Vibration characteristics calculation system, vibration characteristics calculation method, and vibration characteristics calculation program

Abstract

This tool calculates highly accurate vibration characteristics for materials such as urethane foam. [Solution] The vibration characteristic calculation system 10 is a system for calculating the vibration characteristics of a material that contains bubbles and is deformable, wherein the amount of gas contained in the bubbles changes due to deformation. The system comprises an acquisition unit 11 that acquires values ​​indicating the properties of the material used in calculating the vibration characteristics and values ​​indicating the external pressure, and a calculation unit 12 that calculates a value related to the time variation of the gas pressure inside the material when the material is deformed, according to the external pressure, from the values ​​acquired by the acquisition unit 11, and uses the calculated value related to the time variation to calculate a vibration transmittance coefficient corresponding to the vibration frequency as a vibration characteristic.

Description

[Technical Field]

[0001] This invention relates to a vibration characteristic calculation system, a vibration characteristic calculation method, and a vibration characteristic calculation program for calculating the vibration characteristics of a material. [Background technology]

[0002] By mixing polyfunctional isocyanates, polyols, and foaming agents such as water, a sponge-like urethane foam containing fine air bubbles in the polyurethane resin is created. By adjusting the properties of the polyurethane resin portion and the size and continuity of the air bubbles, a variety of functions and characteristics can be expressed in the urethane foam. In automotive seat cushions, as foam thickness is decreasing to improve fuel efficiency, there is a need to improve technology to control the vibration characteristics of the foam in order to improve ride comfort.

[0003] Vibration characteristics are a crucial factor in reducing discomfort caused by vibrations while driving, and there is a need for the development of urethane foam for automotive seat cushions with controlled vibration characteristics. When a car is in motion, vibrations from the ground are transmitted to the human body through the seat cushion. The ratio of the magnitude of vibrations from the ground to the magnitude of vibrations felt by the human body is called the vibration transmission coefficient. The discomfort caused by transmitted vibrations varies depending on the frequency. Therefore, controlling the vibration characteristics, which are the frequency dependence of the vibration transmission coefficient, is important for reducing discomfort caused by vibrations while driving.

[0004] Air permeability, an indicator of the breathability of polyurethane foam, is one of the important parameters that characterize the structure of polyurethane foam, and its relationship with vibration characteristics is being actively studied. Air can move through polyurethane foam through the interconnected pores between microscopic air bubbles. The ease with which air passes through polyurethane foam varies depending on the structure of the bubbles and interconnected pores, and air permeability is used as an indicator of this. Air permeability is defined as the flow rate of air that comes out from one side of the polyurethane foam when a certain pressure is applied from the other side. Polyurethane foam with high air permeability allows air to pass through easily, while polyurethane foam with low air permeability does not allow air to pass through easily. Conventionally, attempts have been made to correlate air permeability with vibration characteristics using physical models (see, for example, Non-Patent Document 1). Air permeability is considered to be a factor that can control vibration characteristics. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] M. Bianchi and F. Scarpa,Smart Mater.Struct.,22,084010(2013) [Overview of the project] [Problems that the invention aims to solve]

[0006] The vibration transmission coefficient of urethane foam, which is a vibration characteristic depending on the vibration frequency, can be calculated using the air permeability based on the conventional method described above. By calculating the vibration transmission coefficient, the material can be evaluated without actually creating the urethane foam, thereby streamlining the development of urethane foam.

[0007] However, the vibration characteristics calculated by the conventional method may differ from the actual behavior depending on the urethane foam and the frequency of vibration. That is, the accuracy of the vibration characteristics calculated by the conventional method was not always sufficient from the viewpoint of, for example, the development of urethane foam for automotive seat cushions. Further, the above problem can also occur with materials other than urethane foam.

[0008] The present invention has been made in view of the above, and an object thereof is to provide a vibration characteristic calculation system, a vibration characteristic calculation method, and a vibration characteristic calculation program capable of calculating highly accurate vibration characteristics for materials such as urethane foam.

Means for Solving the Problems

[0009] In order to achieve the above object, a vibration characteristic calculation system according to the present invention is a vibration characteristic calculation system for calculating the vibration characteristics of a material that contains bubbles and is deformable, and in which the amount of gas contained in the bubbles changes due to deformation, the system comprising: an acquisition unit that acquires a value indicating the properties of the material used for calculating the vibration characteristics and a value indicating the external atmospheric pressure; and a calculation unit that calculates a value related to the time variation of the pressure of the gas in the material when the material is deformed according to the external atmospheric pressure from the values acquired by the acquisition unit, and uses the calculated value related to the time variation to calculate a vibration transmission rate corresponding to the frequency of vibration as the vibration characteristics.

[0010] In the vibration characteristic calculation system according to the present invention, a value related to the time variation of the pressure of the gas in the material when the material is deformed according to the external atmospheric pressure is calculated, and the calculated value related to the time variation is used to calculate the vibration characteristics. By using the value related to the time variation, which affects the vibration characteristics and was not considered in the conventional calculation method, the vibration characteristic calculation system according to the present invention can calculate highly accurate vibration characteristics.

[0011] The calculation unit may calculate a value indicating the time for relaxing the pressure difference between the pressure of the gas in the material and the external atmospheric pressure that occurs when the material is deformed, as a value related to the time variation. Further, the acquisition unit may acquire, as a value indicating the property of the material used for calculating the value related to the time variation, the volume of the gas contained in the material, the area of the surface from which the gas flows out in the material, the path length when the gas flows out from the material, and a coefficient representing the ease of gas passage of the material. Further, the calculation unit uses the following formula [Number] (However, ω: angular frequency [rad / s], A(ω): vibration transmissibility at angular frequency ω [-], τ: time [s] for relaxing the pressure difference between the pressure of the gas in the material and the external atmospheric pressure that occurs when the material is deformed, P0: external atmospheric pressure [Pa], γ: specific heat ratio of the gas [-], μ: viscosity of the gas [Pa·s], m: mass [kg] of the object placed on the material, S: cross-sectional area of the material [m 2 , h0: height of the material [m], E: elastic modulus of the material [Pa], V0: volume of the gas contained in the material [m 3 , L rep : length of the path that the gas in the material travels from the inside to the surface [m], S rep : total area of the portions of the surface of the material where gas flows in and out during deformation [m 2 , K: coefficient representing the ease of gas passage of the material [m 2 ) to calculate the vibration transmissibility according to the frequency of vibration. According to these configurations, vibration characteristics with high accuracy can be calculated appropriately and reliably.

[0012] The material may be urethane foam. According to this configuration, high-precision vibration characteristics can be calculated for urethane foam.

[0013] By the way, the present invention can be described not only as an invention of a vibration characteristic calculation system as described above, but also as an invention of a vibration characteristic calculation method as follows. These are only different in category, but are substantially the same invention and exhibit the same operations and effects.

[0014] That is, the vibration characteristic calculation method according to the present invention is a vibration characteristic calculation method which is a method for operating a vibration characteristic calculation system that calculates the vibration characteristics of a material that contains bubbles and is deformable, wherein the amount of gas contained in the bubbles changes due to deformation, and includes an acquisition step of acquiring a value indicating the properties of the material used to calculate the vibration characteristics and a value indicating the ambient pressure, and a calculation step of calculating a value relating to the time variation of the pressure of the gas inside the material when the material is deformed, according to the ambient pressure, from the values ​​acquired in the acquisition step, and using the calculated value relating to the time variation, calculating a vibration transmittance coefficient according to the vibration frequency as a vibration characteristic.

[0015] Furthermore, the vibration characteristic calculation program according to the present invention is a vibration characteristic calculation program that causes a computer to function as a vibration characteristic calculation system for calculating the vibration characteristics of a material that contains bubbles and is deformable, wherein the amount of gas contained in the bubbles changes due to deformation. The computer functions as an acquisition unit that acquires values ​​indicating the properties of the material used to calculate the vibration characteristics and values ​​indicating the ambient pressure, and a calculation unit that calculates a value related to the time variation of the pressure of the gas inside the material when the material is deformed, in accordance with the ambient pressure, from the values ​​acquired by the acquisition unit, and uses the calculated value related to the time variation to calculate a vibration transmittance corresponding to the vibration frequency as a vibration characteristic. [Effects of the Invention]

[0016] According to the present invention, highly accurate vibration characteristics can be calculated for materials such as urethane foam. [Brief explanation of the drawing]

[0017] [Figure 1] This figure shows the configuration of a vibration characteristic calculation system according to an embodiment of the present invention. [Figure 2] This figure shows an example graph of vibration transmissibility and an overview of vibration transmissibility. [Figure 3] This diagram schematically illustrates the behavior of urethane foam, which is considered when calculating the vibration transmission coefficient. [Figure 4]This graph shows the time-dependent change in the pressure difference between the inside and outside of the polyurethane foam. [Figure 5] This diagram schematically shows the pressure inside and outside the polyurethane foam when air escapes from within the foam. [Figure 6] This diagram shows the breathability of polyurethane foam. [Figure 7] This diagram shows the pressure when air is compressed. [Figure 8] This diagram shows the force generated when polyurethane foam is compressed. [Figure 9] This diagram shows the relationship between vibrations applied to the polyurethane foam, the vibrations of the polyurethane foam itself, and the vibrations of the object (person) resting on the polyurethane foam. [Figure 10] This flowchart shows a vibration characteristic calculation method, which is a process performed by the vibration characteristic calculation system according to an embodiment of the present invention. [Figure 11] This graph shows examples of vibration transmission coefficients and other parameters of urethane foam calculated according to embodiments of the present invention. [Figure 12] This figure shows the configuration of a vibration characteristic calculation program according to an embodiment of the present invention, along with a recording medium. [Modes for carrying out the invention]

[0018] Hereinafter, embodiments of the vibration characteristic calculation system, vibration characteristic calculation method, and vibration characteristic calculation program according to the present invention will be described in detail with reference to the drawings. In the description of the drawings, the same elements are denoted by the same reference numerals, and redundant explanations are omitted.

[0019] Figure 1 shows the vibration characteristic calculation system 10 according to this embodiment. The vibration characteristic calculation system 10 is a system (device) for calculating the vibration characteristics of a material. The material to be used for calculating the vibration characteristics is a deformable material that contains air bubbles, and the amount of gas contained in the air bubbles changes with deformation. The material contains a large number of air bubbles. Multiple air bubbles are connected by connecting holes, and the gas contained within the air bubbles can move between them. Air bubbles are also provided on the surface of the material, and gas can move between the inside and outside of the material. Such a material has cushioning properties.

[0020] In this embodiment, the material whose vibration characteristics are to be calculated is made of resin. Specifically, the material whose vibration characteristics are to be calculated is urethane foam. In particular, the material whose vibration characteristics are to be calculated may be urethane foam for vehicle seats, such as for car seat cushions. Also, in this embodiment, the gas contained in the bubbles of the material and the gas outside the material are air.

[0021] The vibration characteristic to be calculated is the vibration transmittance. Vibration transmittance is the ratio of the magnitude of vibration that the material exerts on the outside to the magnitude of the vibration applied to the material. As shown in the graph in Figure 2(a), the vibration transmittance of a material depends on the vibration frequency. In this graph, the horizontal axis represents the vibration frequency, and the vertical axis represents the vibration transmittance. Furthermore, the vibration transmittance of a material depends on the properties of the material, the mass of the object placed on the material (load), and the conditions of the gases surrounding and contained within the material. The properties of the material also include the shape of the material. The graph in Figure 2(a) shows the vibration transmittance under two conditions. In vibration transmittance, the position of the peak is usually important, so the peak position is indicated by a black circle.

[0022] As shown in Figure 2(b), the vibrations transmitted to the urethane foam used for car seat cushions are the vibrations of the car, and the vibrations transmitted by the urethane foam are vibrations transmitted to the person sitting on the seat cushion. Therefore, the vibration transmission rate affects the ride comfort of the car (e.g., motion sickness, discomfort, and fatigue).

[0023] The vibration characteristic calculation system 10 acquires information indicating conditions related to vibration transmissibility and calculates the vibration transmissibility of urethane foam. According to the vibration characteristic calculation system 10, vibration transmissibility can be evaluated without actually measuring it. Furthermore, if information indicating the properties of the urethane foam used in calculating vibration transmissibility is obtained, vibration transmissibility can be evaluated without actually creating the urethane foam. This makes the development of urethane foam more efficient. In addition, the vibration characteristic calculation system 10 can calculate vibration transmissibility with higher accuracy compared to conventional methods of calculating vibration transmissibility.

[0024] Furthermore, the material used for calculating the vibration transmittance coefficient does not necessarily have to be polyurethane foam; as described above, any material that contains air bubbles and is deformable, where the amount of gas contained in the air bubbles changes with deformation, is acceptable. In addition, the gas contained in the air bubbles of the material and the gas outside the material may be other than air. If the gas is other than air, then in the following description, air should be read as that other gas. Moreover, the purpose of calculating the vibration transmittance coefficient does not have to be for the development of materials that take into account the ride comfort of automobiles as described above; it may be any purpose appropriate to the material for which the vibration transmittance coefficient is being calculated.

[0025] The vibration characteristic calculation system 10 is specifically a computer including hardware such as a CPU (Central Processing Unit) and memory. The various functions of the vibration characteristic calculation system 10, as described later, are performed by the operation of these components by programs, etc. The vibration characteristic calculation system 10 may be implemented by a single computer, or by a computer system consisting of multiple computers connected to each other by a network. The vibration characteristic calculation system 10 may have communication functions for acquiring information necessary for the processing shown below.

[0026] This embodiment explains the concept for calculating the vibration transmittance of a material and provides an example of a formula used for the calculation based on that concept. As described above, the vibration transmittance of a material depends on the properties of the material, the mass of the object placed on the material, and the conditions of the gases surrounding and contained within the material.

[0027] The material properties used to calculate the vibration transmissibility in this embodiment include the elastic modulus and air permeability (ease of air passage). The shape of the material subject to the calculation of vibration transmissibility, the mass of the object placed on the material, and the gas contained in the material are predetermined. In this embodiment, the shape of the material subject to the calculation of vibration transmissibility is a rectangular parallelepiped with a predetermined size. The gas contained in the material is air, as described above.

[0028] Figure 3 illustrates the behavior of the urethane foam 20, which is considered in the calculation of the vibration transmission coefficient in this embodiment. Figure 3 schematically shows the state of the urethane foam 20 and the state of the inside 30 of the urethane foam at that time. Multiple air bubbles 31 exist inside the urethane foam 30.

[0029] As shown in Figure 3, when a force is applied perpendicular to one face of a rectangular urethane foam 20, the urethane foam 20 is compressed in that direction. When the urethane foam 20 is compressed, the pressure inside the urethane foam 20 increases. In addition, the air inside the bubbles 31 inside the interior 30 of the urethane foam 20 is also compressed, and the pressure of that air increases. This creates a pressure difference between the air inside the bubbles 31 inside the interior 30 of the urethane foam 20 and the air outside the urethane foam 20. After the urethane foam 20 is compressed, over time, the above pressure difference causes air to escape from the bubbles 31 inside the interior 30 of the urethane foam 20 (ventilation), and the above pressure difference decreases. In other words, the pressure is relieved by ventilation.

[0030] Figure 4 shows a graph of the pressure difference ΔP(t) over time. In this graph, the horizontal axis represents time, and the vertical axis represents the pressure difference ΔP(t). The pressure difference ΔP(0) is at its maximum value when the urethane foam 20 is compressed (t=0), and gradually decreases over time. The above time variation of the pressure difference is due to the pressure difference between the air inside and outside the urethane foam 20 (material) and the ease with which air (gas) escapes from inside the urethane foam 20.

[0031] The vibration transmittance of the urethane foam 20 depends on the fluctuation of the pressure difference ΔP(t) described above. However, conventional calculations of the vibration transmittance of materials did not take into account the fluctuation of the pressure difference ΔP(t). Conventional calculations assumed that ventilation occurred at the same speed as deformation, and that the deformation speed, the degree of ventilation, and the internal pressure were proportional. In this embodiment, the vibration transmittance is calculated taking into account the fluctuation of the pressure difference ΔP(t) described above. This more faithfully reproduces the actual physical processes compared to conventional methods. Therefore, in this embodiment, it is possible to calculate a vibration transmittance with higher accuracy compared to conventional methods.

[0032] In this embodiment, the vibration transmittance coefficient of the urethane foam 20 is calculated using the time it takes for the pressure difference between the air inside and outside the urethane foam 20 to decrease from its maximum value to a preset value based on that maximum value when the urethane foam 20 deforms. Specifically, the time τ shown in Figure 4 is used when the pressure difference ΔP(t) decreases from its maximum value ΔP(0) to ΔP(0) / e. e is the base of the natural logarithm (Napier's number). Time τ is a value related to the time variation of the gas pressure inside the urethane foam 20 (the material for which the vibration transmittance coefficient is calculated) in response to the ambient air pressure when the urethane foam 20 deforms, and is the time it takes for the pressure difference between the gas pressure inside the urethane foam 20 and the ambient air pressure to ease when the urethane foam 20 deforms. The reduction of the pressure difference occurs when the pressure difference ΔP(t) decreases from its maximum value ΔP(0) to ΔP(0) / e.

[0033] In this embodiment, the vibration transmission rate is calculated by the following formula.

Number

[0034] Hereinafter, the derivation of the above formula will be described. As shown in FIG. 5, when the air (gas) with a volume V0 [m 3 and a pressure P [Pa] = P0 [Pa] + ΔP [Pa] in the urethane foam 20 (material) flows out into the outside air (pressure P0 [Pa]) at a volume flow rate u [m 3 / s], the following formula (1) holds.

Number

[0035] Inside the urethane foam 20, if the temperature is constant, the following formula (2) holds.

Number

[0036] From equations (1) and (2), the pressure change inside the urethane foam 20 is expressed by the following equation (3) using the volumetric flow rate u.

number

[0037] L is the length (characteristic length) of the path that air (gas) in the urethane foam 20 (material) takes to escape from the inside to the surface, relative to the shape of the urethane foam 20. rep [m], and the total surface area (representative surface area) of the surface of the urethane foam 20 (material) through which air (gas) enters and exits during deformation, S rep [m 2 ] is defined. Using these definitions, the volumetric flow rate u can be expressed by the following equation (4) from Darcy's law.

number

[0038] Darcy's Law is a law expressed by the following equation relating to the air permeability (flow rate) v [m / s] of polyurethane foam, as shown in Figure 6.

number

[0039] In reality, if we consider that the pressure difference ΔP with respect to the outside air is the stress ΔP that manifests in the urethane foam 20, then from equations (3) and (4), the following equation (5) holds.

number

[0040] Solving for ΔP yields (6) below.

number

[0041] The relaxation time τ[s], which is the time elapsed until the pressure ΔP[Pa] changes from the compression value P(0)[Pa] to P(0) / e[Pa] due to ventilation, is expressed by the following formula.

number

[0042] Spring constant k of air (gas) in polyurethane foam 20 (material) under adiabatic compression air The spring constant [N / m] (due to the air pressure under deformation) is calculated as follows: As shown in Figure 7, the cross-sectional area S[m 2 When air at atmospheric pressure (external pressure: pressure of the air (gas) outside the urethane foam 20) P0 [Pa] at a height h0 [m] is deformed in the height direction by Δh [m], Poisson's law, shown by the following equation, holds true for the pressure P [Pa] after deformation. Note that the cross-sectional area S [m 2 ] corresponds to the cross-sectional area of ​​the urethane foam 20 (material) on a plane perpendicular to the direction of compression. Also, height h0 corresponds to the length (height) in the direction of compression of the urethane foam 20 (material).

number

number

[0043] When pressure P is applied, the force F [N] acting on the deformation is expressed by the following equation:

number

number

[0044] From the above, the force σ [N] during deformation of the urethane foam 20 shown in Figure 3 can be expressed by the following formula.

number

[0045] In the above equation, ε[m] is the deformation of the urethane foam 20. k0[N / m] is the spring constant of the urethane foam 20, and is expressed by the following equation.

number

[0046] In the above formula, E[Pa] is the modulus of elasticity of the urethane foam 20. E[Pa] is calculated by the following formula.

number

[0047] As described above, the change in force due to air permeability in the urethane foam 20 could be explained using the degree of air permeability and the modulus of elasticity in the same form as the generalized Maxwell model that represents viscoelasticity.

[0048] As shown in Figure 9, the vibration transmissibility A can be calculated using the change in force under the above deformation (step deformation) of the urethane foam 20, under the condition of an object (a person in the example of Figure 9) resting on the urethane foam 20. In Figure 9, ω [rad / s] is the angular frequency of the vibration. Note that angular frequency is a constant multiple of frequency, and the concept of frequency includes angular frequency. X0(t) [m] is the displacement applied to the urethane foam 20 at time t [s]. x0 [m] is the amplitude related to X0(t). X1(t) [m] is the displacement (deformation) of the urethane foam 20 at time t [s] corresponding to the displacement applied to the urethane foam 20. x1 [m] is the amplitude related to X1(t). X2(t) [m] is the displacement of the object (a person in the example of Figure 9) resting on the urethane foam 20 at time t [s] corresponding to the displacement of the urethane foam 20. x2 [m] is the amplitude related to X2(t).

[0049] In the region where viscoelasticity is linear, according to Boltzmann's superposition principle, the resulting force is given by the convolution of the spring constant and the deformation rate. That is, the following equation holds:

number

[0050] Next, the functions of the vibration characteristic calculation system 10 according to this embodiment will be described. As shown in Figure 1, the vibration characteristic calculation system 10 is configured to include an acquisition unit 11 and a calculation unit 12.

[0051] The acquisition unit 11 is a functional unit that acquires values ​​indicating the properties of the material used in calculating vibration characteristics, and values ​​indicating the external pressure. The acquisition unit 11 may acquire values ​​indicating the properties of the material used in calculating values ​​related to time variation, such as the volume of gas contained in the material, the surface area from which the gas flows out of the material, the path length when the gas flows out of the material, and a coefficient representing the gas permeability of the material.

[0052] The information acquired by the acquisition unit 11 is used to calculate the vibration transmissibility. When using the formula for calculating the vibration transmissibility A(ω)[-] described above, the acquisition unit 11 acquires the following information used in the formula. The acquisition unit 11 acquires the cross-sectional area S[m²] of the urethane foam as a value indicating the properties of the urethane foam, which is used to calculate the vibration characteristics. 2 ], height of the urethane foam h0 [m], modulus of elasticity of the urethane foam E [Pa], volume of air (gas) contained in the urethane foam V0 [m³] 3 ], the length of the path L that air takes from the inside to the surface as it flows out of the urethane foam. rep [m], the total area S of the surface of the urethane foam where air enters and exits during deformation. rep [m 2 ], a coefficient K[m] representing the air permeability of urethane foam. 2 Obtain each value of [ ]. The volume of air V0 is the volume when an object is placed on the urethane foam and deformation occurs.

[0053] Furthermore, the acquisition unit 11 acquires the value of the external atmospheric pressure P0 [Pa]. In addition, the acquisition unit 11 acquires the specific heat ratio of air γ [-] and the viscosity of air μ [Pa·s] as values ​​related to the air contained in the bubbles of the urethane foam and the air outside the urethane foam, which are used in the calculation of the vibration transmissibility. Furthermore, the acquisition unit 11 acquires the value of the mass m [kg] of the object placed on the urethane foam as a value related to conditions other than those mentioned above, which is used in the calculation of the vibration transmissibility. All of these values ​​appear in the explanation of the derivation process of the vibration transmissibility A(ω) [-] described above.

[0054] The acquisition unit 11 only needs to acquire values ​​indicating the properties of the material used to calculate the vibration characteristics and values ​​indicating the ambient pressure as information used to calculate the vibration transmissibility, and may acquire values ​​other than those mentioned above depending on the formula used to calculate the vibration transmissibility.

[0055] The acquisition unit 11 acquires information by receiving information transmitted from an external source such as the user's terminal, or by accepting information input operations from the user. The acquisition unit 11 may also acquire information by methods other than those described above. The acquisition unit 11 outputs the acquired information to the calculation unit 12.

[0056] The calculation unit 12 is a functional unit that calculates a value related to the time variation of the gas pressure inside the material when the material deforms, in accordance with the ambient pressure, from the value obtained by the acquisition unit 11, and uses the calculated value related to the time variation to calculate the vibration transmittance coefficient according to the vibration frequency as a vibration characteristic. The calculation unit 12 may also calculate a value as related to the time variation that indicates the time it takes for the pressure difference between the gas pressure inside the material and the ambient pressure that occurs when the material deforms to ease. The calculation unit 12 uses the following formula

number

[0057] The calculation unit 12 stores in advance formulas for calculating vibration transmissibility, such as the formula for calculating τ as described above, and the formula for calculating the vibration transmissibility A(ω)[-] based on τ. The calculation unit 12 receives information to be used in calculating the vibration transmissibility from the acquisition unit 11. The calculation unit 12 calculates the vibration transmissibility using the stored formulas. For example, the calculation unit 12 inputs the value received from the acquisition unit 11 into the formula for calculating the vibration transmissibility A(ω)[-] described above, and calculates the vibration transmissibility A(ω)[-]. In this case, as described above, the calculation unit 12 first calculates τ, a value indicating the time it takes for the pressure difference between the air pressure inside the urethane foam and the outside air pressure to ease when the urethane foam deforms, and then calculates the vibration transmissibility A(ω)[-] using the calculated τ.

[0058] Furthermore, the calculation unit 12 may pre-store the value of the angular frequency ω [rad / s] for which the vibration transmissivity A(ω)[-] is calculated, and use that value of angular frequency ω to calculate the vibration transmissivity A(ω)[-] at that angular frequency ω. Alternatively, the acquisition unit 11 may acquire the value of the angular frequency ω as a value related to conditions other than those mentioned above, and the calculation unit 12 may use that value of angular frequency ω to calculate the vibration transmissivity A(ω)[-] at that angular frequency ω. The calculation unit 12 may also calculate the vibration transmissivity A(ω)[-] at multiple angular frequencies ω. For example, the calculation unit 12 may calculate the vibration transmissivity A(ω)[-] at angular frequencies ω at regular intervals so that a graph like the one shown in Figure 2(a) can be drawn.

[0059] The calculation unit 12 may calculate the vibration transmittance using a method other than the formula used to calculate the vibration transmittance A(ω)[-] described above. The calculation unit 12 may also use a frequency other than the angular frequency as the frequency related to the vibration transmittance. Furthermore, the value related to the time variation of the air pressure inside the urethane foam when the urethane foam deforms, in accordance with the ambient pressure, which is calculated in the process of calculating the vibration transmittance, may be a value other than the above-mentioned τ. The calculation unit 12 can calculate the value related to the time variation of the air pressure inside the urethane foam when the urethane foam deforms, in accordance with the ambient pressure, from at least a part of the information input from the acquisition unit 11, and then calculate the vibration transmittance using the calculated value.

[0060] The calculation unit 12 outputs information indicating the calculated vibration transmissibility. For example, the calculation unit 12 transmits this information to an external device such as a user's terminal. Alternatively, the calculation unit 12 displays this information on a display device provided by the vibration characteristic calculation system 10. The calculation unit 12 may also output this information by other methods and to other output destinations. The vibration transmissibility calculated by the vibration characteristic calculation system 10 is, for example, referenced by the user and used in the development of urethane foam as described above. The above describes the functions of the vibration characteristic calculation system 10 according to this embodiment.

[0061] Next, the vibration characteristic calculation method, which is a process (operation method performed by the vibration characteristic calculation system 10) executed by the vibration characteristic calculation system 10 according to this embodiment, will be explained using the flowchart in Figure 10. In this process, the acquisition unit 11 acquires information necessary for calculating the vibration transmissibility (S01, acquisition step). The information necessary for calculating the vibration transmissibility includes values ​​indicating the properties of the material and values ​​indicating the ambient pressure. Subsequently, the calculation unit 12 calculates a value (for example, τ as described above) related to the time variation of the gas pressure inside the material when the material deforms, according to the ambient pressure, from the values ​​acquired by the acquisition unit 11, and the vibration transmissibility is calculated using the calculated value related to the time variation (S02, calculation step). Subsequently, the calculation unit 12 outputs information indicating the calculated vibration transmissibility (S03). The above is the vibration characteristic calculation method according to this embodiment.

[0062] According to this embodiment, the time-dependent variation in the gas pressure within the material when the material deforms is calculated in accordance with the ambient pressure, and the vibration characteristics are calculated using the calculated time-dependent variation. By using the above-mentioned time-dependent variation, which affects the vibration characteristics and was not considered in conventional calculation methods, this embodiment makes it possible to calculate vibration characteristics with high accuracy.

[0063] As in the embodiment described above, the calculation unit 12 may calculate a value (τ in the example above) that indicates the time it takes for the pressure difference between the gas pressure inside the material and the ambient pressure to ease when the material deforms, as a value related to time variation. The acquisition unit 11 may also acquire a value that indicates the properties of the material used in calculating the value related to time variation, such as the volume of gas contained in the material, the surface area from which the gas flows out of the material, the path length when the gas flows out of the material, and a coefficient representing the gas permeability of the material. Furthermore, the calculation unit 12 may also calculate the vibration transmittance according to the vibration frequency using the formula for calculating the vibration transmittance A(ω)[-] described above. With these configurations, vibration characteristics can be calculated appropriately, reliably, and with high accuracy.

[0064] However, the calculation of the vibration transmissivity by the vibration characteristic calculation system 10 does not necessarily have to be performed in the manner described above. The acquisition unit 11 only needs to acquire at least a value indicating the properties of the material and a value indicating the ambient pressure as information used to calculate the vibration transmissivity. In addition, the calculation unit 12 may calculate a value other than the time it takes for the pressure difference between the gas pressure inside the material and the ambient pressure that occurs when the material deforms to ease, as a value related to time variation. Furthermore, the calculation unit 12 may calculate the vibration transmissivity using a formula other than the formula used to calculate the vibration transmissivity A(ω)[-] described above.

[0065] The material used for calculating the vibration transmissibility may be polyurethane foam. This configuration allows for the calculation of highly accurate vibration characteristics for polyurethane foam. However, the material used for calculating the vibration transmissibility does not have to be polyurethane foam; any material that contains air bubbles and is deformable, where the amount of gas contained in the air bubbles changes with deformation, is acceptable.

[0066] Using Figure 11, an example of the vibration transmittance of urethane foam according to the vibration frequency, calculated by the vibration characteristic calculation system 10 according to this embodiment, will be explained. Figure 11(a) is a graph of the vibration transmittance measured for actual urethane foam. Figure 11(b) is a graph of the vibration transmittance calculated by the vibration characteristic calculation system 10 according to this embodiment. Figure 11(c) is a graph of the vibration transmittance calculated by the conventional calculation method shown in Non-Patent Document 1. Similar to the graph shown in Figure 2(a), the horizontal axis in this graph represents the vibration frequency, and the vertical axis represents the vibration transmittance. The vibration transmittances in each graph shown in Figure 11 are under the same conditions. In addition, each graph in Figure 11 shows the vibration transmittances of multiple urethane foams with different air permeability.

[0067] As indicated by the arrows in the graph of Figure 11(a), the peak position of the vibration transmissibility shifts to a higher frequency as the degree of air permeability decreases. As indicated by the arrows in the graph of Figure 11(b), the peak position of the vibration transmissibility calculated by the vibration characteristic calculation system 10 according to this embodiment is the same as that of the measured vibration transmissibility. This is also true for the peak of the vibration transmissibility when the degree of air permeability is low (the peak around 8Hz indicated by the circle in the graph) in the graph shown in Figure 11.

[0068] On the other hand, as indicated by the arrows in the graph in Figure 11(c), the peak position of the vibration transmissibility calculated using the conventional calculation method does not occur at higher frequencies even when the degree of air permeability is low. In the graph in Figure 11(c), there is no peak at the position around 8Hz, indicated by the circle in the graph, where a peak should be present. Thus, the conventional calculation method cannot explain the vibration characteristics of a particular urethane foam.

[0069] As shown in the specific example above, the vibration characteristic calculation system 10 according to this embodiment can accurately calculate the vibration transmissivity, which could not be accurately calculated using conventional calculation methods. In other words, the vibration characteristic calculation system 10 according to this embodiment enables accurate peak prediction and control of vibration characteristics.

[0070] Next, a vibration characteristic calculation program for executing the processing performed by the series of vibration characteristic calculation systems 10 described above will be explained. As shown in Figure 12, the vibration characteristic calculation program 100 is stored in a program storage area 111 formed on a computer-readable recording medium 110 that is inserted into and accessed by a computer, or is provided by a computer. The recording medium 110 may be a non-temporary recording medium.

[0071] The vibration characteristic calculation program 100 comprises an acquisition module 101 and a calculation module 102. The functions realized by executing the acquisition module 101 and the calculation module 102 are the same as the functions of the acquisition unit 11 and the calculation unit 12 of the vibration characteristic calculation program 100 described above.

[0072] Furthermore, the vibration characteristic calculation program 100 may be configured such that part or all of it is transmitted via a transmission medium such as a communication line, received and recorded (including installation) by other equipment. Also, each module of the vibration characteristic calculation program 100 may be installed on any of multiple computers, not just one. In that case, the series of processes described above will be performed by a computer system consisting of these multiple computers.

[0073] The vibration characteristics calculation system, vibration characteristics calculation method, and vibration characteristics calculation program of this disclosure have the following configurations. [1] A vibration characteristic calculation system for calculating the vibration characteristics of a material that contains air bubbles and is deformable, wherein the amount of gas contained in the air bubbles changes due to deformation, An acquisition unit that acquires values ​​indicating the properties of the material used to calculate vibration characteristics, and values ​​indicating external pressure, A calculation unit calculates, from the values ​​obtained by the acquisition unit, the value relating to the time variation of the gas pressure inside the material when the material deforms, in accordance with the external atmospheric pressure, and uses the calculated value relating to the time variation to calculate the vibration transmittance coefficient corresponding to the vibration frequency as a vibration characteristic. A vibration characteristic calculation system equipped with the following features. [2] The vibration characteristic calculation system according to [1], wherein the calculation unit calculates a value as a value relating to the time variation, which represents the time it takes for the pressure difference between the gas pressure inside the material and the outside air pressure that occurs when the material deforms to ease. [3] The vibration characteristic calculation system according to claim [2], wherein the acquisition unit acquires, as a value indicating the properties of the material used to calculate the value relating to the time variation, the volume of gas contained in the material, the surface area from which the gas flows out of the material, the path length when the gas flows out of the material, and a coefficient representing the gas permeability of the material. [4] The calculation unit is calculated using the following formula

number

[0074] 10...Vibration characteristic calculation system, 11...Acquisition unit, 12...Calculation unit, 100...Vibration characteristic calculation program, 101...Acquisition module, 102...Calculation module, 110...Recording medium, 111...Program storage area.

Claims

1. A vibration characteristic calculation system for calculating the vibration characteristics of a material that contains air bubbles and is deformable, wherein the amount of gas contained in the air bubbles changes due to deformation, An acquisition unit that acquires values ​​indicating the properties of the material used to calculate vibration characteristics, and values ​​indicating external pressure, A calculation unit calculates, from the values ​​obtained by the acquisition unit, the value relating to the time variation of the gas pressure inside the material when the material deforms, in accordance with the external atmospheric pressure, and uses the calculated value relating to the time variation to calculate the vibration transmittance coefficient corresponding to the vibration frequency as a vibration characteristic. A vibration characteristic calculation system equipped with the following features.

2. The vibration characteristic calculation system according to claim 1, wherein the calculation unit calculates a value as a value relating to the time variation, which represents the time it takes for the pressure difference between the pressure of the gas inside the material and the external air pressure that occurs when the material deforms to ease.

3. The vibration characteristic calculation system according to claim 2, wherein the acquisition unit acquires, as a value indicating the properties of the material used to calculate the value related to the time variation, the volume of gas contained in the material, the surface area from which the gas flows out of the material, the path length when the gas flows out of the material, and a coefficient representing the gas permeability of the material.

4. The calculation unit is calculated using the following formula [Math 1] (where ω: angular frequency [rad / s], A(ω): vibration transmission rate at angular frequency ω [-], τ: time [s] for the pressure difference between the pressure of the gas inside the material and the external atmospheric pressure generated when the material is deformed to relax, P ０ : external atmospheric pressure [Pa], γ: specific heat ratio of the gas [-], μ: viscosity of the gas [Pa·s], m: mass [kg] of the object placed on the material, S: cross-sectional area [m ２ of the material, h ０ : height [m] of the material, E: elastic modulus [Pa] of the material, V ０ : volume [m ３ of the gas contained in the material, L ｒｅｐ : length [m] of the path that the gas in the material travels from the inside to the surface until it flows out, S ｒｅｐ : total area [m ２ of the part of the surface of the material where gas flows in and out during deformation, K: coefficient [m ２ representing the ease of gas passage through the material) to calculate the vibration transmission rate according to the frequency of vibration. The vibration characteristic calculation system according to claim 3.

5. The vibration characteristic calculation system according to claim 1 or 2, wherein the material is urethane foam.

6. A vibration characteristic calculation method is a method for operating a vibration characteristic calculation system that calculates the vibration characteristics of a material that contains air bubbles and is deformable, wherein the amount of gas contained in the air bubbles changes due to deformation, An acquisition step to obtain a value indicating the properties of the material used in calculating vibration characteristics, and a value indicating the external pressure, A calculation step in which, from the values ​​obtained in the acquisition step, a value relating to the time variation of the gas pressure inside the material when the material deforms, in accordance with the external atmospheric pressure, is calculated, and the vibration transmission coefficient corresponding to the vibration frequency is calculated as a vibration characteristic using the calculated value relating to the time variation, A method for calculating vibration characteristics, including the method described above.

7. A vibration characteristic calculation program that causes a computer to function as a vibration characteristic calculation system for calculating the vibration characteristics of a material that contains air bubbles and is deformable, and whose amount of gas contained in the air bubbles changes due to deformation, The aforementioned computer, An acquisition unit that acquires values ​​indicating the properties of the material used to calculate vibration characteristics, and values ​​indicating external pressure, A calculation unit calculates, from the values ​​obtained by the acquisition unit, the value relating to the time variation of the gas pressure inside the material when the material deforms, in accordance with the external atmospheric pressure, and uses the calculated value relating to the time variation to calculate the vibration transmittance coefficient corresponding to the vibration frequency as a vibration characteristic. A vibration characteristic calculation program that functions as such.

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