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Numerical Simulation on Hardness Distribution for a FC250 Gray Cast

Iron Brake Disc Casting and Its Experimental Verification

Chun-Ping Yeh1, Weng-Sing Hwang1;* and Chien-Hen Lin2

1Department of Materials Science and Engineering, National Cheng Kung University, Tainan 701, Taiwan, R.O.China2China-Motor Corporation Co. Ltd., Taoyuan 326, Taiwan, R.O.China

The purposes of this study are to develop a technique of numerically simulating the hardness of a FC250 gray cast iron brake disc castingand verified by experimental measurements. As the numerical model is proven reliable, numerical experimentation is then conducted tohomogenize the hardness distribution of a brake disc to obtain better casting quality. The Oldfield’s model was adopted to simulate thenucleation and grain growth during solidification of the casting. A calibration brake disc casting was first made. By comparing the hardness ofthe calibration brake disc casting with the simulated results using different nucleation and growth coefficients ðAe;BeÞ in Oldfield’s model, themost appropriate set of values for Ae and Be was obtained. Then, this set of values was applied to the hardness simulation of a test brake disccasting and confirmed by experimental measurements. Through this approach, a set of nucleation and growth coefficients was obtained for thebrake disc casting. Subsequently, numerical simulations were conducted for the brake disc casting with different shake-out times to evaluate itsdistribution of hardness and an optimized shake-out time was then proposed based on the simulated results. The predictions of hardness werevalidated by comparison with experimental measurements and actual track testing. [doi:10.2320/matertrans.M2009184]

(Received May 22, 2009; Accepted August 10, 2009; Published October 7, 2009)

Keywords: sand casting, hardness distribution simulation, solidification simulation

1. Introduction

The braking system of most modern cars is based on brakediscs, which uses gray cast iron brake discs as the brakingsurfaces. The metallurgical properties of the gray cast irondetermine the strength, noise, wear and braking character-istics of the brake discs. If a brake disc is too soft, it will wearrapidly. On the contrary, if a brake disc is too hard, it is morelikely to crack. In addition, if hardness is uneven, a brake discwill wear unevenly, which then causes a brake judder. It canalso be accompanied by a shuddering or jerky stop duringnormal braking. This creates a multi-million dollar warrantyproblem every year for car manufacturers. To homogenizethe hardness of the brake disc casting, proper control ofshake-out time is of great importance, where shake-out timeis defined as the time interval after the casting is filled andbefore it is shaken out of the mold.

Gray cast iron is hypoeutectic and therefore begins tosolidify by precipitation of primary austenite from the melt.Once eutectic temperature is reached, nucleation of austenite-graphite eutectic cells will occur on or near the primarydendrites and growth of nuclei leads the heat to be extractedand the undercooling increases. Finally, the latent heatreleased by solidification causes the temperature to rise. Afterthe end of nucleation, solidification process only takes placefrom growth of existing particles.

The mechanical properties of brake disc casting arefunction of composition and microstructure. Bates et al.determined that the ultimate tensile strength in gray cast ironcan be modeled using a Griffith’s fracture criterion:1)

�f ¼kffiffiffiffiffiffiffiffifficmax

p ð1Þ

k ¼ffiffiffiffiffiffiffiffiffi2E�

�

rð2Þ

where �f is the ultimate tensile strength, cmax is the maximumgraphite flake length, E is the Young’s modulus and � is theenergy required to produce a new surface. The graphite flakesin gray cast iron grow outward in a radial pattern from theeutectic cell center into the remaining eutectic liquid. It isassumed that the graphite flake does not cross the eutecticcell boundary, the maximum possible graphite flake lengthwould be the largest eutectic cell diameter. Therefore,Brinell hardness (HB) was determined using the followingequation:2)

HB ¼ 0:0284�f expð0:8228� CEÞ ð3Þ

where CE is the carbon equivalent.It was very important that a more even hardness distribu-

tion favored a better optimal use of the material as well asbetter machinability. Several studies have been conductedon the numerical simulations of hardness. Svensson et al.modeled mold filling, solidification process and Brinellhardness of a ductile iron casting.3) It was found that thesilicon gave a more even hardness in the casting. Thehardness range was expected to be somewhat higher than thecastings without copper. Goettsch et al. modeled the temper-ature field and Brinell hardness for a gray cast iron castingof six cylinders of different diameters.2) Xue et al. used anengineering software to model the Vickers hardness of a Ni-based superalloy gas turbine blade casting.4) They found thatwith the decrease in pouring temperature, Vickers hardnessincreased. But with the increase of preheated mold temper-ature, the Vickers hardness decreased. Yoo et al. modeledBrinell hardness of a ductile cast iron casting in as-castconditions by using the rule of mixture since Brinell hardnessof a ductile iron casting is mainly affected by the volumefraction of ferrite and pearlite in the matrix.5) Catalian et al.modeled Brinell hardness of multiple gray cast iron cylinderbar castings having carbon equivalents of 3.8% and 4.1%.6)

In the present study, a numerical model for the hardnessprediction of a FC250 gray cast iron brake disc casting is*Corresponding author, E-mail: [email protected]

Materials Transactions, Vol. 50, No. 11 (2009) pp. 2584 to 2592#2009 The Japan Institute of Metals

http://dx.doi.org/10.2320/matertrans.M2009184

presented. The technique is to employ the Oldfield’s model,obtain the appropriate solidification parameters through acalibration brake disc casting, and conduct numericalexperimentation to find the optimal design to homogenizethe hardness distribution of a brake disc casting. A set ofnucleation and growth coefficients; Ae and Be were firstobtained by comparing the simulated hardness values withthe experimental measurements of the calibration brake disccasting. Then, this set of values was applied to the hardnesssimulation of a test brake disc casting. The simulatedhardness values were compared with the experimentalmeasurements to validate the reliability of the numericalmodel. Subsequently, numerical simulations were conductedfor the brake disc casting with different shake-out times toobserve distribution of hardness and the optimized shake-outtime was then proposed based on the simulated results. Thepredictions of hardness were then validated by comparisonswith experimental measurements and actual track testing.

2. Numerical Model

In order to predict the hardness distribution, the algorithmfor eutectic grains nucleation proposed by Oldfield wasadopted to simulate the nucleation and grains growth ofFC250 gray cast iron brake disc casting. Numerical simu-lation of hardness distribution was coupled with thermalanalysis. A diagram of the brake disc is shown in Fig. 1. Thesimulation system is based on the finite element method(FEM). The whole physical system, which includes thecasting, running system and gating system, was subdividedinto tetrahedral elements. The disc casting cavity included anupper disc casting cavity located at the cope flask and a lowerdisc casting cavity located at the drag flask. The two cavitiesare separated by a middle plate core. FC250 gray cast ironwas selected as the casting alloy. The pouring temperaturewas 1723K and the pouring time was around 12 s. Theambient temperature surrounding the casting was around313K. The shake-out times were 1800 and 7200 s and arereferred to as the calibration brake disc casting case and testbrake disc casting case in this paper. The simulation startedwith a coupled fluid flow and heat transfer analysis for thefilling of casting. Then, a thermal analysis with phase changewas conducted to simulate the solidification and coolingphenomena. Hardness distribution is calculated only after thethermal calculation converges and thus it is calculated onlyonce per timestep. The latent heat release for the energyconservation calculation is based on the solid fraction change

between the last timestep (t-dt) and the step before the lastone (t-2dt). Figure 2 shows the enmeshed solid model ofa brake disc casting. The length, height and depth of thesimulated system are 0.7, 0.6 and 0.484m, respectively.Related thermal and physical properties data as well as theFEM parameters are displayed in Table 1.

As for Oldfield’s model,7) the number of nuclei is apower law of the undercooling. The growth of the grains iscontrolled by thermal undercooling at the solid/liquidinterface. Solutal undercooling is neglected here since solutediffusion during eutectic solidification is negligible. Thethermal undercooling is given by the difference between theeutectic temperature and the actual solid/liquid interfacetemperature. Bulk heterogeneous nucleation occurs at foreignsites which are already present within melt or intentionallyadded to the melt by inoculation. Oldfield used experimentaldata to relate the eutectic cell density with the undercoolingby the following equation;

Neut ¼ Aeð�TÞn ð4Þ

where Neut is the eutectic cell density, Ae is the nucleationcoefficient, �T is the undercooling and n is a constant whichdepends on the effectiveness of inoculation. In this study,n ¼ 2 was adopted. Differentiation of the above equationyields an expression for the nucleation rate as follows:

dNeut

dt¼ �nAeð�TÞn�1 dT

dtð5Þ

Oldfield also studied the growth kinetics in Fe-C eutectics.The growth rate was correlated with interfacial undercoolingas shown in the following equation;

dReut

dt¼ Beð�TÞ2 ð6Þ

where Reut is the radius of spherical particles and Be isthe growth coefficient. Ae and Be are then the nucleationand growth coefficients respectively which depend on thecomposition of the alloy.

After solidification is complete, further cooling reaches theeutectoid temperature. The eutectoid reaction leads to thedecomposition of austenite into ferrite and graphite for thecase of stable eutectoid and to pearlite for metastableeutectoid transformation. Normally, the metastable eutectoid

Fig. 1 Shape and dimensions of a brake disc casting.

weights

mold

jacket

truck

Fig. 2 Enmeshed solid model of a brake disc casting.

Numerical Simulation on Hardness Distribution for a FC250 Gray Cast Iron Brake Disc Casting and Its Experimental Verification 2585

temperature is lower than the stable eutectoid temperature.Slower cooling rates result in more stable eutectoid structure.If the transformation of austenite is not complete when themetastable eutectoid temperature is reached, then nucleationand growth of pearlite takes place. Pearlite forms and growsin competition with ferrite. The Avrami equation is used tocalculate the fraction of pearlite formed:

fpe ¼ 1� exp½�CðTÞtnðTÞ� ð7Þ

where fpe is the pearlite fraction, t is the transition time andexponent of time, nðTÞ, is a function of the temperature, T .Rate constant, CðTÞ, is the shape equation of the TTT curve,which can be described by the following equation:

CðTÞ ¼ exp½aT2 þ bT þ c� ð8Þ

where a, b and c are coefficients. For a given material, thesecoefficients can be determined experimentally.

As mentioned in eq. (3), hardness can be calculated whenultimate tensile strength is known. The ultimate tensilestrength is shown to be related to cell diameter in eq. (1). Inorder to find out cell diameter, Ae and Be must be determinedas shown by eqs. (4) and (6). As a result, values of Ae and Be

were needed for calculating hardness. The computationalcycle is shown in Fig. 3.

3. Experimental Method

The simulation results need to be verified by experimentalmeasurements for the numerical model to become a designtool. Figure 4 shows a schematic diagram of the Brinellhardness test. Brinell hardness test was made according to theASTM E10 standard test method in this study. The Brinellhardness test used a desk top machine to press a 0.01mdiameter, hardened steel ball into the surface of the testspecimen. The machine applied a load of 3000 kg load for10 s. After the impression was made, a measurement of thediameter of the resulting round impression was taken. TheBrinell hardness was calculated according to the followingequation:

HB ¼2F

�DðD�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiD2 � d2

pÞ

ð9Þ

Input appropriate values of Ae and Be

Calculate the Neut

and Reut

Calculate the maxc

Calculate the fσ

Calculate the hardness

Fig. 3 Flow chart of the computational cycle.

Fig. 4 Schematic diagram of Brinell hardness test.

Table 1 Related thermal/physical properties and parameters for numerical simulation of a brake disc casting.

FC250 gray cast iron Silica sand Simulation system

Thermal

conductivity

(Wm�1K�1)

25.0

Thermal

conductivity

(Wm�1K�1)

0.70Number of

nodes302,389

Specific heat

(Jkg�1K�1)840

Specific heat

(Jkg�1K�1)1230

Number of

elements1,464,662

Latent heat

(Jkg�1)2:61� 105 Casting/mold 850

Initial

(s)0.01

Liquidus

temperature

(K)

1478Interface

heat transfer

coefficients

(Wm�2K�1)

Casting/core 300 Calculating

time step

Max. for filling

(s)0.1

Solidus

temperature

(K)

1373 Mold/air 10Max.

(s)1

2586 C.-P. Yeh, W.-S. Hwang and C.-H. Lin

where F is the applied load, D is the diameter of the sphericalindenter and d is the diameter of the indentation. Figure 5shows the eight hardness measured positions of the brake disccasting. Positions (a) to (h) are 0.01m from the outer edge ofthe brake disc.

Track testing was also introduced to evaluate the extentof brake judder. Track testing is conducted on elliptoid-like high-speed runway. First, testing car is accelerated to5.56m/s on the straight line area of the elliptoid-like high-speed runway. The speed is kept for a period of time and thendecelerated to stop on the straight line area in the other sideof the elliptoid-like high-speed runway with four differentdeceleration values: 1m/s2, 2m/s2, 3m/s2, and 4m/s2.Experiments for each deceleration value are repeated threetimes. The total track testing distance is around 1:5� 107 m.During the test, the brake discs are judged by the extent ofbrake judder on whether they fit to pass track testing or not.The judgement for passing the track testing or not isevaluated and determined by well-trained test driver.

4. Results and Discussion

The approach developed in this study was to employ theOldfield’s model in conjunction with a calibration brake disccasting to simulate the hardness distribution of a FC250 graycast iron sand casting. A set of nucleation and growthcoefficients; Ae and Be were first obtained by comparing thesimulated hardness with the experimentally measured one ofthe calibration brake disc casting. The values can then beutilized to simulate the hardness of FC250 gray cast ironcasting under any other design and operating conditions.Then, this set of values was applied to simulate the hardnessof a test brake disc casting and compared with experimentalmeasurements to validate the reliability of the numericalmodel. The results of the different shake-out time designswere again evaluated by with the numerical simulations aswell as the actual track test results.

4.1 Acquisition of the appropriate nucleation andgrowth coefficients

Oldfield’s model had been adopted to simulate grainstructure by several researchers and various values of Ae andBe had been reported as shown in Table 2. Based on the

Oldfield’s model and related references, it was found thatfor FC250 gray cast iron, Ae ranges between 105 and107 m�3K�2 and Be ranges between 10�8 and 10�5 m/sK2.This study used a calibration brake disc casting to find theappropriate values of Ae and Be within this range.

Figure 6 show the grain radius profiles simulated withAe ¼ 105 m�3K�2 and Be ¼ 10�8 m/sK2 for the calibrationbrake disc casting where the shake-out time was 1800 s.It can be seen from Figs. 6(a) and 6(b) that grain radiusof both upper and lower discs are around 3:90� 10�4 to6:40� 10�4 m.

Fig. 5 Hardness measured positions of a brake disc casting.

Table 2 Various values of Ae and Be from the literature.

Researchers Ae (m�3K�2) Be (m/sK2)

Oldfield

(gray cast iron)7Þ9:10� 105

to 7:12� 1062:50� 10�8

to 3:45� 10�7

Goettsch

(gray cast iron)2Þ3:66� 107 3:84� 10�8

Magnin

(gray cast iron)8ÞN/A 3:87� 10�8

Hillert

(white cast iron)9ÞN/A 3:00� 10�5

Stefanescu

(gray cast iron)10ÞN/A

7:25� 10�8

to 9:50� 10�8

Tian

(gray cast iron)11ÞN/A

1:20� 10�8

to 3:10� 10�8

Degand

(Al-11Si alloy)12ÞN/A 10�7 to 10�6

(a)

(b)

Fig. 6 Grain radius profiles simulated with Ae ¼ 105 m�3K�2 and Be ¼10�8 m/sK2 for the calibration brake disc casting; (a) upper disc casting,

(b) lower disc casting.


Figure 7 demonstrates the hardness profiles simulated withthe above conditions for the calibration brake disc casting.Figure 7(a) represents the hardness profiles of the upper disccasting and Fig. 7(b) represents those of the lower disccasting. It should be noted that the lower disc casting isactually presented upside down to the actual arrangement. Itcan be seen from Figs. 7(a) and 7(b) that hardness values ofboth upper and lower discs are around 173 to 192HB.

Table 3 shows the experimental measurements of hardnessfor the calibration brake disc casting. It can be seen fromTable 3 that the measured Brinell hardness values of thecalibration brake disc casting are 206 to 220HB. By

comparing with the above simulated hardness, it was foundthat the simulated hardness is smaller than that of theexperimental result. In order to resemble the experimentalresult, hardness values need to be increased. It implies thatthe grain radius should be decreased. From eq. (4), it showsthat eutectic cell density is proportitional to Ae. As a result, itcan be anticipated that when the value of Ae increases, theeutectic cell density increases, and the grain radius decreases.Then, 107 m�3K�2 was reassigned as the value of Ae as thehigher end of the Ae range (between 105 and 107 m�3K�2)was chosen while the value of Be is fixed at 10�8 m/sK2.

Figure 8 show the grain radius profiles simulated withAe ¼ 107 m�3K�2 and Be ¼ 10�8 m/sK2 for the calibrationbrake disc casting where the shake-out time was 1800 s.It can be seen from Figs. 8(a) and 8(b) that grain radiusof both upper and lower discs are around 1:65� 10�4 to2:59� 10�4 m, which is smaller than that in the Fig. 6.

Figure 9 demonstrates the hardness profiles simulated withAe ¼ 107 m�3K�2 and Be ¼ 10�8 m/sK2 for the calibrationbrake disc casting. Figure 9(a) represents the hardnessprofiles of the upper disc casting and Fig. 9(b) representsthose of the lower disc casting. It can be seen from Figs. 9(a)and 9(b) that hardness values of both upper and lower discsare around 202 to 212HB, which are higher than those inFig. 7. By comparing with the measured hardness, it wasfound that the simulated values are closer to the experi-mental results than the case where Ae ¼ 105 m�3K�2 andBe ¼ 10�8 m/sK2.

(a)

(b)

Fig. 7 Hardness profiles simulated with Ae ¼ 105 m�3K�2 and Be ¼10�8 m/sK2 for the calibration brake disc casting; (a) upper disc casting,


Table 3 Experimental measurements of hardness for the calibration brake

disc casting, where the shake-out time is 1800 s.

PositionExperimental results

(HB)

a 212

b 210

c 206

d 213

e 214

f 206

g 216

h 220

(a)

(b)




From eq. (6), it can be seen that the rate of grain growth isproportitional to Be. As a result, it can be anticipated thatwhen the value of Be increases, the grain radius increases, andthe hardness values decrease. From the literature, it wasfound that Be ranges between 10�8 and 10�5 m/sK2. Toevaluate the effects of Be on hardness values, the value of Be

is reassigned as 10�5 m/sK2 and the value of Ae is fixed at107 m�3K�2.

Figure 10 show the grain radius profiles simulated withAe ¼ 107 m�3K�2 and Be ¼ 10�5 m/sK2 for the calibrationbrake disc casting. It can be seen from Figs. 10(a) and 10(b)that grain radius of both upper and lower discs are around5:00� 10�4 to 1:23� 10�3 m, which is larger than that ofFig. 8. Hardness profiles simulated with Ae ¼ 107 m�3K�2

and Be ¼ 10�5 m/sK2 for the calibration brake disc castingare illustrated in Fig. 11. Figure 11(a) represents the hard-ness profiles of the upper disc casting and Fig. 11(b)represents those of the lower disc casting. From Fig. 11, itreveals that hardness of both upper and lower discs arearound 165 to 185HB, which is smaller than that of Fig. 9. Itimplies that the appropriate set of orders for Ae and Be are107 m�3K�2 and 10�8 m/sK2, respectively.

To resemble the measured hardness even more closely,small adjustments were attempted on the values of Ae and Be.Figure 12 show the grain radius profiles simulated withAe ¼ 5:34� 107 m�3K�2 and Be ¼ 3:91� 10�8 m/sK2 forthe calibration brake disc casting. It can be seen fromFigs. 12(a) and 12(b) that grain radius of both upper andlower discs are around 9:00� 10�5 to 2:50� 10�4 m. The

(a)

(b)

Fig. 9 Hardness profiles simulated with Ae ¼ 107 m�3K�2 and Be ¼10�8 m/sK2 for the calibration brake disc casting, where the shake-out

time is 1800 s; (a) upper disc casting, (b) lower disc casting.

(a)

(b)



(a)

(b)

Fig. 11 Hardness profiles simulated with Ae ¼ 107 m�3K�2 and Be ¼10�5 m/sK2 for the calibration brake disc casting; (a) upper disc casting,



actual average grain size is around 1:30� 10�4 m. Figure 13show the hardness profiles simulated with Ae ¼ 5:34�107 m�3K�2 and Be ¼ 3:91� 10�8 m/sK2 for the calibrationbrake disc casting. Figure 13(a) represents the hardnessprofiles of the upper disc casting and Fig. 13(b) representsthose of the lower disc casting. It can be observed fromFigs. 13(a) and 13(b) that hardness values of both upper andlower discs are around 205 to 222HB.

By comparing with the simulated hardness as shown inTable 4, it was found that the optimum nucleation andgrowth coefficients; Ae and Be for the particular alloy usedwere 5:34� 107 m�3K�2 and 3:91� 10�8 m/sK2, respec-tively. Through continuous repetitive trials on findingappropriate nucleation and growth coefficients, it is discov-ered that although smaller order of the growth coefficient (Be)would lead to fine grains to increase the hardness, small orderof the nucleation coefficient (Ae) also results in less cellnumbers to reduce the overall fine-grained strengtheningeffect, as shown in Fig. 7. Larger order of the nucleationcoefficient (Ae) causes more cell numbers while larger orderof the growth coefficient (Be) coarsens the grains to reducethe hardness, as shown in Fig. 11.

4.2 Simulation of the test brake disc casting and itsexperimental verification

Figure 14 show the grain radius profiles simulated withAe ¼ 5:34� 107 m�3K�2 and Be ¼ 3:91� 10�8 m/sK2 forthe test brake disc casting where the shake-out time is 7200 s.It can be seen that grain radius of both upper and lower discs

are around 8:78� 10�3 to 9:56� 10�3 m. The actual averagegrain size is around 9:30� 10�3 m. From Fig. 14, it can beobserved that the grain radius is larger as compared to thatshown in Fig. 12. Figure 15 illustrates the hardness profilessimulated with the optimal nucleation and growth coeffi-cients obtained from the above section; Ae ¼ 5:34�107 m�3K�2 and Be ¼ 3:91� 10�8 m/sK2 for the test brakedisc casting. Table 5 shows the simulation and experimentalresults of hardness for the test brake disc casting. Goodconsistency between numerical and experimental results canbe observed which indicates the reliability and accuracy ofthe numerical model.

(a)

(b)

Fig. 12 Grain radius profiles simulated with Ae ¼ 5:34� 107 m�3K�2 and

Be ¼ 3:91� 10�8 m/sK2 for the calibration brake disc casting; (a) upper

disc casting, (b) lower disc casting.

(a)

(b)

0.008

0.006

Unit: m

Unit: m

0.008

0.006

Fig. 13 Hardness profiles simulated with Ae ¼ 5:34� 107 m�3K�2 and

Be ¼ 3:91� 10�8 m/sK2 for the calibration brake disc casting, where the

shake-out time is 1800 s; (a) upper disc casting, (b) lower disc casting.

Table 4 Simulation results of hardness for the calibration brake disc

casting, where the shake-out time is 1800 s (Ae ¼ 5:34� 107 m�3K�2 and

Be ¼ 3:91� 10�8 m/sK2).

PositionSimulation results

(HB)

a 216

b 209

c 215

d 212

e 213

f 210

g 219

h 211


From Fig. 15, it can be seen that the hardness of the testbrake disc casting is smaller than that shown in Fig. 13. Itmay be due to the difference between shake-out time; 1800 sfor the calibration brake disc casting and 7200 s for the testbrake disc casting. It means cooling rate of the calibrationbrake disc casting is faster than that of the test brake disccasting, which leads to finer grains as shown in Figs. 12 and14. It can also be found that the grain radius distribution ofthe test brake disc are more uniform over the whole brakediscs than that of the calibration casting. Although thehardness distribution in Fig. 15 shows that different hardnessranges appear near the outer and inner edges of the test brakedisc casting. However, they are beyond the wear areas of theactual brake discs, which are between 0.008m from the outeredge and 0.006m from the inner edge. As a result, thehardness distribution of the test brake disc castings are moreeven over the whole brake discs than the calibration case.This implies that the design of the test brake disc casting caseis better and a better shake-out time design is 7200 s.

In actual track testing, the calibration brake disc castingfailed to pass the test while the test brake disc casting passed.This proves that the 7200 s shake-out time case is a betterdesign for the casting process.

5. Conclusion

A feasible approach has been developed in this study toemploy the Oldfield’s model to simulate the hardness of

FC250 gray cast iron castings. An appropriate set ofnucleation and growth coefficients; Ae and Be, were obtainedby comparing the simulated hardness values with theexperimental measurements of a calibration brake disccasting. Subsequently, this set of values was applied to thehardness simulation of a test brake disc casting. Thepredictions of hardness were validated by comparison withexperimental measurements. Efforts were also made toevaluate the effects of shake-out time on the distribution ofhardness and an appropriate shake-out time was thenproposed based on the simulated results. From those results,the following conclusions can be made:

(a)

(b)

0.008

0.006

Unit: m

Unit: m

0.008

0.006

Fig. 15 Hardness profiles simulated with Ae ¼ 5:34� 107 m�3K�2 and

Be ¼ 3:91� 10�8 m/sK2 for the test brake disc casting, where the shake-

out time is 7200 s; (a) upper disc casting, (b) lower disc casting.

(a)

(b)

Fig. 14 Grain radius profiles simulated with Ae ¼ 5:34� 107 m�3K�2 and

Be ¼ 3:91� 10�8 m/sK2 for the test brake disc casting; (a) upper disc

casting, (b) lower disc casting.

Table 5 Simulation and experimental results of hardness for the test brake

disc casting, where the shake-out time is 7200 s (Ae ¼ 5:34� 107 m�3K�2

and Be ¼ 3:91� 10�8 m/sK2).

PositionSimulation results

(HB)

Experimental results

(HB)

a 204 207

b 201 210

c 207 211

d 202 208

e 205 201

f 203 209

g 206 199

h 199 206


(1) The appropriate values of the nucleation and growthcoefficients of the Oldfield’s model for the sand castingof FC250 gray cast iron are 5:34� 107 m�3K�2 and3:91� 10�8 m/sK2 for Ae and Be, respectively.

(2) A good correlation has been found between the hard-ness of the actual FC250 gray cast iron brake disccasting and the simulated one using the proposedapproach.

(3) 7200 s is a better shake-out time design for the brakedisc casting.

Acknowledgements

The authors would like to thank China-Motor Corporationand National Science Council (NSC 95-ET-7-006-005-ET)in Taiwan for the financial support of this study.

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