Effect of multi-layered induction coils on efficiency and uniformity of surface heating

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1 Effect of multi-layered induction coils on efficiency and uniformity of surface heating Ming-Shyan Huang *, Yao-Lin Huang Department of Mechanical and Automation Engineering, National Kaohsiung First University of Science and Technology, 2 Jhuoyue Road, Nanzih, Kaohsiung City 811, Taiwan, ROC article info abstract Article history: Received 10 February 2009 Received in revised form 23 December 2009 Accepted 23 December 2009 Available online 12 February 2010 Keywords: Coil design Induction heating Multiple physical coupling analyses PCA Principal component analysis Rapid mold surface heating Taguchi method This article explores the effect of the design of the multi-layered coil on the efficiency and uniformity of high-frequency electromagnetic induction surface heating. This work aims to improve the non-uniform temperature distribution of the cross and depth sections of a heated target that is produced by the approximate and skin effects, which often occur in induction heating using a conventional single-layered coil. The goal is to heat rapidly and uniformly the surface of a target. An injection mold plate is used as the target of induction heating; this investigation first utilizes multiple physical coupling analyses in ANSYS software to predict the temperature profile in the various layers of a coil. The Taguchi method and principal component analysis (PCA) are then adopted to determine the best combination of process parameters with a two-layered induction coil. The effects of the multi-layered induction coils on the heating history are further examined, and are compared with those of the single-layered coil in terms of the duration of heating required to yield a surface temperature of over 100 C and the largest heating area at uniform temperature. The experimental results show that the multi-layered coil heats to a uniform temperature more efficiently than the conventional single-layered coil, and the temperature varies within 5 C even upon heating to 190 C. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Recent studies have proven that a high temperature on the surface of an injection mold advantageously shortens the cycle time, improves the replication of micro-features, and reduces the welding lines of injection molding parts [1 4]. The use of high-frequency electromagnetic induction heating in the variothermal control of injection molds has thus attracted considerable attention over the last few years. Induction heating involves placing an induction coil at the proper distance from the front end of a workpiece, and to pass through it a high-frequency electric current. The surface of the workpiece is thus immediately heated to a high temperature. Most induction heating coils are made of such materials as copper or chromium copper. The method of heating changes with the geometry of the workpiece [5 7]. The main considerations in designing an induction heating coil are as follows. (1) Number of stacking layers in the induction coil. In a disctype spiral coil, the lateral uniform distribution of the electric current is made more uniform by controlling the number of central and external turns of the coil [8]. (2) Cross-sectional shape control of the induction coil. The cross-section of a good coil can be designed using the finite element method by considering the relationship between eddy-current and the excitation current density. The hollow effect of a heated stylus on the eddy-current density in a part of which eddy-currents are concentrated can be improved sufficiently [9]. (3) Conduction control of multi-induction coils. The eddy-current loss of a disc-type spiral coil has a non-uniform distribution at its central and external surfaces. This problem can be effectively eliminated using multi-coils that conduct various frequencies [10]. However, this approach requires various high-frequency induction heaters and the control of the various frequencies. (4) Distance of heat from induction coil. The non-uniformity of the lateral distribution of electric current in the cross-section of the conductor due to approximate effects can be effectively eliminated using various heating distances. Also, the uniformity of the temperature of the heated surface can be thus improved [11]. In summary, the above four considerations concern mainly in the design of an induction coil. To realize rapid and uniform heating to high temperature, with a large area of uniform temperature following the surface heating of injection molds, this work aims to design the optimal heating coils for use in high-frequency

2 M.-S. Huang, Y.-L. Huang / International Journal of Heat and Mass Transfer 53 (2010) induction heating. Consequently, the non-uniformity of the heat distributions on the section of a heated conventional disc-type single-layered wound conductor in both transverse and longitudinal directions, resulting from the approximate effect and skin effect, can be eliminated. This study is divided into three parts. (1) Analysis of key design parameters of induction coil: The Taguchi method is used to analyze the effective quantity of circular windings, quantity of layers, spacing, and stacking methods as experimental factors. (2) Design of optimal induction coil and process parameters: This part uses ANSYS software with the Taguchi method to determine the best combination of design parameters that optimize multiple qualities in the case of a uniform heat distribution and a short heating cycle. These qualities are related to but conflict with each other. PCA can be used to convert these related qualities into independent quality indicators, and then a composite quality indicator that represents the multiple quality characteristics can be constructed [12]. This indicator effectively clarifies the relations between the designs of various coils and the physical parameters of induction heating to yield the optimal design that provides a uniform temperature. (3) Experimental evaluation: The multi-layered coil design is verified by considering the performance for various mold temperatures, and the effect of various heating durations. 2. Induction heating theory According to the Faraday induction law, Eq. (1), the electromotive force on the induction coil is produced by the magnetic field inducted by the column, and is called self-induced potential: E ¼ L di ð1þ dt where E is electromotive force; L is self-inductance, and i is electric current. For variously shaped induction coils, Eqs. (2) (4) yield the self-inductance L, mutual inductance M, and mutual instantaneous magnetic flux : L ¼ lan2 ¼ l ol r AN 2 M ¼ lan 1N 2 ð3þ / ¼ lan 1I 1 ð4þ where l, l o and l r are properties of magnetic conductivity; A is cross-sectional area; N 1 and N 2 are the number of turns of the coils; l is length, and I 1 is electric current. A single coil has a self-inductance function, whereas multiple coils have a mutual inductance function. Eqs. (5) and (6) indicate that the mutual inductance function of each coil in a serial array has a connection mutual assistance term L Ta and a connection mutual elimination term L Tb, respectively. L Ta ¼ L 1 þ L 2 þ 2M L Tb ¼ L 1 þ L 2 2M ð2þ ð5þ ð6þ Eq. (7) gives coupling constant K between two coils, which is the ratio of the instantaneous mutual inductance of the coils to the maximum mutual inductance. The value of K is positive if the magnetic fluxes of the two coils are in the same direction, and negative if they are oppositely directed. K ¼ p ffiffiffiffiffiffiffiffiffi M ; jkj < 1 ð7þ L 1 L 2 The above formula indicates that a change in electric current in a coil causes electromagnetic induction in or between the coils. This electromagnetic induction reflects the electromagnetic properties of a coil and between the coils, and can be described in terms of self-inductance and mutual inductance of the coil. The electromotive force associated with self-induction is generated by the coil itself. In Eq. (2), L includes the magnetic conductivity l, so a change in the electric current i results in a change in the l value of the iron core. Thus, L also varies with the i. Moreover, Eqs. (3) and (4) reveal that M between coils is governed by the shape, size and number of turns of the coils and the ferromagnetics, as well as the relative location of the coils referred to Eqs. (5) (7). In this work, the shape, size and number of turns of the coils and the relative location of the coils are considered in the design of the optimal induction coil for rapid and uniform surface heating. 3. Principal component analysis (PCA) PCA enables data that contain information on multi-quality characteristics to be converted into several independent quality indicators. Some of these indicators are then adopted to construct a composite quality indicator, which is a mathematical function of the several required quality characteristics. Initially, data on the multi-quality characteristics were collected and normalized to yield dimensionless values between 0 and 1. Changing the quality requirements changes the corresponding normalization, as shown below [12]. Case1: Larger-is-better. The target value of the quality objectives was uncertain but was expected to be large. Y ij ¼ L ij minðl j Þ maxðl j Þ minðl j Þ Case 2: Smaller-is-better. The target value of the quality objectives was uncertain but was expected to be small. Y ij ¼ maxðl jþ L ij maxðl j Þ minðl j Þ Case 3: Target-is-best. The target value of the quality objectives was known and was expected to be reached. Y ij ¼ 1 jl ij O b j maxfmaxðl j Þ O b ; O b minðl j Þg ð8þ ð9þ ð10þ where L ij and Y ij represent the observed and its normalized values in the ith experimental run of the jth quality characteristics, respectively; max(l j ) and min(l j ) denote the maximum and the minimum observed values of the jth quality characteristics, respectively, and O b is the target value. In this formula, a larger Y ij corresponds to a better quality of a product. These normalized data were used to construct a variancecovariance matrix A, as follows. 2 3 R 1;1 R 1;2... R 1;n R 2;1 R 2;2... R 2;n A ¼ ð11þ 5 R n;1 R n;2 R n;n CovðY i;k R k;l ¼ ; Y i;l qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Þ VarðY i;k ÞVarðY i;l Þ ð12þ where n is the number of quality characteristics. The eigenvectors and eigenvalues of matrix A are computed and represented as V j and j, respectively. In PCA, eigenvector V j is the weighting vector of j quality characteristics of the jth principal component. For instance, when Q j is the jth quality characteristic, the jth principal component w j is

3 2416 M.-S. Huang, Y.-L. Huang / International Journal of Heat and Mass Transfer 53 (2010) Table 1 Eighteen types of two-layered disc-type spiral coils. # Code Diagram Heating direction Coil winding Direction of electric current # Code Diagram Heating direction Coil winding Direction of electric current 1 CNL 1 I 1 Non-reverse L 1 I 1 10 CIL 1 I 1 Reverse L 1 I 1 2 CNL 1 I 2 Non-reverse L 1 I 2 11 CIL 1 I 2 Reverse L 1 I 2 3 CNL 1 I 3 Non-reverse L 1 I 3 12 CIL 1 I 3 Reverse L 1 I 3 4 CNL 2 I 1 Non-reverse L 2 I 1 13 CIL 2 I 1 Reverse L 2 I 1 5 CNL 2 I 2 Non-reverse L 2 I 2 14 CIL 2 I 2 Reverse L 2 I 2 6 CNL 2 I 3 Non-reverse L 2 I 3 15 CIL 2 I 3 Reverse L 2 I 3 7 CNL 3 I 1 Non- reverse L 3 I 1 16 CIL 3 I 1 Reverse L 3 I 1 8 CNL 3 I 2 Non-reverse L 3 I 2 17 CIL 3 I 2 Reverse L 3 I 2 9 CNL 3 I 3 Non-reverse L 3 I 3 18 CIL 3 I 3 Reverse L 3 I 3 CN: Direction of heating from the first layer faces to the target. CI: Heating surface in the reverse direction compared to CN. L 1 : Quantity of the coil windings declines from the outside to the center. L 2 : Quantity of the coil windings declines from the center to outside. L 3 : Quantity of the coil windings declines from both the center and the outsides. I 1 : Direction of the electric current entering the coil winding in a conventional vortex form. I 2 : Direction of the electric current entering the coil winding in a mirror array form. I 3 : Direction of the electric current direction entering the coil winding in a moving array form. treated as a quality indicator with the required quality characteristics that satisfies w j ¼ V 1j Q 1 þ V 2j Q 2 þþv jj Q j ¼ V 0 j Q ð13þ Notably, each principal component w j explains some of the variation of the quality characteristics, called the accountability proportion (AP). A combination of numerous principal components explains more of the quality characteristics, called the cumulative accountability proportion (CAP). In this study, the composite principal component w was defined as the sum of all principal components, w j. The component w j was designated as an individual quality indicator. The composite principal component is a generalized indicator of partial quality characteristics, as presented below. w ¼ XK w j j¼1 ð14þ If a quality characteristic Q j strongly dominates the jth principal component, then this principal component becomes the major

4 M.-S. Huang, Y.-L. Huang / International Journal of Heat and Mass Transfer 53 (2010) Table 2 Material properties of SKD61 used in mold surface heating experiment. AISI H13 (JIS SKD61) Density (1000 kg/m 3 ) 7.76 Poisson s ratio ( C) 10.4 Thermal expansion coefficient (10 6 / C) ( C) 11.5 ( C) 12.2 ( C) 12.4 ( C) 13.1 ( C) 28.6 Thermal conductivity coefficient (w/m K) ( C) 28.4 ( C) 28.4 ( C) 28.7 indicator of that quality characteristic. In this study, PCA is computed using Minitab R14 software to determine the properties of the optimal induction coil. 4. Computer simulation and optimization In this work, the commercial simulation software ANSYS was adopted to analyze induction heating conditions. This software is based on a multiple physical coupling analysis that involves both electromagnetic analysis and thermal analysis; it is useful in simulating the thermal phenomenon associated with various geometrical structures of objects and induction heating settings. The simulation comprises two steps, which are (1) electromagnetic analysis to determine the eddy loss appeared on the surface of the heated target, following by (2) thermal analysis to calculate the mold surface temperature, in which the eddy loss in step 1 is treated as a heat source. In the simulation, the geometries PLANE13 and PLANE55, coded by ANSYS, are used in the electromagnetic and thermal analyses, respectively. The computer used to perform the simulation had a Pentium 43 GHz CPU, with 2 Gbytes of RAM. A 5 mm diameter coil was adopted to produce the multi-layered disc-type spiral coils that were used in this experiment. The multi-layered disc-type spiral coil is classified according to the heating direction to the target, the shape of the coil winding, and the direction of the electric current. For example, the direction of heating from an induction coil to the target defines the coil as either (1) CN type, or (2) CI type, which is like the CN type, but with the heating surface in the reverse direction. The shapes of coil windings define (1) the L 1 type, in which the quantity of the coil windings declines from the outside to the center, (2) the L 2 type, in which the quantity of the coil windings declines from the center Table 3 Inner orthogonal array used for optimally designed two-layered induction coils. Control factors Unit Level 1 Level 2 Level 3 A Inverse of upper and lower layers CN CI - B Course of the coil winding L 1 L 2 L 3 C Number of the upper layer Turn D Number of the lower layer Turn E Direction of the electric current I 1 I 2 I 3 F Distance between the coil and the mold mm surface G Distance between the upper and lower mm layers H Working frequency khz CN: Direction of heating from the first layer faces to the target. CI: Heating surface in the reverse direction compared to CN. L 1 : Quantity of the coil windings declines from the outside to the center. L 2 : Quantity of the coil windings declines from the center to outside. L 3 : Quantity of the coil windings declines from both the center and the outsides. I 1 : Direction of the electric current entering the coil winding in a conventional vortex form. I 2 : Direction of the electric current entering the coil winding in a mirror array form. I 3 : Direction of the electric current direction entering the coil winding in a moving array form. to outside, and (3) the L 3 type, in which the quantity of the coil windings declines from both the center and the outsides. The electric current direction defines three types; (1) I 1 type, in which the direction of the electric current entering the coil winding in a conventional vortex form; (2) I 2 type, in which the direction of the electric current entering the coil winding in a mirror array form; (3) I 3 type, in which the direction of the electric current direction entering the coil winding in a moving array form. In summary, 18 types of two-layered disc-typed spiral coils are studied to eliminate the non-uniformity of heating, as shown in Table 1. The object heated by induction heating in this work is a ferromagnetic, hot working tool made steel SKD61; Table 2 presents its material properties. Since the electromagnetic parameters, thermal properties, and mechanical properties vary with the electromagnetic and thermal fields, these nonlinear properties are considered in the simulation. In this study, the mold temperature is maintained between 100 C and 150 C. Also, the coil windings form a cuboid with a square cross-section; the maximum length of the effective windings in the coil is 70 mm, the number of effective stacking layers does not exceed two, and the dimensions of the mold plate that is heated are 150 mm long 150 mm wide 20 mm thick. To determine the optimal combination of winding parameters and the heating parameters for coil design by the Taguchi method, the quality indicators are defined as (1) minimal duration of Table 4 L 4 outer orthogonal array used for optimally designed induction coils. Diagram The L 4 outer orthogonal array No. of exp. DP P (mm) DP T (mm) DP V (mm) Ideal value Error P T DP T P V DP V P P DP P

5 2418 M.-S. Huang, Y.-L. Huang / International Journal of Heat and Mass Transfer 53 (2010) Table 6 Eigenvalues, eigenvectors, accountability proportion (AP), and cumulative accountability proportion (CAP) computed for the first two major quality indicators. w 1 w 2 Eigenvalue Eigenvector [0.707, 0.707] T [0.707, 0.707] T AP CAP Table 7 ANOVA of composite quality indicator w. SV DOF SS MS F PSS CP(%) Inverse of upper and lower layers Course of the coil winding Number of the upper layer Number of the lower layer Direction of the electric current Distance between the coil and the mold surface Distance between the upper and lower layers Working frequency Error Pooled error (9) (0.162) (0.018) Total SV, source of variation; DOF, degrees of freedom; SS, sum of squares; MS, mean square; PSS, pure of sum squares; CP, contribution percentage. heating to reach the target temperature; and, (2) maximal area of uniform temperature distribution. Table 3 specifies L 18 ( ) Taguchi orthogonal arrays that are used in the simulation of induction heating. The chosen experimental factors were the inverse of upper and lower layers, the course of the coil winding, the number of upper layers, the number of lower layers, the direction of the electric current, the distance between the coil and the mold surface, the distance between the upper and lower layers, and the working frequency. The interactions among various factors affect each row, factor and level as presented in Table 3. Not only do the aforementioned factors affect uniformity of heating, but also the space between coil windings, the distance between the coil and the mold surface, and the variation in the quality of the coil that is associated with the stacking format and the space of the coil are regarded as noise factors. These factors are set in an L 4 external orthogonal table as the external variables, as presented in Table 4. The requirements are to minimize the heating cycle time required to achieve uniform temperature distribution and to maximize the heating area at uniform temperature. Columns 6 and 11 in Table 5 present the normalized and averaged values of these qualities, respectively. They were used to produce the variance-covariance matrix and then to calculate the eigenvalues using PCA. Table 6 presents the obtained eigenvalues, accountability proportions (AP), and eigenvectors. Table 6 shows that the eigenvalue of the first principal component w 1 was 1.44 and AP was 0.72; the eigenvector of the second principal component w 2 was 0.56 and AP was The composite quality indicator was the sum of individual quality indicators, whose cumulative accountability proportion, CAP, is normally set to greater than 0.8. In this case, the composite quality indicator w is the sum of w 1 and w 2, since the CAP of w 1 and w 2 was In Table 6, the heating duration required to yield a uniform temperature distribution and the working range over which the temperature distribution was uniform, with given the weighting vector of the first principal component, yielded the eigenvector [0.707, 0.707] T. This vector was substituted into Eq. (13) to calculate the first principal component w 1 and w 2. The quality observations obtained using the Taguchi method were converted into w 1, w 2 and w using PCA, as shown in columns 12, 13 and 14 in Table 5. Table 7 displays the results of the ANOVA analysis carried out to obtain the w value obtained using the L 18 ( ) Taguchi method. The results show that the direction of the electric current, the number of turns of the coil in the second layer of the coil, the number of turns of the coil in the first layer of the coil, and the distance between the layers significantly affect the values of the composite principal component, so these four factors were treated as the key design parameters. Fig. 1 presents the responses to various levels of factors. The best combination of a two-layered induction coil is A 1 B 3 C 2 D 3 E 1 F 1 G 2 H 2, meaning the CNL 2 I 1 type with one turn in the Table 5 L 18 ( ) simulation results. Exp. no. Heating cycle to achieve uniform temperature (s) Heating area at uniform temperature (mm) w 1 w 2 w y1 y2 y3 y4 Averaged normalized heating duration y1 y2 y3 y4 Averaged normalized working range

6 M.-S. Huang, Y.-L. Huang / International Journal of Heat and Mass Transfer 53 (2010) first layer, four turns in the second layer, a distance to the heated target of 3.5 mm, a distance between layers of 12 mm, and a working frequency of 41 khz. Since the number of turns of the coil in each layer dominates the induction heating performance, as described above, this work further adds a layer of the coil in the stacking direction. Fig. 2 depicts the geometry of the three-layered induction coil. Fig. 3 presents the simulation of the temperature distributions when induction heating is applied the mold surface, using a single-layered coil, a two-layered coil and a three-layered coil. The instantaneous variation in the surface temperature is improved from 44.1 C to 30.4 C when the third layer is added. The temperature variation increases to 58.7 C when only one layer is used. The results indicate that adding one layer in the stacking direction to the best coil, as designed using the Taguchi method, improves heating efficiency and uniformity. 5. Experimental evaluation The experimental evaluation in this study compares the temperature uniformities obtained using induction heating of the mold surface with the three-layered coil, the optimal two-layered coil obtained by the Taguchi method, and the single-layered coil. These temperature uniformities are also predicted by computer simulation analysis. Table 8 presents information on the experimental setup. The injection mold is preheated to 100 C using oil. Then, the mold surface is induction-heated for 8 s and then moved away from the coil until the temperature of the mold surface is being, Fig. 1. S/N response of multiple quality characteristics. Fig. 2. Geometry of three-layered induction coil (unit: mm).

7 2420 M.-S. Huang, Y.-L. Huang / International Journal of Heat and Mass Transfer 53 (2010) Fig. 3. Simulation analysis of instantaneous surface temperature distribution obtained by induction heating using single-layered, two-layered, and three-layered coils. Table 8 Experimental setup. Types of induction coil Single-layered Two-layered Three-layered 1st layer nd layer 1 1 3rd layer 1 Process setting of induction rapid surface heating (Mold preheated to 100 C by oil) Distance 3.5 mm between the coil and the mold surface Working 41 khz frequency Heating duration 8s meaning that the temperature deviation is less than 5 C. As presented in Figs. 4 and 5 and Table 9, (1) overall, the results of the simulation are consistent with experimental results; (2) a multi-layered coil design generates a higher temperature than the conventional single-layered design: the uniform temperatures practically obtained using single-layered, two-layered, and threelayered coils are C, C and C, respectively; (3) the duration for the three-layered coil to reach a uniform temperature is only 3 s, which is much shorter than that required by the other two (8 s and 5 s for the single-layered and the two-layered coils, respectively); however, (4) the area of uniform temperature is only 53 mm (54 mm in the simulation) for the three-layered coil, 60 mm (62 mm in the simulation) for the single-layered coil and 55 mm (56 mm in the simulation) for the two-layered coil. This phenomenon is associated with the effect of waiting time on the heat balance: increasing the waiting time increases the area of uniform temperature but reduces the actual uniform temperature. This work further experimentally studies the uniformity of temperature that corresponds to various mold temperature settings and heating durations. The results in Table 10 are the heating durations required for various temperature settings. An infrared thermal image detector reveals that increasing the heating duration and mold temperature increases the final uniform temperature of the mold surface. To evaluate the stability of induction heating, a repeatability test was also conducted. On the three-layered coil, as an example, 50 mold surface heating tests were performed using the same process settings as were used in the optimal two-layered induction coil in Section 4. In each experimental run, the high-frequency induction heating system is manipulated using a robot. The target value of the mold surface temperature is 190 C, and the temperature difference within u = 50 mm of the mold surface is recorded. The experimental results show that the temperature variation that corresponds to these 50 tests is 4.95 C, which is satisfactory for injection molding. 6. Conclusions A high temperature setting on the surface of injection mold was demonstrated to shorten cycle time, improve the level of filling with melt plastics in microinjection molding, and reduce the number of welding lines in molded parts. However, traditional high-frequency electromagnetic induction heating of a mold surface using a single-layered coil has the disadvantage of producing a non-uniform temperature distribution over the cross and depth sections of the heated target because of approximate and skin effects. Accordingly, this work introduces a multi-layered designed induction coil to increase the efficiency of mold surface heating and the uniformity of the temperature obtained. The following conclusions are drawn. (1) This work uses multiple physical coupling analyses in ANSYS software to predict the thermal effect of induction heating on the surface of the heated target. This model can yield the temperature profile in an optimally designed multi-layered induction coil. (2) A computer simulation is conducted using the Taguchi method and the PCA to optimize the process parameters with a two-layered induction coil in terms of efficiency and uniformity of surface heating. The results demonstrate that the direction of the electric current, the number of turns

8 M.-S. Huang, Y.-L. Huang / International Journal of Heat and Mass Transfer 53 (2010) Fig. 4. Instantaneous surface temperature profiles following induction heating using single-layered, two-layered, and three-layered coils. in the second layer of the coil, the number of turns in the first layer of the coil, and the distance between the layers are the key design parameters. The best combination twolayered induction coil is suggested to be the CNL 2 I 1 type, with one turn in the first layer, four turns in the second layer, a distance to the heated target of 3.5 mm, a distance between layers of 12 mm, and a working frequency of 41 khz. (3) Experimental results reveal that the multi-layered coil more efficiently delivers a uniform temperature than the conventional single-layered coil; the temperature variation, obtained using a three-layered coil for example, can be maintained within 5 C even upon heating up to 190 C. Hence, the application of multi-layered induction coils in injection mold surface heating is feasible in terms of heating efficiency and temperature uniformity. Fig. 5. Temperature history obtained by induction heating using single-layered, two-layered, and three-layered coils.

9 Table 9 Temperature distributions of induction coils designed with various types of induction coil (heating duration: 8 s). Simulation Single-layered coil Two-layered coil Three-layered coil Uniform temperature C C C Area of uniform temperature (T 6 5 C) / 62 mm / 56 mm / 54 mm Experimental Uniform temperature C C C Area of uniform temperature (T 6 5 C) / 60 mm / 55 mm / 53 mm Duration to reach uniform temperature 8 s 5 s 3 s 2422 M.-S. Huang, Y.-L. Huang / International Journal of Heat and Mass Transfer 53 (2010)

10 M.-S. Huang, Y.-L. Huang / International Journal of Heat and Mass Transfer 53 (2010) Table 10 Experimental evaluation of temperature uniformity corresponding to various mold temperature setting and heating duration. Type of induction coil Mold materials/dimensions Distance between the coil and the mold surface Working frequency Temperature measurement equipment SKD 61/150 mm 150 mm 20 mm 3.5 mm 41 khz Infrared thermal detector Mold temperature preheated by oil ( C) Induction heating duration (s) Acknowledgements The authors would like to thank the National Science Council of the Republic of China, Taiwan, for financially supporting this research under Contract No. NSC E Ted Knoy is appreciated for his editorial assistance. References [1] S.C. Chen, W.R. Jong, Y.J. Chang, J.A. Chang, J.C. Cin, Rapid mold temperature variation for assisting the micro injection of high aspect ratio micro-feature parts using induction heating technology, J. Micromechan. Microeng. 16 (2006) [2] S.C. Chen, W.R. Jong, J.A. Chang, Dynamic mold surface temperature control using induction heating and its effects on the surface appearance of weld line, J. Appl. Polymer Sci. 101 (2006) [3] P.C. Chang, S.J. Hwang, Simulation of infrared rapid surface heating for injection molding, Int. J. Heat Mass Transfer 149 (2006) [4] M.-S. Huang, N.-S. Tai, Experimental rapid surface heating by induction for micro-injection molding of light-guided plates, J. Appl. Polym. Sci. 113 (2009) [5] S. Zinn, S.L. Semiatin, Coil design and fabrication: basic design and modifications, Heat Treat. (1998) [6] S. Zinn, S.L. Semiatin, Coil design and fabrication: part 2, specialty coils, Heat Treat. (1998) [7] S. Zinn, S.L. Semiatin, Coil design and fabrication: part 3, fabrication principles, Heat Treat. (1998) [8] C.G. Kang, P.K. Seo, H.K. Jung, Numerical analysis by new proposed coil design method in induction heating process for semi-solid forming and its experimental verification with globalization evaluation, Mater. Sci. Eng. A 341 (2003) [9] T. Todaka, M. Enokizono, Optimum design method with the boundary element for high-frequency quenching coil, IEEE Trans. Magnet. 32 (1996) [10] H. Fujita, N. Uchida, K. Ozaki, Zone controlled induction heating (ZCIH): a new concept in induction heating, Power Conversion Conference-Nagoya, 2007, pp [11] A. Boadi, Y. Tsuchida, T. Todaka, M. Enokizono, Designing of suitable construction of high-frequency induction heating coil by using finiteelement method, IEEE Trans. Magnet. 41 (2005) [12] M.-S. Huang, T.-Y. Lin, Simulation of a regression-model and PCA based searching method developed for setting the robust injection molding parameters of multi-quality characteristics, Int. J. Heat Mass Transfer 51 (2008)