JP2017186178A - Deformation predicting method in producing sanitary ware - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a deformation predicting method in producing sanitary ware, capable of accurately predicting deformation in a drying step and a firing step.SOLUTION: A deformation predicting method in producing sanitary ware produced through a drying step and a firing step includes: performing in deformation prediction in the drying step, a first test for acquiring a relation between a time course and a shrinkage amount using a test piece, a second test for obtaining a degree of elasticity of every moisture content of the test piece, and a third test for obtaining a creep in every moisture content of the test piece; performing simulation using a heat conduction analysis, on the basis of the results of the first test, the second test, and the third test, so as to obtain a relation between a moisture change and a shrinkage ratio of non-machine strain; performing simulation so as to obtain a relation between a moisture change and creep deformation and elastic deformation of non-machine strain due to a visco-plastic material; and obtaining changes over time of dry shrinkage/deformation, considering a physical property change based on a moisture change from the simulation results so as to specify the shape when the drying step is completed.SELECTED DRAWING: Figure 9

Description

  The present invention relates to a deformation prediction method at the time of manufacturing sanitary ware.

  Conventionally, sanitary ware such as urinals, urinals, wash basins, hand-washers, etc. are cast and molded using a gypsum mold or a resin mold, and then molded into a predetermined shape. It is manufactured through a drying process for evaporating water inside the product at ℃ and a firing process for sintering the product at several hundreds of ℃.

  Here, in the drying process (drying process), about 3% shrinkage deformation occurs due to evaporation of moisture inside the product, and in the firing process (baking process), about 10% shrinkage deformation occurs due to rapid densification due to heating. . Further, in these drying and firing processes, creep deformation also occurs due to the weight of the product.

  As described above, sanitary ware has a complicated deformation at the time of manufacture, and it is difficult to capture an accurate shape after the product is completed. For this reason, conventionally, for example, a drying process is performed so that deformation is predicted by relying on the skill of a skilled engineer based on experience, etc., so that a desired product shape is obtained after completion, and cracks and other defects do not occur. The product shape is adjusted before the firing process.

  On the other hand, a general structural analysis program such as the finite element method is used based on this by conducting experiments on sanitary ware bases in advance to obtain deformation characteristics for each predetermined time segment in each step of the drying process and firing process. A technique for predicting the deformation that occurs by performing a simulation for each time segment using the method has been proposed and put into practical use (see, for example, Patent Document 1).

JP 2002-187863 A

  However, in the conventional method for predicting deformation at the time of manufacturing sanitary ware, as shown in FIG. 18, the prediction is performed based on the deformation characteristics obtained for each predetermined time segment in each process of the drying process and the firing process. I have to. For this reason, in the drying process, the drying speed varies depending on the part of the product, but such inhomogeneous material property change is not taken into consideration. In the firing process, changes in material properties that change with density change rate and temperature are not considered at all.

  Thereby, even if the deformation | transformation prediction method at the time of manufacture of the conventional sanitary ware is used, the deformation | transformation prediction of the product in a drying process and a baking process cannot be performed with sufficient precision. In addition, it is impossible to perform stress evaluation for predicting crack generation using this prediction method.

  An object of this invention is to provide the deformation | transformation prediction method at the time of manufacture of the sanitary ware which makes it possible to predict the deformation | transformation in a drying process or a baking process with sufficient precision in view of the said situation.

  In order to achieve the above object, the present invention provides the following means.

  The method for predicting deformation at the time of manufacturing sanitary ware according to the present invention is a method for predicting deformation at the time of manufacturing sanitary ware manufactured through a drying process and a firing process. The first test to obtain the relationship between the passage of time and the amount of shrinkage using the test specimens, the second test to obtain the elastic modulus for each moisture content of the sanitary ware raw material test specimen, and the sanitary ware raw material test specimen A third test for obtaining a creep for each moisture content is performed, and based on the results of the first test, the second test, and the third test, a simulation using a heat conduction analysis is performed to determine moisture change and non-mechanical strain. In addition to determining the relationship between the shrinkage rate and the simulation, the relationship between the moisture change and the creep and elastic deformation of non-mechanical strain due to the viscoplastic material is determined, and the physical property change based on the moisture change is considered from these simulation results. Seeking the drying shrinkage-aging deformation, characterized in that so as to identify the shape of the drying process is complete.

  Moreover, in the deformation | transformation prediction method at the time of manufacture of the sanitary ware of this invention, the elastic characteristic depending on the moisture content at the time of a drying process can be identified using the following formula | equation (1) from the result of the said 2nd test. desirable.

Here, the equation (1) is a moisture concentration-dependent elastic modulus constitutive law, E (γ _m ) is a moisture content-dependent elastic modulus, γ _m is a water concentration, and H _E , W _E , and E _C are coefficients. .

  Furthermore, in the deformation prediction method at the time of manufacture of the sanitary ware of the present invention, the creep characteristic depending on the moisture concentration is obtained from the result of the third test using the following formula (2), and the identification analysis is performed to obtain the formula. It is desirable to identify the coefficient of (2).

Here, γ _m is moisture concentration, Δγ is creep strain, σ _eq is von Mises equivalent stress, t is time, C ₁ , C ₂ , C ₃ , XA, f _c , W _c , and γ _c are coefficients. is there.

  In the method for predicting deformation during the manufacture of sanitary ware according to the present invention, in the deformation prediction for the firing process, the behavior in the firing process of the raw material after the drying process is represented by elastic deformation, creep deformation, thermal expansion / contraction deformation, and sintering phenomenon. It is divided into four deformation factors of deformation accompanying the above, and the relationship between the time and temperature of each deformation factor and the density change of the raw material is obtained by a test, a simulation is performed based on the test result, and the density change of the raw material is considered. The change with time of deformation was obtained, and the shape when the firing process was completed was specified.

Furthermore, in the method for predicting deformation at the time of manufacturing sanitary ware according to the present invention, the time evolution of the creep deformation rate is expressed as follows using the creep multiplier γ (above) ^vp and the flow vector N = s / || s || The creep multiplier was obtained using the following equation (4) in consideration of the dependence of the equivalent stress σ _eq , time t, temperature T, and relative density ρ _rel .

Where d ^vp is the creep deformation rate tensor, s is the deviation stress, δh is the displacement, C ₁ , C ₂ , C ₃ , C ₄ , T ₀ , W are the creep parameters (coefficients), and T ₀ is the creep deformation. It is the reference temperature that begins to occur.

  In the deformation prediction method at the time of manufacturing the sanitary ware according to the present invention, the coefficient is identified based on the first test, the second test, and the third test in the drying process, and the deformation is predicted. It is possible to perform deformation prediction.

  Moreover, in the deformation | transformation prediction method at the time of manufacture of the sanitary ware of this invention, the whole behavior of material (raw material) is made into four factors, elasticity, creep, thermal expansion (contraction), and a sintering phenomenon in a baking process. It is possible to perform very good deformation prediction by performing the deformation prediction considering the decomposition.

In the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning one Embodiment of this invention, it is a figure which shows the 1st test performed for the deformation | transformation prediction by a drying process. In the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning one Embodiment of this invention, it is a figure which shows the 2nd test performed for the deformation | transformation prediction by a drying process. In the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning one Embodiment of this invention, it is a figure which shows the result of the 2nd test performed for the deformation | transformation prediction by a drying process. In the deformation prediction method at the time of manufacture of sanitary ware according to an embodiment of the present invention, the relationship between elastic modulus and water content (an example of a characteristic curve) obtained from the result of the second test performed for deformation prediction by the drying process is as follows. FIG. In the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning one Embodiment of this invention, it is a figure which shows the 3rd test performed for the deformation | transformation prediction by a drying process. In the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning one Embodiment of this invention, it is a figure which shows the relationship between the time obtained from the result of the 3rd test performed for the deformation | transformation prediction by a drying process, and a deformation | transformation amount, and an identification analysis result. is there. In the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning one Embodiment of this invention, it is a figure which shows the analysis model of the simulation (unsteady heat transfer analysis) using heat conduction analysis. In the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning one Embodiment of this invention, it is a figure which shows the analysis model of the simulation (unsteady static analysis) using the deformation | transformation analysis according to moisture concentration. It is a figure which shows an example of the deformation | transformation prediction result by the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning one Embodiment of this invention. It is a figure which shows the dimension measurement location of the experiment conducted in order to confirm the predominance of the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning one Embodiment of this invention. It is a figure which shows the experimental result performed in order to confirm the predominance of the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning one Embodiment of this invention, and is the figure which compared the measurement dimension and prediction result of an actual machine. It is a figure which shows the change of the temperature and the relative density with respect to time in the baking process of the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning one Embodiment of this invention. In the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning one Embodiment of this invention, it is a figure which shows the heat curve of the baking process, and the obtained amount of axial displacement. In the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning one Embodiment of this invention, it is a figure which shows the relationship between the densification speed | rate of a sintered area, and a relative density. In the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning one Embodiment of this invention, it is a figure which shows the relationship between the ultimate relative density in a baking process, and the preset temperature in each isothermal process. In [[rho] [ ^infinity] (T)-[rho] _rel ([delta] h)] and ln [| [epsilon] (above) s (T, T) in the sintering step of the deformation prediction method during the manufacture of sanitary ware according to an embodiment of the present invention. It is a figure which shows the relationship of (delta h) |]. It is a figure which shows the relationship of (omega) (T) / 3 and n (T) in the sintering process of the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning one Embodiment of this invention. It is a figure which shows the deformation | transformation prediction method at the time of manufacture of the conventional sanitary ware.

  Hereinafter, with reference to FIG. 1 to FIG. 17, a deformation prediction method at the time of manufacturing a sanitary ware according to an embodiment of the present invention will be described.

  First, sanitary ware (ceramic ceramic products) such as urinals, urinals, wash basins, hand-washers, etc., is formed by forming slurry (raw material) as a raw material into a predetermined shape using a plaster mold or a resin mold. Manufactured through a drying process for evaporating the water inside the product at a temperature of from 110 ° C. to 110 ° C. and a baking process for sintering the product at a few hundreds of degrees C.

  In this drying process, about 3% shrinkage deformation occurs due to evaporation of moisture inside the product, and in the baking process, about 10% shrinkage deformation occurs due to rapid densification by heating. Further, in these drying and firing processes, creep deformation also occurs due to the weight of the product. For this reason, there are many cases in which a product having a desired shape cannot be manufactured with high accuracy by shrinkage deformation or creep deformation even if it is molded into a predetermined shape using a mold.

  The method for predicting deformation at the time of manufacturing sanitary ware according to the present embodiment accurately predicts deformation of the pottery product in such a drying process and firing process, and as a result, the desired product without causing defects such as cracks. It relates to a method for making it possible to produce a finished product of shape.

  Specifically, in the deformation prediction method at the time of manufacturing sanitary ware according to the present embodiment, the deformation behavior in the drying process and the firing process in the manufacturing process of sanitary ware is clarified and prediction is performed using CAE (finite element method). .

And the deformation | transformation prediction method at the time of manufacture of the sanitary ware of this embodiment is utilized as follows.
First, mold design is performed, deformation prediction in the drying process and firing process is performed by the deformation prediction method at the time of manufacturing the sanitary ware of the present embodiment using CAE, the mold is corrected based on this prediction, and the corrected mold Is used to manufacture products. As a result, even if deformation occurs in the drying process and the firing process, since the deformation is taken into account, a finished product of a sanitary ware having a desired shape with high accuracy and no defects such as cracks is preferable. Can be manufactured.

<Prediction of deformation during drying process>
More specifically, the deformation prediction method during the drying process will be described.

  In the present embodiment, a slurry (raw material) obtained by mixing raw materials, moisture, and a peptizer (dispersant) is formed into a predetermined shape using a mold and dried in a drying step.

  And in the deformation | transformation prediction method at the time of manufacture of the sanitary ware of this embodiment, in the drying process in which the water | moisture content of this slurry evaporates and decreases, 1) The shrinkage | contraction by a water content (moisture content) reduction | decrease, 2) It depends on a water content Experiments (first test, second test, third test) are performed in advance on the three phenomena of creep that depend on the amount of moisture and 3) moisture content, and data of material characteristics of each phenomenon is acquired.

[Experiment on shrinkage due to water content (water content) reduction: first test]
In this embodiment, 1) In the measurement of the shrinkage rate due to the decrease in the amount of water, the relationship between the passage of time and the amount of shrinkage in the longitudinal direction and the relationship between passage of time and mass are obtained. For example, as shown in FIG. 1, using a test body 10 having a rectangular parallelepiped of 100 × 10 × 10 mm and an initial moisture content of about 18%, the displacement of both ends of the test body 10 is measured with the laser sensor 1 over time, The mass change of the test body 10 is measured with the electronic balance 2 over time.

In this embodiment, equation (5) indicating the water vapor diffusion rate is linearly approximated as equation (6) from the experimental result, and A and B are identified from the experimental result. Thus, by linearly approximating Equation (5) as Equation (6), it is possible to prevent the surface diffusivity D from divergence to ∞ due to the decrease in the moisture concentration C.
Q is the water vapor diffusion rate (g / sec · mm ² ), C is the water concentration (g / mm ³ ), C∞ is the equilibrium water concentration (g / mm ³ ), and D _surf is the surface diffusivity (mm / sec). ).

  For example, A and B can be identified from the experimental results such as A = −5.3282E−1, B = 2.8287E-4, and the like.

  Thereby, the shrinkage rate dependent on the amount of water can be obtained from the change in the amount of water and the shrinkage rate. In other words, the constituent side of the shrinkage deformation can be obtained from the coefficient of thermal expansion with respect to the change in the temperature degree of the specimen as the shrinkage ratio with respect to the moisture concentration. In addition, the evaporation speed from the surface can be obtained by changing the moisture amount with time.

[Experiment on elasticity depending on moisture content: second test]
Next, in this embodiment, 2) the measurement of the moisture amount-dependent elastic modulus is performed using, for example, a rectangular parallelepiped test body 10 of 115 × 15 × 10 mm. Here, four specimens 10 having a moisture content of 19.5%, 18.9%, 17.6%, and 15.8% were used.

For example, as shown in FIG. 2, a test is performed using a three-point bending test apparatus 3 that applies a load to the center while supporting the test body 10 with a span of 100 mm, and the elastic modulus is measured. In the three-point bending test, the center of the test body 10 is pushed by the load cell 4 at a pushing speed of 1.5 mm / min, and the relationship between the center vertical direction displacement and the load is measured.
That is, a creep test for each moisture content is performed using the three-point bending test apparatus 3.

Then, the elastic modulus is obtained from the test results as shown in FIG. 3 (from the inclination at the initial stage of deformation), and the water content is calculated using the equation (7), which is an equation of the water content-dependent elastic modulus (E (γ _m )). The dependent elastic properties are identified (see FIG. 4). Expression (7) is a constitutive law of elastic modulus depending on the water concentration, γ _m is the water concentration (g / mm ³ ), and H _E , W _E , and E _C are coefficients.

  Thereby, for example, as shown in FIG. 4, the relationship (characteristic curve) between the elastic modulus and the moisture content can be obtained.

[Experiment on creep depending on moisture content: Third test]
In the present embodiment, 3) the measurement of moisture content-dependent creep characteristics is performed using, for example, a rectangular parallelepiped test body 10 of 221 × 33.5 × 6.5 mm. In addition, four specimens having a moisture content of 17.3%, 14.6%, 11.7%, and 9.1% were used here. Further, in the measurement of the moisture content-dependent creep characteristics, for example, as shown in FIG. 5, the center time history vertical displacement is measured by the laser sensor 5 while supporting the test body 10 with a span of 180 mm.

And in the deformation | transformation prediction method at the time of manufacture of the sanitary ware of this embodiment, said test result is applied to Formula (8), and an elastic modulus and a moisture concentration dependence creep characteristic are calculated | required using this Formula (8).
In equation (8), Δγ is creep strain, σ _eq is equivalent stress, and t is time. C ₁ , C ₂ , C ₃ , XA, f _c , W _c , and γ _c are coefficients. Also, equation (8) is a constitutive equation using a hyperbolic function based on Norton's law in order to express that the characteristic changes suddenly at a certain moisture concentration as in the case of the elastic modulus described above. Yes.

  Then, as shown in FIG. 6, identification analysis by DE (Differential Evolution) is performed on the test results of each moisture content, the identification analysis is turned to minimize errors, and each of the equations (8) of the creep evolution law Identify coefficients.

  In the method for predicting deformation during the manufacture of sanitary ware according to the present embodiment, based on the results of the first test, the second test, and the third test, first, as shown in FIG. At the same time, a simulation using heat conduction analysis (unsteady heat transfer analysis) is performed to express the water evaporation speed from the surface during the drying process of the product in terms of heat conductivity, and the change rate of moisture change and non-mechanical strain Seeking a relationship.

  In addition, as shown in FIG. 8, a simulation (unsteady static analysis) using a deformation analysis according to the moisture concentration is performed, and the water deformation during the product drying process and the non-mechanical strain creep deformation due to the viscoplastic material. And the relationship of elastic deformation.

  Based on these simulation results, as shown in FIG. 9, the time during the drying process based on the results of the first test, the second test, and the third test, which is the sum of shrinkage deformation, elastic deformation, and creep deformation due to a decrease in the amount of water, The total deformation can be obtained. That is, it is possible to obtain a change with time in drying shrinkage / deformation in consideration of a change in physical properties based on a change in moisture, and it becomes possible to accurately identify / predict the shape when the drying process is completed.

  Here, the deformation | transformation prediction of the flush toilet is performed using the deformation | transformation prediction method at the time of manufacture of the sanitary ware of this embodiment, and the result of having compared with the actual machine is demonstrated.

  First, the dimension measurement location of the flush toilet (sanitary ware / raw material) of the product is shown in FIG.

  And FIG. 11 is the result of having compared the deformation | transformation prediction method at the time of manufacture of the sanitary ware of this embodiment in each measurement location, and the measurement result of an actual machine, From this result, the deformation | transformation at the time of manufacture of the sanitary ware of this embodiment is carried out. As a result of the prediction using the prediction method, it was confirmed that the average measurement error at the seven measurement points was about 0.74% with respect to the actual machine.

  Therefore, according to the deformation prediction method at the time of manufacturing the sanitary ware of the present embodiment, the coefficient is identified based on the first test, the second test, and the third test as described above in the drying process, and the deformation prediction is performed. This makes it possible to perform excellent deformation prediction with high accuracy.

<Deformation prediction during firing process>
Next, a deformation prediction method during the firing process of the present embodiment will be described.

  In the baking process, the product after the drying process is further contracted by about 10% due to rapid densification by heating. Further, since the creep deformation due to the weight of the product is large, not only the deformation prediction is further complicated, but also a defect such as a crack may occur locally due to the residual stress inside the product.

  On the other hand, in this embodiment, the deformation of the product in the baking process is numerically predicted. At this time, the material constitutive law capable of reproducing the material characteristics in the material firing step and the identification method of the parameters were established and predicted.

  Specifically, a constitutive law capable of predicting deformation in the firing process is constructed in substantially the same manner as the drying process.

  First, rapid shrinkage deformation in the sintering zone is treated as non-mechanical linear using the densification rate equation, and the creep constitutive law is formulated in the framework of finite deformation theory. Then, an STC test (Stairway Thermal Cycle test) is performed to identify material parameters related to sintering strain.

  Next, as for the elastic properties of the material, a three-point bending test of a specimen that has not been performed conventionally is performed in the firing process, and the temperature-dependent elastic properties are determined from the tangents of the obtained stress-strain curves in each temperature range. .

  Furthermore, thermal expansion / contraction characteristics and creep characteristics are tested separately, and the material parameters are determined (identified parameters) using an optimization method based on metaheuristics.

[Mechanical phenomena in the firing process]
Here, a mechanical phenomenon in the firing process will be described.

  First, FIG. 12 shows changes in temperature and relative density with respect to time in the firing step. The relative density is a dimensionless quantity used as an alternative index of density obtained by dividing the current density by the density at the stage where the firing test is completed.

  At this time, the pottery exhibits different dynamic behaviors in the three regions indicated by the arrows at the top of the figure.

  In the firing start stage, which is the first region R1, thermal expansion deformation of the material occurs as the temperature increases, and the density decreases due to the effect of the volume increase due to expansion deformation.

  In the second region R2, the high temperature state of the sintered region is reached, and rapid shrinkage deformation of the material occurs. This is a material sintering phenomenon, and rapid densification occurs in this region. At the same time, creep deformation is dominant because it is in a high temperature state in this region, and as a whole, it appears as a much larger deformation than other regions.

  Thereafter, when reaching the third region R3, the sintering is completed, and heat shrinkage deformation occurs as the temperature decreases, so that the density gradually increases.

  The inventors of the present application have found that the overall behavior of the material (raw material) in such a firing process is considered to be decomposed into four factors of elasticity, creep, thermal expansion (shrinkage), and sintering phenomenon. It was. That is, the main deformation factors in the firing process of the ceramic material are rapid shrinkage deformation characteristics and creep deformation characteristics with respect to temperature increase, and these factors have strong dependence on time, temperature and density change. Based on this, it was thought that deformation prediction in the firing process could be performed.

[Setting kinematic variables]
In order to realize this, first, in this embodiment, kinematic variables are set.
The total deformation gradient F is multiplied and decomposed as in the following equation (9). F ^mi is a non-mechanical deformation gradient, and F ^m is a mechanical deformation gradient.

It is assumed that F ^im develops as isotropic volume expansion and is defined as in equation (10). ε ^t and ε ^s are thermal expansion strain and sintering strain, respectively.

Next, to describe the development of mechanical deformation, the addition degrades the elastic deformation rate tensor d ^e and creep deformation rate tensor d ^vp mechanical deformation rate tensor d _m of Equation (11).

[Relative density]
Next, the material behavior in the firing process strongly depends on the density change. For this reason, in this embodiment, on the premise that a thermomechanical analysis (thermomechanical analysis not conventionally used: hereinafter referred to as TMA) is performed on a sample having a measurement direction length of h, Relative density is introduced to consider density dependence.

With reference to the pre-firing stage defined as mass density, ie, the initial arrangement density ρ _s , the density of the current arrangement, which continuously changes in the firing process, is calculated from the sample length used for TMA by the following equation (12): It expresses like this. Here, J is a Jacobian, and is calculated by the following equation (13) using the pre-test specimen length h _s and the displacement δh, assuming isotropic deformation in the firing step.

  Then, when the equation (13) is substituted into the equation (12), the density is given by the following equation (14) as a function of the displacement amount.

In general, when considering the influence of density on the material constitutive law, a dimensionless quantity such as strain is desirable, and therefore a relative density ρ _rel defined by the following equation (15) is introduced. ρ _f is the density after firing, and is calculated by the following equation (16) with respect to the length h _f of the sample in the room temperature environment after the end of the test.

  Since the relative density depends on the dimensional change in the measurement axis direction of the sample as shown in Equation (15), it changes while being indirectly influenced by the temperature history (or heat curve) and its speed. Therefore, it is necessary to calculate the relative density every time when data of different heat curves and temperature rising rates are used. The relative density is always 100% after the test is completed.

[Non-mechanical deformation]
It is assumed that the proportional relationship shown in the following equation (17) holds between the thermal expansion strain, which is non-mechanical deformation, and the rate of change in sintering time. Here, α _T is a thermal expansion coefficient. Further, assuming that the thermal expansion amount is different between the thermal expansion region and the thermal contraction region, different thermal expansion coefficients are used.

Next, the time change rate of the sintering strain is expressed by the following equation (18) using the densification rate ρ (upward) / ρ which means the relative time change rate of the density. Here, the negative sign in equation (18) means that the sintering strain is calculated as the shrinkage with respect to the density increase. For this densification rate, the following relational expression (19) is used. ρ ^∞ _rel (T) is an ultimate relative density which is a relative density when the material finally settles in an isothermal environment at a certain temperature T, and Ω (T) and n (T) are temperature-dependent material parameters.

  By substituting equation (19) into equation (18), the final development law at the time of sintering strain becomes the following equation (20).

  In this embodiment, since the sintering deformation is an amount that develops only in the sintering region and is dominant with respect to the thermal expansion deformation, only the development of the sintering strain is considered in the sintering region, and the thermal expansion is considered. In the region and heat shrinkage region, only the thermal expansion strain development was considered.

[Mechanical deformation]
Next, the mechanical deformation, stress rate sigma to elastic deformation rate tensor d ^e (above ▽) = sigma Equation nitrous elastic constitutive law with -wσ + σw (· above) (21) is used.

  Here, in the firing process, isotropic elastic deformation is assumed, but in order to take into account that the stiffness changes depending on the temperature, temperature dependence is imparted to the Young's modulus. However, the Poisson's ratio is given as a constant.

  On the other hand, the time evolution of the creep deformation rate is assumed to follow the flow law of the following equation (22) using the creep multiplier γ (upper) vp and the flow vector N = s / || s ||.

Where s is the deviation stress. Similarly to the drying step, Norton's law that can express the initial and steady creep phenomenon generally used for metal materials is adopted for this creep multiplier, and von-Miss equivalent stress σ _eq = √ ( 3/2 × s: s: s), time t, temperature T, and the following equation (23) that takes into account all the dependencies of relative density ρ _rel are used.

Here, C ₁ , C ₂ , C ₃ , C ₄ , T ₀ , and W are creep parameters (coefficients), respectively. A hyperbolic tangent function was used as the temperature term in consideration of the fact that creep progresses predominantly in a high temperature range after the reference temperature T ₀ where creep deformation starts to occur. Moreover, the relative density term of Arrhenius rule was diverted to the relative density term.

[Identification of material parameters for non-mechanical deformation]
Next, identification of material parameters relating to non-mechanical deformation will be described.

[Time evolution of sintering strain]
Parameters related to the time evolution law of the sintering strain were identified from the STC test (special firing test).

  The STC test method changes the temperature stepwise while maintaining an isothermal state at regular intervals in the sintering zone. In such a firing test, the effects of an instantaneous isothermal state of the material and a temperature increase are alleviated as compared with the case where a linear temperature change is set. For this reason, unique temperature perturbations inside the material are difficult to be reflected in the measurement, accurate density changes during sintering can be measured, and there is little information to identify the functional form of the time evolution law of sintering strain There is an advantage that it can be done.

  And in this embodiment, after shaping | molding and drying BC slurry using a gypsum mold, the test body 10 whose dimensions are 20 mm in height x 4.5 mm in length x 4.5 mm in width is produced, and on the upper surface of the test body 10 An STC test was performed using a TMA test apparatus while applying a load of 98 N.

FIG. 13 shows the heat curve and the obtained axial displacement.
After linearly heating at about 94 min up to a temperature level of 900 deg in the sintering zone, a TMA test was performed with an isothermal zone of 10 min every 30 deg from temperature 900 deg as shown in the figure. The amount of axial displacement in the height direction of the specimen obtained in this way is indicated by a broken line in the figure.

  Thereafter, the parameter of the densification rate is determined using this.

  First, in order to calculate the densification rate from the axial displacement of the specimen obtained from this firing test, it is assumed that the sintering strain rate is equivalent to the time change rate of the axial strain εz of the specimen. It is set as Formula (24). The axial strain is defined by the logarithmic strain of the following equation (25).

  Then, if εz at the time for each time increment Δt is determined from this equation (25) and FIG. 13 and ε (up) s = ε (up) ・ z is calculated from the forward difference, equation (18) The densification rate at each time is calculated from Equation (26).

  FIG. 14 shows the relationship between the densification rate of the sintered area calculated in this way and the relative density.

  From FIG. 14 obtained in this way, it can be confirmed that the densification rate is decreasing in each isothermal step. In the present embodiment, each decrease curve is stretched in the direction of the relative density axis, and the intersection (see the broken line in FIG. 14), that is, the value of the ultimate relative density in Expression (18) is obtained.

  FIG. 15 shows the relationship between the ultimate relative density thus determined and the set temperature in each isothermal process.

  Due to densification by sintering, it can be seen in FIG. 15 that the ultimate relative density increases rapidly after 1000 deg. When this relation is approximated by a hyperbolic tangent function using the method of least squares, the following equation (27) is obtained. In the formula (27), a, b, c, and d are constants.

  Next, in order to identify the remaining two parameters n (T) and Ω (T) in the equation (18) of the time evolution law of sintering strain, the time of sintering strain is expressed as in the following equation (28). The absolute value and the natural logarithm are taken on both sides of the equation (18) of the evolution law.

Then, using equations (27) and (28) (FIGS. 14 and 15), ln [ρ ^∞ (T) −ρ _rel (δh)] and ln [| ε (above) s in each temperature range. FIG. 16 shows the relationship between (T, δh) |] calculated.

Since Ω (T) / 3 and n (T) in equation (28) are the intercept and slope of this figure, respectively, they are calculated by linearly approximating plots in each temperature range. The obtained n (T) and Ω (T) are shown in FIG. Using this plot point, two function forms were identified as Equation (29) and Equation (30) by the method of least squares.
It should be noted that a, b, c, d, e, f, g, h, i, j, k, l, m, n, p, q, r, u, v in formula (29) and formula (30). , W, x, y, z are constants.

 As a result, all parameters (coefficients) relating to the time evolution law of sintering strain have been identified (can be identified).

[Thermal expansion coefficient]
Next, the thermal expansion coefficient may be identified by numerical analysis using a differential evolution method that is one method of metaheuristics.

  For example, first, CAE (finite element analysis) is performed on each particle having different identification target parameters under the same conditions as in the experiment. An error is calculated by comparing the calculated physical quantity with an experimental value, and a particle that minimizes the error is searched for.

  And about a thermal expansion coefficient, it identifies using the result of the baking test of the test body in a no-load state using a TMA test device.

  Therefore, in the deformation prediction method at the time of manufacturing the sanitary ware according to the present embodiment, the coefficient is identified based on the first test, the second test, and the third test in the drying process, and the deformation is predicted. This makes it possible to perform very good deformation prediction.

  Moreover, in the deformation | transformation prediction method at the time of manufacture of the sanitary ware of this embodiment, four factors of elasticity, creep, thermal expansion (shrinkage), and a sintering phenomenon are considered as the overall behavior of the material (raw material) in the firing process. It is possible to perform very good deformation prediction by performing the deformation prediction considering the above.

  And according to the deformation prediction method at the time of manufacturing the sanitary ware of the present embodiment, for example, when manufacturing a flush toilet, predict deformation according to the skill of a skilled engineer based on experience as in the past, Compared to the case of correction / adjustment, it is possible to shorten the manufacturing period (yield reduction) for a long period of 6 months or more.

  As mentioned above, although one embodiment of the deformation | transformation prediction method at the time of manufacture of the sanitary ware concerning this invention was described, this invention is not limited to said one embodiment, It can change suitably in the range which does not deviate from the meaning. It is.

DESCRIPTION OF SYMBOLS 1 Laser sensor 2 Electronic scale 3 Three-point bending test apparatus 4 Load cell 5 Laser sensor 10 Test body

Claims (5)

A method for predicting deformation during the manufacture of sanitary ware manufactured through a drying process and a firing process,
In the deformation prediction for the drying process, the first test for obtaining the relationship between the passage of time and the shrinkage amount using the sanitary ware raw material specimen, and the second for obtaining the elastic modulus for each moisture content of the sanitary ware raw material specimen. The test and the third test to find the creep for each moisture content of the sanitary ware raw material specimen,
Based on the results of the first test, the second test, and the third test, a simulation using heat conduction analysis is performed to obtain the relationship between the moisture change and the non-mechanical strain shrinkage rate, and the simulation is performed to determine the moisture content. The relationship between the change and the creep deformation and elastic deformation of non-mechanical strain due to the viscoplastic material is obtained. A method for predicting deformation during the manufacture of sanitary ware characterized by being specified. In the deformation prediction method at the time of manufacture of the sanitary ware according to claim 1,
A method for predicting deformation during the manufacture of sanitary ware, wherein elastic properties depending on the amount of water during the drying process are identified from the results of the second test using the following formula (1).
Here, the equation (1) is a moisture concentration-dependent elastic modulus constitutive law, E (γ _m ) is a moisture content-dependent elastic modulus, γ _m is a water concentration, and H _E , W _E , and E _C are coefficients. . In the deformation | transformation prediction method at the time of manufacture of the sanitary ware of Claim 1 or Claim 2,
From the results of the third test, the creep characteristics depending on the moisture concentration are obtained using the following formula (2), and the deformation prediction method at the time of manufacturing sanitary ware is performed by performing identification analysis to identify the coefficient of formula (2) .
Here, γ _m is moisture concentration, Δγ is creep strain, σ _eq is von Mises equivalent stress, t is time, C ₁ , C ₂ , C ₃ , XA, f _c , W _c , and γ _c are coefficients. is there. In the deformation prediction method at the time of manufacture of sanitary ware according to any one of claims 1 to 3,
In the deformation prediction for the firing process, the behavior of the raw material after the drying process in the firing process is divided into four deformation factors: elastic deformation, creep deformation, thermal expansion / contraction deformation, and deformation accompanying the sintering phenomenon. The relationship between the time, temperature, and density change of the raw material is obtained by testing, and simulation is performed based on the test result, the change with time of deformation considering the density change of the raw material is obtained, and the shape at the completion of the firing process is specified. A method for predicting deformation during the manufacture of sanitary ware characterized by the above. In the deformation | transformation prediction method at the time of manufacture of the sanitary ware of Claim 4,
The time evolution of the creep deformation rate is obtained in accordance with the flow law of the following equation (3) using the creep multiplier γ (upper) ^vp and the flow vector N = s / || s ||. A deformation prediction method at the time of manufacturing sanitary ware, which is obtained by using the following formula (4) in consideration of the dependence of σ _eq , time t, temperature T, and relative density ρ _rel .
Where d ^vp is the creep deformation rate tensor, s is the deviation stress, δh is the displacement, C ₁ , C ₂ , C ₃ , C ₄ , T ₀ , W are the creep parameters (coefficients), and T ₀ is the creep deformation. It is the reference temperature that begins to occur.