JP2012176529A - Physical properties simulation method after vulcanization of laminated rubber - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a simulation method that can forecast physical properties of the laminated rubber after the vulcanization at the large deformation.SOLUTION: There is provided a physical property parameter function in which the physical property parameters after the vulcanization of the rubber member are approximated and the temperature and the vulcanization degree are made parameters (106) by making a test body which holds the rubber member with two iron plates (100), and obtaining a vulcanization degree of the test body obtained by vulcanizing in various temperature histories and a shear elastic modulus after the vulcanization (102). A temperature of each element and the time change with the vulcanization degree are forecasted by giving the vulcanization condition to a three dimension FEM model and analyzing the heat transfer (110 and 112). The physical property parameter that is calculated by giving the predicted values of the temperature and the vulcanization degree of the element of the rubber member obtained to each element are given to each element that composes the rubber member of three dimension FEM model, (114), and the structure analysis is performed by giving a boundary condition and the physical property of each element of the rubber member is presumed (116).

Description

  The present invention relates to a method for simulating physical properties after vulcanization of a laminated rubber formed by laminating a rubber member and an iron plate using a finite element method.

  In recent years, as a method of joining superstructures such as buildings and bridge girders and substructures such as foundation piles and bridge piers to support them, instead of conventional rigid joints, in order to control earthquake and seismic isolation, Joining methods using joining, rolling bearings, sliding bearings or laminated rubber for seismic isolation have been adopted. Although the above-mentioned seismic isolation laminated rubber is a large industrial rubber product, its performance such as shear rigidity and damping constant is relatively higher than other large rubber products such as fenders and flexible joints. High accuracy is required.

  Moreover, optimization of vulcanization is mentioned as a technical subject at the time of manufacturing a large-sized and thick rubber product like the laminated rubber used for the said seismic isolation. In other words, in the vulcanization process using a mold as described above, the heat source is limited to the outer periphery, so the internal vulcanization state tends to be uneven in large rubber products, which greatly affects the physical properties of the product. Resulting in.

  Therefore, a simulation method for predicting physical properties of a rubber material after vulcanization related to the performance of the laminated rubber, such as an elastic modulus and a damping coefficient, and identifying appropriate vulcanization conditions is known (Patent Document). 1).

JP 2007-203591 A

  However, the method described in Patent Document 1 has a problem that only physical properties in a deformation region that can be regarded as simple deformation can be predicted.

  The present invention has been made to solve the above problems, and provides a post-vulcanization physical property simulation method for a laminated rubber capable of predicting the physical properties of the laminated rubber after vulcanization during large deformation. Objective.

  In order to achieve the above object, the post-vulcanization physical property simulation method for laminated rubber according to the present invention is a method for simulating physical property values after vulcanization of a laminated rubber formed by laminating a plurality of rubber members and iron plates. The test body obtained by sandwiching the rubber member constituting the laminated rubber with the steel material constituting the iron plate and vulcanizing it with various temperature histories was obtained. The first step of determining the physical property value later, and the physical property parameters obtained by approximating the physical property parameters after vulcanization of the rubber member using the data of the obtained specimen, and using the temperature and the degree of vulcanization as parameters A second step of creating a parameter function; and a heat transfer analysis by applying a vulcanization condition to a first numerical analysis model obtained by dividing the laminated rubber into a finite number of elements, and each of the first numerical analysis models Temperature of each element constituting the rubber member And a second step of predicting the time change of the degree of vulcanization and the degree of vulcanization, and the predicted value of the temperature of the rubber member element and the degree of vulcanization obtained for each element in the third step as parameters. The physical property parameter calculated by giving to the physical property parameter function created in the step is given to each element constituting the rubber member of the second numerical analysis model obtained by dividing the laminated rubber into a finite number of elements, and And a fourth step of estimating a physical property value of each element of the rubber member by performing a structural analysis by giving boundary conditions to the second numerical analysis model.

  The method for simulating vulcanized physical properties of a laminated rubber according to the present invention includes a fifth step of calculating a product performance value of the laminated rubber based on physical properties of each element of the rubber member estimated in the fourth step. Whether the difference between the target performance value and the calculated product performance value is within a predetermined range by comparing the product performance value obtained in the fifth step with a preset target performance value. A sixth step of determining whether or not, and when the difference exceeds a predetermined range, the process returns to the third step to change the vulcanization condition, and from the third step to the third step. Steps up to step 6 can be repeated to specify the vulcanization condition that gives the target performance value.

  The physical property value according to the present invention can be the shear modulus of the rubber material.

  The second numerical analysis model according to the present invention can be common to the first numerical analysis model.

  As described above, according to the post-vulcanization physical property simulation method for laminated rubber of the present invention, the first numerical analysis model is subjected to heat transfer analysis by giving vulcanization conditions, and each element of the rubber member after vulcanization is analyzed. After predicting the temperature and the degree of vulcanization, physical property parameters calculated using the predicted temperature and the degree of vulcanization are given to each element of the second numerical analysis model, and the second numerical analysis model is bounded. By performing structural analysis under conditions and estimating the physical property value of each element of the rubber member, it is possible to predict the physical property of the laminated rubber after vulcanization at the time of large deformation.

It is the schematic which showed the simulation apparatus which concerns on embodiment of this invention. It is a figure which shows schematic structure of the laminated rubber for seismic isolation. It is a figure for explaining vulcanization processing of laminated rubber for seismic isolation. It is a flowchart which shows the physical property simulation method after vulcanization | cure of the laminated rubber for seismic isolation which concerns on embodiment of this invention. It is a schematic diagram of the test body for the post-vulcanization characteristic measurement which concerns on embodiment of this invention. It is a figure which shows an example of a vulcanization physical property function. It is a figure which shows a mode that the simple shear was given to the model. It is a graph which shows the relationship between a shear strain and a shear stress. It is a figure which shows a three-dimensional FEM model. It is a figure which shows the example of calculation of the temperature distribution in the laminated rubber for seismic isolation. (A) The figure which shows the example of calculation of the time series change of each element of the laminated rubber for seismic isolation, The figure which shows the example of calculation of the time series change of the shear elastic modulus of each element of the (B) laminated rubber for seismic isolation It is. It is a figure which shows each element of the laminated rubber for seismic isolation. It is a figure which shows the example of calculation of the shear elastic modulus distribution in the laminated rubber for seismic isolation. It is a contour figure which shows distribution of the shear stress in the laminated rubber for seismic isolation at the time of 400% shear deformation.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

  As shown in FIG. 1, a simulation device 50 that executes a post-vulcanization physical property simulation of a laminated rubber according to an embodiment of the present invention is a process described later by a simulation program for executing the post-vulcanization physical property simulation of the laminated rubber. It is comprised by the computer arithmetic processing system which performs. Such a computer system includes, for example, a CPU, a ROM, a RAM, a hard disk, an input / output terminal, and other necessary units. The simulation program is stored in advance on a hard disk or the like.

  FIG. 2 is a diagram showing a schematic configuration of the seismic isolation laminated rubber 10 analyzed by the post-vulcanization physical property simulation method of the laminated rubber according to the present embodiment. The seismic isolation laminated rubber 10 is obtained by alternately laminating a plurality of rubber members 11 and iron plates 12, and as shown in FIG. 3, the unvulcanized rubber member 11 and the iron plate 12 having been subjected to adhesion treatment are laminated. The product is put into a vulcanizing mold 20 comprising an annular mold 21 and upper and lower molds 22 and 23, and heated from above, underside and side surfaces of the vulcanizing mold 20, and the rubber member 11 is heated. It is obtained by causing a crosslinking reaction between the rubber molecules and sulfur and performing a vulcanization treatment for bonding the rubber member 11 and the iron plate 12 together. By this vulcanization treatment, desired physical property values can be given to the rubber member 11 constituting the seismic isolation laminated rubber 10 such as shear modulus, and the adhesive strength between the rubber member 11 and the iron plate 12 is ensured. be able to. The actual seismic isolation laminated rubber 10 has a configuration in which the whole is further covered with an outer rubber made of EPDM rubber, but the outer rubber is omitted for the sake of simplicity.

  Next, a method of simulating the physical properties after vulcanization of the seismic isolation laminated rubber 10 will be described based on the flowchart of FIG.

  First, a test body 30 in which a designer holds a rubber member 32 made of the same component as the rubber member 11 between two iron plates 31 made of the same steel material as the iron plate 12 as shown in FIG. Many are prepared (step 100), and the designer vulcanizes these specimens 30 under various vulcanization conditions to obtain the degree of vulcanization of the rubber member, and performs a shear test on the specimen 30. Thus, the shear modulus after vulcanization is obtained (step 102).

The simulation device 50 then uses a vulcanization function G that approximates the vulcanization shear modulus of the rubber member 32 from the vulcanization conditions, the obtained vulcanization degree data, and the measured shear modulus data. _eq (C _d , T) is created (step 104). This vulcanization function G _eq (C _d , T) is expressed by a function of two variables having the temperature T and the vulcanization degree C _d as parameters as shown in the following equation (1), and is a schematic diagram of FIG. As shown in FIG. 3, the surface is represented by a curved surface on three-dimensional coordinates.

In this example, the vulcanization function G _eq (C _d , T) is normalized not to the shear modulus G itself but to the shear modulus G ₀ when vulcanized under predetermined vulcanization conditions as 1. (G / G ₀ ) was used. In addition, the boundary of the color-coded region in the figure represents the contour line of the shear modulus.

Next, the simulation apparatus 50 performs shearing after vulcanization of the rubber member 32 when a simple shear γ is given from the above vulcanization conditions, the obtained degree of vulcanization data and the measured shear modulus data. Physical property parameter functions a (C _d , T) and b (C _d , T) approximating the physical property parameters in the equation of the curve representing the elastic modulus G (γ) are created (step 106).

  Here, the superelasticity of the rubber is a model represented by the following equation (2).

  When a simple shear γ as shown in FIG. 7 is given to the model given by the above equation (2), the strain energy function is expressed by the following equation (3), as shown in FIG. The τ-γ curve is expressed by the following equation (4).

Based on the above equation (1), the physical property parameters a and b are defined as a function of the ultimate temperature T and the degree of vulcanization C _d so that G (γ = 100%) = G _eq, and a (C _d , T), b (C _d , T).

  Next, the designer creates a three-dimensional FEM model for heat conduction analysis and large deformation structure analysis (step 108). As the three-dimensional FEM model, a three-dimensional model 40 obtained by dividing the seismic isolation laminated rubber 10 into a large number of 8-node quadrangular prism elements as shown in FIG. 9 is used, and the rubber of the three-dimensional model 40 is used. A thermal conductivity or a thermal diffusion coefficient is given to the element 41, the iron plate element 42, and the outer rubber element 43, and the rubber element 41 is further provided with a vulcanization reaction activation energy for considering the heat generated by the vulcanization reaction. give.

Then, the designer sets the vulcanization conditions (temperature history) (step 110), the simulation device 50 performs the heat conduction analysis, and sets the temperature and the degree of vulcanization of each rubber element 41 for each time step. Calculate and predict the temperature rise of each rubber element 41 and the change in the degree of vulcanization, and the predicted C _d and T of the vulcanization function G (C _d , T) created in step 104 above. Substituting the vulcanization degree and the ultimate temperature of the element, respectively, the shear elastic modulus which is the physical property of the rubber element 41 is estimated (step 112).

Next, the simulation apparatus 50 calculates the vulcanization degree of each rubber element 41 to C _d and T of the physical property parameter functions a (C _d , T) and b (C _d , T) created in step 106. And the temperature reached, the physical property parameters a and b of each rubber element 41 are calculated, and the above equation (4), to which the calculated physical property parameters a and b are applied, is used as a strain energy function to correspond to each rubber element. 41 (step 114).

  Then, the boundary condition (load condition) is set, and the simulation apparatus 50 performs a large deformation structure analysis, calculates the shear elastic modulus of each rubber element 41 for each time step, and determines the physical properties of each rubber element 41. A certain shear modulus is estimated (step 116).

  Then, the simulation apparatus 50 calculates a numerical value representing the product performance of the laminated rubber based on the estimated shear modulus of each rubber element 41 (step 118). The numerical value representing the product performance is used to determine whether the vulcanization conditions set in step 110 are appropriate. For example, the numerical value indicating the volume average of the shear modulus or the uniform distribution of the shear modulus It is a numerical value indicating sex.

  After calculating the numerical value representing the product performance, the designer examines whether or not to change the vulcanization conditions (step 120), and if so, return to step 110 to set new vulcanization conditions. A heat conduction analysis and a large deformation structure analysis are performed again to obtain a numerical value representing the product performance. If the vulcanization conditions are not changed, this simulation process is terminated.

  As described above, according to the present embodiment, the vulcanization conditions are given to the three-dimensional FEM model, the heat conduction analysis is performed, and the temperature and the degree of vulcanization of each element of the rubber member after vulcanization are predicted. A physical property parameter calculated using the predicted temperature and degree of vulcanization is given to each element of the three-dimensional FEM model, and boundary conditions are given to the three-dimensional FEM model to perform a large deformation structure analysis, and a rubber member By estimating the physical property values of each element, the physical properties of the laminated rubber after vulcanization at the time of large deformation can be predicted.

  In addition, physical property parameters can be predicted from heat conduction analysis performed with vulcanization conditions, and large deformation structure analysis can be performed continuously to predict the characteristic values of laminated rubber under various force conditions. It becomes possible.

In the above embodiment, the case where the physical property value after vulcanization is the shear modulus has been described as an example. However, the present invention is not limited to this, and the physical property value after vulcanization includes an equivalent damping coefficient and the like. Other physical property values may be used. In this case, similarly to the above-mentioned shear modulus, the physical property value after vulcanization estimated by creating a separate specimen is measured, and the physical property after vulcanization of the rubber member when simple shear γ is given. What is necessary is just to create the physical property parameter functions a (C _d , T) and b (C _d , T) that approximate the physical property parameters in the equation of the curve representing the values.

  Further, in step 120, a standard for changing the vulcanization condition is not particularly provided, and the designer has determined the change of the vulcanization condition. The product performance value obtained in step 120 is compared with a preset target performance value. Then, it is determined whether or not the difference is within a predetermined range, and when the difference exceeds the predetermined range, the process may return to step 110 to change the vulcanization conditions. Alternatively, a plurality of vulcanization conditions may be simply set, and all product performance values under each vulcanization condition may be obtained.

  Various strain energy functions can be used. For example, strain energy functions such as Neo-Hookean model, Mooney-Rivlin model, Yeoh model, Ogden model and the like proposed as a material model of rubber can be used.

  In addition, the case where a single three-dimensional FEM model is used as an example has been described as the first numerical analysis model for heat conduction analysis and the second numerical analysis model for large deformation structure analysis. However, the first numerical analysis model for heat conduction analysis and the second numerical analysis model for large deformation structure analysis may be used separately.

  In addition, the creation of the vulcanization function in step 104 and the calculation of the physical property values in the heat conduction analysis in step 112 may be omitted.

  Seismic isolation with a cylindrical rubber member layer with an outer diameter of φ1600mm, an inner diameter of 0, and a single layer thickness of 6.0mm, and a steel plate (material: SPHC) layer with the same planar shape and a thickness of 4.4mm The internal temperature, degree of vulcanization, temperature change of shear modulus, and physical properties of the laminated rubber under various boundary conditions were simulated using a finite element method.

  The model dimensions are shown in Table 1 below.

The parameters necessary for the calculation are as follows.

(1) Properties of rubber and steel plate ・ Rubber quality of rubber member Internal rubber: High damping rubber material Outer rubber: EPDM rubber ・ Rubber (common to inner rubber and outer rubber), thermal diffusion coefficient of steel plate κ
・ Vulcanization reaction activation energy for rubber (common to inner rubber and outer rubber) ・ Standard vulcanization conditions for rubber (common to inner rubber and outer rubber) (best cure time)
・ Volume elastic modulus of rubber (common to inner rubber and outer rubber) ・ Young's modulus of steel sheet ・ Poisson's ratio of steel sheet (2) Vulcanization conditions Initial temperature and upper and lower ends of laminated rubber and end of outer rubber for a predetermined time Sulfur conditions were set.
(3) Boundary conditions Table 2 below shows the boundary conditions used in the large deformation structure analysis.

The temperature distribution 1.5 hours after the start of vulcanization is shown in FIG. 11A and 11B show time series changes in the temperature and shear modulus of the seismic isolation laminated rubber up to 10 hours. In the figure, the solid line represents the time series change of the rubber element A located near the heat source, the fine broken line represents the time series change of the rubber element C located farthest from the heat source, and the broken lines represent A and C. Is a time-series change of the rubber element B located approximately in the middle (see FIG. 12).

  In addition, FIG. 13 shows the distribution of the shear modulus immediately after the end of vulcanization. Further, FIG. 14 shows a contour diagram showing the distribution of the shear stress when the shear deformation is 400%.

  Since the distribution of physical properties of the seismic isolation laminated rubber during large deformation can be predicted as shown in FIG. 14 above, the physical properties after vulcanization of the seismic isolation laminated rubber can be easily predicted by performing the simulation according to the present invention. Was confirmed.

DESCRIPTION OF SYMBOLS 10 Seismic isolation laminated rubber 11 Rubber member 12 Iron plate 20 Vulcanization mold 30 Specimen 31 Iron plate 32 Rubber member 40 Three-dimensional model 41 Rubber element 42 Iron plate element 43 Skin rubber element 50 Simulation device

Claims (4)

A method for simulating physical property values after vulcanization of a laminated rubber formed by laminating a plurality of rubber members and an iron plate,
A test body in which a rubber member constituting the laminated rubber is sandwiched between steel members constituting the iron plate is produced, and the degree of vulcanization and vulcanization of the test body obtained by vulcanizing the specimen at various temperature histories. A first step for obtaining physical property values;
A second step of creating a physical property parameter function using temperature and degree of vulcanization as parameters, approximating physical property parameters after vulcanization of the rubber member, using the data of the obtained specimen;
The first numerical analysis model obtained by dividing the laminated rubber into a finite number of elements is subjected to heat transfer analysis by giving vulcanization conditions, and the temperature and the temperature of each element constituting each rubber member of the first numerical analysis model are added. A third step of predicting the time change of the sulfur content,
The physical property parameters calculated by giving to the physical property parameter function created in the second step, using as parameters the predicted values of the temperature and the degree of vulcanization of the element of the rubber member obtained for each component in the third step , The laminated rubber is divided into a finite number of elements to each element constituting the rubber member of the second numerical analysis model, and the structural analysis is performed by giving boundary conditions to the second numerical analysis model, A fourth step of estimating a physical property value of each element of the rubber member;
A method for simulating physical properties of a laminated rubber after vulcanization. A fifth step of calculating a product performance value of the laminated rubber based on a physical property value of each element of the rubber member estimated in the fourth step;
Whether the difference between the target performance value and the calculated product performance value is within a predetermined range by comparing the product performance value obtained in the fifth step with a preset target performance value And a sixth step of determining
When the difference exceeds a predetermined range, the process returns to the third step to change the vulcanization condition, and repeats the third step to the sixth step to obtain the target performance value. 2. The method for simulating vulcanized physical properties of a laminated rubber according to claim 1, wherein the vulcanizing conditions to be given are specified.   The method for simulating vulcanized physical properties of laminated rubber according to claim 1 or 2, wherein the physical property value is a shear modulus of the rubber material.   The vulcanization physical property simulation method according to any one of claims 1 to 3, wherein the second numerical analysis model is common to the first numerical analysis model.