the stress is calculated by Formula 2. After that, the main strain coordinate system and the main strain rate coordinate system are converted into the overall coordinate system, and the stress is updated by the following mathematical formula 3. (Formula 3) Where K: bulk modulus, ε _v : volume strain,
σ _ij : Stress in the global coordinate system.

Further, a viscoelastic model considering the viscosity of the viscoelastic material is used to derive different viscous resistances in the strain loading state and in the strain unloading or restoring state to obtain strain, strain rate, and strain loading. Since the relationship between viscous resistance when the state is unloaded and when the strain is unloaded or restored is input to the product model for simulation, the physical property value indicating the non-linearity of the viscoelastic material depends on the speed and magnitude of material deformation. It is possible to accurately represent a phenomenon that changes nonlinearly depending on the size. In addition, since the strain, strain rate, and stress values used in the simulation are measured under conditions that assume the actual usage state of products made of viscoelastic materials, they can be used for various deformation states of actual viscoelastic materials. The simulation can be performed. Therefore, the relationship between strain and strain rate changes depending on the deformed state of the material, and it is possible to accurately predict the performance by simulation even for products made of viscoelastic materials whose material properties such as loss coefficient show non-linearity. ing.

In this simulation method, the momentary values of strain, strain rate, and stress occurring in the viscoelastic material are measured under measurement conditions assuming the actual use state of the product made of the viscoelastic material. Specifically, the measurement conditions are determined assuming that the viscoelastic material is deformed by the external force applied to the product when the product is actually used. Under the above measurement conditions, the values of strain, strain rate, and stress occurring in the viscoelastic material are measured every moment to obtain time history data. Therefore, it is possible to obtain information on the state of deformation of the viscoelastic material when an external force assuming the actual use state is applied to the viscoelastic material from the time history data of strain, strain rate, and stress. As a result, it is possible to accurately predict the physical properties of a viscoelastic material accompanied by high-speed and large-deformation behavior due to impact load.

The above-mentioned values of strain, strain rate and stress are preferably measured under a plurality of different measurement conditions. By changing the magnitude of the external force applied to the product and setting the measurement conditions for multiple patterns, it is possible to obtain data for various patterns regarding strain, strain rate, and stress, and improve the accuracy of the simulation input values. be able to. In addition, as much as possible, in order to obtain data for as many patterns as possible, the strain, strain rate, and stress values are
It is preferable to measure until the strain becomes almost zero after the strain is generated by applying an external force to the viscoelastic material, and the shorter measurement time interval is better from the viewpoint of simulation accuracy.

As the viscoelastic model considering the viscosity of the viscoelastic material, a viscoelastic model including a spring and a dashpot is preferable. Since such a viscoelastic model can simplify the viscosity of the viscoelastic material, it is possible to easily consider the influence of the viscosity on the deformed state of the material.
Specifically, a Maxwell model, a Voigt model, or a combination of a plurality of springs and dashpots may be used. The two-element model is preferable from the viewpoint of model simplification. In such a viscoelastic material model, the viscous resistance η of the dashpot and the rigidity of the spring (longitudinal elastic coefficient E or shear coefficient (horizontal elastic coefficient)) are made variable. The shear modulus is a physical property value determined by the longitudinal elastic modulus (Young's modulus) E and the Poisson's ratio.

From the above-mentioned time history data of strain, strain rate, and stress and a viscoelastic model considering the viscosity of the viscoelastic material, the strain is applied to the viscoelastic material and the strain is unloaded or restored. Time history data of different viscous resistances are derived. Specifically, according to the viscoelastic model, the strain generated in the viscoelastic material, the strain rate, the longitudinal elastic modulus of the viscoelastic material, and the viscous resistance that differs between the strain loading state and the strain unloading or restoring state Each relationship of is formulated. By formulating in this way, the viscous resistance is expressed as a function of strain and strain rate. Then, the longitudinal elastic modulus of the viscoelastic material is derived from the strain and stress generated in the viscoelastic material obtained by the above measurement, and along with the strain and the strain rate, it is substituted into the above function by the strain load state and the strain removal. Different values of viscous resistance are derived depending on the load or the restored state. In the above measurement,
Since the time history data regarding strain, strain rate, and stress is obtained, the corresponding time history data can be similarly obtained regarding viscous resistance. In this way, the viscous resistance is determined by the values of strain and strain rate, and the viscous resistance also changes according to the time change.

A product made of the viscoelastic material is set as a product model to be analyzed, and the product model including the product model
Input data for calculation including constraint conditions (or input
data), the strain, strain rate, and the relationship of the viscous resistance that differs between the strain load state and the strain unloading or restoring state are entered, and the change in the viscous resistance due to the strain and strain rate differences is considered. We are doing a simulation. At the time of simulation calculation, the above-mentioned strain, strain rate, and the relationship of viscous resistance that is different between the strain loading state and the strain unloading or restoring state are input to the product model. And the two-dimensional data of the relationship between strain and viscous resistance can be input and calculated. Further, the relationship between strain, strain rate, and viscous resistance can be made into three-dimensional data, and the viscous resistance can be input as data into a function and calculated.

For each two-dimensional data of the relation between strain and strain rate and the relation between strain and viscous resistance, the above relations are used to calculate strain, strain rate and corresponding strain under load and strain unloading. Alternatively, a viscous resistance different from that in the restored state is written as input data. Specifically, under a plurality of measurement conditions, strain, strain rate, etc. are measured, and for each pattern under different measurement conditions,
From the time series data of strain and strain rate, record the correspondence between strain and strain rate. The value of the viscous drag corresponding to each curve is also recorded. By arranging these three correspondences of strain, strain rate, and viscous resistance, the viscous resistance at a certain strain and strain rate is accurately derived and calculated.

Since the physical properties of the viscoelastic material can be more accurately realized as the number of measurements under different strains and strain rates is increased, the strains, strain rates, etc. can be measured under a plurality of different measurement conditions as described above. It is preferable to carry out. However,
Since more measurement data requires more calculation time during simulation, it is preferable to calculate the viscous resistance using interpolation when the strain and strain rate are not the same as the measurement data measured under the specified measurement conditions. . The above-mentioned interpolation is, for example, various methods such as linear interpolation from two values of viscous resistance under the conditions of close strain and strain rate, or interpolation using individual measured values under all measured conditions. Can be done by. By performing such an interpolation operation, the viscous resistance can be calculated corresponding to the changes in strain and strain rate that occur in the material due to the difference in measurement conditions.

According to the present simulation method, even if the viscoelastic material is a material whose physical properties are non-linear,
It is possible to accurately simulate the physical properties of materials and the deformation behavior assuming actual usage. Even in a material in which the physical properties of the viscoelastic material are not linearly linear and exhibit strong nonlinearity accompanied by changes in the deformation rate and the magnitude of deformation, as described above, the viscous resistance is strained and the strain rate is
Non-linearity can be considered by calculating the viscous drag using a viscoelastic model that is determined by two values. In this simulation method, particularly in a material exhibiting a strong nonlinearity with a loss coefficient, it is possible to accurately perform a simulation and predict the performance of a product assuming an actual use state.

The simulation method of the present invention is performed by the finite element method as shown below. When performing the simulation by the finite element method analysis, a large number of nodes and elements are set in the product model. That is, when simulating a product composed of a viscoelastic material by the finite element method and predicting the material properties, the stiffness (longitudinal elastic modulus or shear coefficient) of the spring of the viscoelastic model is determined, and the viscous resistance indicating the viscosity is determined. As described above, by determining the strain and strain rate generated in each element for each element, it is possible to represent the material physical properties under the conditions of appropriate strain and strain rate for each element. It should be noted that instead of inputting the longitudinal elastic modulus, a shearing coefficient may be input from the relationship with the Poisson's ratio. Whether to input the longitudinal elastic coefficient or the shear coefficient can be changed according to the specifications of the finite element method program.

The above strain, strain rate and stress are measured by a split Hopkinson bar tester. Using the Split Hopkinson bar tester, a test piece can be subjected to high-speed and large-deformation strain at a high speed of 10,000 minutes or several thousandths of a second, and the amount of deformation is also tens of percent.
Time series data of strain, strain rate and stress of viscoelastic material under high speed and large deformation condition can be obtained. If the measurement conditions of the split Hopkinson rod tester are strains that occur in the viscoelastic material when an impact load is applied to the product, and conditions equivalent to the strain rate, high-speed large deformation state of the viscoelastic material caused by external force, etc., It is possible to obtain the material properties of the viscoelastic material corresponding to various states. Therefore, the accuracy of the simulation can be improved by using the material properties measured by this split Hopkinson bar tester.

The split Hopkinson bar tester can measure the material properties of the test piece in various strain and strain rate regions simply by changing the impact speed of the striking rod that impacts the test piece. Therefore, it is possible to easily obtain material properties in various strain and strain rate patterns.

The split Hopkinson bar tester was originally used for evaluating the impact behavior of metallic materials.
In the present invention, the split Hopkinson bar tester is modified and used for evaluation of viscous viscoelastic materials. The measuring method and the like of the split Hopkinson bar tester will be described later.

If it is possible to apply a strain of large deformation to the test piece at a high speed and the physical properties of the material can be measured under the conditions of strain and strain rate under the conditions in which the product is actually used, It goes without saying that the physical properties of the material may be determined by a measuring method other than the split Hopkinson bar.

The maximum value of the strain generated in the viscoelastic material at the time of measuring the strain, strain rate, and stress under measurement conditions assuming the actual use state of the product made of the viscoelastic material is 0.05 to 0. And / or the maximum value of the strain rate is 500 / s to 10000 / s,
It is preferably in the range of 500 / s to 5000 / s. The maximum value of the above-mentioned strain, the range of the maximum value of the strain rate, the strain that occurs during high-speed large deformation of the viscoelastic material, since the condition of the strain rate, to predict the performance of the product during high-speed large deformation, It is preferable to use three time-series data of strain, strain rate, and stress under the conditions.

The viscoelastic material is a golf ball material, and the product model is a golf ball. Golf balls are products made of viscoelastic materials that are subject to external forces such as impact loads when subjected to high-speed deformation or large deformation during actual use. The high-speed, large-deformation state has a large effect on the performance of the golf ball itself. Exert. Therefore, the analysis by the simulation method of the present invention is very useful for predicting the performance of the golf ball, and the performance of the golf ball can be predicted with high accuracy without trial production. Can be realized.

Simulation of a collision phenomenon between the golf ball and a hitting object assuming a golf club head,
The behavior of the golf ball at the time of the collision is predicted. In practice, the golf club head can predict the material properties of the viscoelastic material that composes the golf ball under the same strain, strain rate, and stress conditions as when the golf ball is hit. It is possible to predict the behavior of the golf ball such as the coefficient of restitution and the state of deformation of the golf ball when hit.

The above-mentioned golf ball may be a so-called one-piece golf ball which is composed of a unit such as a crosslinked rubber layer, or a so-called two-piece golf ball in which a core is covered with a cover such as a crosslinked rubber layer, or 3 It may be a so-called multi-piece golf ball composed of layers or more, and is applicable to golf balls of any structure made of a viscoelastic material.

The viscoelastic material includes all materials having viscoelasticity. Examples thereof include thermoplastic resins, thermosetting resins, various elastomers, rubbers, and the like, and these can be used alone or as a mixture. Further, these simple substances and mixtures include a colorant, a deterioration inhibitor,
Various additives such as a cross-linking agent may be blended as necessary. It can be applied to any material as long as it can measure strain, strain rate, and stress under actual use conditions of the product.

Specifically, synthetic resins such as ionomer resins used as constituent materials for golf balls, polybutadiene (butadiene rubber), natural rubber, polyisoprene, styrene-butadiene copolymers, ethylene-propylene-diene copolymers. (EPDM), urethane rubber and the like.

Examples of the viscoelastic material include rubber balls, rubber belts, or tires used in printing machines such as printers, as well as golf balls, and other viscoelastic materials such as sports goods for tennis and golf. To be As a product made of a viscoelastic material, a viscoelastic material may be used for at least a part of the product, and it may be a composite molded product with another material such as a metal material. It is also possible to predict the performance of the part corresponding to. In particular, it is suitable for a product that receives an impact load and exhibits a large amount of deformation at high speed during use, and the performance and dynamic behavior of the product can be accurately predicted by this simulation method.

In this simulation method, the strain, strain rate, longitudinal elastic modulus or shear coefficient is input to the calculation input data including the product model, and the longitudinal elastic coefficient or shear due to the difference in strain or strain rate is input. By considering the change in the coefficient, it is possible to perform accurate analysis even for viscoelastic materials whose longitudinal elastic coefficient changes depending on the deformation state (strain, magnitude of strain rate, etc.) of the material, further improving the accuracy of simulation. Can be made. Further, depending on the case, it is possible to divide the case into a stress-loaded state and a stress-loaded state.

[0043]

DETAILED DESCRIPTION OF THE INVENTION Embodiments of the present invention will be described below with reference to the drawings. In the simulation method of the first embodiment of the present invention, a material containing butadiene rubber, which is a constituent material of a golf ball, as a main component is used as a viscoelastic material exhibiting nonlinearity. Using a material containing the butadiene rubber as a main component as a test piece, a split Hopkinson rod tester improved for measuring viscoelastic materials was used under high-speed, large-deformation measurement conditions assuming actual use of a golf ball, The strain, strain rate, and stress generated in the material containing butadiene rubber as the main component are measured every moment. The measuring method using the split Hopkinson bar tester will be described later.

The split Hopkinson rod tester can measure the physical properties of materials in various strain and strain velocity regions by changing the impact velocity of the striking rod. In this embodiment, four patterns of collision speeds (7 m / s, 14 m / s)
s, 20 m / s, 25 m / s) is adopted, and measurement is performed under four measurement conditions, and strain, strain rate, and time history data of stress are obtained for each collision pattern. The time history data of strain ε, strain rate ε ′, and stress σ are shown in FIGS. 1, 2, and 3, respectively.

After the striking rod was made to collide with the split Hopkinson rod tester, as shown in FIG. 1, the material containing butadiene rubber as a main component was distorted, and the strain value increased until a certain time. , And then gradually decreased. Further, as shown in FIG. 2, the strain rate shows a positive value until the strain reaches the maximum value, and shows a negative value after the maximum strain value. As shown in FIG. 3, the stress value also changes with time.

FIG. 4 shows a strain-stress diagram drawn from the strain time history data and the stress time history data. In the strain-stress diagram of FIG. 4, using the strain ε _max when the strain value is the maximum and the value of the stress σa at that time, the longitudinal elastic modulus E of the test piece is calculated for each collision pattern by the following mathematical formula 4. It is calculated. (Equation 4) E = [sigma] _a / [epsilon] _max --- (4) In the material containing butadiene rubber as the main component used in the present embodiment, the impact velocity of the striking rod was changed in the split Hopkinson rod tester. However, the longitudinal elastic modulus in each collision pattern shows almost the same value.

For a product made of a viscoelastic material, a viscoelastic model considering the viscosity of the viscoelastic material is set in order to perform a simulation in which the viscosity is taken into consideration. Specifically, in this embodiment, a basic two-element Voigt model is used as a viscoelastic model including a spring and a dashpot as shown in FIG. That is, in the viscoelastic material model, the dashpot viscous resistance η and the spring rigidity (longitudinal elastic modulus E or shear coefficient) are used in a variable manner.

As shown in FIG. 5, a two-element Voigt (Vo
igt) model, the response generated by the spring
Force σ₁, The stress generated in the dashpot is σ_TwoAnd
The stress σ generated as a whole can be expressed by Equation 5 as follows.
it can. (Formula 5) σ = σ₁+ Σ_Two = Eε + ηε ′ −−− (5)

Therefore, from the above formula 5, the viscous resistance η can be expressed by the following formula 6 in such a viscoelastic model. (Equation 6) η = (σ−Eε) / ε ′ −−− (6)

Therefore, the viscous resistance η corresponding to the strain ε and the strain rate ε ′ is calculated from the time history data of the strain ε, the strain rate ε ′ and the stress σ shown in FIGS. 1, 2 and 3 and the above mathematical formula 3. It can be calculated moment by moment. Here, as described above, the strain, the strain rate, and the value of the stress are changing with the passage of time, and the strain state generated in the viscoelastic material is the "load state" in which the applied strain increases in the compression direction. "
And the “restored state” in which the amount of compression gradually decreases. Therefore, when the viscous resistance is calculated, the strain state generated in the viscoelastic material is divided into two states, that is, the load state and the unloading (or restoring) state.
As shown in, the time history data of viscous resistance is obtained at each collision velocity.

As described above, after determining the longitudinal elastic modulus E of the viscoelastic material from the strain and stress obtained by the measurement under the high-speed large-deformation condition, the above mathematical formula derived from the viscoelastic model considering the viscosity is obtained. By virtue of 6, the viscous resistance η is calculated separately for the loaded state and the unloading (or restoring) state, and the viscous resistance η is different between the strain loading state and the strain unloading or restoring state. Apply to simulation.

FIG. 7 shows the relationship between strain and viscous resistance based on the time history data of strain and the time history data of viscous resistance. As shown in FIG. 7, the value of the viscous resistance is different between the strain applied state and the unloaded (or restored) state even when the strain is the same value. Further, FIG. 8 shows the relationship between strain and strain rate based on the time history data of strain and the time history data of strain rate. in this way,
The viscous resistance changes depending on the strain and strain rate, and shows different values during the strain loading state and the unloading (or restoring) state. Therefore, the viscous resistance can be determined by the strain and strain rate. The viscous resistance is divided into a strain-loaded state and a strain-unloaded state and used as a function of strain and strain rate. In FIG. 8, the data of the four collision velocities seem to overlap with each other on the display in the negative region of the strain velocity, but the actual values are different strains and strains for each collision velocity. It is the speed value.

The relationship between the strain and the viscous resistance shown in FIG. 7 and the relationship between the strain and the strain rate shown in FIG. 8 are respectively written as input data in each collision pattern as described later, and the above is obtained by the finite element method analysis. The simulation is performed in consideration of the change in viscous resistance due to the difference in strain and strain rate, that is, the change in viscous resistance due to the difference between the loaded state and the unloaded (or restored) state of strain.

In this embodiment, a golf ball model is set as a product model made of a viscoelastic material, and a simulation is performed assuming a collision of a golf club head (hit object) with a golf ball. As shown in FIG. 9, the golf ball model 10 assumes a one-piece ball containing butadiene rubber as a main component, and has a spherical shape having a diameter of 42.8 mm.

In performing the finite element method analysis, initial conditions are set in the product model. That is, the initial conditions such as the size, shape, and structure of the golf ball model 10 are set, and the golf ball model 10 is divided into a large number of elements 11
And a large number of nodes 12 are obtained. The number of elements in all ranges of the golf ball model is preferably 1000 to 100,000, more preferably 2500 to 20000 in the whole model. The upper limit is
This is because the capacity of the computer at the present stage is taken into consideration. As the capacity of the computer is improved in the future, the upper limit range can be easily imagined because the analysis time is shortened.

Based on the above set conditions, the data of the golf ball model 10 and the relation between the strain, the strain rate, and the viscous resistance are written in the input data during the simulation calculation. When the calculation is executed, an appropriate viscous resistance is calculated for each element every moment, and the formula is calculated using the viscous resistance. In this simulation, the two-dimensional data of the relationship between strain and strain rate, and the relationship between strain and viscous resistance, which are divided into the case of strain loading and the case of unloading (or restoring), are input and calculated. There is. From the time series data of strain and strain rate for each of the four patterns with different measurement conditions, record the correspondence between strain and strain rate, and write the strain, strain rate and corresponding viscous resistance as input data. Become. In the case of strains and strain rates that are not the same as the strain and strain rate measurement data measured under the four measurement conditions, linear interpolation is performed using viscous resistance binary values under the conditions of adjacent strain and strain rate. ing.

More specifically, when focusing on one element, the magnitude of the strain (norm) occurring in that element
Is calculated and compared with the norm of the previous step at the time of simulation, if the norm is increasing, it is judged to be the load, and if the norm is decreasing, it is judged to be the unloading. Judgment is made and information on strain and strain rate considering the material state is obtained. Next, from the relationship between the strain and strain rate of each collision case (measurement case) obtained from the measurement, refer to the value of the strain rate when the strain of the same value occurs in each case, and We search for two cases with strain rate values close to the strain rate values. When the strains corresponding to these two cases have the same value, the values of the strain rate and the viscous resistance can be used to calculate the appropriate value of the viscous resistance corresponding to the strain and strain rate generated in the element by interpolation. it can. In the present embodiment, interpolation is performed by such simple primary interpolation. In this way, by determining the viscous resistance that differs between loading and unloading for each element depending on the strain and strain rate occurring in that element, the material properties under the conditions of appropriate strain and strain rate for each element. Is represented.

Further, the strain and strain rate of the global coordinate system generated for each element are decomposed into a deviation component and a volume component, and the strain and strain rate of the deviation component are converted from the global coordinate system to the main strain coordinate system and the main strain rate. Converted to the coordinate system, and using the converted main strain of deviation and main strain velocity of deviation, as described above, from each of the coordinate axes shown in FIGS. Different viscous resistances are determined depending on the state, and the stress and strain of the deviation component considering the viscoelasticity from the viscous resistances are calculated by the mathematical formulas 1, 2, and 3. After that, the stress and strain of the deviation component are reconverted to the global coordinate system, and the stress and strain of each element are calculated from the stress and strain of the volume component and the stress and strain of the deviation component.

That is, the strain 6 components generated for each element are converted into the main strain coordinate system to obtain the strain 3 components in the main axis direction. The strain and strain rate of the global coordinate system generated for each element are decomposed into a deviation component and a volume component, and viscoelasticity is considered in the deviation component. Six components of strain and strain velocity deviations that have been decomposed are converted from the global coordinate system to the main strain coordinate system and the main strain velocity coordinate system, and the main strain coordinate system and the main strain velocity coordinate system deviate the main strain and the deviation main strain velocity system. Using each of the three components of, the viscous resistance is determined for each axis in the main strain coordinate system and the main strain velocity coordinate system, even if the strain is the same value, when the strain is loaded and when the strain is unloaded or restored. is doing.

In the present embodiment, specifically, FIG. 10 (A)
(B) As shown in (C), golf ball model 10
In addition, as a hitting object, a cylindrical hollow bar model 20 of 200g (same as the weight of a golf club head)
The physical properties of the golf ball model 10 when the golf ball is collided at a speed of 45 m / s are analyzed by the finite element method, and simulation is performed. With this, the amount of strain generated in each element 11 of the golf ball model 10 is calculated for a predetermined time from the time of impact of the impacting object to the predetermined time.

Mass is distributed to each node constituting one element, each node is replaced with a mass point, and the velocity of each node is divided as the velocity of the mass point to obtain the total velocity.
That is, the velocity Vbi of the ball after impact (i = x,
y, z) is calculated by the following equation 7: The total momentum of the ball is considered to be the sum of the momentums of all masses, and the total momentum divided by the total weight is defined as the ball ejection velocity Vbi.

(Equation 7) Here, N and M are the number of nodes of the ball, the total mass, Vni,
Mn is the n-th translational velocity, the mass of the element containing the node divided by the number of nodes contained in that element.

The circular surface 20a of the aluminum hollow bar model 20 is used as a collision surface, and the collision surface is flat.
It is a flat frontal collision with the golf ball model 10. In addition, the circular surface 2 of the aluminum hollow bar model 20
The center point 20b of 0a is the first golf ball model 10
The collision is made so that it becomes a collision point with.

The speed of the aluminum hollow rod model 20 and the golf ball 10 before and after the collision is calculated by the above method, and the coefficient of restitution of the golf ball 10 is calculated and predicted from the respective speeds and weights.

As described above, the main strain coordinates and the main strain rate of the deviation component obtained by decomposing the strain and the strain rate into the volume component and the deviation component and converting them into the main strain coordinate system and the main strain rate coordinate system are used. For each axis of the system and the main strain rate coordinate system, even if the strain is the same value, different viscous resistances are determined in the strain loading state and the strain unloading or restoring state, and the viscous resistances for each element are The three axial components are variable. Therefore, the analysis considering the viscoelasticity of the viscoelastic material can be accurately performed in the three-dimensional direction, and the accuracy of the simulation can be improved.

In addition, the viscous resistance which is divided into the strain loading state and the unloading (or restoration) state is strained,
It is determined as a function of strain rate, and the relationship among the three factors of strain, strain rate, and viscous resistance is input to a golf ball model, and simulation is performed by the finite element method analysis. Therefore, the viscous resistance corresponding to each strain and strain rate of each element can be calculated, and the viscous resistance value takes into consideration the difference between the strain load state and the unloading (or restoring) state. The properties of viscoelastic materials with strong nonlinearity can be predicted very accurately even under high-speed and large deformation conditions.

Therefore, the performance such as the coefficient of restitution of a golf ball model made of a viscoelastic material, the dynamic behavior, etc., under the same conditions as when hit by an actual golf club head,
It can be grasped accurately without making a prototype.

Further, as shown in FIG. 11, the phase angle δ is calculated from the stress-strain curve by using the following formula 8.
The loss coefficient (tan δ) can be calculated from the phase angle δ. (Equation 8) δ = sin ⁻¹ ((σ _a −σ _b ) / σ _max ) −−− (8)

(Measurement of Material Properties by Split Hopkinson Bar Tester) FIG. 12 is a schematic front view showing a split Hopkinson bar tester improved for measuring viscoelastic materials.

The split Hopkinson rod tester shown in FIG. 12 comprises a striking rod 51, an input rod 53 and an output rod 55, which are arranged on a straight line. Input rod 53
The first strain gauge 57 and the second strain gauge 59.
Is attached. A third strain gauge 61 and a fourth strain gauge 63 are attached to the output rod 55. The rear end 53a of the input rod 53 and the front end 55a of the output rod 55
A columnar test piece 70 is sandwiched between and.

The test piece 70 may be formed by molding the viscoelastic material to be measured into the shape of the test piece, or may be cut out from the molded product state of the viscoelastic material. In this embodiment, the length of the test piece 70 (that is, the distance between the rear end 53a of the input rod 53 and the front end 55a of the output rod 55) is 4 mm, and the cross-sectional diameter of the test piece 70 is 18 mm.

The striking rod 51, the input rod 53 and the output rod 55 are cylinders made of polymethylmethacrylate and have a cross-sectional diameter of 20 mm, a longitudinal elastic modulus of 5300 MPa and a specific gravity of 1.
It is 19. The striking rod 51 has a length of 100 mm.
The length of the input rod 53 and the output rod 55 (hereinafter, the input rod 53 and the output rod 55 are also referred to as “stress rods”) is 2
It is 000 mm. The first strain gauge 57 is the input rod 53.
It is attached at a position 900 mm from the rear end 53a, and the second strain gauge 59 is attached at a position 600 mm from the rear end 53a of the input rod 53. In addition, the third strain gauge 61 is connected to the front end 55a of the output rod 55 by 300
It is attached at the position of mm and the fourth strain gauge 6
3 is attached at a position 600 mm from the front end 55a of the output rod 55.

As described above, the split Hopkinson rod tester of FIG. 12 has the striking rod 51, the input rod 53, and the output rod 5.
5 is a synthetic resin made of polymethylmethacrylate, the striking rod 51 and the input rod 53 are as large as 2000 mm, and the first strain gauge 57 and the rear end 5 of the input rod 53.
3a and the distance between the second strain gauge 59 and the rear end 53a of the input rod 53 are large, so that strain, strain rate, and stress of viscoelastic materials such as crosslinked rubber used for golf balls can be measured. Suitable for

The above-mentioned first strain gauge 57, second strain gauge 59, third strain gauge 61, and fourth strain gauge 6
A strain gauge for uniaxial plastic is used as 3, and in this embodiment, KFP-5-350 manufactured by Kyowa Denki Co., Ltd.
-C1-65 is used to attach the input rod 53 and the output rod 55 to the above-mentioned positions. The mounting positions of the first strain gauge 57 to the fourth strain gauge 63 on the input rod 53 and the output rod 57 are on the same line in the length direction.

In the measurement of strain, strain rate, and stress by this split Hopkinson rod tester, first, the striking rod 51 collides with the front end 53a of the input rod 53 at a predetermined velocity. As a result, an incident distorted wave is generated, and this incident distorted wave travels toward the rear end 53a of the input rod 53. A part of the incident strain wave is reflected at the rear end 53a of the input rod 53 and becomes a reflected strain wave, which proceeds toward the front end 53b of the input rod 53. A part of the incident strain wave passes through the test piece 70 from the rear end 53a of the input rod 53, further propagates to the output rod 55 to become a transmitted strain wave, and the rear end 55b of the output rod 55.
Head towards.

The incident strain wave is actually measured by the first strain gauge 57 and the second strain gauge 59. The measured incident distorted wave is passed through a low-pass filter for 10
High frequencies above kHz are removed. Further, the time history of the incident distorted wave is subjected to zero correction with its baseline value set to zero. First strain gauge 57 thus obtained
And the time axis strains in the second strain gauge 59 are Fourier transformed to obtain the frequency axis strain. The first strain gauge 57 and the second strain gauge 5
From the frequency axis strain at 9, the transfer function is derived. While considering the ratio (X1: X2) of the distance X1 between the first strain gauge 57 and the rear end 53a of the input rod 53 and the distance X2 between the second strain gauge 59 and the rear end 53a of the input rod 53, Based on the transfer function, the rear end 53 of the input rod 53
The frequency axis strain at a is estimated. This frequency axis distortion is subjected to inverse Fourier transform, so that the input rod 53
The time axis strain (time history of strain) εi of the incident strain wave at the rear end 53a is obtained.

Similarly, the reflected strain wave reflected by the rear end 53a of the input rod 53 and traveling toward the front end 53b is measured by the second strain gauge 59 and the first strain gauge 57. From the measured reflected distortion wave, the rear end 53 of the input rod 53
The time base strain (time history of strain) εr of the reflected strain wave at a is obtained.

Further, the third strain gauge 61 of the output rod 55
Also, the transmitted strain wave propagated to the output rod 55 through the test piece 70 is measured by the fourth strain gauge 63, and the time-axis strain of the transmitted strain wave at the front end 55a of the output rod 55 is measured from the measured transmitted strain wave ( Time history of strain) ε
t is obtained.

From the thus obtained εi, εr and εt, the strain rate ε ′ of the test piece 70 is calculated by the following mathematical formula 9.
Is calculated. (Equation 9) ε '= (C ₀ / L) · (εi-εr-εt) = ((E / ρ) ^1/2 / L) · (εi-εr-εt) ----- (9) (Equation 9) 9, C ₀ represents the propagation velocity (m / s) of the strain wave in the input rod and the output rod (stress rod), L represents the length (m) of the test piece, and E represents the longitudinal elasticity of the stress rod. Coefficient (N /
m ² ) and ρ represents the density of the stress rod (kg / m ³ ).

Further, the strain ε of the test piece 70 is calculated from εi, εr and εt by the following mathematical formula 10.

(Equation 10) (In Formula 10, C ₀ represents the propagation velocity (m / s) of the strain wave in the input rod and the output rod (stress rod), L represents the length (m) of the test piece, and E represents the stress rod. Longitudinal elastic modulus (N
/ M ² ), and ρ represents the density (kg / m ³ ) of the stress rod)

Further, the stress σ of the test piece 70 is calculated from εi, εr, and εt by the following formula 11. (Equation 11) σ = (E · A / (2As)) · (εi + εr + εt) = (E · D ² / (2 (Ds) ² )) · (εi + εr + εt) −−− (11) (Equation 11 represents E Represents the longitudinal elastic modulus (N / m ² ) of the stress rod composed of the input rod and the output rod, A represents the cross-sectional area (m ² ) of the stress rod, and As represents the cross-sectional area (m of the test piece.
² ), D represents the diameter (m) of the stress rod, and Ds represents the diameter (m) of the test piece).

The strain time history of the test piece 70 thus obtained is shown in the graph of FIG. As shown in FIG. 13, the curve is gentle for a while after the peak P, but thereafter becomes uneven. A point S at a smooth stage after the peak P is selected, a tangent to the curve at this point S is drawn, the relaxation time λ is derived from the intersection of this tangent and the time axis, and the curve obtained by the following formula 12 is used as a point. By setting the curve after S, the entire strain time history can be a smooth curve (shown by a dotted line in FIG. 13).
This makes it possible to eliminate the influence of noise on the finally obtained material properties. (Formula 12) ε (t) = ε ₀ · e ^{−t / λ} −−− (12) (In Formula 12, ε ₀ represents strain at the contact)

Similarly, the following equation 13 makes it possible to make the entire stress time history into a gentle curve, and thereby remove the influence of noise on the finally obtained physical properties of the material. (Formula 13) σ (t) = σ ₀ · e ^{−t / λ} −−− (13) (In Formula (13), σ ₀ represents stress at the contact)

As described above, the strain time history and the stress time history of the test piece 70 are corrected.

By the above method, the time history data of strain, the time history data of strain rate, and the time history data of stress at the time of high-speed large deformation are obtained by the split Hopkinson bar tester.

Examples of the present invention and comparative examples will be described in detail below. First, a golf ball was manufactured using a material containing urethane rubber as a main component. A material containing urethane as a main component was compression-molded at 160 ° C. for 30 minutes with a mold having a diameter of 42.8 mm to obtain a one-piece ball.

The split Hopkinson rod tester was used to measure the strain, strain rate, and stress of the material containing urethane rubber as the main component, and the impact velocity of the striking rod was 7 m / s, 1
It measured about 4 patterns of 4 m / s, 20 m / s, and 25 m / s (room temperature 23 degreeC, relative humidity 50%). The maximum strain and maximum strain rate during measurement are shown below. Collision velocity 7m / s (maximum strain 0.12, maximum strain velocity 1378 / s) Collision velocity 14m / s (maximum strain 0.24, maximum strain velocity 2703 / s) Collision velocity 20m / s (maximum strain 0.35, Maximum strain velocity 3898 / s) Collision velocity 25m / s (maximum strain 0.43, maximum strain velocity 4716 / s) Since the measurement is performed with four patterns of collision velocity, the value of the phase angle δ at each collision velocity is as follows. It shows in Table 1.

[0089]

[Table 1]

(Example) Time history data of strain, strain rate, and stress measured by a split Hopkinson bar tester using a material mainly containing urethane rubber as a test piece, and the same viscoelasticity as in the first embodiment. The simulation was performed using the model and considering the viscous resistance. First above
In the simulation method of the embodiment, the change in the longitudinal elastic coefficient due to the difference in the strain and the strain rate is considered by further inputting the relationship among the strain, the strain rate, and the longitudinal elastic coefficient into the product model. The software used is the general-purpose software Ls-dyna94 manufactured by Japan Research Institute, Ltd.
It was set to 0. The phase angle δ predicted by the simulation of the example is shown in Table 1 above.

Comparative Example Strain, strain rate, measured by a split Hopkinson bar tester using the same material containing urethane rubber as the main component as in the above example as a test piece.
Each time history data of stress was used. The longitudinal elastic modulus was made variable, and the simulation was performed using the strain, strain rate and viscous resistance of the load under load. Except for the points described above, the same procedure as in the example was performed. The phase angle δ predicted by the simulation of the comparative example is shown in Table 1 above.

According to the finite element method analysis, a golf ball made of a material containing urethane rubber as the main component is
Simulating the performance of the golf ball and the deformed state of the material when a 0 g (same as the weight of the head) aluminum hollow rod model is made to collide at three initial velocities of 35, 40 and 45 m / s, The coefficient of restitution in golf ball analysis was calculated by the method described above. The coefficient of restitution in the analysis of Examples and Comparative Examples of the golf balls made of the above-mentioned urethane rubber-based material is shown in Table 2 below.
Shown in.

[0093]

[Table 2]

In addition, the actual coefficient of restitution of the golf ball was measured by the following method by an experiment using an actual golf ball molded from the material containing urethane rubber as the main component. Difference (%) between the coefficient of restitution in the analysis of the above Examples and Comparative Examples and the coefficient of restitution in the experiment using the following actual products
Is shown in Table 2 above.

(Measurement of Restitution Coefficient by Experiment Using Actual Golf Ball) As a method of measuring the restitution coefficient of a golf ball, a golf ball made of the above material was used in place of the head of a golf club at room temperature of 23 ° C. As 20
A hollow rod made of aluminum (0 g (same as the weight of the head)) was made to collide at three speeds of 35, 40 and 45 m / s. The velocities of the hollow rod and the golf ball before and after the collision were measured, and the coefficient of restitution of the golf ball was calculated from the respective velocities and weights. The collision surface of the aluminum hollow rod was flat, and the collision surface was a flat frontal collision with the golf ball. Since the golf ball does not rotate at the time of collision because the collision surface does not have an angle like a golf club head, only the resilience performance of the golf ball can be evaluated.

As shown in Table 1, the phase angle δ in the analysis of the example was almost the same as the phase angle δ of the experimental result at each collision velocity. On the other hand, the phase angle δ in the analysis of the comparative example
Since the simulation is performed using a load and a load curve, the energy loss in the stress-strain curve is smaller than that of the example, and the value of the phase angle δ of the comparative example is smaller than that of the example at each collision velocity. The value was smaller and the difference was larger than the experimental results. Therefore, it was confirmed that the example could accurately simulate the actual experimental result.

Further, as shown in Table 2, the value of the coefficient of restitution in the analysis of the examples is the value of the coefficient of restitution in the experiment obtained by actually making a golf ball as a trial, and which hollow bar Even in the case of speed, there was a good agreement. The difference between the example and the actual test result was -4.82% to -5.98%, and it was confirmed that the actual test result was accurately simulated. On the other hand, the value of the restitution coefficient in the analysis of the comparative example was larger than the experimental value because the value of the phase angle δ was small, and the difference was also larger than that of the example. Specifically, the difference between the comparative example and the actual test result is 16.
It was 1% to 22.2%, which was significantly different from the experimental result.

From the above, when the strain is applied and when the strain is unloaded or restored, the viscosity is the same even when the strain has the same value, when the strain is loaded and when the strain is unloaded or restored. By performing the simulation of the present invention in consideration of the difference in resistance, it has been confirmed that the performance of the product made of a viscoelastic material whose material properties show non-linearity under actual use conditions can be accurately predicted by simulation.

[0099]

As is apparent from the above description, according to the present invention, the strain generated in each element, in order to consider the viscoelastic characteristics in the deviation component of the strain rate, the strain
Each axis of the main strain coordinate system and the main strain rate coordinate system is decomposed into the volume component and the deviation component and converted into the main strain coordinate system and the main strain rate coordinate system using the main strain and the main strain rate of the deviation component. The viscous resistance is determined for each element, and the viscous resistance is made variable for each element in the three axial directions. Therefore, the analysis considering the viscoelasticity of the viscoelastic material can be accurately performed in the three-dimensional direction, and the accuracy of the simulation can be improved.

Further, using a viscoelastic model considering the viscosity of the viscoelastic material, the viscous resistance is derived by dividing it into the strain loading state and the strain unloading or restoration state, and the strain, strain rate, Since the relationship between viscous resistance when strain is applied and when strain is unloaded or restored is input to the product model for simulation, it is possible to accurately capture the actual material state. It is possible to accurately represent the phenomenon that the physical property value indicating the non-linearity of changes non-linearly depending on the deformation speed and size of the material.

Furthermore, since the values of strain, strain rate, and stress used in the simulation are measured under the conditions that assume the actual use state of the product made of the viscoelastic material, various deformations of the actual viscoelastic material will occur. The simulation corresponding to the state can be performed.

Therefore, depending on the deformed state of the material, strain,
Even in the case of a product made of a viscoelastic material in which the relationship between strain rates changes and the material properties such as the loss coefficient show nonlinearity, the performance and the dynamic behavior of the product can be accurately analyzed by simulation.

With a golf club head, an actual impact test can be accurately simulated under the conditions of strain and strain rate equivalent to when the golf ball is impacted, and in a state close to the actual impact. The performance and deformation behavior of the golf ball can be accurately predicted. This makes it easy to understand the physical properties of the material that affect the performance of the golf ball, which not only helps improve the performance of the product,
In the design stage of a golf ball, it is possible to reduce the number of actual ball trials and reduce the cost and time required for trial production.

[Brief description of drawings]

FIG. 1 is a diagram showing time history data of strain ε.

FIG. 2 is a diagram showing time history data of strain rate ε ′.

FIG. 3 is a diagram showing time history data of stress σ.

FIG. 4 is a diagram showing a strain-stress diagram and a method of calculating a longitudinal elastic modulus.

FIG. 5 is a diagram showing a two-element Voigt model used as a viscoelastic model of the present embodiment.

FIG. 6 is a diagram showing time history data of viscous resistance.

FIG. 7 is a diagram showing a relationship between strain and viscous resistance.

FIG. 8 is a diagram showing a relationship between strain and strain rate.

FIG. 9 is a diagram showing how a golf ball model is divided by meshes.

FIG. 10 shows a collision state of an aluminum hollow rod model with a golf ball model, (A) before collision, and (B).
Is a diagram during a collision, and (C) is a diagram after the collision.

FIG. 11 is a diagram showing a method of calculating a loss coefficient.

FIG. 12 is a schematic front view showing a split Hopkinson bar tester.

FIG. 13 is a diagram showing a state of strain time history of a test piece.

[Explanation of symbols]

10 golf club models 11 elements 12 nodes 20 Aluminum hollow bar model

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Masataka Shiraishi             3-6-9 Wakihama-cho, Chuo-ku, Kobe-shi, Hyogo               Sumitomo Rubber Industries, Ltd. F-term (reference) 2G061 AA13 AB04 BA19 CA10 DA11                       EA03 EA04

Claims (6)

[Claims] 1. The strain, strain rate, and momentary values of stress occurring in the viscoelastic material are measured under measurement conditions that assume the actual use state of a product made of a viscoelastic material, and the strain, strain rate, From the time history data of stress and a viscoelastic model considering the viscosity of the viscoelastic material, the viscoelastic resistance of the viscoelastic material can be divided into a strain-loaded state and a strain-unloaded or restored state. Derivation of time history data, the product consisting of the viscoelastic material is set as a product model to be analyzed, the product model is divided into a number of elements, the strain, strain rate, the relationship of viscous resistance is input, When performing the analysis by the finite element method in consideration of the difference in the viscous resistance between the strain loading state and the strain unloading or restoring state, when predicting the performance of the product model made of the viscoelastic material, Up Decompose the strain and strain rate of the global coordinate system that occurs for each element into the deviation component and the volume component, and convert the strain and strain rate of the above deviation component from the global coordinate system to the main strain coordinate system and the main strain rate coordinate system. , Using the converted main strain of deviation and main strain velocity of deviation, for each coordinate axis of the main strain coordinate system and the main strain velocity coordinate system, even if the strain is the same value, when the strain is in the loaded state and when the strain is unloaded or restored. A simulation method for predicting the performance of a product made of a viscoelastic material, characterized in that different viscous resistances are determined by and. 2. The norm which is the magnitude of the principal strain is calculated for each element and compared with the norm of the previous step at the time of simulation, and when the norm increases, the load and the norm decrease. The simulation method for predicting the performance of a product made of a viscoelastic material according to claim 1, wherein the load is determined to be unloaded, and the strain load and the unloaded state are determined. 3. The simulation method for predicting the performance of a product made of a viscoelastic material according to claim 1 or 2, wherein the viscoelastic material is a material whose material properties exhibit non-linearity. 4. The strain, strain rate, and stress are measured by a split Hopkinson bar tester.
A simulation method for predicting the performance of a product made of the viscoelastic material according to claim 3. 5. The maximum value of the strain generated in the viscoelastic material during the measurement is in the range of 0.05 to 0.50, and / or the maximum value of the strain rate is 500 / s to.
A simulation method for predicting the performance of a product made of the viscoelastic material according to any one of claims 1 to 4, which is in the range of 10000 / s. 6. The viscoelastic material is a golf ball material, the product model is a golf ball, and a collision phenomenon between the golf ball and a hitting object assuming a golf club head is simulated, and the golf ball at the time of the collision is simulated. Claim 1 thru | or Claim 5 which has predicted the behavior of a ball.
A simulation method for predicting the performance of a product made of the viscoelastic material according to any one of 1.