INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 7, pp. 1085-1093 JULY 2012 / 1085 DOI: 10.1007/s12541-012-0142-z

1. Introduction

Energy-savings considerations in manufacturing processes have been drawing a great attention to the designers and manufactures because of the ecological issues, cost-saving pressure, and new environmental legislations.1 Manufacturing companies have been trying to produce more with less,2 so the improvement of machining and process efficiency for manufacturing is one of the promising solutions.3,4 Induction heating process has been considered as a high productivity, repeatable quality, and green heating technology compared to fuel-fired furnaces. This is the reason why the induction heating, a best available heating technology, is preferred in the forging industry.5,6 Induction heating prior to hot forging, namely induction through heating, requires a huge amount of electrical energy for heating a steel workpiece with large volume from the ambient temperature to approximate 1150~1250C. Therefore, the increase in the electrical efficiency of the heating system significantly saves the consumed energy.

Similar to other manufacturing technologies, energy-saving solutions for induction heating are important issues that the manufacturers and researchers always pay their attention. Solutions for saving energy for industrial induction heating may include the energy management, innovative components of induction devices,

energy recovery, and adaptive control.7 One of the effective ways to resolve the energy-savings problem in induction heating is carrying out the optimization process through parameter studies. Diverse published works devoted to the optimization of induction heating,8-14 but most of them focused on how to minimize the temperature deviation at the end of the heating process. Studies on minimizing the energy consumption for particular manufacturing processes have been still dimmed although the producers of induction heaters are trying to increase the efficiency of their products. In addition, issues related to the billets temperature distribution and power distribution along the heating line is a controversial problem that is rarely discussed in the literature.15 Therefore, studying the influence of process parameters on the energy consumption and finding the potential optimization of the in-line induction heating system are the purposes of this research.

2. State of the research Within the International Collaborative R&D Program

Development of information technology-based manufacturing process system for energy savings hosted by KITECH, we have been carrying out the sub-project Holistic process chain

Optimization of the In-line Induction Heating Process for Hot Forging in Terms of Saving Operating Energy

Hong-Seok Park1,# and Xuan-Phuong Dang1 1 School of Mechanical and Automotive Engineering, University of Ulsan, San 29, Mugeo 2-dong, Namgu, Ulsan, Korea, 680-749

# Corresponding Author / E-mail: phosk@ulsan.ac.kr, TEL: +82-52-259-1458, FAX: +82-52-259-1680

KEYWORDS: Optimization, Induction heating, Hot forging, Energy-savings

Improving the efficiency of the manufacturing process is one of the ways to resolve the ecological issues, cost-saving pressure, and new environmental legislations. This paper presents the study on the in-line induction heating process prior to hot forging of an automotive crankshaft in order to find the potential solutions for improving the energy efficiency. The heating strategy that divides the induction heating line into groups for flexible control and saving operating energy was introduced. Optimization of the operating parameters of the induction heating system, including voltages and frequencies, was done using design of experiment in conjunction with numerical simulation, approximation, and genetic algorithm optimization techniques. In addition, thermal insulation was proposed to reduce the heat losses. The research results show that the energy can be saved through process parameter optimization approximately 6%. Furthermore, if the insulating covers at the open spaces between adjacent heaters are used, roughly 4% of additional amount of the energy consumption can be reduced.

Manuscript received: November 30, 2011 / Accepted: April 22, 2012

KSPE and Springer 2012

1086 / JULY 2012 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 7

optimization for forging production of automotive parts in terms of manufacturing efficiency and saving operation energy. In this project, the whole manufacturing processes, including induction heating, forging, and cooling are considered holistically by involving the interactions among manufacturing steps. This sub-project aims at increasing 8% of the energy efficiency for the hot forging production of automotive crankshafts. In addition, productivity and quality of the product must be the same or better than the current state.

As previously mentioned, induction heating step is the one that consumes a great amount of energy compared to other stages in the forging process. It also the first step of the manufacturing process so that we focus this step in the first phase of the project. The in-line induction system with of seven heaters for heating a long steel bar with a diameter of 97 mm is shown in Fig. 1. The steel bar moves continuously through the in-line heaters, and the velocity of the heated bar is decided by a predetermined cycle time of the forging process. In every cycle time, the heated steel bar is cut into 460-mm-long by the hot shearing before moving to the crankshaft forging die.

Practical analysis shows that there is a potential improvement of the induction system for increasing the energy efficiency by optimization. We also carried out the investigation into the existent induction system and found that the heat losses caused by convection and radiation at the open spaces where the heated billet exposes to the ambient air account for a significant amount of energy. In addition, to heat the billet from the initial temperature to the target temperature around 1220C using several heaters (see Fig. 2), there are many different temperature profiles or heating patterns

along the heating line. One may put more power into some heaters at the beginning of the heating line or vice versa. It is clear that different heating pattern strategies result in different energy efficiencies and final temperature distributions at the end of the heating process. In practice, the strategy of power distribution along the heating line is mainly based on the rules of thumb.15 Therefore, the systematic analysis of the influences of power distribution along the in-line heaters on the energy efficiency is imperative. In this project, we do not focus on improving the hardware or equipment such as power supplies, inverters, or induction coils that were made by the induction heater manufacturer. Instead, the optimum voltages and frequencies, which are the changeable process parameters of the heaters in the induction heating line, must be figured out by a scientific approach and elaborated study rather than practice or experience.

3. Research methodology and systematic procedure for optimizing the heating process

To save the experimental costs, the numerical simulation

method was used instead of performing a set of expensive physical experiments. In addition, it is impossible to measure the temperature distribution inside the heated workpiece by a pyrometer while the workpiece moves continuously. In the case of induction through-heating, the accuracy of the simulation result is very high when the material properties and the simulation modeling are well-defined.16,17 Therefore, numerical simulation is an appropriate choice for studying the behavior of the induction heating system in this work.

The systematic procedure for optimizing the process parameters of the induction heating is presented in Fig. 3. Firstly, we defined the design variables, design constraints and performed the design of experiments (DOE). Secondly, the numerical model of the induction heating was developed, and the virtual experiments were then carried out with different combinations of inputs in the design matrix. Thirdly, the data obtained from the simulations was used to

Fig. 1 In-line induction heat a long bar prior to forging thecrankshaft

0

200

400

600

800

1000

1200

1400

0 100 200 300 400 500Time (s)

Tem

pera

ture

(C

)

Center (3) Surface (1) Average (2)

1

Heater 1

Heater 2

Heater 3

Heater 4

Heater 5

Heater 6

Heater 7

2

3

Target temperature

Initial temperature

Fig. 2 A typical temperature profile in the heated bar when usingin-line induction heating

Fig. 3 Systematic procedure for optimizing the heating process

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 7 JULY 2012 / 1087

construct the approximate mathematical relations between inputs and outputs using the second-order response surface model (RSM). The approximate model was verified the fidelity before carrying out the optimization process. Finally, the optimization was then solved based on the regressive explicit equations obtained by the previous approximation. This method is called metamodel-based optimization approach. The algorithm of metamodel-based optimization is shown in Fig. 4. The brief descriptions of above steps are presented in the next sections.

4. Mathematical and numerical modeling of the induction heating process

Induction heating is a complex electromagnetic and heat-

transfer process because of the temperature dependency of electromagnetic, electrical, and thermal properties of material as well as skin effect. The temperature profile of the heated workpiece and the energy consumption are complicated functions of the current density, frequency, material properties, coil design, the coupling between coils and workpiece, and the characteristic of the power supply. The layout of the induction heating system and its principle are depicted in Fig. 5. In the physical aspect, electromagnetic field and heat-transfer are complicated, and the transient simulation takes a long computational time. To simplify the numerical model, four acceptable assumptions are made in this study: (i) ignore the helixcity of the coil (inductor),18,19 (ii) 2D modeling is adequate for a spiral inductor,20,21 (iii) ignore the moving effect of the heated billet, and (iv) heat transfer by conduction in the axial direction is not taken into account.12,22 The

theoretical background of the mathematical and numerical modeling of electromagnetic field governed by Maxwells equations and the heat-transfer process are well presented in the literature.23,24 Therefore, a brief presentation of the theoretical background of the induction heating is presented in this paper.

The global system of equation modeling the electromagnetic field is based on the Maxwells equations in the differential forms:

BEt

= (Faradays law) (1)

DH Jt

= + (Amperes law) (2) 0B = (3) D = (4) where E and H are the electric field intensity and magnetic field intensity, respectively; B and D are the magnetic flux density and electric flux density, respectively; J is the current density, is the electric discharge; and denote the curl operator and divergence operator, respectively.

The system of Maxwells equations is couple with following constitutive relations:

D = E (5) B = H (6) J = E (Ohms law) (7) where is the dielectric constant, and are the magnetic permeability and electrical conductivity, respectively. They are temperature independent parameters.

By taking Eqs. (5) and (7) into account, Eq. (2) can be rewritten as

EH Et = + (8)

In most application of induction heating of common metals, the frequency of the current is less than 10MHz, the induced conduction current J is much greater than the displacement current density / ,D t so the last term in the right-hand side the Eq. (8) can be neglected. Therefore, the Eq. (8) can be rewritten as

H = E (9) Taking some vector algebra manipulations using Eqs. (1), (2),

and (6), it is possible to show that

Stop

Organizing the design of experiments

Performing a set of simulations

Finding temperature distribution, temperature derivation, power consumption, and energy efficiency

Fitting the metamodel by RSM method

Is the metamodel adequate?

Performing optimization

Is the accuracy satisfactory?

Evaluating the optimized results

Con

tinuo

us i

mpr

ovem

ent o

r ch

ange

the

met

amod

el t

ype

Yes

No

Yes

No

Fig. 4 Algorithm of metamodel-based optimization

Fig. 5 Layout of induction heating and the electromagnetic principle

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1 HHt

= (10)

01

r

EEt

=

(11)

where 0 and r are the relative magnetic permeability and permeability of free space 0( ).r =

Since the magnetic flux B satisfies the zero divergence condition (Eq. 3), it can be expressed in terms of a magnetic vector potential A

B = A (12) From (1) and (12), we obtain

0AEt

+ = (13)

By introducing the electric scalar potential that satisfies ( ) 0 = using vector identity, Eq. (13) can be integrated as

AEt

+ = (14)

or

AEt

= (15)

Substituting Eqs. (5), (6), (7), and (12) to Eq. (13), we obtain

21 EA Et = (16)

Substituting Eqs. (15) to (16), the electromagnetic field equation in terms of A and can be expressed as

2

22

1 A AAt t t

= + + + (17)

where sJ = is the source current density in the coil or the conduction current density, A

t is the eddy or induced current

density, and 2

2

At t

+ is the displacement current density.

Because the induction heating applied to hot forging operate in low frequency, the hysteresis loss can be neglected. Thus, the displacement current density can be omitted. The Eq. (17) can be simplified as

21 0sAA Jt

+ = (18)

When electromagnetic field quantities are harmonically oscillating functions with a single frequency, J and A can be expressed as

0 0j t j t

sJ J e and A A e = = (19)

where 1;j = A0 and J0 are the amplitude of magnetic vector potential and source current density, respectively; is the angular frequency ( 2 ).f =

Substituting A and Js into Eq. (18) we obtain

2 0 0 01 0A J j A + = (20)

For the axisymmetric condition or cylindrical coordinate, Eq. (20) is rewritten as

2 2

0 0 0 00 02 2 2

1 1A A A A J j AR R R Z R

+ + = +

(21)

It is necessary to see how the Eq. (20) applies region by region. In induction heating application, there are three distinct regions for consideration: the workpiece, the coil, and the surrounding air.

Since the coil is connected to an external source, the current density consists of two components: impressed part and induced part. The impressed part, which is refer to as Js, is due to an external source and is defined by the gradient of the electric scalar potential (Js ).E = = The induced part is generated by the time-varying magnetic field B in the coil itself. Therefore, in the coil we obtain:

2 sA j A J = (22) In the workpiece, there is an induced current denoted by Js, but

there is no source term. The equation for this region is

2 0A j A = (23) For the air region, there is no current, so Eq. (20) simplifies to

2 0A = (24) The source current density must be input to Eq. (22). When the

induction coil is fed by a voltage source, JS is the second unknown. In this case, the computation of the equivalent impedance of the coil-workpiece using circuit analysis is necessary.

The eddy currents derived from the electromagnetic model induce the heat dissipated within the workpiece due to the Joule heat effects. Temperature evolution within the workpiece is governed by the classical heat transfer equation

2Tc k T Et

= (25)

In the case of heating a cylindrical workpiece and the cylindrical coordinate (R,,Z), Eq. (25) can be rewritten as

21T T T Tc k kR Et Z Z R R R

= (26)

where , c, k, are the material density, specific heat, and the thermal conductivity, respectively.

The right side of Eq. (26) is the heat source due to eddy current.

22

2 200

( ) ( )j t

j tA A eE j A et t

= = = (27)

The specific heat and thermal conductivity are temperature dependent. The thermal dependent material properties of the workpiece (SCM440 steel) were obtained by using JMAT-pro software and the data from the forging company.

Equation (25), with suitable boundary condition and initial condition, represents the temperature distribution at any time and any point in the workpiece. The initial temperature condition refers to the temperature profile within the workpiece at time t = 0; therefore, that condition is required only when dealing with

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 7 JULY 2012 / 1089

transient heat transfer problem in which the temperature is not only a function of the space coordinate but also a function of time.

Different kinds of boundary conditions for temperature can be prescribed at interfaces, including convection and radiation between the workpiece and the surrounding air

4 4( ) ( )air emi b airTk h T T T Tn

= + (28)

where h is the convection coefficient, emi is the radiation emissivity, and b is the Stefan-Boltzmann constant.

The energy dissipated in both the workpiece and the coil. The energy dissipated per cycle in these two components is given by

2 2

0

T

coil workpiece

J JQ dv dv dt = + (29)

Due to the complex of the electromagnetic and heat-transfer process, the exact analytical method is very difficult to implement. Thus, general-purpose FEM was employed to simulate the induction heating process.

The FEM-based model of the induction heating process was developed using APDL (ANSYS Parametric Design Language). To reduce the computational time, only one turn of the coil is considered. This simplification is sufficient when modeling an induction heating system with a classical solenoidal inductor.19 Because the input of the Maxwells equations is the current density meanwhile the induction heaters are fed by voltage supplies, the circuit-coupled FEM model was employed as shown in Fig. 6. The current flowing through the inductor turn depends on the impedance of the system.

The movement of the billet through the heating line (space variable) and the time dependence of the heating process (time variable) are modeled by changing the boundary and initial conditions. The output temperature distribution of the previous step time is the initial condition for the subsequent step time. By this manner, the radial and axial temperature distributions in the heated workpiece are determined as a continuous steady state along the whole heating line. In case of the in-line induction heating, the time axis represents the length of the induction line.

Because the induction heating and hot forging line are working on production, it is not allowed to disturb the manufacturing process by physical experiments in the actual system. To validate

the numerical simulation model, the surface temperatures of the workpiece which are calculated by simulation after moving through each induction heater are compared with the temperatures measured in the existent workpiece. The temperature data were collected in the factory when the induction heating line was operating with the designated process parameters. The maximum error between the temperatures obtained by simulation and those measured by the pyrometer can be acceptable in mechanical engineering (54C, equivalent to 4.5% of maximum relative error between measured temperatures and simulation temperatures). It can be concluded that the simulation model is currently adequate to replace for the expensive physical experiments.

5. Heating strategy and energy efficiency analysis Flexible manufacturing requires the induction heating systems

to have an ability of adapting to the change of the throughput while keeping a reasonable energy efficiency. In addition, the energy efficiency depends on the heating pattern along the heating line as previously mentioned in the research hypothesis in Section 2. Therefore, the seven heaters are divided into three groups with the strategy described in Fig. 7. The group 1, including two heaters, heats the billet below and around the Curies temperature. The group 2 with three heaters is responsible for heating above Curies temperature and gives a large portion of heat energy that transfers from the surface of the billet to the center (through heating). The group 3, including two heaters, just gives a small remaining portion of energy to heat the billet up to the target temperature and mainly compensates the heat loss caused by convection and radiation at the hot billets surface at the final heating stage.

All the groups of heaters are fed the same voltage but different frequencies. For voltage-fed induction heater, low frequency generates more heat energy than high frequency. The frequencies f1 and f2 of group 1 and 2, respectively, are parametric studied. The frequency f3 is estimated by an iteration algorithm in order to obtain the target temperature. As the result, there are three design variables, including voltage U, frequencies f1, and frequencies f2.

Fig. 6 Circuit-coupled FEM model of induction heating simulation

Fig. 7 Heating strategy that divides the heaters into three groupsfed by independent power supplies

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The electrical energy efficiency is defined as the ratio of the heat absorbed by the workpiece per unit time and the electric power (voltage current) fed into the coils. This efficiency can also be calculated by using power or heat energy.

w w e losste e e

P Q Q QP Q Q

= = = (30)

where e, Qw, Qe, Qloss are the total electrical and thermal efficiency, the heat stored in the workpiece, electric energy, and heat losses, respectively.

The heat losses and the energy flow in the induction heating process are depicted in Fig. 8. The heat losses cause by the conduction into the equipment in the heating line is ignored because they account for a small portion in comparison with other components. The required electrical power, the Joule heat, the thermal loss, and the heat absorbed by the workpiece can be obtained in every step time by the simulation program. Thus, the energy efficiency of every heater is obtained conveniently.

6. Simulation, approximation, and optimization results Full factorial design matrix was applied for parametric studies.

Three process parameters were chosen including voltage U, frequency f1, frequency f2 as previously mentioned in Section 5. The range of U, f1, and f2 are 45050 V, 7001100 Hz, and 9001300 Hz, respectively. Each parameter (factor) is divided into three levels, so there are 33 = 27 experiments. Initial and final temperatures of the workpiece are 25C and 1220C, respectively. The emissivity or coefficient of radiation is selected as 0.75, and the ambient air temperature is 25C. The temperatures of the inner surface of the refractory inside the heaters were assumed to be lower than the surface temperature of the workpiece 150C. The billet moves with a speed of 460 mm per 25 seconds. The length of each heater is 1000 mm, and the distance between adjacent heaters is 300 mm. The geometry of the billet and the coil are partly demonstrated with FEM model in Fig. 5.

The data obtained from simulation was used to construct the relations between U, f1, f2 and all necessary outputs by using RSM model (a type of meta-model25) and a systematic procedure as presented in Section 3. Practically, there are some popular meta-models such as RSM, radial basis function, and Kriging model. However, RSM is a well-known method and easy to use. The second-order RSM model is suitable for modeling the moderate nonlinear behavior with the low number of design variables (5~10 design variables). The benefit of RSM model is that the number of experiment points is less than that of other models if the orthogonal design of experiment method is applied. Because the induction heating simulation is an extremely expensive computing cost (takes about 11 hours for each simulation in this work), a reduction of the number of simulations is necessary. In addition, the number of simulations can be run on different computers to reduce the total required simulation time. For these reasons, RSM model can be considered as an appropriate approach.

Table 1 The normalized coefficients (when the inputs and responses are scaled in [-1,1] range) of the approximate RSM equations

Energy efficiency Temperature deviationIntercept -0.15183 -0.84387

f1 0.85436 -0.51830 f2 0.73895 -0.91653 U -1.37908 1.18687 f12 -0.35786 1.22150 f22 -0.04397 1.11538 U2 0.15400 3.20126

f1f2 0.17307 1.57210 f1U 0.31595 -3.57457 f2U -0.11266 -3.66501

Electromagnetic losses due to

coupling

Heat losses transfer to

cooling system

Losses caused by conduction into equipment

convection and radiation losses

Useful heat stored in the workpiece

Input

electr

ical e

nergy

tIUQin = 2 00=

f

i

dcmQ peff

Fig. 8 The diagram of energy flow in the induction heating process

Fig. 9 Error analysis of the approximate models using cross-validation method

The considered outputs include current, power, heat losses,

temperature distribution in the radial and axial direction, temperature deviation in the cross-section of the workpiece at the end of heating, and the energy efficiency. Second-order RSM model for three design variables was applied to generate the approximate relation between the process parameters and the target outputs such as energy efficiency and temperature deviation.

3 3 2 3

20

1 1 1 1i i ii i ij i j

i i i j iy x x x x

= = = = += + + + + (31)

where 0, i, ii, ij are the coefficients that are shown in Table 1. The fidelity of the approximate models was verified by the

cross-validation method.25 The model accuracy or the goodness of fit of the response surface model is assessed by four error measures: averages absolute error, maximum error, root mean square error, and R-squared (R2). Figure 9 shows the result of the error analysis

R2=0.97 R2=0.96

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 7 JULY 2012 / 1091

Fig. 10 The approximate relation between frequencies and the total efficiency (a); frequencies and the temperature deviation (b)

using cross-validation method. It can be seen that the R2 values are close to 1. It means that the errors between observed and approximated values are small; therefore, the selected RSM model is adequate. The visual relation between inputs and outputs is shown in Fig. 10.

In hot forging, both energy efficiency and the quality related to the uniformity of temperature distribution in the workpiece are important criteria. This research aims at saving the operating energy. The energy efficiency is the most important criterion. Hence, the energy efficiency is the objective function. Small temperature deviation assures the heating quality of the workpiece. However, after building the approximate relations between process parameters and energy efficiency as well as the temperature deviation, we found that minimizing the temperature deviation will decrease the energy efficiency. In practice, it is unnecessary to reduce the temperature deviation down to a too small value. Therefore, temperature deviation is treated as a technical constraint. In case of hot forging automotive crankshaft, the temperature deviation across the cross-section of the billet is practically chosen in the range of 23 C, a strict value for a reasonable heating quality.

The optimization problem is stated as follows: Maximize the energy efficiency subject to: 2 temperature deviation 3, 700 f1 1100,

900 f2 1300, and 450 U 550. To solve the optimization problem, genetic algorithm26 (GA)

optimization technique was used. GA is a global optimization search that can avoid the local optimum compared to other gradient search methods such as quadratic programming, generalize reduced gradient, modified feasible direction, etc. Although GA can reach the global optimum point, this method requires a lot of iterations for function evaluation. Fortunately, the computer can perform thousands of function evaluations per second when the explicit meta-model (RSM model) is adopted. Therefore, the combination of RSM and GA is the best choice for the intensive simulation-based optimization in this case.

Figure 11 shows the history of the optimization process using genetic algorithm. It was found that the optimum values of voltage, frequency f1, and f2 are 457 V, 1000 Hz, and 1274 Hz, respectively. The frequency f3 was estimated at 1179 Hz. The maximum energy efficiency is 63.5% (see Fig. 12), greater than the worse case in 27 experiments 6.8% (63.5% compared to 56.7%). Temperature deviation is 3.0C in comparison with 10.6C of the worse case. It can be seen that optimizing process parameters helps the induction

Fig. 11 History of objective function and constraint using GA

Table 2 Optimization results of the cases without insulating cover (a) and with insulating cover at the open spaces between heaters (b) Optimum

resultsVoltage

U Frequency

f1 Frequency

f2 Total

efficiencyTemperature

deviation(a) 457 1000 1274 63.5% 3.0C (b) 452 912 1206 67.9% 2.9C

Fig. 12 Electromagnetic efficiency and the total energy efficiency

heating system significantly increase the energy efficiency and the heating accuracy.

Although the optimization was done, the total efficiency of the heating system is still low compared to its common range (60% to 80%).21 One of the main reasons is the thermal losses due to convection and radiation at the open spaces between adjacent heaters (see Fig. 1). The simulation result shows that the heat losses account for 6.9%, equivalent to 60.8 kW for the optimal case. Reducing this number can increase the energy efficiency significantly. Using proper insulating covers which reduce the convection and radiation losses can increase about 4.4% of energy efficiency compared to the case without the insulating covers (see Table 2 for comparison).

7. Conclusion and future work In summary, this paper investigates an in-line induction heating

process prior to hot forging. Simulation-assisted approach in conjunction with DOE, approximation, and GA technique were applied in order to optimize the process parameters of the induction heating system. Through the optimization, the energy efficiency can increase up to around 6%, and the temperature uniformity is better than the un-optimized case. Specially, if the insulating devices are used to reduce the radiation and convection at the open spaces

89.6

79.8

63.3 59.955.3

49.944.4

62.9

89.984.0

71.6 71.8 72.4 72.6 72.878.3

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

Heater1

Heater2

Heater3

Heater4

Heater5

Heater6

Heater7

Total

Effic

ienc

y (%

)

Thermal & electrical efficiencyElectromagnetic efficiency

0

200

400

600

800

1000

1200

1400

Ave

rage

bill

et's

tem

pera

ture

(C

)

63.5

Run counter Run counter (a) (b)

Temp

Devia

tion

Temp

Devia

tion

1092 / JULY 2012 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 7 between heaters, around 4% of energy can be saved after optimization compared to the case without insulating cover. We also found that increasing the heating accuracy (lowering the temperature deviation) will decrease the energy efficiency. We suggest that it is unnecessary to minimize the temperature deviation below a certain value around 2~3C. Because the difficulties of the testing condition, the verification of the results of numerical simulation and optimization will be done by physical experiments at the forging factory in the future work.

ACKNOWLEDGEMENT This work was supported by the Ministry of Knowledge

Economy, Korea, under the International Collaborative R&D Program hosted by the Korea Institute of Industrial Technology.

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