The Method of Optimizing the Drying Process of an Oak Blank in a Radiofrequency Electromagnetic Field

The Method of Optimizing the Drying Process of an Oak Blank in a

Radiofrequency Electromagnetic Field

SLOVAC Francisc

, COMAN Simina

, GORDAN Mircea

1 _{University of Oradea, Romania,}

Faculty of Electrical Engineering and Information Technology, 1 Universitatii Street, 410087 Oradea, Romania

2 _{University of Oradea, Romania,} Faculty of Environmental Protection,,

26 Gen. Magheru Street, 410059, Oradea, Romania, E-mail: simina_vicas@yahoo.com

Abstract - This paper presents some aspects concerning the modeling of heating some moving oak blanks in a radiofrequency electromagnetic field, which has been coupled with an optimization method based on a statistical model. The Response Surface Method and Central Composite Design type of experiment have been employed.

Keywords: modeling, radiofrequency field, heating, optimization.

I. INTRODUCTION

The development of software dedicated to modeling electromagnetic phenomena allowed us to perform a numerical analysis on the problem of converting the energy of the electromagnetic field into thermal energy.

The results of such modeling provide detailed information as regards the parameters of the heating process, as well as elements of computer-aided design for such installations [1], [2], [3].

In certain situations, such as the modeling of the radiofrequency heating process of certain blanks, is recommended to develop software able to couple the electromagnetic and the thermal fields, as well as mass and movement problems of the blank processed. We have found useful, in this respect, the following software using hybrid numerical techniques: the Finite Element Method (FEM) and The Boundary Element Method (BEM), in 2D and 3D, with significant advantages in situations when the blank is moved [4], [5].

We should point out here that most dedicated software does not include optimization modules; therefore, several running of the software mentioned have been necessary, in order to obtain an appropriate correlation between requirements associated with the heated/dried blank, the input electrical parameters and the geometry of the applicator [6].

The Response Surface Method is a set of experimental design techniques (DOE), which contribute to a better understanding and optimization of the response. The Response Surface Methodology is often employed in order to build refined models, after

determining important factors with the help of Analysis of Variance, ANOVA. The experiments of the response surface type are: Central Composite and Box Behnken. Central Composite Design fits a full quadratic model and, unlike Box Behnken, which has 3 levels for each factor, it uses five levels [7].

Central Composite Design is a type of experiment that uses hubs that are part of an axial points group called Star Points, which allows the estimation of curvature [8], [9].

II. MATERIALS AND METHODS USED

In order to model the heating process, the FEM-BEM.3D-RFmove_term_masa.for software has been employed, using an applicator made up of 5 pairs of electrodes with a diameter of 10 [mm] and the length of 150 [mm] [4].

The dimensions of the oak blank processed in the applicator are as follows: on the Ox axis - 80[mm], on the Oy axis - 100 [mm] and on the Oz axis - 10 [mm].

The following input data have been used for numerical simulations:

 voltage - U [V], which may have the values: 1150[V], 1240[V], 1340[V], 1380[V], 1490[V], 1550[V], 1610[V], 1690[V], 1820[V];

 time - T[s], with values between 1000 and 10000[s];

 distance - D [mm] – with values between 10 and 200[mm].

Figures1 and 2 show the 5 pairs of electrodes, the oak blank and the representation of the input size – distance, where A represents the center of the blank at the beginning of the running and B is its center at the end of the running, while O marks the center of the applicator. The distance crossed by the blank between A and B is symmetrical to the O point that, as shown above, represents the center of the applicator.

Journal of Electrical and Electronics Engineering 73

Fig.1 The geometry of the applicator

Fig.2 The geometry of the applicator in plan view

In order to optimize the heating process in a radiofrequency field, the Surface Response Method and the Central Composite Design experiment type have been used. Taking into account the input data, the experiment used have had a number of 3 factors and 2 responses. At the beginning, the input data have been introduced in Minitab software, and thus, for each factor, a five-level table has been generated, the letters A, B and C representing the three factors (see Table 1).

TABLE 1. Values generated by the optimization software

A B C

0 1.68179 0

0 0 0

0 0 0

0 0 0

-1 -1 1

-1 1 -1

0 -1.6818 0

0 0 0

1 -1 1

0 0 0

0 0 -1.6818

0 0 1.68179

0 0 0

-1 1 1

-1 -1 -1

-1.6818 0 0

1.68179 0 0

1 1 1

1 -1 -1

1 1 -1

Looking at the values presented in Table 1, the five levels of each factor can be observed. Next, the 5 values,

corresponding to each level in particular, have been converted to values corresponding to the problem defined. In order to achieve the conversion of the values generated by Minitab with the modeling values, the following notations have been established:

- the "-1.6818"value corresponds to level 1; - the "-1" value corresponds to level 2; - the "0" value corresponds to level 3; - the "1" value corresponds to level 4; - the "1.6818" value corresponds to level 5.

Thus, the following levels have been established for each factor:

1. the voltage factor - U[V]: - for level, it1 has the value 1150[V], for level 2 – it has the value 1340[V], for level 3 – it has the value 1490 [V], for level 4 – it has the value 1610[V] and for level 5 – it has the value 1820 [V].

2. the time factor - T[s] – for level 1 it has the value of 1000[s], for level 2 - the value of 3000[s], for level 3 - the value of 5000 [s], for level 4 - the value of 8000 [s] and for level 5 - the value of 10000 [s].

3. The distance factor - D[mm] – for level 1 it has the value of 10[mm], for level 2 – the value of 40[mm], for level 3 – the value of 100 [mm], for level 4 – the value of 140 [mm] and for level 5 – the value of 200 [mm].

Next, the values from Table 1 have been replaced with the values presented above and thus the input data for 20 numerical simulations have been obtained. Both the input data and the results of numerical simulations are presented in Table 2.

TABLE 2. Input and output data

U [V]

T [s]

D [mm]

Humidity [%]

Max. temp.

[°C]

1490 10000 100 0.1 80.19

1490 5000 100 0.1 83.45

1490 5000 100 0.1 83.45

1490 5000 100 0.1 83.45

1340 3000 140 0.31 68.96

1340 8000 40 0.1 69.09

1490 1000 100 0.1 80.19

1490 5000 100 0.1 83.45

1610 3000 140 0.22 90.03

1490 5000 100 0.1 83.45

1490 5000 10 0.1 77.91

1490 5000 200 0.22 76.43

1490 5000 100 0.1 83.45

1340 8000 140 0.1 69.37

1340 3000 40 0.21 72.75

1150 5000 100 0.21 58.98

1820 5000 100 0.1 109.99

1610 8000 140 0.1 87.09

1610 3000 40 0.1 92.36

1610 8000 40 0.1 89.42

The next stage of the optimization process focused on the introduction of data obtained as a result of running in Minitab software. Thus, a series of analyses

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concerning the influence/importance of factors on responses can be achieved.

III. RESULTS AND THEIR INTERPRETATION

ANOVA - Analysis of Variance allows one to study the importance of factors in relation to output data. With this view, the One-Way ANOVA has been used, which, by the p parameter, outlines the more or less relevant contribution of input data to the optimization process. The data we have obtained are presented in Table 3.

TABLE 3. Contribution of input data

Response versus Factor Value of p

Humidity versus U 0.281

Humidity versus T 0.071

Humidity versus D 0.199

Maximum temp. versus U 0.000

Maximum temp. versus T 0.99

Maximum temp. versus D 0.957

After analyzing the obtained results for the p value, the following conclusions can be drawn:

 the U factor has a significant influence on the Maximum temp. factor and, to a certain extent, on the humidity factor.;

 the T factor is very important especially for the humidity response, with a value of the p parameter of 0.071;

 the D factor has the most significant contribution to the Humidity response.

Another important means of analysis is represented by normality and residual plots. For the normality plot, the requirement is that all fields of a specific answer should be normally distributed along a line, while the residual test requires that data should be equally distributed on both sides of the line.

Further on, we present the normality and the residual plots.

Fig.3 The normality plot for the Humidity response

Fig.4 The residual plot for the Humidity response

Fig.5 The normality plot for the Maximum temp. response

Fig.6 The residual plott for the Maximum temp. response

Figures 3 and 4 present the normality and the residual plots for the Humidity response, while figures 5 and 6 for the Maximum temp. response.

The images above show that, for the normality plots, the data are distributed along the line, exactly as required by the test. As regards the resitual test, again the conditions for the good and correct development of the optimization process have been fulfilled.

A final analysis of factors has been achieved by means of the effect plots. Figures 7 and 8 show the effect of factors on the two responses.

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Fig.7 The effect plot for the Maximum temp. response

Fig.8 Effects plot for the Humidity response

By analyzing the effects plots, the following conclusions can be drawn: the U factor has a significant effect on the Maximum temp. response, a fact also proved by ANOVA - One-Way analysis; the most important effect for the Humidity response is represented by the T factor.

In order to obtain the final solution, the Response Optimizer from Minitab has been used during this optimization. Within this tool, it has been imposed that the maximum temperature of the oak blank should not be above 85[°C], as the quality of the charge can be affected beyond this value. At the same time, minimizing the value of the processing time has also been imposed.

The results obtained after applying all the constraints are: voltage - 1490[V]; time - 1000[s]; distance - 100[mm].

Running these input data, the following results have been obtained: maximum temperature - 80.19 [°C] and humidity - 0.1%. Analyzing the data obtained as a result of the optimization process, using the Response Surface optimization model and the Central Composite type of experiment, it can be said that the results meet all the constraints imposed.

IV. CONCLUSIONS

The results of modeling the heating process in a radiofrequency field, using FEM-BEM.3D-RFmove_term_masa.for software, coupled with the

Response Surface optimization method, for a moving oak blank, emphasize the following:

 the value of the applicator’s voltage has an

important influence on the temperature and the humidity parameters;

 the input value, time of heating/drying, correlated to the initial position of the oak blank as related to the entry to the applicator, further highlights other useful features for the design of such equipment

 the optimized results have been validated with the help of one more simulation, using the the software mentioned.

The results obtained represent a continuation of similar research undertaken with the aim of obtaining optimal designs of radiofrequency equipment.

REFERENCES

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Numerical Modeling of the Heating Process in a Radiofrequency Electromagnetic Field Using Comsol

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Engineering, University of Oradea, Vol.7, nr. 2, pp.17-20, May 2014.

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