JP2007093596A - Method and program for measuring relaxation modulus, recording medium with program recorded, and manufacturing method of forming mold - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for measuring relaxation module, capable of easily and correctly measuring the relaxation module necessary for keeping dimensional precision, after molding a glass lens. <P>SOLUTION: In the step for Laplace transforming the discreet data of the creep function, obtained by an experiment, after applying an approximation using an arbitrary formula capable of Laplace transformation performs the Laplace transform, the numerical solution obtained in an image space is subjected to inverse-Laplace transformation. The Laplace transforms can be analytically performed, and on the Laplace image space, the operation of the Laplace transformation can be performed mechanically. From the measured relaxation module of the viscoelastic body, the forming mold for forming the glass lens is manufactured. The dimensional precision of the glass lens after press forming can be maintained, and generation of breakages and cracks of the glass lens may happen, at press forming, can be prevented. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a relaxation modulus measurement method for measuring a relaxation modulus of a viscoelastic body, a relaxation modulus measurement program, a recording medium on which the program is recorded, and a mold manufacturing method.

  In recent years, with the development of IT technology, the demand for optical devices and optical communication devices such as DVD optical pickups and digital cameras is increasing. As these optical devices and optical communication devices, high precision such as miniaturization or aspherical surface, improvement in production efficiency, or reduction in production cost is desired. Among these, there is a glass optical device which is a viscoelastic body having optical characteristics excellent in a high refractive index, a low birefringence, a low chromatic aberration, and the like as compared with a plastic device used in an optical apparatus.

  However, processing processes such as direct grinding, chemical polishing, CVD, and lithography are used for production of the glassy optical device. And it is easy to process glass into a general spherical lens shape by these processing processes, but the shape is composed of a lot of fine and discontinuous curved surfaces such as aspherical lenses, micro Fresnel lenses or diffraction gratings. However, it is not easy to process, and it takes time for processing.

  For this reason, a technique for producing a glass lens, which is an optical device made of glass, by press molding with a high-temperature press using a mold is known, and aspherical lenses and the like are mass-produced by this press molding (for example, , See Patent Document 1).

Specifically, in high-temperature press molding of a glass lens, a glass material is set in a mold, and then the glass material is heated and pressure is applied to the mold to change the shape of the mold to a glass material. The glass lens is manufactured by cooling after transferring and removing from the mold.
JP-A-8-301624

  However, in the above-described high-temperature press molding of a glass lens, it is not easy to grasp the optimum conditions related to press molding of a glass lens. For example, when simulating numerical values in the press molding process, not only nonlinear contact and large deformation between the mold and the glass material become a problem, but also the elastic modulus of the glass material is a thermoviscoelasticity that depends on temperature and time. Need to be considered.

  That is, since the constitutive equation (elastic coefficient) of the glass material that is the material of the glass lens depends on each of temperature and time, it is not easy to determine optimum molding conditions. In addition, since the contact condition between the glass lens and the mold changes with time, it is not easy to accurately grasp the temperature change inside the glass lens. For this reason, it is not easy to handle various numerical values that should be grasped at the time of high-temperature press molding of a glass lens.

  Therefore, at the time of high-temperature press molding of this glass lens, there is a problem that cracks and cracks occur in the glass material and it is not easy to maintain the dimensional accuracy of the glass lens after molding.

  The present invention has been made in view of such points, and a relaxation modulus measurement method and relaxation modulus that can easily and accurately measure the relaxation modulus necessary for maintaining the dimensional accuracy of a viscoelastic body after molding. It is an object of the present invention to provide a measurement program, a recording medium on which the program is recorded, and a method for manufacturing a mold.

  The method for measuring the relaxation elastic modulus according to claim 1 is such that the relational expression between stress and strain of the viscoelastic body is approximated by an arbitrary expression capable of Laplace transform, and the relation approximated by an arbitrary expression capable of Laplace transform. The equation is subjected to Laplace transform, the Laplace transformed relational equation is calculated as Laplace transform of relaxation elastic modulus, and the Laplace transform of the relaxation elastic modulus is converted into Laplace inverse.

  The method for measuring the relaxation elastic modulus according to claim 2 measures a displacement amount with respect to a time history under a load of the viscoelastic body, and calculates a stress and strain of the viscoelastic body from the displacement amount with respect to the measured time history. A relational expression is obtained, and this relational expression is approximated by an arbitrary expression that can be converted to Laplace, the relational expression approximated by an arbitrary expression that can be converted to Laplace is subjected to Laplace conversion, The Laplace transform of the relaxation elastic modulus is calculated, and the relational expression calculated for the Laplace conversion of the relaxation elastic modulus is inversely converted to Laplace.

  The method for measuring relaxation elastic modulus according to claim 3 is the method for measuring relaxation elastic modulus according to claim 1 or 2, wherein the relational expression between the stress and strain of the viscoelastic body is obtained from a creep test of the viscoelastic body. It is a creep function.

  The method for measuring relaxation elastic modulus according to claim 4 is an arbitrary expression capable of Laplace transform based on the relaxation elastic modulus of the viscoelastic body measured by the method for measuring relaxation elastic modulus according to any one of claims 1 to 3. Is a power function.

  The method for measuring the relaxation modulus according to claim 5 is an arbitrary expression capable of Laplace transform based on the relaxation modulus of the viscoelastic body measured by the method for measuring relaxation modulus according to any one of claims 1 to 3. Is a function obtained by modeling a relational expression between stress and strain of a viscoelastic body using a Forked model.

  The relaxation elastic modulus measurement program according to claim 6 approximates the relational expression between the stress and strain of the viscoelastic body by an arbitrary expression capable of Laplace transform and an arbitrary expression capable of Laplace transform. Laplace transforming the relational expression, Laplace transform of the Laplace transformed relational expression into Laplace transform of relaxation modulus, and Laplace inverse transform of the relational expression computed into the relaxation modulus Laplace transform Steps.

  The relaxation elastic modulus measurement program according to claim 7 includes a step of measuring a displacement amount with respect to a time history under a load of the viscoelastic body, and a stress and strain of the viscoelastic body from the displacement amount with respect to the measured time history. A step of approximating the relational expression with an arbitrary expression capable of Laplace transform, a step of performing Laplace transform on the relational expression approximated with an arbitrary expression capable of Laplace transform, A step of calculating the Laplace transformed Laplace transform, and a step of performing Laplace inverse transform on the Laplace transform of the relaxed elastic modulus.

  The relaxation modulus measurement program according to claim 8 is the relaxation modulus measurement program according to claim 6 or 7, wherein the relational expression between stress and strain of the viscoelastic body is obtained from a creep test of the viscoelastic body. This is the obtained creep function.

  The relaxation elastic modulus measurement program according to claim 9 is the relaxation elastic modulus measurement program according to any one of claims 6 to 8, wherein an arbitrary expression capable of Laplace transform is a power function.

  The relaxation elastic modulus measurement program according to claim 10 is the relaxation elastic modulus measurement program according to any one of claims 6 to 8, wherein an arbitrary expression capable of Laplace transform is a relational expression between stress and strain of a viscoelastic body. Is a function modeled by the Forked model.

  A recording medium recording a relaxation elastic modulus measurement program according to an eleventh aspect of the present invention records the relaxation elastic modulus measurement program according to any one of the sixth to tenth aspects of the invention in a computer-readable manner.

  The method for producing a mold according to claim 12 is characterized in that the viscoelastic body is made of a material based on the relaxation elastic modulus of the viscoelastic body measured by the method for measuring the relaxation elastic modulus according to any one of claims 1 to 5. A mold for molding the molded product is manufactured.

  A method for manufacturing a mold according to claim 13 is characterized in that the viscoelastic body is made of a material based on the relaxation elastic modulus of the viscoelastic body measured by the relaxation elastic modulus measurement program according to any of claims 6 to 10. A mold for molding the molded product is manufactured.

  The method for producing a mold according to claim 14 is the method for producing a mold according to claim 12 or 13, wherein the viscoelastic body is a glass material, the molded product is an optical element, and the mold is the glass material. Is a press die for molding the optical element.

  The method for producing a mold according to claim 15 is the method for producing a mold according to claim 12 or 13, wherein the viscoelastic body is an engineering plastic, the molded article is an optical element, and the molding die is the engineering plastic. Is a press die for molding the optical element.

  According to the method for measuring the relaxation elastic modulus according to claim 1, after the Laplace transform is performed after approximating the relational expression between the stress and the strain of the viscoelastic body with an arbitrary formula capable of Laplace transform, Since the relational expression calculated for the Laplace transform of the relaxation elastic modulus is inversely converted to Laplace, the relaxation elastic modulus necessary for maintaining the dimensional accuracy of the viscoelastic body after molding can be measured easily and accurately.

  According to the method for measuring the relaxation modulus according to claim 2, the relational expression between the stress and strain of the viscoelastic body obtained from the displacement with respect to the time history measured under the load of the viscoelastic body can be arbitrarily converted to Laplace. Approximate with Laplace transform after approximating with formula, then calculate Laplace transform of relaxation modulus and Laplace inverse transform the relational formula computed for Laplace transform of relaxation modulus, so dimensional accuracy after molding of viscoelastic body Can be measured easily and accurately.

  According to the method for measuring the relaxation elastic modulus according to claim 3, in addition to the effect of the method for measuring the relaxation elastic modulus according to claim 1 or 2, the creep function is obtained from the creep test of the viscoelastic body, Since the relational expression between the stress and strain of the viscoelastic body is used, this relational expression can be easily and accurately measured by a simple test, so that the relaxation elastic modulus of the viscoelastic body can be measured more easily and accurately.

  According to the method for measuring relaxation elastic modulus according to claim 4, in addition to the effect of the method for measuring relaxation elastic modulus according to any one of claims 1 to 3, by using a power function as an arbitrary expression capable of Laplace transform Since the Laplace transform can be executed analytically and the calculation in the Laplace image space can be performed mechanically, the relaxation elastic modulus of the viscoelastic body can be measured more easily.

  According to the method for measuring the relaxation elastic modulus according to claim 5, in addition to the effect of the method for measuring the relaxation elastic modulus according to any one of claims 1 to 3, the stress and strain of the viscoelastic body can be expressed as an arbitrary expression capable of Laplace transformation. By using a function modeled by the Forked model, the relation between the stress and strain of the viscoelastic body can be approximated more accurately, Laplace transformation can be executed analytically, and the Laplace image Since calculation in space can also be performed mechanically, the relaxation elastic modulus of the viscoelastic body can be measured more easily and accurately.

  According to the relaxation modulus measurement program according to claim 6, after the Laplace transform is performed after approximating the relational expression between the stress and strain of the viscoelastic body with an arbitrary formula capable of Laplace transform, the Laplace of the relaxation modulus is obtained. Since the relational expression calculated for the Laplace transform of the relaxation elastic modulus is inversely converted to Laplace, the relaxation elastic modulus necessary for maintaining the dimensional accuracy of the viscoelastic body after molding can be measured easily and accurately.

  According to the program for measuring the relaxation modulus according to claim 7, the relational expression between the stress and strain of the viscoelastic body obtained from the displacement with respect to the time history measured under the load of the viscoelastic body can be arbitrarily converted to Laplace. Approximate with Laplace transform after approximating with formula, then calculate Laplace transform of relaxation modulus and Laplace inverse transform the relational formula computed for Laplace transform of relaxation modulus, so dimensional accuracy after molding of viscoelastic body Can be measured easily and accurately.

  According to the relaxation elastic modulus measurement program according to claim 8, in addition to the effect of the relaxation elastic modulus measurement program according to claim 6 or 7, the creep function is obtained from the creep test of the viscoelastic body, Since the relational expression between the stress and strain of the viscoelastic body is used, this relational expression can be easily and accurately measured by a simple test, so that the relaxation elastic modulus of the viscoelastic body can be measured more easily and accurately.

  According to the relaxation modulus measurement program according to claim 9, in addition to the effect of the relaxation modulus measurement program according to any one of claims 6 to 8, by using a power function as an arbitrary expression capable of Laplace transform Since the Laplace transform can be executed analytically and the calculation in the Laplace image space can be performed mechanically, the relaxation elastic modulus of the viscoelastic body can be measured more easily.

  According to the relaxation modulus measurement program according to claim 10, in addition to the effect of the relaxation modulus measurement program according to any one of claims 6 to 8, as an arbitrary expression capable of Laplace transform, the stress of the viscoelastic body and By using a function in which the relational expression of strain is modeled by the Forked model, the relational expression of stress and strain of the viscoelastic body can be approximated more accurately, Laplace transformation can be executed analytically, and Laplace Since the calculation in the image space can also be performed mechanically, the relaxation elastic modulus of the viscoelastic body can be measured more easily and accurately.

  According to the recording medium on which the relaxation elastic modulus measurement program according to claim 11 is recorded, the relaxation elastic modulus is obtained by operating the computer according to the recorded relaxation elastic modulus measurement program according to any one of claims 6 to 10. Can be measured easily and accurately.

  According to the method for manufacturing a mold according to claim 12, the viscoelastic body is made of a material based on the relaxation elastic modulus of the viscoelastic body measured by the method for measuring the relaxation elastic modulus according to any one of claims 1 to 5. By producing a molding die for molding the molded product, it is possible to maintain the dimensional accuracy of the molded product after molding the viscoelastic body using this molding die. It is possible to prevent the occurrence of cracks and cracks in the molded product, which may occur when molding the molded product using as a material.

  According to the method for manufacturing a mold according to claim 13, the viscoelastic body is made of a material based on the relaxation elastic modulus of the viscoelastic body measured by the relaxation elastic modulus measurement program according to claim 6. By producing a molding die for molding the molded product, it is possible to maintain the dimensional accuracy of the molded product after molding the viscoelastic body using this molding die. It is possible to prevent the occurrence of cracks and cracks in the molded product, which may occur when molding the molded product using as a material.

  According to the method for manufacturing a mold according to claim 14, in addition to the effect of the method for manufacturing a mold according to claim 12 or 13, the dimensional accuracy of the optical element after press molding of the glass using the press mold is maintained. Therefore, it is possible to prevent the optical element from being cracked or cracked, which may occur when the optical element is press-molded with glass as a material in this press mold.

  According to the method for manufacturing a mold according to claim 15, in addition to the effect of the method for manufacturing a mold according to claim 12 or 13, the dimensional accuracy of an optical element after press molding of engineering plastic using a press mold is maintained. Therefore, it is possible to prevent the optical element from being cracked or cracked, which may occur when the optical element is press-molded using the engineer plastic as a material.

  Hereinafter, an embodiment of a method for measuring a relaxation elastic modulus of the present invention will be described with reference to FIGS.

  First, in order to grasp the mechanical behavior of a thermo-viscoelastic body such as a glass lens as an optical element, two mechanical behaviors called creep and stress relaxation are examined. Here, creep refers to a phenomenon in which strain increases with time when a certain stress is applied to and held on a viscoelastic body. Stress relaxation is a phenomenon in which stress decreases with time when a certain strain is applied to a viscoelastic body.

  The mechanical behavior of creep and stress relaxation depends on the creep function J (t) and the relaxation elastic modulus k (t) as the relaxation elastic modulus, as shown in FIGS. 2 (a) and 2 (b). Can be described. Here, the creep function is a time variation of strain when a unit step-like stress is applied and held from time t = 0 in a uniaxial load state. In addition, the relaxation modulus (Relaxation Modulus) refers to a time variation when a unit step-like strain is applied and held from time t = 0.

  Here, H (t) in FIGS. 2 (a) and 2 (b) is a unit step function of Heviside that becomes 0 when t <0 and becomes 1 when t> 0.

  Next, when the viscoelastic body is handled as a linear viscoelastic body in which handling of strain and stress is easy, in order to calculate the strain generated when several loads act simultaneously, FIG. As shown in 3 (b), the principle of superposition is used.

  Specifically, when stress σ (0) is applied at t = 0, strain ε = σ (0) J (t) occurs. Here, if some stress is further applied at t = τ, the corresponding applied stress is applied to time t after time τ. As a result, the added strain generated is proportional to Δσ (τ) and similarly depends on the creep function J (t). In this case, since it must be expressed in a coordinate system with t = τ as a reference, such as J (t−τ), the total strain for time t after τ is ε (t) = σ (0) J ( t) + Δσ (τ) J (t−τ).

  Furthermore, the initial stress σ (0) is applied at t = 0, after which σ varies as an arbitrary function σ (t). Then, as shown in FIG. 4, the strain response to the stress diagram includes the strain response σ (0) J (t) to the initial stress portion σ (0) H (t) and the infinitesimal step portion dσ (τ) H ( The strain response σ (τ) J (t−τ) with respect to t−τ can be continuously superimposed.

  For this reason, the constitutive equation, which is the relational expression between the stress σ (t) and the strain ε (t) acting on the elastic body, is determined by the linear viscoelasticity theory of relaxation elastic modulus. It can be expressed as an integral system of integration.

  Here, k (t) in Equation 1 is a relaxation elastic modulus, and means a time variation of stress when a unit step-like strain input is applied at t = 0. Further, when this equation 1 is rewritten using a strain time variation, ie, a creep function J (t), which is a strain response when a unit step-like stress is applied, equation 2 is obtained.

  Further, when each of Equation 1 and Equation 2 is Laplace transformed, Equation 3 and Equation 4 are obtained.

  Here, s in Equation 3 and Equation 4 is a Laplace conversion parameter, and Laplace conversion of each physical quantity is indicated by a superscript “添 え”. As initial conditions, ε (0) = 0 and σ (0) = 0 were given.

  As a result, as shown in Equations 3 and 4, the relationship of Equation 5 is established between the Laplace transform of the creep function and the Laplace transform of the relaxation elastic modulus.

  Therefore, if the creep function of the viscoelastic body that is the target material can be obtained through experiments, the relaxation elastic modulus necessary for the analysis can be easily and reliably measured by applying Laplace transform. In addition, since this calculation goes through a process in the Laplace image space and a numerical Laplace inversion process, a problem under bad conditions generally occurs and many errors are superimposed.

  Therefore, after approximating the creep function obtained in the experiment using an arbitrary expression that can be Laplace transformed, for example, a power function, analytical Laplace transformation is performed, and an operation defined by Equation 4 is performed on the Laplace image space. The relaxation elastic modulus of a viscoelastic body such as a glass material is calculated by performing a numerical Laplace inverse transform using the so-called Hosono method.

  Specifically, a creep function, which is discrete data measured by experiment, is approximated by a power series sum as a power function as shown in Equation 6, for example, as a first method.

Here, k ₀ is the instantaneous elastic modulus, that is, the Young's modulus at room temperature. The power function order N is set to 10. The initial conditions were J (0) = 1 / k (0), (k (0): instantaneous elastic modulus). Next, when Equation 6 is Laplace transformed, Equation 7 is obtained.

  Therefore, based on Equation 7, Laplace transform of relaxation elastic modulus in the Laplace image space can be obtained as in Equation 8.

  As a result, it is possible to obtain the relaxation elastic modulus k (t) of the viscoelastic body in real time by performing numerical Laplace inverse transformation using the Hosono method on the Laplace transformation of the obtained relaxation elastic modulus. it can.

  Further, for example, as a second method, as shown in FIG. 5, the creep function is approximated by a function modeled by a Forgt model.

Forked model is one unit consisting of a spring k _i that is an elastic element and a dashpot η _i that is a damping element connected in parallel, and a plurality of (N) units are connected in series. Consider a model in which an elastic element k ₀ corresponding to ₀ is added in series.

  The displacement when a unit step-like stress is applied to this generalized Forked model, that is, the creep function in the Forked model is as shown in Equation 9.

Here, a _{λ i = η i / k i} , k 0 is the instantaneous modulus of elasticity of the material, that is, Young's modulus at room temperature.

A displacement response to a unit step stress, that is, a creep function is obtained by a creep test. The unknown parameters k _i and λ _i (or η _i ) are obtained by search calculation so that the creep function of the Forked model given by the equation (9) matches the experimental result.

  Here, when the Laplace transform is performed on Formula 9 that is a general formula of the Forked model, Formula 10 is obtained.

  The Laplace transform of the relaxation elastic modulus is obtained as shown in Equation 11 by the equation of Equation 10 and the equation of Equation 5 in the above embodiment.

  Then, by applying the numerical Laplace inverse transformation to the equation of Equation 11 thus obtained, the relaxation elastic modulus k (t) in real time can be obtained.

  Next, the relaxation modulus at each measurement temperature was determined using the method described above. As shown in FIG. 6, when the horizontal axis is the logarithm of time and the vertical axis is the relaxation modulus, the relaxation modulus at each temperature. Are similar to each other along the time axis, and can be combined into a single curve, that is, a master curve, by parallel translation on the logarithmic time axis. This master curve is the relaxation elastic modulus at the reference temperature.

  That is, it has been found that by quantitatively expressing the shift amount, which is the parallel movement amount of the master curve, the effect of temperature can be replaced with time, and the analysis of a thermo-viscoelastic body accompanying a temperature change can be facilitated.

  Here, in thermoviscoelastic materials such as glass and plastic, the constitutive equation depends not only on time but also on temperature. A time-temperature conversion rule is established between the relaxation elastic modulus, the temperature T, and the time t, and can be generalized as in Expression 12.

That is, the relaxation elastic modulus k (t, T ₀ ) between the relaxation elastic modulus k (t, T) and the reference temperature T ₀ at an arbitrary time t is related by the time-temperature transfer factor α _T0 (T). Attached. The time temperature transfer factor α _T0 (T) is a function of the temperature T with respect to the reference temperature T ₀ and is generally called a shift factor. When the real time t of Formula 12 is rewritten by the conversion time t ′ using Formula 13, Formula 14 is obtained.

  Therefore, it becomes possible to replace the influence of temperature with time by describing using the conversion time t ′, and the constitutive equation of the thermo-viscoelastic body is expressed by the following equation (15). It can be obtained by replacing with '.

  Further, when the creep function is experimentally obtained and the relaxation elastic modulus is measured, the creep function measured in the experiment is approximated using the linear polynomial approximation expressed by Equation 16.

  Then, each of the relaxation elastic modulus and the master curve can be calculated by substituting the equation (16) into the equation (5) after performing Laplace transform. Further, the master curve is approximated by a Maxwell model expressed by Equation 17 for use in FEM (Finite Element Method) analysis.

  However, n in Expression 16 was set to 10, and N in Expression 17 was set to 5.

Furthermore, the shift factor indicating the time-temperature conversion rule was calculated from the shift amount of the relaxation modulus using the reference temperature T ₀ as the glass transition temperature of the glass material.

  On the other hand, the master curve can be obtained by fixing the relaxation elastic modulus at the reference temperature on the logarithmic axis and translating and overlapping the relaxation elastic modulus at other temperatures. That is, if this master curve can be obtained, the relaxation elastic modulus at other temperatures and times can be expressed by parallel movement of the master curve.

  For example, when a curve at a glass transition point T = 680 ° C. in FIG. 6 is used as a reference and a graph of another temperature is translated so as to overlap this curve, as shown in FIG. Can be aggregated. In FIG. 1, curves approximated by the Maxwell model are also shown.

Further, when the movement amount logα _T0 in the time axis direction in FIG. 1 is the vertical axis and the reciprocal of the absolute temperature is the horizontal axis, it can be shown as in FIG. It can be confirmed from FIG. 7 that the measurement data of the shift factor are arranged almost linearly. Therefore, by using the Narayanaswamy definition formula (not shown), the activation energy ΔH of the viscous flow velocity and the shift factor α _T0 can be related as shown in Equation 18.

Here, R is a gas constant (= 8.31 × 10 ⁻³ kJ / mol). T ₀ is a reference temperature, and the glass transition temperature T _g is 953K. In the actual FEM analysis, the activation energy ΔH is given as a calculation condition. H / R is a slope when 1 / T is a variable.

  Furthermore, ΔH = 481.45 kJ / mol was obtained by linearly approximating each point in FIG. 7 by the least square method and obtaining the slope thereof. Finally, the shift factor at an arbitrary temperature can be calculated by substituting the activation energy obtained by the approximate straight line into Equation 18.

  Furthermore, the relaxation elastic modulus calculated | required by the creep test mentioned later is approximated using a Maxwell model. The Maxwell model is one of mechanical models showing viscoelastic characteristics.

Specifically, as shown in FIG. 8, the Maxwell model includes springs k ₁ , k ₂ ,..., K ₅ that are elastic elements and dashpots λ ₁ , λ ₂ ,. , λ ₅ connected in series as one unit, these one unit are connected in parallel to a plurality of rows, for example, five units, and an elastic element k _∞ corresponding to time infinity is added to a total of 11 It is a model of freedom.

Then, considering the relationship between time and stress when strain is applied to a Maxwell model composed of n elements, k _i is an elastic coefficient and η _i is a viscosity coefficient. However, i = 1, 2,..., N. Further, the stress in the entire of each element and sigma _i, and the strain with epsilon _i, spring _{k 1, k 2, ......,} k 5 and dashpot _{λ 1, λ 2, ......,} λ 5 each strain epsilon _E, when the epsilon _D, these spring _{k 1, k 2, ......,} k 5 and dashpot lambda _1, lambda _2, ......, since lambda ₅ are connected in series, the number 19 to number 21 become that way.

  Further, when these formulas 19 to 21 are arranged as strain time derivatives, formulas 22 to 24 are obtained.

Here, when substituting Equation 22 and Equation 23 into Equation 24 and then multiplying both sides by k _i , Equation 25 is obtained.

When λ _i = η _i / k _i , Equation 25 is expressed as Equation 26.

  Further, assuming that the stress in the entire Maxwell model is σ and the strain is ε, each unit is connected in parallel, and therefore can be expressed as in Expression 27 and Expression 28.

Here, each of Equations 25, 27, and 28 is Laplace transformed. At this time, since k _i and λ _i are constants, they are expressed by the following equations 29 to 31.

  Furthermore, by substituting Equations 29 and 31 into Equation 30, Equation 32 can be obtained.

  Here, assuming that the strain acting on the Maxwell model is a unit step-like strain, Equation 33 is obtained.

  As a result, Expression 32 can be expressed as Expression 34.

  Then, when this equation 34 is inversely transformed by Laplace, equation 35 can be obtained.

  That is, the stress fluctuation of the n-unit Maxwell model with respect to the step strain ε = H (t), that is, the relaxation elastic modulus k (t) is expressed as shown in Expression 36 when one of the relaxation times λ is infinite. Can do.

Here, springs k ₁ , k ₂ ,..., K ₅ and dashpots λ ₁ , λ ₂ ,..., Λ ₅ in FIG. 8 are undetermined coefficients corresponding to each unit of the Maxwell model. . K _∞ represents the elastic modulus after elapse of infinite time.

Furthermore, when the relaxation elastic modulus approximated by the Maxwell model shown in FIG. 8 is schematically shown, it can be shown as in FIG. That is, each unit (k _i, λ _i) over time stepwise relaxation occurs in each, to converge to the final k _∞. Therefore, in approximation by the Maxwell model, spring k _1, k _2, ......, it is given as a known quantity for k _5, dashpot lambda ₁ which defines the relaxation _rate, lambda _2, ...... lambda ₅ only unknown parameter For example, the search was performed by the Newton method.

The elastic modulus k _{∞ at} time infinity can be obtained from the final shape of the sample piece in the creep test. Further, all the relaxation elastic moduli satisfy the conditional expression established between the instantaneous elastic modulus k ₀ , that is, Expression 37.

As a result of the above, a Maxwell model of relaxation modulus can be finally specified by performing search calculation with respect to the remaining unknown amounts of dashpots λ ₁ , λ ₂ ,... Λ ₅ .

  Next, a method for measuring the linear expansion coefficient used for measuring the relaxation elastic modulus will be described.

  As a glass material which is a thermoviscoelastic body, the linear expansion coefficient of the glass sample TaF-3 was measured with a thermal analysis measurement apparatus (TA50-WS: manufactured by Shimadzu Corporation) 1 shown in FIG. Here, the thermal analysis measuring apparatus 1 includes a sample setting portion 3 having a bottomed cylindrical storage recess 2 in which a columnar sample piece B which is a thermoviscoelastic body as a viscoelastic body is stored. . A differential transformer 5 having a displacement detection rod 4 whose lower end can be inserted into the accommodation recess 2 is attached above the accommodation recess 2 of the sample setting portion 3. Here, the displacement detection rod 4 is installed in a state where the axial direction is along the vertical direction, and the differential transformer 5 is concentrically attached to the upper end portion of the displacement detection rod 4. A coil 6 is attached to the outer periphery of the differential transformer 5 so as to surround the differential transformer 5.

  An electric furnace 7 for heating the sample piece B installed in the housing recess 2 is attached to the outer periphery of the housing recess 2 of the thermal analysis measuring device 1. Further, the accommodation recess 2 is attached with a lower end portion of a thermocouple 8 for measuring the temperature of the sample piece B installed in the accommodation recess 2 and heated in the electric furnace 7 being inserted.

  And this thermal analysis measuring device 1 heats the sample piece B installed in the accommodation recessed part 2 of the sample installation part 3 in the electric furnace 7, and the sample piece B generated in the heating in this electric furnace 7 Measure dimensional changes. Specifically, the lower end portion of the displacement detection rod 4 connected to the differential transformer 5 is in contact with the upper portion of the sample piece B while applying a fine constant pressure. Therefore, the relative position of the differential transformer 5 and the coil 6 changes with the dimensional change of the sample piece B, and the dimensional change of the sample piece B is detected by detecting the output of the differential transformer 5. Furthermore, by measuring each of the dimensional change and temperature change of the sample piece B, the thermal expansion coefficient can be measured.

  Since the linear expansion coefficient, which is a linear expansion coefficient, depends on the temperature in a predetermined temperature range, the average linear expansion coefficient at each temperature is obtained from the obtained displacement, and then the obtained average linear expansion coefficient is obtained. The rate data was approximated by a function that should be a fourth-order linear polynomial, as shown in Equation 38.

  Next, a creep test necessary for measuring the relaxation elastic modulus will be described.

  First, the constitutive equation of the glass material composing the sample piece B is experimentally measured by measuring the amount of displacement with respect to the time history under load, that is, the uniaxial compression creep test, with the glass material that is a viscoelastic body as the sample piece B. Can be requested. That is, the creep test is one of methods for experimentally obtaining a master curve of a viscoelastic body that is a thermoviscoelastic body and a shift factor indicating a time-temperature conversion rule, and is a constant tensile load or compressive load. The relaxation elastic modulus is calculated from the creep function obtained by measuring the time history of the deformation amount of the sample piece B. Furthermore, the shift factor can be calculated by conducting a creep test under various temperature environments.

  Here, most materials that exhibit viscous properties such as plastics and glass materials are viscoelastic bodies whose viscous behavior depends on temperature. Therefore, it is necessary to perform a similar creep test under various temperature environments and measure a shift factor representing a conversion rule between temperature and time. For measurement of the relaxation elastic modulus, the thermoviscoelastic properties of the sample piece B were measured, that is, identified using a creep test apparatus 11 shown below.

  Specifically, the creep test apparatus 11 is an apparatus for a tensile test, and includes a plate 12 which is an installation table installed horizontally as shown in FIG. On the plate 12, an elongated columnar column 13 having a longitudinal direction in the vertical direction is erected. A longitudinal center portion of the elongated columnar lever 14 is attached to the upper end portion of the support column 13 so as to be horizontally rotatable along the vertical direction. In addition, a disc-shaped weight installation plate 15 on which a predetermined weight W can be installed is attached via a rod-like body 16 to a distal end portion which is one end portion in the longitudinal direction of the lever 14.

  In addition, a load mechanism 17 that compresses and applies a load to the specimen B, which is a specimen to be tested in a creep test, is attached between the base end that is the other end in the longitudinal direction of the lever 14 and the plate 12. ing. Here, as the sample piece B, for example, a cylindrical glass material having a diameter dimension of 10 mm and a length dimension of 10 mm is used.

  Further, the load mechanism 17 is provided with a displacement meter 18 for measuring the crushing of the sample piece B installed in the load mechanism 17, that is, the displacement. As the displacement meter 18, for example, a load cell (DTH-A-5: manufactured by Kyowa Denki Co., Ltd.) or a data logger (remote scanner Jr. DC3100: manufactured by NEC Sanei Co., Ltd.) is used.

  The displacement meter 18 is connected to a data recorder 19, and the data recorder 19 is connected to a computer 21 as control means. The computer 21 receives displacement record information measured by the displacement meter 18 and recorded by the data recorder 19, and calculates a creep function based on the displacement record information.

  On the other hand, an electric furnace 22 for heating the sample piece B installed in the load mechanism 17 is attached to the load mechanism 17. As the electric furnace 22, for example, an electric furnace (manufactured by Shimadzu Corporation) having a maximum allowable temperature of 1100 ° C. is used. A temperature controller 23 is connected to the electric furnace 22, and heating of the sample piece B by the electric furnace 22 is controlled by the temperature controller 23. In other words, the heating temperature by the electric furnace 22 is controlled by the temperature controller 23. As the temperature controller 23, for example, a temperature controller (EC5600: manufactured by Okura Electric Co., Ltd.) is used.

  Then, in a state where the sample piece B is installed in the load mechanism 17 of the creep test apparatus 11, while the load mechanism 17 is controlled by the temperature controller 23 and heated in the electric furnace 22, A test is performed to convert the tensile load on the sample piece B into a compressive load by installing a weight W. At this time, a fixed load is applied to the sample piece B by setting the weight W on the weight setting plate 15, and the degree of collapse of the sample piece B at this time, that is, the displacement amount is measured by the displacement meter 18. And measure it as a time history.

  Next, a numerical simulation using the method for measuring the relaxation elastic modulus will be described.

  First, as an analysis model of a press molding simulation of a glass lens that is molded with a glass material 51 that is a viscoelastic body, as shown in FIGS. 12A and 12B, for example, a spherical glass material 51, A spherical lens is molded using a model of a press die 54 which is a molding die constituted by two upper and lower molds 52 and 53.

  Then, the pressure acting on the upper surface of the upper mold 52 is controlled to simulate the press molding process of the lens from the glass material 51 by numerical analysis based on nonlinear contact analysis in consideration of large deformation. Further, as the linear expansion coefficient of the glass material 51, a value measured by approximation of the relaxation elastic modulus according to the above-mentioned Maxwell model is used.

  Then, for example, a numerical simulation simulating a process with different temperature conditions and pressure conditions is performed. In actual molding, heat exchange occurs between the glass material 51 and the molds 52 and 53, and between the glass material 51 and the molds 52 and 53 and the external region, and as a result, the glass material. A temperature distribution occurs inside 51. It is assumed that the mold 52, 53 and the glass material 51 always have a uniform temperature field that matches the temperature sequence, and the temperature distribution and heat transfer in the mold 52, 53 and the glass material 51 are not considered. It was supposed to be.

  As described above, according to the above embodiment, at the stage of adopting the Maxwell model having eleven degrees of freedom and performing Laplace transform on the discrete data of the creep function obtained by the experiment, a power function, a Forked model, etc. After applying an approximation using an arbitrary expression capable of Laplace transform, analytical Laplace transform is performed, and then the obtained numerical solution in the image space is Laplace inverse transformed. In other words, by using an approximation by an arbitrary expression that can perform Laplace transform, Laplace transform can be performed not only analytically but also mechanically in Laplace image space.

  As a result, since the accuracy of the final relaxation modulus measurement can be improved as compared with the existing method for measuring the relaxation modulus, the relaxation modulus can be measured with extremely high accuracy. For this reason, it is possible to easily and accurately measure the relaxation elastic modulus necessary for maintaining the dimensional accuracy of the viscoelastic body such as the glass material 51 after molding.

  Furthermore, based on the relaxation elastic modulus of the viscoelastic body measured by the method of measuring the relaxation elastic modulus, a press die 54 for molding a molded article such as a lens made of a viscoelastic body such as the glass material 51 is provided. By manufacturing, the dimensional accuracy of the lens after molding the glass material 51 using the press die 54 can be maintained. Therefore, it is possible to prevent the occurrence of cracking or cracking of the lens, which may occur when the lens is formed using the glass material 51 by the press die 54.

  In other words, in the cooling process at the time of molding, it is possible to prevent residual stress and residual deformation from occurring in the lens, and it is possible to prevent deterioration of the dimensional accuracy of the molded product, so that a lens that can achieve the desired optical performance can be easily manufactured. it can. Therefore, it is not necessary to make correction after manufacturing the press die 54 for high-temperature press molding of the lens made of the glass material 51, so that the design and manufacture of the press die 54 can be facilitated.

  Furthermore, by modeling the obtained relaxation elastic modulus, obtaining the elastic parameters in advance using a general-purpose finite element method code, and performing a search for only the coefficient corresponding to the relaxation time, it is possible to measure the relaxation elastic modulus. Since highly accurate parameters can be estimated, a faithful model of relaxation modulus can be obtained as a result. In addition, as a result of the contact between the press die 54 and the glass material 51 and the large deformation analysis, the lens shape and residual stress after molding largely depend on the temperature drop condition due to the thermo-viscoelastic properties of the glass material 51. I understood.

  When the creep function is approximated by a power function, calculation and the like are simplified and measurement is easy.When the creep function is approximated by a Forked model, it is suitable for more accurate approximation of the creep function, and the relaxation elastic modulus. Can be measured more easily and accurately.

  Next, an example of a method for specifying the Maxwell model used in the method for measuring the relaxation elastic modulus will be described.

For example, a master curve of the Maxwell model is obtained by curve fitting with respect to a relaxation elastic modulus of glass transition temperature T _g = 680 ° C. = 953 K. The various constants of the finally identified Maxwell model are as follows.

k ₁ = k ₂ = k ₃ = k ₄ = 30.88 GPa, k ₅ = 1.248 GPa, k _∞ = 1.97 GPa, λ ₁ = 7.0 ms, λ ₂ = 9.0 ms, λ ₃ = 10.0 ms , Λ ₄ = 11.0 ms, λ ₅ = 30.0 ms

  At this time, this master curve is indicated by a broken line in FIG. That is, the specified Maxwell model curve almost coincides with the relaxed elastic modulus of each shifted temperature, and thus high approximation accuracy can be achieved by approximation using the Maxwell model.

  Next, an example of the measurement of the linear expansion coefficient used in the method for measuring the relaxation elastic modulus will be described.

  A rectangular parallelepiped glass material having a width of 4 mm, a depth of 4 mm, and a height of 10 mm was used as the sample piece B, and the test temperature was raised from 50 ° C. to 710 ° C. at 10 ° C./min and held at 710 ° C. for 5 minutes.

  The circles in FIG. 13 indicate the relationship between the measured temperature and thermal strain. Furthermore, as shown in FIG. 13, in the range from room temperature (20 ° C.) to 700 ° C., it was found that the linear expansion coefficient, which is the linear expansion coefficient, depends on the temperature.

Here, in the above formula 38, the coefficients α ₀ , α ₁ ,..., Α ₄ are set to the following values.

α ₀ = 5.48 × 10 ⁻⁶ K ⁻¹ , α ₁ = 3.16 × 10 ⁻⁹ K ⁻² , α ₂ = 4.87 × 10 ⁻¹¹ K ⁻³ , α ₃ = −1.78 × 10 ⁻¹³ K ⁻⁴ , α ₄ = 1.69 × 10 ⁻¹⁶ K ⁻⁵

  Next, an example of a creep test used in the method for measuring the relaxation elastic modulus will be described.

  While the specimen piece B is placed on the load mechanism 17 of the creep test apparatus 11, the weight mechanism plate 15 is heated to a predetermined weight while being heated by the electric furnace 22 while being controlled by the temperature controller 23. A test is performed to convert the tensile load on the sample piece B into a compression load by installing the weight W. At this time, by installing the weight W on the weight setting plate 15, a constant load of, for example, 98.1 N and stress: 1.25 MPa is applied to the sample piece B, and the degree of crushing of the sample piece B at this time That is, the displacement amount was measured with the displacement meter 18 and measured as a time history.

As this sample piece B, TaF-3 which is a typical glass material used for a glass lens was used. In this TaF-3 is at 680 ° C. The glass transition temperature _{T g} is a density ρ is 4711kg / ^{m 3,} the Young's modulus _{k 0} is the instantaneous elastic modulus is 124.8GPa. Furthermore, the creep test results of the sample piece B at the test temperatures of 660 ° C., 670 ° C., and 680 ° C. are as shown in FIG.

  Next, an example of press forming analysis in numerical simulation using the above-described relaxation modulus measurement method will be described.

  First, as an analysis model of a press molding simulation of a glass lens molded with a glass material 51 that is a viscoelastic body, a spherical lens having a radius of curvature of 25 mm was formed with the glass material 51 having a diameter of 10 mm. The press die 54 was divided into a total of 826 elements of 479 elements, with the glass material 51 being 347 elements using a quadratic secondary element.

  Then, the pressure acting on the upper surface of the upper mold 52 was controlled to simulate the press molding process of the lens from the glass material 51. At this time, the general-purpose finite element method code ANSYS ver. 8.0 (trade name) was used for the numerical analysis, and a non-linear contact analysis considering a large deformation was performed. Further, the thermoviscoelastic properties of the glass material 51 were calculated from the above master curve and shift factor, and the Poisson's ratio was set to 0.3. Further, as the linear expansion coefficient of the glass material 51, a value measured by approximating the relaxation elastic modulus by the Maxwell model described above was used.

Further, the materials of the upper and lower molds 52 and 53 of the press mold 54 are made of carbide, the Young's modulus of each of these molds 52 and 53 is 630 GPa, the Poisson's ratio is 0.2, and the linear expansion coefficient is 4.6 ×. 10 ⁻⁶ K ⁻¹ .

And as press molding analysis, numerical simulation was performed using the molding conditions shown in FIG. In this press molding process, the analysis was started from the state in which the temperature of the glass material 51 and the molds 52 and 53 were both T ₀ = 680 ° C. A molding pressure P ₀ of about 20 MPa is applied to the upper surface of the upper mold 52, and press molding with the glass material 51 is held in the molds 52 and 53 for a molding time t _P seconds, and the spherical glass material 51 is made into a lens. Formed into a shape. Thereafter, the pressure acting on the upper surface of the upper mold 52 was reduced, and the temperature of the mold 52 was lowered to 20 ° C., which is room temperature. The time for pressurization and pressure reduction was 10 seconds each, and the time required for the temperature drop was 300 seconds. As a result, the action time of the pressure, ie was discussed deformation of the glass material 51 in the case of changing between up to 80 seconds forming time t _p of 30 seconds and the residual stress.

FIG. 16 and FIG. 17 show the distribution of residual stress (Mises equivalent stress), which is an isotropic pressure after the end of forming, in each of the forming times t _p = 40 and t _p = 70, respectively. . As a result, as shown in FIG. 16, when t _p = 40, it was confirmed that a gap was formed between the upper and lower molds 52 and 53, and the molding time was insufficient. Further, when compared with the result in the case of t _p = 70, a clear difference was observed in the distribution of the equivalent stress inside the glass material 51.

  Further, as shown in FIG. 16, when the molding time is short and the molding is completed without the upper and lower molds 52 and 53 being in contact, the surface point on the central axis of the lens molded from the glass material 51 is used. The stress is maximized at a slightly inner position. On the other hand, as shown in FIG. 17, when molding is performed so that the upper and lower molds 52 and 53 are in contact with each other, the stress on the surface layer of the glass material 51 in contact with the molds 52 and 53 is increased. A tendency to increase was shown, and it was found that the equivalent stress was maximum at a position about 0.6 mm inside from the outer periphery of the lens molded from the glass material 51.

Further, the maximum value of the residual stress in the case of changing the six at 10 second intervals over the molding time t _p from 30 seconds to 80 seconds, in the center of the lens to be molded from glass material 51 thickness The relationship with the change is shown in FIG. As a result, as shown in FIG. 18, the molding time t _p is 60 seconds or less in the region not in contact upper and lower molds 52 and 53 due to the molding time is short, the glass material 51 as a result The thickness of the molded lens will be larger than the design dimension of 2 mm. Also, t until _p reaches 60 seconds, the residual stress tended to decrease with increasing molding time. Further, in the region where t _p > 60 seconds, as shown in FIG. 17, the stress distribution shape itself changes, and the maximum value of the stress distribution shape converges to a constant value of around 0.3 MPa. I understood.

Further, 19 the relationship between the curvature radius and the molding time t _P of the central portion of the lens to be molded from the glass material 51. At this time, the radius of curvature R of the designed lens was set to 25 mm. Furthermore, it has been found that, on average, a change in curvature of about 0.6% occurs due to thermal shrinkage accompanying cooling when the glass material 51 is press-formed. Further, it was confirmed that the curvature change due to the thermal contraction due to cooling when the glass material 51 is press-molded is minimized when the molding time t _P is in the vicinity of 60 seconds.

  Next, another embodiment of the press forming analysis in the numerical simulation using the method for measuring the relaxation elastic modulus will be described.

In one embodiment of the press forming analysis in the numerical simulation, the numerical simulation was performed using the forming conditions shown in FIG. In this press molding analysis, the molding temperature was set higher than in one embodiment of the press molding analysis, and the time required for press molding was shortened. Specifically, from the state where the temperature T ₁ of the glass material 51 and the molds 52 and 53 are both 710 ° C., a molding pressure P ₀ of about 20 MPa is applied to the upper surface of the upper mold 52, and this state is maintained for t ₁ second. Held. Thereafter, the temperature T ₂ is lowered to 610 ° C. for t ₂ seconds while the pressure on the upper mold 52 is left as it is, and the glass is kept at a constant temperature gradient for 300 seconds. The temperature of each of the material 51 and the molds 52 and 53 was returned to room temperature, that is, 20 ° C.

Incidentally, in the actual lens molding process reference, even when returning to room temperature for each of these glass materials 51 and the mold 52, 53 temperature, it was added a correction of P _0/10 = 2MPa. Further, by changing the holding time t ₁ at the temperature T ₁ = 710 ° C. and the time t ₂ required for the temperature T ₁ to drop from the temperature T ₁ to T ₂ , the deformation of the lens is performed in the same manner as in the embodiment of the press molding analysis. We focused on residual stress.

FIG. 21 shows the analysis result of the residual stress when the molding times t ₁ = 10 s and t ₂ = 10 s. FIG. 22 shows the analysis result of the residual stress when the molding times t ₁ = 30 s and t ₂ = 10 s. Both FIG. 21 and FIG. 22 show the distribution of Mises-equivalent stress, which is the residual stress generated in the lens after completion of molding.

As a result, as shown in FIG. 21, when the molding time t ₁ is short, because the molding in a state where the upper and lower molds 52 and 53 are not in contact is completed, substantially the same as an embodiment of the press forming analysis It turned out to be a stress distribution. Further, by setting the molding time t ₁ appropriately, as shown in FIG. 22, the molding is completed in a state in which the upper and lower molds 52 and 53 are in contact, resulting in an embodiment of the press forming analysis It turned out that it becomes the stress distribution of the same tendency as FIG.

In the above example, the maximum stress value in FIG. 17 was about 0.374 MPa, and the pressing time t _P was 70 s. In contrast, in this example, the maximum stress value in FIG. 22 was about 0.345 MPa, and the pressing time (t ₁ + t ₂ ) was 40 s. For this reason, it was found that by setting the press time in a high temperature range, the total time required for molding can be shortened and the residual stress can be reduced.

23 (a) to 23 (c) show tensile stresses σ _x , σ _y and shear stress τ _xy generated in the lens after completion of molding when the pressurization time t ₁ = 30 s and t ₂ = 10 s. The distribution of. As a result, it has been found that the stress generated in the lens is based on the tensile stress. Further, it was found that a slightly high compressive residual stress of about 0.3 MPa was generated at the surface point of this lens. Further, FIGS. 24 and 25 show the maximum value of the residual stress after the end of molding when the pressing time t ₁ is changed from 10 seconds to 30 seconds, or the pressing time t ₂ is changed from 10 seconds to 110 seconds, respectively. The relationship between the lens thickness and the pressing times t ₁ and t ₂ is shown.

As a result, as shown in FIG. 24, the residual stresses, the line connecting the points _{(t 1, t 2)} = a point _{(25,10) (t 1, t} 2) = (10,90) It becomes a boundary line for judging the quality of molding conditions. That is, it has been found that a glass lens with high dimensional accuracy can be formed by determining these t ₁ and t ₂ in the regions where t ₁ and t ₂ on the side exceeding the boundary line are large. . As shown in FIGS. 24 and 25, it was found that the total lens molding time can be shortened by setting t ₁ longer than the pressurizing time t ₂ . In addition, by increasing each of these t ₁ and t ₂ , each of the residual stress and the amount of residual deformation can be reduced. However, when priority is given to the molding efficiency, the processing time in the high temperature range should be increased. I understood that.

  Therefore, the Laplace transform of the creep curve is used to measure the relaxation modulus in the Laplace image space, and by performing the inverse numerical Laplace transform using the so-called Hosono method, a simple and accurate method for deriving the relaxation modulus can be established. It was. Furthermore, the shift factor could be calculated by obtaining a master curve from the relaxation modulus at each temperature. Further, the linear expansion coefficient of the glass material 51 was measured by experiment and approximated using linear polynomial approximation.

  Each of the operations in the above-described embodiments and examples can be a computer-readable relaxation modulus measurement program, a mold design or manufacturing program, and can be automatically calculated by a computer. Software for measuring relaxation elastic modulus or for designing or manufacturing a mold can be used.

  In each of the above embodiments and examples, the creep function is not only approximated by a power function or a Forked model, but can be approximated by an arbitrary expression capable of Laplace transform such as a polynomial or a step function. It is possible to play. In particular, when the creep function is approximated by a step function, the data obtained by measuring the time history in the first embodiment can be input as it is when digital processing is performed by a computer using the relaxation modulus measurement program or the like. Therefore, it is more advantageous than the case of approximating with other functions.

  Furthermore, these programs and software can be stored in an optical disk, a magnetic disk, or other recording medium on which the program or software is recorded, and the recording medium can be used to automatically operate the computer. Further, a relaxation elastic modulus measuring device, a mold designing device, a manufacturing device, or the like provided with a mechanism or means for performing the operations in the above embodiments and examples may be used.

  In each of the above embodiments and examples, the glass material 51 is used as the sample piece B that is a viscoelastic body. However, for example, viscoelasticity other than the glass material 51 such as thermoplastic plastic, thermosetting plastic, or engineering plastic. Even the body can be used in correspondence. Moreover, even if it is an optical element other than a lens or a press-molded product other than a lens having a non-curved surface, it can be used correspondingly as long as it is a molded product that can be molded by press-molding a viscoelastic body.

It is a graph which shows the master curve used for the measuring method of the relaxation elastic modulus of one embodiment of this invention. It is a graph used for the measuring method of a relaxation elastic modulus same as the above, (a) is a graph of a creep function, (b) is a graph of a relaxation elastic modulus. It is a graph used for the measuring method of a relaxation elastic modulus same as the above, (a) is a graph of an additional strain, (b) is a graph in which an additional strain is dependent on a creep function. It is a graph which shows the superposition of step input. It is explanatory drawing which shows a forked model. It is a graph which shows the relaxation elastic modulus in each temperature. It is a graph which shows a shift factor. It is explanatory drawing which shows a Maxwell model. It is a schematic diagram which shows the relaxation elastic modulus approximated by the Maxwell model same as the above. It is explanatory drawing which shows a thermal analysis measuring device. It is explanatory side view which shows a creep test apparatus. It is a block diagram which shows the analysis model of the shaping | molding die of press molding simulation, (a) is a perspective view of a shaping | molding die, (b) is a front view which shows a part of shaping | molding die. It is the graph which measured one Example of the linear expansion coefficient used for the measuring method of the relaxation elastic modulus of this invention with the said thermal analysis measuring device. It is a graph which shows one Example of the displacement amount in the said creep test apparatus used for the measuring method of the relaxation elastic modulus of this invention. It is a graph which shows the molding conditions in one Example of the press molding analysis of this invention. It is a diagram showing the distribution of molding time t _{P =} 40 seconds Mises equivalent stress in the case of in ibid press forming analysis. It is a diagram showing the distribution of molding time t _{P =} 70 seconds Mises equivalent stress in the case of in ibid press forming analysis. It is a graph which shows the relationship between the maximum value of the residual stress with respect to the shaping | molding time in a press molding analysis same as the above, and the lens thickness. It is a graph which shows the relationship between the curvature radius in the center part of the lens in a press molding analysis, and molding time same as the above. It is a graph which shows the molding conditions in other examples of press molding analysis of the present invention. It is a diagram showing the distribution of the Mises equivalent stress in the case of molding time t _{1 =} 10 sec and t _{2 =} 10 seconds in the same as above press forming analysis. It is a diagram showing the distribution of molding time t _{1 =} 30 sec and t _{2 =} in the case of 10 seconds Mises equivalent stress in ibid press forming analysis. It is a diagram in the case where the pressing time t _{1 =} 30s and t _{2 =} 10s in ibid press forming analysis, (a) represents a distributed view of the tensile stress sigma _x occurs in the lens after completion of the molding, (b) is FIG. 5C is a distribution diagram of tensile stress σ _y , and FIG. 5C is a distribution diagram of shear stress τ _xy . The maximum value of residual stress and squeezing time t _1, is a graph showing the relationship between t _2. Between thickness and pressurization of the lens t _1, it is a graph showing the relationship between t _2.

Explanation of symbols

51 Glass materials as viscoelastic bodies
54 Press mold as mold B Sample piece as viscoelastic body

Claims (15)

Approximate the relational expression between stress and strain of viscoelastic body with an arbitrary expression that can be converted to Laplace,
The above relational expression approximated by an arbitrary expression that can be converted to Laplace is Laplace converted,
The Laplace transformed relational expression is calculated into a relaxation modulus Laplace transform,
A Laplace inverse transform is performed on the relational expression calculated for the Laplace transform of the relaxation elastic modulus. Measure the displacement with respect to the time history under the load of the viscoelastic body,
From the amount of displacement relative to the measured time history, a relational expression between the stress and strain of the viscoelastic body is obtained,
This relational expression is approximated by an arbitrary expression that can be converted to Laplace,
The above relational expression approximated by an arbitrary expression that can be converted to Laplace is Laplace converted,
The Laplace transformed relational expression is calculated into a relaxation modulus Laplace transform,
A Laplace inverse transform is performed on the relational expression calculated for the Laplace transform of the relaxation elastic modulus. The relational expression between the stress and strain of the viscoelastic body is a creep function obtained from a creep test of the viscoelastic body. The relaxation elastic modulus measuring method according to claim 1 or 2. The method for measuring the relaxation elastic modulus according to any one of claims 1 to 3, wherein the arbitrary expression capable of Laplace transform is a power function. 4. The relaxation elastic modulus measurement according to claim 1, wherein the arbitrary expression capable of Laplace transform is a function obtained by modeling a relational expression between stress and strain of a viscoelastic body using a Forked model. Method. Approximating a relational expression between stress and strain of a viscoelastic body with an arbitrary expression capable of Laplace transform;
Laplace transforming the relational expression approximated by an arbitrary formula capable of Laplace transform;
Calculating the Laplace transformed relational expression into a relaxation elastic modulus Laplace transform;
A program for measuring the relaxation elastic modulus, comprising: a step of inversely transforming the relational expression calculated for Laplace conversion of the relaxation elastic modulus. Measuring a displacement with respect to a time history under the load of the viscoelastic body;
From the amount of displacement relative to the measured time history, obtaining a relational expression between stress and strain of the viscoelastic body,
Approximating this relational expression with an arbitrary expression capable of Laplace transform;
Laplace transforming the relational expression approximated by an arbitrary formula capable of Laplace transform;
Calculating the Laplace transformed relational expression into a relaxation elastic modulus Laplace transform;
A program for measuring the relaxation elastic modulus, comprising: a step of inversely transforming the relational expression calculated for Laplace conversion of the relaxation elastic modulus. The relaxation elastic modulus measurement program according to claim 6 or 7, wherein a relational expression between stress and strain of the viscoelastic body is a creep function obtained from a creep test of the viscoelastic body. The program for measuring relaxation elastic modulus according to any one of claims 6 to 8, wherein the arbitrary expression capable of Laplace transform is a power function. 9. The measurement of relaxation elastic modulus according to claim 6, wherein the arbitrary expression capable of Laplace transform is a function obtained by modeling a relational expression between stress and strain of a viscoelastic body by a Forked model. program. 11. A recording medium storing a relaxation elastic modulus measurement program, wherein the relaxation elastic modulus measurement program according to claim 6 is recorded so as to be readable by a computer. A mold for molding a molded article made of the viscoelastic body is manufactured based on the relaxation elastic modulus of the viscoelastic body measured by the method for measuring the relaxation elastic modulus according to any one of claims 1 to 5. A method for producing a mold, characterized by: A mold for molding a molded article made of the viscoelastic material is manufactured based on the relaxation elastic modulus of the viscoelastic body measured by the relaxation elastic modulus measurement program according to any one of claims 6 to 10. A method for producing a mold, characterized by: The viscoelastic body is a glass material,
The molded product is an optical element,
The mold according to claim 12 or 13, wherein the mold is a press mold for pressing the glass material to mold the optical element. The viscoelastic body is engineering plastic,
The molded product is an optical element,
The method for manufacturing a molding die according to claim 12 or 13, wherein the molding die is a press die for pressing the engineering plastic to mold the optical element.