Di

Za

b

a

ARRAA

KHSMI

1

aaimfawcHne

m(psist

0d

Journal of Materials Processing Technology 211 (2011) 1432–1440

Contents lists available at ScienceDirect

Journal of Materials Processing Technology

journa l homepage: www.e lsev ier .com/ locate / jmatprotec

etermination of heat transfer coefficients by extrapolation and numericalnverse methods in squeeze casting of magnesium alloy AM60

hizhong Suna,∗, Henry Hua, Xiaoping Niub

Department of Mechanical, Automotive & Materials Engineering, University of Windsor, 401 Sunset Ave., Windsor, Ontario N9B 3P4, CanadaPromatek Research Centre, Cosma International, Brampton, Ontario L6T 5R3, Canada

r t i c l e i n f o

rticle history:eceived 18 October 2010eceived in revised form 12 March 2011ccepted 15 March 2011vailable online 22 March 2011

eywords:

a b s t r a c t

In this work, a different wall-thickness 5-step (with thicknesses as 3, 5, 8, 12, 20 mm) casting mold wasdesigned, and squeeze casting of magnesium alloy AM60 was performed under an applied pressure 30,60 and 90 MPa in a hydraulic press. The casting–die interfacial heat transfer coefficients (IHTC) in the5-step casting were determined based on thermal histories throughout the die and inside the castingwhich were recorded by fine type-K thermocouples. With measured temperatures, heat flux and IHTCswere evaluated using the polynomial curve fitting method and numerical inverse method. For numerical

eat transfer coefficientqueeze castingagnesium alloy

nverse method

inverse method, a solution algorithm was developed based on the function specification method to solvethe inverse heat conduction equations. The IHTCs curves for five steps versus time were displayed. Asthe applied pressures increased, the IHTC peak value of each step was increased accordingly. It can beobserved that the peak IHTC value decreased as the step became thinner. Furthermore, the accuracy ofthese curves was analyzed by the direct modeling calculation. The results indicated that heat flux andIHTCs determined by the inverse method were more accurately than those from the extrapolated fitting

method.

. Introduction

Compared to other conventional casting processes, the mostttractive features of squeeze casting (SC) are slow cavity fillingnd pressurized solidification. Before the solid fraction of the cast-ng becomes high enough, the applied pressure squeezes liquid

etal feed into the air or shrinkage porosities effectively. There-ore, squeeze casting can make castings virtually free of porositynd usually have excellent as-cast quality, and are heat treatable,hich is difficult to achieve with other conventional casting pro-

esses. Despite many squeeze casting research activities of Cho andong (1996) and Yu (2007), certain fundamental questions stilleed to be answered and the process must be optimized so as toxpand its application, especially for emerging magnesium alloys.

To solve the obstacles of squeeze casting application, the opti-ized process parameters and interfacial heat transfer coefficients

IHTCs) at the metal–mold interface need to be further studied. Therocess parameters, such as the applied hydraulic and local pres-

ures, pouring temperatures, and die initial temperatures, have annfluence on the formation of pressure-transfer path, which con-equently affects heat transfer at the metal–mold interface andhe finial quality of squeeze castings. In various casting processes,

∗ Corresponding author. Tel.: +1 519 2533000.E-mail address: sun1l@uwindsor.ca (Z. Sun).

924-0136/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2011.03.014

© 2011 Elsevier B.V. All rights reserved.

the contact between the liquid metal and die inner surface is usu-ally imperfect because of coating applied on the die surface andair gap caused by shrinkage. These thermal barriers may decreasethe heat transfer between metal and die and cooling rates of thecasting surface, which influence microstructure and quality of thecasting significantly. Hence, precise determination of heat transfercoefficients at the metal–mold interface is essential to accuratelysimulate solidification process and model microstructure evolutionof die castings. Especially, for thin-wall castings, Guo et al. (2008)described that the accuracy of IHTCs is critically vital due to verylimited solidification time.

Although the IHTC has been studied extensively by manyresearchers, rare experiment has been carried on to determine theIHTC in squeeze die casting processes because it is hard to performand the operation procedure is complicated for magnesium alloys.Cho and Hong (1996) estimated heat transfer coefficients at themolten metal–die interface in aluminum alloy (Al–4.5%Cu) squeezecasting. The IHTC values were about 1000 W/m2 K prior to pressur-ization which rapidly increased to around 4700 W/m2 K at a singlehydraulic pressure (50 MPa) for a cylindrical casting with a heatedsteel die. Then, it was concluded that IHTC increased with the appli-

cation of pressure. Kim and Lee (1997) investigated the tube shapecasting and found that the heat transfer coefficients at the interfaceof the inner mold decreased temporarily and then increased, whilethe one at the outer interface of the mold decreased monotonously.Browne and O’Mahoney (2001) carried out experiments with dif-

cessing Technology 211 (2011) 1432–1440 1433

fttmaI

tfl(grma(dAca

mAtimilap2st

tptI7

amtdItfott3

cBwmm

gtprTcIum

Z. Sun et al. / Journal of Materials Pro

erent solidification ranges of aluminum alloys. After investigatinghe effect of alloy solidification ranges, metal static heads, initial dieemperatures and interface geometry shapes, they found that the

etal static head affected IHTC significantly for long freezing rangelloys and initial temperatures also had alloy-dependent effects onHTC.

By applying the Laplace Transform of the heat conduction equa-ion, Broucaret et al. (2001) estimated the unidirectional heatux exchanged between plate shape die and aluminum–siliconAS7G06) casting. Dour et al. (2005) developed a heat-transferage which used an infrared probe incorporated into a Pyromet-ic chain. They claimed that the inside die temperature and moltenetal surface temperature can be measured accurately without

ny intrusion into the casting. By this method, Dargusch et al.2007) measured surface die temperature and determined IHTCuring high pressure die casting of magnesium alloy AZ91 andl–9%Si–3%Cu alloy. The results showed that the peak IHTC reachedlose to 9000 W/m2 K and 8500 W/m2 K for aluminum alloy A380nd magnesium alloy AZ91, respectively.

Hamasaiid et al. (2007) measured IHTC peak values in per-anent mold casting of aluminum alloys Al–9Si–3Cu (A380) andl–7Si–0.3Mg (A356) are 3000 W/m2 K and 4000 W/m2 K, respec-

ively. In high pressure die casting process, Guo et al. (2008)nvestigated the IHTC of a step-shape high pressure die casting in

agnesium alloy AM50 and aluminum alloy ADC12. The resultsndicated that the IHTC value increased during initial stage, fol-owed by fluctuation period of the peak values, then droppedbruptly until a much lower level. Within the peak value fluctuationeriod, the maximum IHTC values are 12,900 W/m2 K for AM50 and0,760 W/m2 K for ADC12, respectively. In thinner steps, a fasterhot velocity led to a higher IHTC peak value. The higher initial dieemperatures, the lower the IHTC peak values for the thick sections.

Yu (2007) studied the IHTC of a cylindrical shape coupon inhe squeeze casting of magnesium alloy AM50. When the appliedressure changed from 30 to 90 MPa, the IHTC peak values of theop coupon varied from 8400 W/m2 K to 10,090 W/m2 K, and theHTC peak values of the side casting varied from 6900 W/m2 K to257 W/m2 K, accordingly.

Aweda and Adeyemi (2009) carried out the experiments oncylindrical shape squeeze casting of commercially pure alu-inum. With the measured temperatures inside a steel die,

he die surface temperature was deducted by extrapolating toie–metal interface by polynomial curve fitting technique. The

HTC obtained by extrapolating method under no pressure applica-ion was 2998 W/m2 K, which agreed with 2975 W/m2 K obtainedrom numerical inverse method. He also observed that the effectf applied pressure became more significant at temperature closeo the liquidus temperature. Within this temperature range,he measured peak values of IHTC varied from 3000 W/m2 K to400 W/m2 K with the applied pressure range from 0 to 85 MPa.

Beck (1970) and Beck et al. (1996) proposed the function specifi-ation method which can be used for linear or non-linear problems.riefly, the method was to minimize the sum of squares functionith respect to heat flux (q) and the errors between calculated andeasured data. It was concluded that the function specificationethod gave the similar results avoid time-consuming calculation.However, these studies only focused on castings with simple

eometries. Little attention has been paid to variation of castinghicknesses and hydraulic pressures. Actually, in the die castingractice, the different thicknesses at different locations of castingsesults in significant variation of the local heat transfer coefficients.

herefore, it would be important to investigate the influence ofasting thickness, pressure value, and process parameters on theHTC. In this study, a special 5-step squeeze casting was designed fornderstanding casting thickness-dependant IHTC. The temperatureeasuring units to hold multiple thermocouples simultaneously

Fig. 1. The 3-D model of 5-step casting with the round-shape gating system. (A) XZview; (B) YZ view; and (C) isometric view.

and the pressure transducers were employed to accurately measurethe temperatures and the local pressures during squeeze casting ofmagnesium alloy AM60.

2. Experiments

2.1. Step casting model

Fig. 1 shows the 3-D model of 5-step casting, which consists of5 steps (from top to bottom designated as steps 1–5) with dimen-sions of 100 mm × 30 mm × 3 mm, 100 mm × 30 mm × 5 mm,100 mm × 30 mm × 8 mm, 100 mm × 30 mm × 12 mm,100 mm × 30 mm × 20 mm accordingly. The molten metal wasfilled the cavity from the bottom cylindrical shape sleeve withdiameter 100 mm.

2.2. Configuration of die and installation of measurement unit

To measure the temperatures and pressures at the casting–dieinterface accurately and effectively, a special thermocouple holderwas developed. It hosted 3 thermocouples simultaneously toensure accurate placement of thermocouples in desired locationsof each step. The thermocouple holders were manufactured usingthe same material P20 as the die to ensure that the heat transferprocess would not be distorted. Fig. 2 illustrates schematically theconfiguration of the upper die (left and right parts) mounted onthe top ceiling of the press machine. It also reveals the geomet-ric installation of pressure transducers and thermocouple holders.Pressures within the die cavity were measured using Kistler pres-sure transducers 6175A2 with operating temperature 850 ◦C andpressures up to 200 MPa.

As shown in Fig. 2, pressure transducers and temperature ther-mocouples were located opposite each other so that measurementsfrom sensors could be directly correlated due to the symmetry ofthe step casting. Five pressure transducers and temperature mea-suring unit were designated as PT1–PT5, TS1–TS5, respectively.Each unit was inserted into the die and adjusted until the front wallof the sensor approached the cavity surface. The geometry shapeof thermocouples holders was purposely designed the same as the

pressure transducer, so that they could be exchangeable at differentlocations.

The thermocouples (Omega KTSS-116U-24) installed inside thedie and casting surface were type K with 1/16 in. diameter, stain-less steel sheath, ungrounded junction, and 24 in. sheath length. To

1434 Z. Sun et al. / Journal of Materials Processing Technology 211 (2011) 1432–1440

installation of thermocouples and pressure transducers.

mimdifimipbmpel(dbificd

Fp

Table 1Chemical composition of magnesium alloy AM60.

Fig. 2. Configuration of upper-dies and geometric

easure the casting surface temperature, the thermocouples werenserted into the cavity through the center hole of each temperature

easuring unit. As shown in Fig. 3, the thermocouple head was bentown to 90◦ and attached to the die surface tightly. The designed

nstallation method minimized the disturbance of the temperatureeld in the step casting cavity. On the right part of the die, the ther-ocouples was installed to measure casting surface (T-surf) and

nside die temperatures (T1, T2, T4). To ensure the accuracy, tem-erature measurements were also carried out simultaneously inoth the right and the left parts of the die. During the simultaneouseasurements, the bended thermocouple was absent in the left

art of the die, but was inserted only in the right part. The differ-nce in the measured temperatures for step 4 between the right andeft parts of the die was 1.97 ◦C, which gave the percentage error(T1L − T1R)/T1L) of 0.64%. For the thinnest step 1, the temperatureifference is 4.82 ◦C and the percentage error is 2.77%. Thus, usingended thermocouples in the cavity to measure the surface cast-

ng temperature caused almost no interference on the temperature

eld in the casting and heat transfer inside the die. This thermo-ouple head bending method enables to acquire relatively accurateata of the casting surface temperature.

ig. 3. Installation of thermocouples measuring casting surface and inside die tem-eratures.

Mg Al (%) Mn (%) Si (%) Cu (%) Zn (%)

Balance 5.5–6.5 0.13 0.5 0.35 0.22

2.3. Casting process

The integrated casting system consisted of a 75 tons laboratoryhydraulic press, a two halves split upper die forming a 5-step cavity,one cylindrical sleeve lower die, an electric resistance furnace anda data acquisition system. The 75-ton heavy duty hydraulic pressmade by Technical Machine Products (TMP, Cleveland, Ohio, USA)used in the experimental study. The die material was P20 steel.Commercial magnesium alloy AM60 was used in experiment. Thechemical composition of AM60 is shown in Table 1. Table 2 givesthe thermal properties of the related materials in this study. Basedon Yu’s (2007) work, the thermal conductivity (K) of AM60 hasthe linear relationship with its temperature and follows equations(K = 192.8 − 0.187T) in semisolid temperature range (540–615 ◦C);(K = 0.0577T + 60.85) below the solidus temperature (<540 ◦C), and(K = 0.029T + 59.78) for the liquid temperature range (>615 ◦C).

◦

Before the pouring, the dies were pre-heated to 210 C usingfour heating cartridges installed inside the dies. The experimentalprocedure included pouring molten magnesium alloy AM60 intothe bottom sleeve with a pouring temperature 720 ◦C, closing thedies, cavity filling, squeezing solidification with the applied pres-

Table 2Thermophysical properties of magnesium alloy AM60.

Properties Mg alloy AM60

Solid Liquid

Thermal conductivity (W/m K) 62 90Specific heat (J/kg K) 1020 1180Density (kg/m3) 1790 1730Latent heat (KJ/kg) 373Liquidus temperature at 0 MPa (◦C) 615Solidus temperature at 0 MPa (◦C) 540

Z. Sun et al. / Journal of Materials Processing Technology 211 (2011) 1432–1440 1435

der a

sdtKtb

ctTtA9ws

3

td

h

wTtbtdnotumies

Fig. 4. 5-Step castings solidifying un

ure, lowering the sleeve die, splitting the two parts of the upperie, Finally the 5-step casting can be shaken out from the cavity. Theemperatures inside the die and casting were measured by OmegaTSS-116U thermocouples with response time below 10 ms. Real-

ime in-cavity local pressures and temperature data were recordedy a LabVIEW- based data acquisition system.

The mold coating used in step castings is boron nitride lubri-ation (type Sf) which was sprayed manually onto the surface ofhe mold cavity before heating the dies to the initial temperature.o minimize the thermal barrier effect of mold coating, the coatinghickness applied in this study was relatively thin (below 50 �m).s shown in Fig. 4, totally 15 castings were poured with 30, 60 and0 MPa pressurized solidification. The chill vent and all five stepsere filled completely. X-ray radioscopic examination reveals the

oundness of the step castings.

. Mathematical modeling of IHTC

Based on the principle of heat transfer, the interfacial heatransfer coefficients (IHTC) between metal and die surface can beetermined by Eq. (1):

(t) = q(t)Tcs − Tds

(1)

here h is IHTC; q is heat flux at the metal–die interface; Tcs andds are the casting surface temperature and die surface tempera-ure, respectively; and t is the solidification time. With the knownoundary conditions in the form of temperatures or the heat fluxes,he temperature field inside the die or casting can be obtained byirect heat conduction method. But the values of Tcs and Tds can-ot be measured directly because the insertion of thermocouplesf finite mass at the interface may distort the temperature field athe interface. Further, the heat flow at the interface may not be

nidirectional due to complex geometry shape. Therefore, deter-ination of IHTC using measurements of Tcs, Tds, and q(t) directly

s difficult. As a result, inverse heat conduction method needs to bemployed to determine the IHTC based on the temperatures mea-ured inside the die or casting. To solve the direct heat conduction

pplied pressure 30, 60, and 90 MPa.

and inverse heat conduction problems, the numerical or analyticalmethod needs to be employed.

From the measured interior temperature histories, the transientmetal–die interface heat flux and temperature distribution wereestimated by two different techniques in this work: (1) polynomialextrapolation; and (2) inverse algorithm using function specifica-tion model, coupling with implicit finite difference method (FDM).

3.1. Inverse method

Because solidification of squeeze casting of magnesium alloyinvolves phase change and its thermal properties are temperature-dependent, the inverse heat conduction is a non-linear problem.To evaluate the IHTC effectively as a function of solidification timein the squeeze casting process, the finite difference method (FDM)was employed based on the Beck’s algorithm.

Since the thickness of each step was much smaller than thewidth or length of the step, it can be assumed that the heat trans-fer at each step was one-dimensional. The heat transfer across thenodal points of the step casting and die is shown in Fig. 5. The tem-peratures were measured at 2, 4, 8 mm beneath die surface and theheat flux transferred to the die mold can be evaluated by the inversemethod. Then, the temperatures at different locations were calcu-lated by the direct model. Compared to the actual temperaturesmeasured, the calculated errors at all locations were evaluated,which were less than 10 ◦C.

The heat flux for both the casting and die interface can be calcu-lated from the temperature gradient at the surface and sub-surfacenodes by Eq. (2):

q(t) = −kdT

dx= −k

Ttm − Tt

m−1

�x(2)

where k is thermal conductivity of the casting or die materials; Ttm

is the temperature value on time t at the nodal point m. With theheat flux value, the segregated IHTC value can be evaluated fromEq. (1).

1436 Z. Sun et al. / Journal of Materials Processing Technology 211 (2011) 1432–1440

e cast

3

t(

�

wtcd

l

T

q

T

wcmtispcd

TTEE

(

Fig. 5. One-dimensional heat transfer at the interface between th

.1.1. Heat transfer inside the dieThe heat transfer inside the die at each step is transient conduc-

ion through one-dimensional steps which can be described by Eq.3):

c(T)∂T(x, t)

∂t= ∂

∂x

(k(T)

∂T(x, t)∂x

)(3)

here � is density of conducting die, T is the temperature, t is theime and x is the distance from the die surface to the node point;(T), k(T) are specific heat capacity and thermal conductivity of theie changed with temperature, respectively.

The initial and boundary conditions were described by the fol-owing Eqs. (4a)–(4c):

(x, 0) = Ti(x) (4a)

(0, t) = −k(T)∂T

∂x

∣∣∣∣x=0

(4b)

(L, t) = Y(L, t) (4c)

here Ti is the initial temperature of the die; q is the heat flux at theasting–die interface; L is the distance from the last temperatureeasurement point to the die surface; Y is the measured tempera-

ure at distance L from die surface. The measured region (0 ≤ x ≤ L)n the die is divided into M equal size meshes (L = M�x), and n sub-cripts are used to designate the x location of the discrete nodaloint. With the proper time step (�t), the time can also be dis-retized as t = p�t. Thus, the finite differential format to the timeerivatives of Eq. (3) can be expressed as Eq. (5).

∂T

∂t

∣∣∣∣m

≈ Tp+1m − Tp

m

�t(5)

The superscript p was used to denote the time dependence of. The subscript m means the number of the discrete nodal points.he implicit form of a finite difference method was applied to solve

q. (3). For the surface node of the die, Eq. (3) can be rearranged asq. (6a):

1 + 2F0)Tp+10 − 2F0Tp+1

1 = 2F0�x

kq0 + Tp

0 (6a)

ing and die, where temperature measurements were performed.

For any interior node of the die, Eq. (3) can be solved as Eq. (6b):

(1 + 2F0)Tp+1m − F0(Tp+1

m−1 + Tp+1m+1) = Tp

m (6b)

where F0 is a finite different form of the Fourier number:

F0 = ˛�t

(�x)2= k

c�

�t

(�x)2(6c)

The heat flux at the casting–die interface (q) at each time stepcan be obtained by the Beck’s function specification method. At thefirst time step, a suitable initial value of heat flux q was assumedwhich was maintained constant for a definite integer number(u = 2–5) of the subsequent future time steps. According to Eqs.(6a)–(6c), with the measured initial die temperature (p = 0), thetemperature distribution at each node of the next time step wascalculated with this assumed q. The assumed heat flux value waschanged by a small value (εq) where ε was a small fraction and thenew temperature distribution value corresponding to (q + εq) wasdetermined accordingly. Thus, the sensitivity coefficient (X) can becalculated by Eq. (7). To minimize the calculation error, the calcu-lated temperatures were compared with measured temperature atthe same position, and the assumed heat flux (q) was corrected byEq. (8). The corrected heat flux of the same time step was obtainedby Eq. (9):

Xp+j−1 = ∂T

∂q= Tp+j−1

est (qp + εqp) − Tp+j−1est (qp)

εqp(7)

�qp =∑u

j=1(Yp+j−1mea − Tp+j−1

est )Xp+j−1

∑uj=1(Xp+j−1)2

(8)

qpcorr = qp + �qp (9)

where Test (q) was estimated temperatures on p time step at themeasuring node points inside die with a boundary constant heatflux q; Ymea was measured temperatures at the same measuringnode points. The corrected heat flux and the new temperature dis-tribution were used as initial value for next cycle of calculation.

The calculation process was repeated until the following conditiongiven by Eq. (10) was satisfied:

�qp

qp≤ ε (10)

Z. Sun et al. / Journal of Materials Processing Technology 211 (2011) 1432–1440 1437

e dete

tTpsgttta(Bcn

3

cche

�

S

wcE

�

it

X1, X2, X3, and X4. Fig. 7 shows the calculated temperaturesagainst distance X which were fitted and extrapolated by a polyno-mial trendline. The temperature at the die surface (T0 = 308.43 ◦C,t = 4.1 s) was determined by substituting the value of X = 0 in the

Fig. 6. Flow chart showing an algorithm for th

Therefore, for all time steps, the surface heat flux and die surfaceemperature were determined according to the above procedures.he flow chart shown in Fig. 6 gives an overview of the solutionrocedure. The j in Eq. (7) is the integer subsequent future timeteps (j = 1, 2, . . ., u) and j should not bigger than u (a definite inte-er number). The inverse modeling is to calculate heat flux (q) usinghe present temperatures and the future temperatures. The futureemperatures are the calculated temperatures at time steps greaterhan the present time steps estimated using the known bound-ry condition T(L, t) = T1, T4 and the assumed constant heat fluxqp = qp+1 = . . . = qp+j−1), which set some future qp+1 is equal to qp+j−1.ut p is the present time steps for all nodal points. Only after thealculated heat flux satisfied Eq. (10), the present time can go toext step (p = p + 1).

.1.2. Heat transfer inside the castingTo evaluate the IHTC, the temperatures inside the casting, espe-

ially the surface temperatures need to be estimated. Due to phasehange of the casting, the heat source term related with the latenteat of solidification must be added to Eq. (3). The heat transferquation can be rewritten as Eq. (11):

c(T)∂T(x, t)

∂t= ∂

∂x

(k(T)

∂T(x, t)∂x

)+ Sl (11)

l = � l∂fs∂t

(12)

here l is the latent heat of fusion and fs is the solid fraction in theasting. Substitution of Eq. (12) into Eq. (11) led to the formation ofq. (13):[

c(T) − l∂fs

]∂T(x, t) = ∂

(k(T)

∂T(x, t))

(13)

∂T ∂t ∂x ∂x

The term ∂fs/∂T can be calculated at each step of the casting byts solidification curve. With the measured temperature data insidehe step casting, the temperature profile on the surface of the step

rmination of IHTC at the casting–die interface.

casting can be determined by applying Eqs. (6a)–(6c) given in theprevious section.

3.2. Polynomial curve fitting method

Beneath the die surface, as Fig. 5 shown, thermocouples werepositioned at X1 = 2 mm, X2 = 4 mm, X3 = 6 mm, and X4 = 8 mm awayfrom the die surface. From the temperature versus time curvesobtained at each position inside the die, the temperature at thedie surface (X0 = 0 mm) can be extrapolated by using polynomialcurve fitting method.

After the completion of filling, by selecting a particular timeof solidification process, for example t = 4.1 s, the values of tem-peratures were read from the temperature–time data at position

Fig. 7. Polynomial curve with various measured temperatures at a time of 4.1 s ofsolidification process.

1438 Z. Sun et al. / Journal of Materials Processing Technology 211 (2011) 1432–1440

Fs

pv

y

tefif

4

4

ma3

ig. 8. Typical temperature versus time curves (step 4, 30 MPa) at metal surface, dieurface, and various positions inside the die.

olynomial curve fitting Eq. (14) obtained from the temperaturealues at various distances inside the die at a chosen time of 4.1 s.

= 0.0635x3 + 0.1759x2 − 16.495x + 308.43 (14)

This procedure was repeated for a number of time incrementso get series of such temperatures with corresponding times. Thextrapolated temperature curve versus time was drawn at die sur-ace (X0 = 0 mm) as “Die-surface-T0-polynomial” in Fig. 8, whichndicated the dynamic temperature change at the metal–die inter-ace.

. Results and discussion

.1. Heat flux (q) and IHTC (h) curves

Fig. 8 shows typical temperatures versus time curves at theetal–die interface of step 4 for solidifying magnesium alloy AM60

nd steel die respectively with an applied hydraulic pressure of0 MPa. The following analysis was also based on this typical

Fig. 10. The interfacial heat flux (q) and the heat transfer coefficient (IHTC)

Fig. 9. Comparison of calculated temperature curve at the die surface by the inversemethod and the extrapolated fitting method.

data at step 4 with pressure 30 MPa. This information includesmeasurements of the casting surface temperature in addition totemperature measurements obtained at different depths under thedie surface. Since molten metal filled the cavity from the bottom,pre-solidification occurred upon the completion of cavity filling. Nodie surface temperatures exceeded 340 ◦C, and the highest temper-ature of the casting surface was 532.97 ◦C.

Fig. 9 shows the comparison of calculated temperatures at thedie surface (T0) by the inverse method and the extrapolated fittingmethod. The curves obtained by these two methods are in rela-tively poor agreement and their deviation values ranges from 0.46to 57 ◦C, which was indicated by temperature difference (Inv-Poly)curve in Fig. 9. The peak temperature value (321.61 ◦C) obtained byextrapolated fitting method was found to be lower than that tem-perature (327.97 ◦C) estimated by the inverse method. Compared

to inverse method, the temperature estimated by the extrapolatedfitting method reached its peak point 1.8 s later.

Inserting the estimated die surface temperature (T0) and themeasured temperature at T1 = 2 mm into Eq. (6), the interfacial heatflux (q) was calculated. Fig. 10 shows the interfacial heat flux (q) and

curves estimated by extrapolated fitting method and inverse method.

Z. Sun et al. / Journal of Materials Processing Technology 211 (2011) 1432–1440 1439

Fp

tmofl67Fiohc

4

eesta(l

tStn

Fs

ig. 11. The residual error of temperatures evaluated by the inverse method at theosition X1 = 2 mm.

he heat transfer coefficient (IHTC) versus solidification time esti-ated by extrapolated fitting method and inverse method, based

n the data in Fig. 8. By extrapolated fitting method, the peak heatux value was 3.31E + 05 W/m2, and the peak value of IHTC was450 W/m2 K. By the inverse method, the peak heat flux value was.38E + 05 W/m2, and the peak value of IHTC was 6005 W/m2 K.rom Fig. 10, it can be observed that the heat flux and IHTC ofnverse method curves reached to their peak value faster than thosef extrapolated fitting method. The inverse method resulted in aigh peak heat flux value and a low peak heat transfer coefficientompared with the extrapolated fitting method.

.2. Accuracy verification

The accuracy of IHTC evaluation by the inverse method andxtrapolated fitting method was analyzed based on the residualrror between the evaluated temperatures and the actual mea-ured temperatures at various locations. With the die surfaceemperature and heat flux evaluated by two methods as a bound-ry condition, direct heat transfer modeling was applied to Eqs.6a)–(6c) and recalculated the temperature distribution at differentocations (X2 = 4 mm, X3 = 6 mm, X4 = 8 mm) inside the die.

From Fig. 11, the residual error of temperatures evaluated by

he inverse method was less than 0.2 ◦C at the position X1 = 2 mm.ince the extrapolated fitting method needs to take the measuredemperature at X1 as the initial input data, the residual error couldot be evaluated.

ig. 12. The residual error between the evaluated temperatures and the actual mea-ured temperatures at X2 = 4 mm beneath the die surface.

Fig. 13. The residual error between the evaluated temperatures and the actual mea-sured temperatures at X3 = 6 mm beneath the die surface.

As shown in Figs. 12–14, the residual error of temperature eval-uated by the inverse method was below 7.4 ◦C at the positionX2 = 4 mm, while that residual error achieved 14.9 ◦C evaluatedby the extrapolated fitting method. The residual error of tem-perature evaluated by the inverse method was less than 3.3 ◦Cat the position X3 = 6 mm, and that residual error increased to33.2 ◦C when evaluated by the extrapolated fitting method. At theposition X4 = 8 mm, the residual error of temperature evaluatedby the inverse method was below 0.7 ◦C. But that residual errorwas as high as 55.2 ◦C when the extrapolated fitting method wasemployed.

For the inverse method, the residual error of temperature at X1and X4 was less than one degree, which indicates that the ther-mal history was estimated accurately by the inverse method. Forthe extrapolated fitting method, the residual error increased from14.9 ◦C to 55.2 ◦C with the depth below the die from 4 mm to 8 mm.Thereafter, the heat flux (q) and IHTC calculated by the extrapo-lated fitting method could not accurately represent the actual heattransfer at the metal–die interface.

Fig. 15 shows that the heat transfer coefficient (IHTC) curves of5 steps estimated by inverse method. For all steps, IHTC began withincreasing stage and reached their peak value, then dropped grad-ually until the value became a low level. From steps 1 to 5 with30 MPa pressure, the peak IHTC values varied from 2807 W/m2 K,

2962 W/m2 K, 3874 W/m2 K, 6005 W/m2 K to 7195 W/m2 K, indicat-ing that the closer contact between the casting and die surface atthicker steps. Therefore, the wall thickness affected IHTC peak val-ues significantly. The peak IHTC value decreased as the step became

Fig. 14. The residual error between the evaluated temperatures and the actual mea-sured temperatures at X4 = 8 mm beneath the die surface.

1440 Z. Sun et al. / Journal of Materials Processin

Fig. 15. The heat transfer coefficient (IHTC) curves of 5 steps estimated by inversemethod with applied pressure 30 MPa.

Fp

t8ptls

pvss27t6paflpaf

5

1

tube-shaped casting and metal mold. Int. J. Heat Mass Transfer 40,3513–3525.

Yu, A., 2007. Mathematical Modeling and experimental study of squeeze cast-ing of magnesium alloy AM50A and aluminum alloy A356. Ph.D. dissertation.Dept. of Mechanical, Automotive & Materials Engineering, University ofWindsor.

ig. 16. The peak IHTC values of 5 steps estimated by inverse method with appliedressure 30, 60 and 90 MPa.

hinner. For the steps 1, 2, 3, 4 and 5, it took 4.1, 4.2, 4.7, 6.1, and.2 s to reach their peak values, respectively. Beside the differenteak values, the time for IHTC to obtain the peak value during ini-ial stage increased as the step became thicker. Thicker step spentonger time to reach its peak IHTC value and its IHTC curve droppedlower to a low level as well.

Fig. 16 shows the IHTC peak values at step 1–5 with appliedressure 30, 60 and 90 MPa. Similar characteristics of IHTC peakalues can be observed at 30, 60 and 90 MPa applied pres-ures. With applied pressure 60 MPa, the peak IHTC values atteps 1, 2, 3, 4, and 5 (section thickness 3, 5, 8, 12, and0 mm) varied from 4662 W/m2 K, 5001 W/m2 K, 5629 W/m2 K,871 W/m2 K and 8306 W/m2 K. With applied pressure 90 MPa,he peak IHTC values varied from 5623 W/m2 K, 5878 W/m2 K,783 W/m2 K, 9418 W/m2 K and 10649 W/m2 K. With the appliedressure increased, the IHTC peak value of each step was increasedccordingly. It can be observed that the peak IHTC value and heatux increased as the step became thick. The large difference in tem-eratures between the melt and the die with thick cavity sections well as relatively high localized pressure should be responsibleor the high peak IHTC values observed at the thick steps.

. Conclusions

. The heat flux and IHTC at metal–die interface in squeeze castingwere successfully determined based on the numerical inversemethod and extrapolated fitting method.

g Technology 211 (2011) 1432–1440

2. For the inverse method, a solution algorithm has been developedbased on the function specification method to solve the inverseheat conduction equations.

3. The IHTC curve increased and reached its peak value, thendropped gradually. For applied pressure 30 MPa, the peak IHTCvalues at steps 1, 2, 3, 4, and 5 (section thickness 3, 5, 8, 12, and20 mm) varied from 2807 W/m2 K, 2962 W/m2 K, 3874 W/m2 K,6005 W/m2 K to 7195 W/m2 K. With applied pressure 60 MPa,the peak IHTC values varied from 4662 W/m2 K, 5001 W/m2 K,5629 W/m2 K, 7871 W/m2 K and 8306 W/m2 K. With appliedpressure 90 MPa, the peak IHTC values varied from 5623 W/m2 K,5878 W/m2 K, 6783 W/m2 K, 9418 W/m2 K and 10649 W/m2 K.The peak IHTC value decreased as the step became thinner. Withthe applied pressure increased, the IHTC peak value of each stepwas increased accordingly.

4. For the steps 1, 2, 3, 4 and 5, it took 4.1, 4.2, 4.7, 6.1, and 8.2 s toreach their peak values, respectively. Beside the different peakvalues, the time for IHTC to obtain the peak value during initialstage increased as the step became thicker.

5. To verify estimation results, temperature distribution inside thedie was recalculated by the direct modeling based on the esti-mated heat flux (q). After comparison with experimental data,the result showed that the heat flux and IHTC evaluated by theinverse method were more accurately than those of the extrap-olated fitting method.

Acknowledgements

The authors would like to thank the Natural Sciences and Engi-neering Research Council of Canada, and University of Windsor aswell as Cosma International for supporting this work.

References

Aweda, J., Adeyemi, M., 2009. Experimental determination of heat transfer coef-ficients during squeeze casting of aluminum. J. Mater. Process. Technol. 209,1477–1483.

Beck, J., 1970. Nonlinear estimation applied to the nonlinear inverse heat conductionproblem. Int. J. Heat Mass Transfer 13, 703–715.

Beck, J., Blackwell, B., Haji-sheikh, A., 1996. Comparison of some inverse heatconduction methods using experimental data. Int. J. Heat Mass Transfer 39,3649–3657.

Broucaret, S., Michrafy, A., Dour, G., 2001. Heat transfer and thermo-mechanicalstresses in a gravity casting die influence of process parameters. J. Mater. Process.Technol. 110, 211–217.

Browne, D., O’Mahoney, D., 2001. Interface heat transfer in investment casting ofaluminum. Metall. Mater. Trans. A 32A, p3055–3063.

Cho, I., Hong, C., 1996. Evaluation of heat-transfer coefficients at the casting/dieinterface in squeeze casting. Int. J. Cast Metals Res. 9, 227–232.

Dargusch, M., Hamasaiid, A., Dour, G., Loulou, T., Davidson, C., StJohn, D., 2007. Theaccurate determination of heat transfer coefficient and its evolution with timeduring high pressure die casting of Al–9%Si–3%Cu and Mg–9%Al–1%Zn alloys.Adv. Eng. Mater. 9 (11), 995–999.

Dour, G., Dargusch, M., Davidson, C., Nef, A., 2005. Development of a non-intrusiveheat transfer coefficient gauge and its application to high pressure die casting.J. Mater. Process. Technol. 169, 223–233.

Guo, Z., Xiong, S., Liu, B., Li, M., Allison, J., 2008. Effect of process parame-ters. Casting thickness, and alloys on the interfacial heat-transfer coefficientin the high-pressure die casting process. Metall. Mater. Trans. 39A,2896–2905.

Hamasaiid, A., Dargusch, M., Davidson, C., Tovar, S., Loulou, T., Rezai-aria, F., Dour, G.,2007. Effect of mold coating materials and thickness on heat transfer in perma-nent mold casting of aluminum alloys. Metall. Mater. Trans. A 38A, 1303–1316.

Kim, T., Lee, Z., 1997. Time-varying heat transfer coefficients between

本文献由“学霸图书馆-文献云下载”收集自网络，仅供学习交流使用。

学霸图书馆（www.xuebalib.com）是一个“整合众多图书馆数据库资源，

提供一站式文献检索和下载服务”的24 小时在线不限IP

图书馆。

图书馆致力于便利、促进学习与科研，提供最强文献下载服务。

图书馆导航：

图书馆首页 文献云下载 图书馆入口 外文数据库大全 疑难文献辅助工具