JP7516990B2 - Physical quantity estimation device, physical quantity estimation method, physical quantity estimation program, and recording medium - Google Patents

Description

The present invention relates to a physical quantity estimation technology, for example, a technology that is effective when applied to a physical quantity estimation device that estimates physical quantities related to a material being mixed in a mixer.

JP 2016-49739 A (Patent Document 1) describes technology related to a simulation method that can evaluate the kneading state of a viscous liquid.

JP 11-77666 A (Patent Document 2) describes a technique for controlling mixing in a mixer.

JP 2016-49739 A Japanese Patent Application Publication No. 11-77666

Viscous flowable materials (viscous fluids) such as rubber and resin before vulcanization are mixed with various additives and compounding materials, for example, by a Banbury mixer or kneading machine, to produce the desired material (kneaded product). In the process of producing such kneaded products, it is important to mix the viscous fluid and various materials uniformly in a short time, and the rotor of the kneading machine is selected and the kneading conditions are considered so that the viscous fluid and various materials can be mixed uniformly in a short time. The selection of the rotor and the consideration of the kneading conditions require repeated prototyping and evaluation of the kneading machine, which takes a lot of time and increases the manufacturing cost. For this reason, in recent years, a method has been proposed in which the kneading behavior of the kneaded product is predicted by computer-based simulation before prototyping and evaluation are carried out.

However, performing detailed analysis using computer simulation requires many calculation points and a large number of calculations, and due to the calculation costs, long-term analyses corresponding to actual mixing times have not been performed at present.

In particular, physical quantities such as the temperature and viscosity of the mixture during the kneading process are important in understanding the state of kneading of the mixture, and estimating these physical quantities after the actual kneading time has elapsed is extremely useful in considering the kneading conditions.

The object of the present invention is to provide a technology that can estimate physical quantities related to the material being mixed in a mixer up until the end of the mixing time without incurring significant calculation costs.

The physical quantity estimation device in one embodiment is configured to estimate a physical quantity based on a relational expression that represents the time evolution of a physical quantity related to a material mixed in a mixer, the relational expression including parameters related to the mixer tank or the material. Here, the physical quantity estimation device includes a parameter determination unit configured to determine the value of the parameter based on experimental data related to the physical quantity from the first time to the second time, and a physical quantity estimation unit configured to estimate the physical quantity at a time after the second time from the time evolution of the physical quantity represented by the relational expression into which the parameter value determined by the parameter determination unit is substituted.

In one embodiment, the physical quantity estimation method estimates a physical quantity based on a relational expression that represents the time evolution of a physical quantity related to a material mixed in a mixer, the relational expression including a parameter related to the mixing tank of the mixer or the material. Here, the physical quantity estimation method includes a parameter determination step of determining a parameter value based on experimental data related to the physical quantity from a first time to a second time, and a physical quantity estimation step of estimating a physical quantity at a time after the second time from the time evolution of the physical quantity represented by the relational expression into which the parameter value determined in the parameter determination step is substituted.

The physical quantity estimation program in one embodiment is a program for causing a computer to execute a process of estimating a physical quantity based on a relational equation that represents the time evolution of a physical quantity related to a material mixed in a mixer and includes parameters related to the mixer tank or the material. Here, the physical quantity estimation program includes a parameter determination process that determines the value of a parameter based on experimental data related to the physical quantity from a first time to a second time, and a physical quantity estimation process that estimates a physical quantity at a time after the second time from the time evolution of the physical quantity represented by the relational equation into which the parameter value determined in the parameter determination process is substituted.

This physical quantity estimation program is recorded on a computer-readable recording medium.

According to one embodiment, it is possible to estimate physical quantities related to the material being mixed in the mixer over a long period of time until the end of the mixing time without incurring significant calculation costs. As a result, according to one embodiment, it is possible to estimate the mixing conditions before prototyping the mixer.

FIG. 2 is a diagram showing a schematic configuration of a kneader. 1 is experimental data showing the relationship between the temperature of the kneaded material and time. 3 is a graph comparing a time-temperature curve obtained from the experimental data shown in FIG. 2 up to the kneading end time (1500 [s]) with a time-temperature curve obtained from the simulation results in this embodiment. FIG. 2 is a diagram illustrating an example of a hardware configuration of a physical quantity estimation device. FIG. 2 is a functional block diagram showing functions of the physical quantity estimation device. 1 is a flowchart illustrating a physical quantity estimation method. 13 is a flowchart illustrating the method described in <<Further Improvements>>.

In all drawings used to explain the embodiments, the same components are generally given the same reference numerals, and repeated explanations will be omitted. In addition, hatching may be used even in plan views to make the drawings easier to understand.

ROOM FOR IMPROVEMENT
For example, a method has been proposed for evaluating the physical quantities of a kneaded material by simulation using a computer. According to this method, it is possible to estimate the kneading conditions based on the results of the simulation before prototyping and evaluating a kneader. Therefore, the simulation method is useful in that it can save a lot of time that would otherwise be spent on prototyping and evaluating a kneader, and also in that it can reduce manufacturing costs.

In regard to this point, the current mainstream simulations are mixing simulations using particle methods, finite element methods, etc. This simulation has the advantage that by setting calculation points over the entire mixture, physical quantities can be evaluated taking into account the complex flow and variation of the mixture.

However, the more calculation points there are, the higher the cost of calculation. For this reason, it is currently difficult to perform long-term analysis corresponding to the actual kneading time due to the problem of calculation costs. That is, to estimate the kneading conditions, it is important to obtain the physical quantities at the end of the kneading time, but with current simulation technology, it is difficult to perform long-term analysis corresponding to the actual kneading time, and therefore it is not possible to fully evaluate the kneading conditions. In other words, with current simulation technology, there is room for improvement in terms of performing long-term analysis of physical quantities corresponding to the actual kneading time without incurring huge calculation costs.

Therefore, in this embodiment, we have implemented measures to address the room for improvement that exists in current simulation technology. The technical ideas behind these measures are explained below.

<Basic Concept of the Embodiment>
The basic idea of the present embodiment is to determine the parameters included in the relational equation based on experimental data related to the physical quantities from a first time to a second time in a simulation technique for estimating the physical quantities based on the relational equation, which is a relational equation expressing the time evolution of the physical quantities related to the material kneaded by the kneader and includes parameters related to the kneading tank of the kneader or the material, for example. Then, the basic idea is to estimate the physical quantities at times after the second time from the time evolution of the physical quantities represented by the relational equation into which the parameter values determined based on the experimental data are substituted.

In this basic concept, the physical quantities estimated from the time evolution of the physical quantities represented by the relational expressions into which parameter values determined based on experimental data are substituted are average values when viewed from the entire kneaded material. In other words, the simulation technology based on this basic concept cannot evaluate the flow of the kneaded material or the variations in the physical quantities, as in the current simulation technology described above. However, since it calculates only average physical quantities, it is possible to estimate the physical quantities at the end of kneading, which are an important factor in evaluating the kneading conditions, without incurring significant calculation costs. In other words, the basic concept has great technical significance in that it can estimate the physical quantities at the end of kneading, which is difficult to achieve with current simulation technology, without incurring calculation costs.

The following describes how this basic concept is embodied in this embodiment.

In this embodiment, the above-mentioned basic concept is explained using an example of a simulation technique for estimating physical quantities related to a material kneaded in a kneading machine. In particular, an example of estimating the temperature of the material is explained, but the basic concept of this embodiment can be applied not only to physical quantities related to a material kneaded in a kneading machine, but also to simulation techniques for estimating physical quantities for a wide variety of objects.

<Configuration of the kneader>
First, before describing the specific contents of the simulation technique for estimating the temperature of the kneaded material, a schematic configuration of the kneader will be briefly described.

Figure 1 shows a schematic diagram of a kneading machine.

In FIG. 1, the kneader 1 has a kneading tank 10 having a hollow portion 10a. The hollow portion 10a of the kneading tank 10 is provided with two rotatable rotors 11a and 11b. Furthermore, the hollow portion 10a contains a kneaded material 12. This hollow portion 10a is sealed with a top cover 13. The kneaded material 12 placed in the sealed hollow portion 10a is kneaded by the two rotating rotors 11a and 11b. In this way, the kneader 1 can knead the kneaded material 12. The kneaded material 12 kneaded in the kneader 1 is used, for example, as an insulating material (coating material) for covering cables.

For example, the kneaded material 12 used as the insulating material for covering the cable is composed of ethylene-vinyl acetate copolymer (EVA), maleic acid modified polymer, a filler made of magnesium hydroxide, and a cross-linking aid made of trimethylolpropane acrylate (TMPT). That is, in the kneader 1, the ethylene-vinyl acetate copolymer, the maleic acid polymer, the filler, and the cross-linking aid are kneaded to form the kneaded material 12.

It is important to knead this kneaded material 12 uniformly in a short time in order to realize the properties of the insulating material. This creates a need to evaluate the kneading conditions in the kneader 1 that kneads the kneaded material 12. For example, the temperature of the kneaded material 12 is an important physical quantity for understanding the kneading condition of the kneaded material 12, and estimating the temperature of the kneaded material 12 throughout the kneading time is very important in evaluating the kneading conditions. Therefore, the specific details of the simulation technology for estimating the temperature of the kneaded material 12 throughout the kneading time will be described below.

<Specific details of simulation technology>
<<Relationship formula showing the time evolution of the temperature of the kneaded material>>
First, in this embodiment, in order to estimate the temperature of the kneaded material based on a relational equation that represents the time evolution of the temperature of the kneaded material being kneaded in a kneader and that includes parameters related to the kneading tank of the kneader or the kneaded material, the following formula (1) is adopted as the relational equation.

Here, the parameters included in formula (1) are as follows:

ρ: density of the kneaded product [kg/m ³ ]
C _p : specific heat of the kneaded material [J/kg/°C]
h: heat transfer coefficient between the kneaded material and the kneading tank [W/m ² /°C]
S: contact area between the kneaded material and the kneading tank [m ² ]
V: Volume of the kneaded product [m ³ ]
T: Temperature of the kneaded material [°C]
_Tw : Temperature of the wall of the kneading tank [°C]
t: time [s]
η: Viscosity of the kneaded product [Pa s]
dγ/dt: shear rate in the kneading tank [1/s]

Equation (1) is the energy conservation equation for a kneaded material made of a viscous fluid, and is a relational equation that qualitatively has the following content. That is, the left side of equation (1) indicates the change in the amount of heat applied to the kneaded material over time. On the other hand, the first term on the right side of equation (1) indicates the amount of heat flowing into or out of the kneaded material based on the difference between the temperature of the kneaded material and the temperature of the kneading tank. For example, the first term on the right side of equation (1) indicates that when the temperature of the kneaded material is lower than the temperature of the kneading tank, an amount of heat proportional to the temperature difference between the temperature of the kneaded material and the temperature of the kneading tank flows from the kneading tank into the kneaded material. On the other hand, when the temperature of the kneaded material is higher than the temperature of the kneading tank, an amount of heat proportional to the temperature difference between the temperature of the kneaded material and the temperature of the kneading tank flows out from the kneaded material to the kneading tank. Furthermore, when the temperature of the kneaded material and the temperature of the kneading tank are equal, the first term on the right side of equation (1) is "0", so there is no flow of heat between the kneaded material and the kneading tank.

Next, the second term on the right side of formula (1) indicates the amount of heat supplied to the kneaded material by the rotation of the rotor. In other words, the second term on the right side of formula (1) indicates that part of the rotational energy of the rotor becomes heat energy added to the kneaded material as a result of kneading by the rotation of the rotor.

From the above, formula (1) is a relational equation that expresses that the change over time in the amount of heat applied to the kneaded material (left side) is equal to the sum of the transfer of heat based on the difference between the temperature of the kneaded material and the temperature of the kneading tank (first term on the right side) and the thermal energy supplied to the kneaded material based on the rotational energy of the rotor (second term on the right side). Since formula (1) is a differential equation related to the temperature of the kneaded material, it can be seen that it expresses the evolution of the temperature of the kneaded material over time.

<<Calculation of the relationship between viscosity and shear rate>>
Next, the viscosity (η) included in the formula (1) generally depends on the temperature (T) and the shear rate (dγ/dt). For this reason, it is considered to express this viscosity as a relational expression between temperature and shear rate. Here, it is known that the viscosity generally has a relationship shown in the following formula (2) with temperature and shear rate as variables.

Here, "a", "b", and "n" in formula (2) are fitting coefficients.

In the following, in order to calculate the fitting coefficients, in this embodiment, first, the viscosity of the kneaded product is measured. Specifically, the relationship between shear rate and viscosity at multiple temperatures is obtained as plot data. After that, the three fitting coefficients included in formula (2) are calculated by fitting the obtained plot data with the relational expression shown in formula (2). This makes it possible to determine the viscosity characteristics specific to the material of the kneaded product.

<<Substituting Formula (2) into Formula (1)>>
Next, the three fitting coefficients included in the formula (2) are calculated, and the viscosity indicated by the formula (2) in which the three fitting coefficients have been determined is substituted into the formula (1). This results in the following formula (3).

Here, the parameters included in formula (3) are as follows:

α1=hS/ρ/C _p /V
β(T)=a×e ^−bT
α2=(dγ/dt) ⁿ⁺¹ /2/ρ/C _p

This formula (3) is a differential equation related to the temperature of the kneaded material, and represents the time evolution of the temperature of the kneaded material. In this formula (3), the unknown parameters are "parameter α1", "parameter α2", and "temperature of the wall surface of the kneading tank (T _w )". Note that "parameter β(T)" is not an unknown parameter. This is because "a" and "b" included in "parameter β(T)" are fitting coefficients that have already been obtained.

<<Determination of unknown parameters>>
In the following, experimental data is used to determine the unknown parameters.

Figure 2 shows experimental data showing the relationship between the temperature of the kneaded material and time.

For example, after the material is put into the kneader (hollow portion) at 75% of its volume and the rotor rotation speed is set to 30 rpm, kneading of the material is started (first time), and the kneading process is terminated when the temperature of the material measured by the thermocouple reaches 160° C. (second time). At this time, the temperature _Tw of the wall surface of the kneading tank is set to 70° C. Thus, the "temperature ( _Tw ) of the wall surface of the kneading tank" is first determined.

Next, we will explain the method for determining the "parameter α1" and "parameter α2" included in formula (3) based on the experimental data shown in Figure 2.

First, by time integrating Equation (3) from the first time t _i to the second time t _f , the following Equation (4) is obtained.

2, for example, temperature _T0 at time t0 (=0 [s]), temperature _T1 at time t1 (=100 [s]), and temperature _T2 at time _t2 (=480 [s]) are obtained. Then, in formula (4), temperature _T0 at time _t0 (t _i = temperature T0 ₎ and temperature _T1 at time _tf = temperature _T1 are substituted, and approximation is performed by replacing T(t) included in the integrand functions of the first and second terms on the _right -hand side with a constant _T0 .

This gives us the following formula (5):

Similarly, in equation (4), temperature _T1 at time t _i = time t ₁ and temperature _T2 at time t _f = t ₂ are substituted, and an approximation is performed by replacing T(t) included in the integrand functions of the first and second terms on the right-hand side with the constant T ₁ .

This gives us the formula (6) shown below.

In this way, two simultaneous equations (equations (5) and (6)) relating to the unknown parameters "parameter α1" and "parameter α2" can be obtained based on the experimental data shown in Figure 2 and equation (4). As a result, by solving the two simultaneous equations composed of equations (5) and (6), the two unknown parameters "parameter α1" and "parameter α2" can be determined.

In this embodiment, when formula (5) and formula (6) are derived, an approximation is performed in which T(t) included in the integrand function of the first term and the second term on the right side of formula (4) is replaced with a constant _T0 or a constant _T1 . However, the approximation method is not limited to this, and for example, when formula (5) is derived, an approximation can be performed in which T(t) included in the integrand function of the first term and the second term on the right side of formula (4) is replaced with a constant ( _T0 + _T1 )/2. Similarly, for example, when formula (6) is derived, an approximation can be performed in which T(t) included in the integrand function of the first term and the second term on the right side of formula (4) is replaced with a constant ( _T1 + _T2 )/2.

<<Substitution of Determined Parameters into Equation (3)>>
The "temperature of the wall surface of the kneading tank (T _w )" is substituted into the formula (3) together with the "parameter α1" and "parameter α2" calculated as described above. As a result, the time evolution of the temperature of the kneaded material is completely regulated by the formula (3). Therefore, the time dependency of the temperature of the kneaded material is determined based on the formula (3). As a result, if a time is specified, the temperature of the kneaded material at the specified time can be estimated. For example, if the kneading end time is 1500 [s], the temperature of the kneaded material at the kneading end time can be estimated by setting the time to 1500 [s]. In this way, according to the simulation technique in this embodiment, the temperature of the kneaded material can be estimated even at the kneading end time, which is a time later than the second time at which no experimental data is obtained.

The shear rate (dγ/dt) included in "parameter α2" in formula (3) is a parameter determined by the shape of the mixer, the shape of the rotor, the rotor rotation speed, etc., but in this embodiment, "parameter α2" including this shear rate is calculated based on experimental data. Therefore, the mixing conditions represented by the rotor rotation speed are automatically incorporated into "parameter α2". As a result, this embodiment has the advantage of being able to estimate the temperature of the mix while appropriately reflecting the mixing conditions.

<<Verification of simulation results>>
Next, verification of the simulation results in this embodiment will be described.

Figure 3 is a graph comparing the time-temperature curve obtained from the experimental data shown in Figure 2 up to the end of kneading (1500 [s]) with the time-temperature curve obtained from the simulation results of this embodiment. In Figure 3, the solid line shows the experimental data, while the dashed line shows the simulation results of this embodiment.

In FIG. 3, in the experimental data shown by the solid line, the temperature of the kneaded material at the end of kneading is 188.5°C, whereas in the simulation results shown by the dashed line, the temperature of the kneaded material at the end of kneading is 187.2°C. As a result, it can be seen that the simulation in this embodiment proves that the temperature of the kneaded material at the end of kneading can be estimated with an accuracy of less than 1%.

<<Further improvements>>
In the simulation of this embodiment, the unknown parameters are calculated using _the temperature _T0 at time t0 (=0 [s]). In this regard, as shown in Fig. 3, in the experimental data, the temperature of the kneaded material drops immediately after the kneading start time in the vicinity of time _t0 , whereas this phenomenon is not reflected in the simulation of this embodiment.

This is thought to be due to the fact that in an actual mixer, the temperature of the entire mixer tank drops when resin is poured into the mixer, which is already at a high temperature. As a result, the simulation in this embodiment is unable to reflect this phenomenon, and it is presumed that the error with the experimental data becomes large immediately after the start of mixing.

Therefore, the following ideas can be considered to reduce the error between the experimental data and the simulation, and these ideas will be explained below.

Specifically, this ingenuity involves changing the values of times t0, t1, and t2 and repeating the process described above in "<<Determination of unknown parameters>>" until the value of the area enclosed by the temperature-time curve from the first time to the second time determined from the experimental data _and the temperature-time curve from the _first time to the _second time determined from the calculation results of the simulation becomes equal to or less than a predetermined value.

This innovation makes it possible to bring the simulation results closer to the experimental data than a configuration that does not repeat the process described in "<<Determining unknown parameters>>", thereby improving the accuracy of the simulation calculations.

<<Modifications>>
For example, in this embodiment, an example is described in which the "parameter α1" and the "parameter α2" included in the formula (3) are calculated by the method described in "<<Determination of Unknown Parameters>>". However, it is also possible to approximate the formula (3) expressing the time evolution of the temperature of the kneaded material by other methods. Specifically, the formula (3) can be approximated by the following formula (7) obtained by substituting the viscosity expressed by the formula (2) into the formula (1) and discretizing time.

Here, the parameters included in equation (7) are as follows:

A=hS/ρ/ _Cp /V
B=1/2/ρ/C _p ×a×(dγ/dt) ⁿ⁺¹

The "parameter A" and "parameter B" included in formula (7) can be determined by fitting to the experimental data shown in Figure 2. For example, fitting to the experimental data can be performed using the least squares method or regression analysis.

<Features of the embodiment>
Next, features of this embodiment will be described.

The feature of this embodiment is that the parameters included in the formula (1) that represents the time evolution of the temperature of the mixture being mixed in the mixer are determined based on experimental data from the first time to the second time, and then the temperature of the mixture at a time after the second time is estimated using the formula (1) with the determined parameters.

This makes it possible to obtain the first advantage described below. That is, when the parameters are determined based on experimental data, the temperature of the kneaded material estimated based on this formula (1) is the average value when viewed as a whole kneaded material. That is, unlike general simulation techniques using particle methods, finite element methods, etc., the simulation technique according to this embodiment does not perform element analysis, so it is not possible to evaluate the flow of the kneaded material or the variation in physical quantities. On the other hand, according to the characteristic points of this embodiment, since only the average physical quantities are calculated, it is possible to estimate the temperature of the kneaded material at the end of kneading, which is an important factor when evaluating the kneading conditions, without incurring a large calculation cost. That is, according to the characteristic points of this embodiment, it is possible to estimate the temperature of the kneaded material at the end of kneading, which is difficult to achieve with current simulation techniques, without incurring a large calculation cost, and this has a great advantage.

Next, we will explain the second advantage brought about by the features of this embodiment.

For example, when estimating the temperature of a kneaded material by substituting formula (2) into formula (1) which represents the time evolution of the temperature of the kneaded material, seven parameters contained in formula (1) ("ρ", "C _p ", "h", "S", "V", "T _w ", "dγ/dt") and three fitting coefficients contained in formula (2) ("a", "b", "n") must be determined.

In this regard, in the present embodiment, first, Equation (2) showing the relationship between viscosity and shear rate is substituted into Equation (1), and then Equation (1) is transformed to obtain Equation (3). When estimating the temperature of the kneaded material in Equation (3), it is necessary to determine three parameters included in Equation (3) ("parameter α1", "parameter α2", and "T _w ") and three fitting coefficients included in Equation (2) ("a", "b", and "n").

However, the "parameter α1" includes "h", "S", "ρ", " _Cp ", and "V", and the "parameter α2" includes "ρ", "Cp", and "dγ/dt". For this reason, even when estimating the temperature of the kneaded material simply based on the formula (3) in which the parameters are determined, it is basically necessary to determine seven parameters ("ρ", "Cp", "h", "S", "V", "Tw", and "dγ/dt") and three fitting coefficients ("a", "b", and "n"), similarly to the case in which the temperature of the kneaded material is estimated based on the formula (1) in which the parameters are determined.

Here, in the feature of this embodiment, experimental data on the temperature of the kneaded material (partial experimental data from the first time to the second time, not experimental data until the end of kneading) is used when determining the parameters included in the formula (3). This point is important. That is, in this embodiment, the parameters included in the formula (3) are determined so as to match the experimental data on the temperature of the kneaded material. In this case, in order to analyze the time evolution of the temperature of the kneaded material based on the formula (3), it is not necessary to determine each of the seven physically meaningful parameters ("ρ", "Cp", "h", "S", "V", "Tw", and "dγ/dt"), and it is sufficient to determine the "parameter α1" and the "parameter α2", which are combinations of these parameters, from the experimental data on the temperature of the kneaded material. In other words, if the experimental data on the temperature of the kneaded material is used to determine the parameters, in order to estimate the temperature of the kneaded material from the formula (3), it is sufficient to determine only the "parameter α1", the "parameter α2", and the "T _w " included in the formula (3).

Therefore, according to the characteristic feature of this embodiment, the number of parameters to be determined can be reduced, which has the advantage that the temperature of the kneaded material can be easily estimated based on formula (3) without the need to determine all the parameters.

This advantage is particularly useful when parameters that are difficult to determine are included. For example, "h", which indicates the heat transfer coefficient between the kneaded material and the kneading tank, and "dγ/dt", which indicates the shear rate in the kneading tank, are difficult to determine. In this regard, according to the feature of this embodiment, "parameter α1" and "parameter α2", which include "h" and "dγ/dt", which are difficult to determine, are determined based on experimental data. Therefore, when the feature of this embodiment, in which parameters are determined using experimental data, is adopted, it becomes easy to estimate the temperature of the kneaded material based on the time evolution of a relational expression including a parameter that is difficult to determine. Furthermore, since "h" and "dγ/dt", which are difficult to determine, are determined to match the experimental data, values that accurately reflect the actual "h" and "dγ/dt" are automatically adopted. Therefore, according to the feature of this embodiment, not only does it become easy to estimate the temperature of the kneaded material based on a relational expression including parameters that are difficult to determine, but the accuracy of the estimated temperature of the kneaded material can also be improved because the actual "h" and "dγ/dt" are accurately reflected.

In this way, the feature of this embodiment in which parameters are determined using experimental data is particularly effective when applied to a simulation technique that estimates the temperature of a kneaded material based on the time evolution of a relational equation that includes parameters that are difficult to determine.

Next, we will explain the third advantage brought about by the features of this embodiment.

For example, the "parameter α2" in formula (3) includes "dγ/dt", which indicates the shear rate. This "dγ/dt" depends on the rotational speed of the rotor. Therefore, when the "parameter α2" including "dγ/dt" is determined based on experimental data as in this embodiment, the rotational speed of the rotor is automatically reflected.

Therefore, by performing multiple simulations to determine the "parameter α2" based on experimental data when the rotor rotation speed is different, the relationship between the rotor rotation speed and the "parameter α2" including "dγ/dt" can be understood from these multiple simulations. For example, a first simulation is performed to determine the "parameter α2" as a first value based on experimental data when the rotor rotation speed is 30 [rpm] and estimate the temperature of the kneaded material. Then, a second simulation is performed to determine the "parameter α2" as a second value based on experimental data when the rotor rotation speed is 50 [rpm] and estimate the temperature of the kneaded material. Then, a data set of (30 [rpm], first value) and (50 [rpm], second value) can be obtained as a data set of (rotor rotation speed, "parameter α2").

Then, by further performing a simulation to determine "parameter α2" based on experimental data at different rotor rotation speeds, multiple sets of data (rotor rotation speed, "parameter α2") can be obtained. As a result, for example, by performing linear regression on the multiple sets of data obtained (rotor rotation speed, "parameter α2"), it is possible to derive the relationship between the rotor rotation speed and "parameter α2".

In this case, for example, even when the rotor rotation speed is an untested rotation speed, the value of "parameter α2" can be determined from the linearly regressed relationship between the rotor rotation speed and "parameter α2". This means that, according to the feature of this embodiment, by repeating simulations under kneading conditions with different rotor rotation speeds, the value of "parameter α2" can ultimately be determined even when the rotor rotation speed is an untested rotation speed. Therefore, according to this embodiment, it is possible to obtain the advantage that the temperature of the kneaded material can be estimated when the kneaded material is kneaded at an untested rotor rotation speed.

<Physical quantities estimated in the embodiment>
As described above, in the simulation of the present embodiment, the temperature of the kneaded material is listed as a physical quantity to be estimated. However, the technical idea of the present embodiment is not limited to the temperature of the kneaded material, and other physical quantities related to the kneaded material can also be estimated.

For example, the viscosity (η), shear stress (τ), and time integral of shear stress (Σ) of the kneaded material are important in evaluating the kneading conditions, and the simulation in this embodiment can estimate these physical quantities as well as the temperature of the kneaded material.

Specifically, the viscosity (η) of the kneaded product can be calculated based on formula (2).

The shear stress (τ) can be calculated using the following formula (8):

Here, in this embodiment, since the "parameter α2" is determined, if "ρ" and "C _p " are known, then "dγ/dt" included in the formula (8) can be obtained. As a result, it is necessary to actually measure "ρ" and "C _p " or to use literature values, but in the simulation in this embodiment, the shear stress (τ) can also be estimated.

Furthermore, the time integral of the shear stress (Σ) can be calculated using the following formula (9):

As described above, in the simulation of this embodiment, it is possible to estimate the shear stress (τ), and by integrating this shear stress (τ) over time, it is also possible to estimate the time integral of the shear stress (Σ).

<Configuration of the physical quantity estimation device>
<<Hardware configuration>>
First, a hardware configuration of the physical quantity estimating device according to the present embodiment that executes the above-mentioned simulation will be described below.

Figure 4 is a diagram showing an example of the hardware configuration of the physical quantity estimation device 100 in this embodiment. Note that the configuration shown in Figure 4 is merely an example of the hardware configuration of the physical quantity estimation device 100, and the hardware configuration of the physical quantity estimation device 100 is not limited to the configuration shown in Figure 4, and may be other configurations.

In FIG. 4, the physical quantity estimation device 100 in this embodiment includes a CPU (Central Processing Unit) 101 that executes a program. This CPU 101 is electrically connected to, for example, a ROM (Read Only Memory) 102, a RAM (Random Access Memory) 103, and a hard disk drive 112 via a bus 113, and is configured to control these hardware devices.

The CPU 101 is also connected to input devices and output devices via the bus 113. Examples of input devices include the keyboard 105, the mouse 106, the communication board 107, and the scanner 111. Examples of output devices include the display 104, the communication board 107, and the printer 110. The CPU 101 may also be connected to, for example, a removable disk device 108 and a CD/DVD-ROM device 109.

The physical quantity estimation device 100 may be connected to, for example, a network. For example, when the physical quantity estimation device 100 is connected to other external devices via a network, the communication board 107 constituting a part of the physical quantity estimation device 100 is connected to a LAN (local area network), a WAN (wide area network), or the Internet.

The RAM 103 is an example of a volatile memory, and the recording media of the ROM 102, the removable disk device 108, the CD/DVD-ROM device 109, and the hard disk device 112 are examples of non-volatile memory. These volatile and non-volatile memories constitute the storage device of the physical quantity estimation device 100.

The hard disk device 112 stores, for example, an operating system (OS) 201, a group of programs 202, and a group of files 203. The programs included in the group of programs 202 are executed by the CPU 101 using the operating system 201. The RAM 103 also temporarily stores at least some of the programs of the operating system 201 and application programs executed by the CPU 101, as well as various data required for processing by the CPU 101.

The ROM 102 stores a BIOS (Basic Input Output System) program, and the hard disk drive 112 stores a boot program. When the physical quantity estimation device 100 is started, the BIOS program stored in the ROM 102 and the boot program stored in the hard disk drive 112 are executed, and the operating system 201 is started by the BIOS program and the boot program.

The program group 202 stores programs that realize the functions of the physical quantity estimation device 100, and these programs are read and executed by the CPU 101. In addition, the file group 203 stores information, data, signal values, variable values, and parameters indicating the results of processing by the CPU 101 as each item of a file.

The files are stored in a recording medium such as the hard disk drive 112 or memory. The information, data, signal values, variable values, and parameters stored in the recording medium such as the hard disk drive 112 or memory are read by the CPU 101 into the main memory or cache memory, and are used for the operations of the CPU 101, such as extraction, search, reference, comparison, calculation, processing, editing, output, printing, and display. For example, during the above-mentioned operations of the CPU 101, the information, data, signal values, variable values, and parameters are primarily stored in the main memory, registers, cache memory, buffer memory, etc.

The functions of the physical quantity estimation device 100 may be realized by firmware stored in ROM 102, or may be realized by software alone, by hardware alone such as elements, devices, boards, and wiring, a combination of software and hardware, or even a combination with firmware. The firmware and software are stored as programs on a recording medium such as the hard disk drive 112, a removable disk, a CD-ROM, or a DVD-ROM. The programs are read and executed by the CPU 101. In other words, the programs cause the computer to function as the physical quantity estimation device 100.

In this manner, the physical quantity estimation device 100 in this embodiment is a computer that includes a CPU 101 as a processing device, a hard disk drive 112 and memory as storage devices, a keyboard 105, a mouse 106, and a communication board 107 as input devices, and a display 104, a printer 110, and a communication board 107 as output devices. The functions of the physical quantity estimation device 100 are realized by using the processing device, the storage device, the input device, and the output device.

<<Function block configuration>>
Next, a functional block configuration of the physical quantity estimation device 100 will be described.

Figure 5 is a functional block diagram showing the functions of the physical quantity estimation device.

In FIG. 5, the physical quantity estimation device 100 has an input unit 301, a parameter determination unit 302, a physical quantity estimation unit 306, an output unit 307, and a data storage unit 308.

The input unit 301 is configured to input, for example, a relational expression that represents the time development of a physical quantity related to the kneaded material kneaded by the kneader, including a parameter related to the kneading tank of the kneader or the kneaded material. For example, the relational expression can be the energy conservation equation of the kneaded material expressed by the mathematical formula (1) (mathematical formula (3)). The input unit 301 is also configured to input the relational expression between the viscosity and the shear rate expressed by the mathematical formula (2). Furthermore, the input unit 301 is configured to input plot data (measurement data) of the shear rate and the viscosity actually measured at a plurality of temperatures, and is also configured to input experimental data showing the relationship between the time from the first time to the second time and the temperature of the kneaded material. The input unit 301 is also configured to input data related to the temperature of the kneading tank wall surface ("T _w "). The input unit 301 is also configured to input the relational expressions shown in the mathematical formulas (4) to (9).

The relational expressions shown in formulas (1) to (9), the plot data, the experimental data, and the temperature of the wall surface of the kneading tank ("T _w ") input to the input unit 301 are stored in a data storage unit 308. Note that the relational expressions shown in formulas (1) to (9), the plot data, the experimental data, and the temperature of the wall surface of the kneading tank ("T _w ") may be stored in advance in the data storage unit 308.

The parameter determination unit 302 is configured to realize the following two functions. That is, the first function is a function to determine three fitting coefficients ("a", "b", "n") included in the formula (2) based on the plot data stored in the data storage unit 308. The second function is a function to determine the values of two parameters ("parameter α1", "parameter α2") included in the formula (3) based on the experimental data from the first time to the second time stored in the data storage unit 308.

To realize the second function, the parameter determination unit 302 has a fitting unit 303. This fitting unit 303 is configured to determine, by fitting, the "parameter α1" and the "parameter α2" contained in the following formula (3) obtained by substituting the viscosity expressed by formula (2) into formula (1) based on the experimental data stored in the data storage unit 308.

This fitting unit 303 has a temperature calculation unit 304 and a parameter calculation unit 305.

The temperature calculation unit 304 is configured to calculate temperatures _T0 , _T1 , and T2 at times t0, _t1 , and _t2 between the first and _second times from the experimental data stored in the data storage unit ₃₀₈ (see Figure 2).

The parameter calculation unit 305 is configured to calculate the “parameter _α1” and the “parameter _α2” by solving simultaneous equations derived based on the formula (3), which are composed of the following formula (5) for the temperature _T0 to the temperature _T1 and the following formula (6) for the temperature T1 to the temperature T2.

When "<Modification>" is realized, the parameter determination unit 302 has a fitting unit 303 configured as shown below. That is, the fitting unit 303 that realizes "<Modification>" is configured to determine, by fitting, "parameter A" and "parameter B" included in formula (7) obtained by substituting the viscosity expressed by formula (2) into formula (1) and discretizing time based on the experimental data stored in the data storage unit 308. Specifically, this fitting unit 303 is configured to determine "parameter A" and "parameter B" included in formula (7) by the least squares method or regression analysis method.

Next, the physical quantity estimation unit 306 is configured to estimate the temperature of the kneaded material at a time later than the second time from the time evolution of the temperature of the kneaded material represented by the relational expression into which the values of the parameters determined by the parameter determination unit 302 are substituted. For example, the physical quantity estimation unit 306 is configured to estimate the temperature at the kneading end time, which is a time later than the second time, based on the time evolution of the temperature represented by the mathematical expression (3) into which the values of "parameter α1" and "parameter α2" calculated by the parameter calculation unit 305 are substituted.

The physical quantity estimation unit 306 can also be configured to estimate physical quantities other than the temperature of the kneaded material. For example, it can estimate the viscosity of the kneaded material based on formula (2), the shear stress based on formula (8), and the time integral of the shear stress based on formula (9).

The output unit 307 is configured to output information related to the physical quantity estimated by the physical quantity estimation unit 306. For example, the output unit 307 is configured to output information related to the temperature of the kneaded material estimated by the physical quantity estimation unit 306 (see the dashed line in FIG. 3).

<Physical quantity estimation method (operation of physical quantity estimation device)>
The physical quantity estimation device 100 is configured as described above, and a physical quantity estimation method using this physical quantity estimation device 100 will be described below with reference to the drawings.

Figure 6 is a flowchart explaining the physical quantity estimation method.

First, it is assumed that the relational expressions shown in the formulas (1) to (9), the plot data, the experimental data, and the temperature of the wall surface of the kneading vessel (“T _w ”) are stored in advance in the data storage unit 308 .

The parameter determination unit 302 of the physical quantity estimation device 100 performs fitting with the curve shown in formula (2) based on plot data (measurement data) of shear rate and viscosity actually measured at multiple temperatures (S101), and determines the three fitting coefficients ("a", "b", "n") included in formula (2) (S102).

Next, the parameter determination unit 302 of the physical quantity estimation device 100 obtains temperatures _T0 , T1, and T2 at times _t0 , _t1 , and _t2 between the first time and the second time from the experimental data stored in the data storage unit 308, and then calculates the simultaneous equations shown in the formulas (5) and (6) using the obtained temperatures _T0 , _T1 , and _T2 ( _S103 ). After that, the parameter determination unit 302 determines parameters ("parameter _α1 " and "parameter α2") by solving the simultaneous equations consisting of the formulas (5) and (6) (S104). Note that the parameter determination unit 302 may determine "parameter A" and "parameter B" included in the formula (7) based on the experimental data stored in the data storage unit 308, for example, by using the least squares method or regression analysis method.

Next, the physical quantity estimation unit 306 determines the time evolution of the temperature of the kneaded material represented by a relational expression into which the parameter values determined by the parameter determination unit 302 are substituted (S105), and estimates the temperature of the kneaded material at a specified time based on the determined time evolution of the temperature of the kneaded material (S106). For example, the physical quantity estimation unit 306 estimates the temperature at the kneading end time, which is a time later than the second time, based on the time evolution of the temperature represented by the formula (3) into which the values of "parameter α1" and "parameter α2" determined by the parameter calculation unit 305 are substituted.

Thereafter, the output unit 307 outputs information regarding the physical quantity estimated by the physical quantity estimation unit 306 (S107). For example, the output unit 307 outputs information regarding the temperature of the kneaded material estimated by the physical quantity estimation unit 306.

In this manner, the physical quantity estimation method in this embodiment is realized.

Below, we will explain the method described in "<<Further Improvements>>".

Figure 7 is a flowchart explaining the method described in "<<Further Improvements>>".

In FIG. 7, first, the physical quantity estimation device 100 acquires a temperature-time curve from the experimental data relating to the temperature of the kneaded material from the first time to the second time stored in the data storage unit 308 (S201). The physical quantity estimation device 100 also acquires a temperature-time curve from the first time to the second time among the temperature-time curves grasped from the calculation results of the simulation (S202). Then, the physical quantity estimation device 100 calculates the area enclosed by the temperature-time curve grasped from the experimental data and the temperature-time curve grasped from the calculation results of the simulation (S203). Next, the physical quantity estimation device 100 determines whether the calculated area is equal to or smaller than a predetermined value (S204).

When the physical quantity estimation device 100 determines that the area is equal to or smaller than the predetermined value, it ends the process. On the other hand, when the physical quantity estimation device 100 determines that the area is not equal to or smaller than the predetermined value, it changes the values of time _t0 , time _t1 , and time _t2 , and repeats the process by the temperature calculation unit 304 and the process by the parameter calculation unit 305 until the area becomes equal to or smaller than the predetermined value.

Specifically, the temperature calculation unit 304 changes the values of time _t0 , time _t1 , and time _t2 , respectively, and obtains temperatures _T0 , _T1 , and _T2 at the new times t0, _t1 , and t2. Then, the parameter calculation unit 305 uses the temperatures _T0 , _T1 , and _T2 newly obtained by the temperature calculation unit ₃₀₄ to solve the _simultaneous equations consisting of formulas (5) and (6), thereby re-determining the "parameter α1" and the "parameter α2" (S205).

Next, the physical quantity estimation unit 306 determines the time evolution of the temperature of the kneaded material based on the re-determined "parameter α1" and "parameter α2" (S206). The physical quantity estimation device 100 then obtains a new temperature-time curve again from the calculation results of the simulation based on the time evolution of the temperature of the kneaded material. Thereafter, the process of calculating the area enclosed by the temperature-time curve grasped from the experimental data and the temperature-time curve grasped from the recalculation results of the simulation, and the process of determining whether the calculated area is equal to or smaller than a predetermined value are repeated.

In this way, the method described in "<<Further Improvements>>" is realized.

<Physical quantity estimation program>
The physical quantity estimation method performed by the above-described physical quantity estimation device 100 can be realized by a physical quantity estimation program that causes a computer to execute a physical quantity estimation process.

For example, in the physical quantity estimation device 100 consisting of a computer shown in FIG. 4, the physical quantity estimation program of this embodiment can be introduced as one of the programs 202 stored in the hard disk device 112. Then, by having the computer that is the physical quantity estimation device 100 execute this physical quantity estimation program, the physical quantity estimation method of this embodiment can be realized.

The physical quantity estimation program that causes a computer to execute each process for creating data related to the physical quantity estimation process can be recorded on a computer-readable recording medium and distributed. Recording media include, for example, magnetic storage media such as hard disks and flexible disks, optical storage media such as CD-ROMs and DVD-ROMs, and hardware devices such as non-volatile memories such as ROMs and EEPROMs.

The invention made by the inventor has been specifically described above based on the embodiment thereof, but it goes without saying that the invention is not limited to the above embodiment and can be modified in various ways without departing from the gist of the invention.

Reference Signs List 1 Kneader 10 Kneading tank 10a Cavity 11a Rotor 11b Rotor 12 Kneaded material 13 Upper lid 100 Physical quantity estimation device 101 CPU
102 ROM
103 RAM
104 Display 105 Keyboard 106 Mouse 107 Communication board 108 Removable disk device 109 CD/DVD-ROM device 110 Printer 111 Scanner 112 Hard disk device 201 OS
202 Program group 203 File group 301 Input section 302 Parameter determination section 303 Fitting section 304 Temperature calculation section 305 Parameter calculation section 306 Physical quantity estimation section 307 Output section 308 Data storage section

Claims (11)

A physical quantity estimation device configured to estimate a physical quantity based on a relational expression expressing time evolution of a physical quantity related to a material kneaded by a kneader, the relational expression including a parameter related to a kneading tank of the kneader or the material,
a parameter determination unit configured to determine a value of the parameter based on experimental data relating to the physical quantity from a first time to a second time;
a physical quantity estimation unit configured to estimate the physical quantity at a time later than the second time from a time evolution of the physical quantity represented by the relational expression into which the value of the parameter determined by the parameter determination unit is substituted;
Equipped with
The relational expression is expressed by the following mathematical expression (1):
The viscosity in the formula (1) has a relationship obtained by fitting the relationship between the shear rate and the viscosity actually measured at a plurality of temperatures to the following formula (2):
the parameter determination unit has a fitting unit configured to determine, by fitting, parameters α1 and α2 included in the following formula (3) obtained by substituting the viscosity expressed by the formula (2) into the formula (1) based on experimental data indicating a relationship between time and a temperature of the kneaded material.

here,
ρ: density of the kneaded material C _p : specific heat of the kneaded material h: heat transfer coefficient between the kneaded material and the kneading tank S: contact area between the kneaded material and the kneading tank V: volume of the kneaded material T: temperature of the kneaded material T _w : temperature of the wall of the kneading tank t: time η: viscosity of the kneaded material dγ/dt: shear rate in the kneading tank

here,
a: fitting coefficient b: fitting coefficient n: fitting coefficient

here,
α1=hS/ρ/C _p /V
β(T)=a×e ^−bT
α2=(dγ/dt) ⁿ⁺¹ /2/ρ/C _p 2. The physical quantity estimation device according to claim 1,
The fitting portion is
a temperature calculation unit configured to calculate temperatures _T0 , _T1 , and T2 at times _t0 , _t1 , and _t2 between the first time and the _second time from the experimental data;
a parameter calculation unit configured to calculate the parameters α1 and α2 by solving simultaneous equations consisting of the following equation (5) for the temperature _T0 to the temperature _T1 and the following equation (6) for the temperature _T1 to the temperature _T2 , which are derived based on the equation (3);
A physical quantity estimation device comprising:

3. The physical quantity estimation device according to claim 2,
the physical quantity estimation unit is configured to estimate a temperature at a kneading end time, which is a time later than the second time, based on the time evolution of temperature expressed by the formula (3) into which the value of the parameter α1 and the value of the parameter α2 calculated by the parameter calculation unit are substituted. 4. The physical quantity estimation device according to claim 3,
the physical quantity estimation device is configured to change the values of the times t 0 , t 1 , and t 2, and repeat processing by the temperature calculation unit and processing by the physical quantity estimation unit, until a value of an area surrounded by a temperature-time curve from the first time to the _second time determined from the experimental data and a temperature-time curve from the first time to the _second time of the temperature-time curve determined from a calculation _result by the physical quantity estimation unit becomes equal to or less than a predetermined value. A physical quantity estimation device configured to estimate a physical quantity based on a relational expression expressing time evolution of a physical quantity related to a material kneaded by a kneader, the relational expression including a parameter related to a kneading tank of the kneader or the material,
a parameter determination unit configured to determine a value of the parameter based on experimental data relating to the physical quantity from a first time to a second time;
a physical quantity estimation unit configured to estimate the physical quantity at a time later than the second time from a time evolution of the physical quantity represented by the relational expression into which the value of the parameter determined by the parameter determination unit is substituted;
Equipped with
The relational expression is expressed by the following mathematical expression (1):
The viscosity in the formula (1) has a relationship obtained by fitting the relationship between the shear rate and the viscosity actually measured at a plurality of temperatures to the following formula (2):
the parameter determination unit has a fitting unit configured to determine, by fitting, a parameter A and a parameter B included in the following formula (7) obtained by substituting the viscosity expressed by the formula (2) into the formula (1) and discretizing time based on experimental data indicating a relationship between time and a temperature of the kneaded material:

here,
ρ: density of the kneaded material C _p : specific heat of the kneaded material h: heat transfer coefficient between the kneaded material and the kneading tank S: contact area between the kneaded material and the kneading tank V: volume of the kneaded material T: temperature of the kneaded material T _w : temperature of the wall of the kneading tank t: time η: viscosity of the kneaded material dγ/dt: shear rate in the kneading tank

here,
a: fitting coefficient b: fitting coefficient n: fitting coefficient

here,
A=hS/ρ/ _Cp /V
B=1/2/ρ/C _p ×a×(dγ/dt) ⁿ⁺¹ 6. The physical quantity estimation device according to claim 5,
The physical quantity estimation device, wherein the fitting unit is configured to determine the parameter A and the parameter B by a least squares method or a regression analysis method. A physical quantity estimation method, comprising: estimating a physical quantity based on a relational expression expressing time evolution of a physical quantity related to a material kneaded in a kneader, the relational expression including a parameter related to a kneading tank of the kneader or the material,
a parameter determining step of determining a value of the parameter based on experimental data relating to the physical quantity from a first time to a second time;
a physical quantity estimating step of estimating the physical quantity at a time later than the second time from a time evolution of the physical quantity represented by the relational expression into which the value of the parameter determined in the parameter determining step is substituted;
Equipped with
The relational expression is expressed by the following mathematical expression (1):
The viscosity in the formula (1) has a relationship obtained by fitting the relationship between the shear rate and the viscosity actually measured at a plurality of temperatures to the following formula (2):
the parameter determination step includes a fitting step configured to determine, by fitting, parameters α1 and α2 included in the following formula (3) obtained by substituting the viscosity expressed by the formula (2) into the formula (1) based on experimental data indicating a relationship between time and a temperature of the kneaded material.

here,
ρ: density of the kneaded material C _p : specific heat of the kneaded material h: heat transfer coefficient between the kneaded material and the kneading tank S: contact area between the kneaded material and the kneading tank V: volume of the kneaded material T: temperature of the kneaded material T _w : temperature of the wall of the kneading tank t: time η: viscosity of the kneaded material dγ/dt: shear rate in the kneading tank

here,
a: fitting coefficient b: fitting coefficient n: fitting coefficient

here,
α1=hS/ρ/C _p /V
β(T)=a×e ^−bT
α2=(dγ/dt) ⁿ⁺¹ /2/ρ/C _p A physical quantity estimation method, comprising: estimating a physical quantity based on a relational expression expressing time evolution of a physical quantity related to a material kneaded in a kneader, the relational expression including a parameter related to a kneading tank of the kneader or the material,
a parameter determining step of determining a value of the parameter based on experimental data relating to the physical quantity from a first time to a second time;
a physical quantity estimating step of estimating the physical quantity at a time later than the second time from a time evolution of the physical quantity represented by the relational expression into which the value of the parameter determined in the parameter determining step is substituted;
Equipped with
The relational expression is expressed by the following mathematical expression (1):
The viscosity in the formula (1) has a relationship obtained by fitting the relationship between the shear rate and the viscosity actually measured at a plurality of temperatures to the following formula (2):
the parameter determination step is configured to determine, by fitting, a parameter A and a parameter B included in the following formula (7) obtained by substituting the viscosity expressed by the formula (2) into the formula (1) and discretizing time based on experimental data indicating a relationship between time and a temperature of the kneaded material:

here,
ρ: density of the kneaded material C _p : specific heat of the kneaded material h: heat transfer coefficient between the kneaded material and the kneading tank S: contact area between the kneaded material and the kneading tank V: volume of the kneaded material T: temperature of the kneaded material T _w : temperature of the wall of the kneading tank t: time η: viscosity of the kneaded material dγ/dt: shear rate in the kneading tank

here,
a: fitting coefficient b: fitting coefficient n: fitting coefficient

here,
A=hS/ρ/ _Cp /V
B=1/2/ρ/C _p ×a×(dγ/dt) ⁿ⁺¹ A physical quantity estimation program for causing a computer to execute a process of estimating a physical quantity based on a relational expression representing time evolution of a physical quantity related to a material kneaded in a kneader, the relational expression including a parameter related to a kneading tank of the kneader or the material, the program comprising:
a parameter determination process for determining a value of the parameter based on experimental data relating to the physical quantity from a first time to a second time;
a physical quantity estimation process of estimating the physical quantity at a time later than the second time from a time evolution of the physical quantity represented by the relational expression into which the value of the parameter determined in the parameter determination process is substituted;
Equipped with
The relational expression is expressed by the following mathematical expression (1):
The viscosity in the formula (1) has a relationship obtained by fitting the relationship between the shear rate and the viscosity actually measured at a plurality of temperatures to the following formula (2),
the parameter determination process is performed by fitting parameters α1 and α2 included in the following formula (3) obtained by substituting the viscosity expressed by the formula (2) into the formula (1) based on experimental data showing the relationship between time and the temperature of the kneaded material, the parameter determination being performed by fitting the parameters α1 and α2 included in the following formula (3) obtained by substituting the viscosity expressed by the formula (2) into the formula (1).

here,
ρ: density of the kneaded material C _p : specific heat of the kneaded material h: heat transfer coefficient between the kneaded material and the kneading tank S: contact area between the kneaded material and the kneading tank V: volume of the kneaded material T: temperature of the kneaded material T _w : temperature of the wall of the kneading tank t: time η: viscosity of the kneaded material dγ/dt: shear rate in the kneading tank

here,
a: fitting coefficient b: fitting coefficient n: fitting coefficient

here,
α1=hS/ρ/C _p /V
β(T)=a×e ^−bT
α2=(dγ/dt) ⁿ⁺¹ /2/ρ/C _p A physical quantity estimation program for causing a computer to execute a process of estimating a physical quantity based on a relational expression representing time evolution of a physical quantity related to a material kneaded in a kneader, the relational expression including a parameter related to a kneading tank of the kneader or the material, the program comprising:
a parameter determination process for determining a value of the parameter based on experimental data relating to the physical quantity from a first time to a second time;
a physical quantity estimation process of estimating the physical quantity at a time later than the second time from a time evolution of the physical quantity represented by the relational expression into which the value of the parameter determined in the parameter determination process is substituted;
Equipped with
The relational expression is expressed by the following mathematical expression (1):
The viscosity in the formula (1) has a relationship obtained by fitting the relationship between the shear rate and the viscosity actually measured at a plurality of temperatures to the following formula (2):
the parameter determination process is performed by substituting the viscosity expressed by the formula (2) into the formula (1) based on experimental data showing the relationship between time and the temperature of the kneaded material, and fitting parameters A and B included in the following formula (7) obtained by discretizing time, to determine the parameters.

here,
ρ: density of the kneaded material C _p : specific heat of the kneaded material h: heat transfer coefficient between the kneaded material and the kneading tank S: contact area between the kneaded material and the kneading tank V: volume of the kneaded material T: temperature of the kneaded material T _w : temperature of the wall of the kneading tank t: time η: viscosity of the kneaded material dγ/dt: shear rate in the kneading tank

here,
a: fitting coefficient b: fitting coefficient n: fitting coefficient

here,
A=hS/ρ/ _Cp /V
B=1/2/ρ/C _p ×a×(dγ/dt) ⁿ⁺¹ A computer-readable recording medium having the physical quantity estimation program according to claim 9 or 10 recorded thereon.

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