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Q2  v2 A'2

A' v A'2 v2 v3 A3  v2 A'2  v3  2 2 v3 A–3  '2  v3 Kinetics S. Roy – U. K. Maity – A. K. Pramanick P. vK. of liquid metal flow in gating design of investment Acasting production 2 ADatta 3

=> PV = nMRCT [RU = MRC] [M = molecular weight] => RTvCaT3 =[nM vgT = m] [m=mass] P1V1PV =mmR and V =V ]  1 temperature  1 a [ m At ambient Ta, P1V1 = m11TRa 2 [P1 = Patm] P2V2 m2 RTm  2Tm At high temperature Tm, m RT PP21V12 = m TRT  T 1=V2]  P2  P112 2 amm 1aPgas[mP1P2and  PV atm  Pgas P2V2 m2 RT Q=vg. Ag 1Tma 2TTm P1V1 m1 RT a   1 a [ m   and V1=VQ2] = v . A = C .v . A f f g D g g T P2V2 m2RT  Tm  P2  P1 2 m  2Pgas  P1  P2  Patm  Pgas 1Ta T  P2  P1 2 m  Pgas  P1  P2  Patm  Pgas 1Ta 2 P   cos  r (iii) Stefanescu’s approach for capillary mold: The resistance to flow through a channel of radius r, can be 2 P   cos  calculated r as [10]: 2γ 2  cosθ ∆P Pγ = − cos

Velocity at section -3: v3 A3 = v2 A'2 ∴ v3 = A'2 v2 v3 = vg

Velocity at section -3 is known as gate velocity: v3 = vg Now, applying surface2 tension correction factor final velocity P v f  [v g 

will be, v f = [vg 2 −

∆Pγ

ρliq

]

liq Q=vg. Ag

.A Qf =g.vfA g = CD .vg. Ag Initial Discharge Rate [11]: Q=v g Corrected Discharge Rate: Qf = v f. Ag = CD .vg. Ag

Filling Time: t f =

Vm Qf

The velocity will be checked by Reynold’s No [12]. For liquid metal, flow will be considered as laminar flow, if, Re < 20000. Sprue design: For first part of Dam Sprue d z rr Aspiration correction, AS  z Cu  A1  z 0 ,, hence hence S  4 0 d z A z A z d z A z A z g Cu G Cu 2 1 hence Where γ is the surface energy between the ,  4 21  Cu S 3 0 AS z Cu liquid z 0 and A1 metal dS z0 4    d z , hence  A z A ' z Thus cup diameter d can be calculated. d AG D z S cu A 2 z 2 3 hence g D z 2 3 its vapor phase, and θ is the contactA angle between zS A0 the zmetal d Cu z1 , P 2 4  Cu  3  Cu 1 (2) v12 the v2mold.  P v2  [v12   ] dD z3 AD zS A' 2 z3 and For first part of Dam Sprue, the dam is considered as cup. liq P Now, energy balance 1 and 2: 2 2 2between d z A z A z (2) g v1  v2  P v2  [v1  ] Aspiration correction, G  Cu  3  2 ,, hence hence  4 2  v liq ∆Pγ 2 2 2 CD  2 ρvv112 = ρvv222 +∆PPγ v2  v2[=v12 [v1P− ]ρ ] v(2) 1 v liq liq CD  2 v Correction Ratio of final to initial velocity: v1CD = 2

(2)

dD AD zS A' 2 z3 z2 Volume Thus cup diameter, M C  dCu can be calculated. z3 Area Volume MC 

Area

v1 v2 v = v . A [A = Area of Gate at ‘1’] Initial Discharge Rate: Q 1 Pgas i 1 g g

Riser design: Volume Modulus of the casting,MM C=Volume

Qi  Ag  gz 

Let, Mr = Modulus of riser = 1.2 Mc [13]. Assume cylindrical riser, riser height (dr) = riser height (zs),

CD 

Qi  Ag  gz 

Pgas 

 Pgas Q f  v2 Ag  CDv1 Ag  CDQi Final rate: Q f = v2 Ag = C D v1 Ag = C D Qi Qi  Adischarge g  gz   Q f  v2 Ag  CDv1 Ag  CDQi

  d r  d r  zs d r Volume of Riser Mr     4dr  d d rr  Volume of Riser Heat dissipatin g Area  zzss  d r 4 Mr   Heat dissipating Area 4  d r  z s 4

Pgas P P 2 Q f  Ag  [v1 P ]  Ag  [ gzP  ] gas  2 Q  v A  C v1Ag P ]CliqDQi Q f  Ag  [v1   liq]  Afg  [2gzg D liq  liq  liq  liq Vm Pgas P  2 t P= Filling Time: V Q f  Ag  [v1  tf ]V Amg  [ gz   ] f liq Qmf  liq  liq

t f  Qf Qf V Gating design of t f  m casting using dam sprue The actual sprue (Fig. 2) in actual casting is divided into three Q f

parts, (i) Sprue pipe; (ii) Dam shaped well; (iii) Sprue Gate. The design has been planned to avoid aspiration as well as floatation of dross for the supply of clean metal into the gating system. The experimental results incorporate the proposed model when liquid brass (60/40) was used in clay molded investment casting. Assume, Volume of the casting = Vm Heat dissipating area of the casting = Am Gating design: Assumptions: Top gating Liquid metal Viscosity = µ and Density = = ρliq Cup area (at 0) = ACu =A0, Sprue area (at 1) = A S = A1, Dam area (at 2) =AD = A’2 Gate area at 3 = Ag= A 3 Velocity and Discharge calculation: Velocity at section -0: v 0 = 0 (consider constant head) (Fig. 2). Velocity at section -1:

VCasting Weight  100% Yield of of casting casting VCastingCasting Yield Yield of casting VCasting  VSprue 100%  100% VCasting  VSprue Weight of liquid metal poured Yield of casting 

VCasting VCasting  VSprue

 100%

liq

A1v1 = A2 v2 ∴ v2 =

A1v1  A2 v2  v2 

A1v1 A2

Q2  v2 A'2 Flow from the Area A 2’ is: Q2 = v2 A'2 A' v v3 A3  v2 A'2  v3  2 2 A3

v3 = vg

Casting Weight Casting Weight Yield of casting   100% Yield of casting  Weight of liquid metal poured  100% Weight of liquid metal poured

Pgas

Velocity at section -2: Apply Continuity Equation [11]:

150

  d r  d r  zs d r Hence drVolume can beofcalculated. Riser Mr    Heat molded dissipatinginvestment Area 4 casting, 4 d r  zs In the clay separate risers are not used by artisans. Riser and sprue are combined together in practice. VTotal = VCasting + VSprue =Casting VCasting VSprue Volume of all items: VTotal VTotal =V ++ VSprue 1.21.2 (VCasting +V ) ×) ×ρmρ Hot metal required: (VCasting + Sprue VSprue 1.2 (VCasting + VSprue) × ρm m [Considering 20% extra metal for drossing & spilling, the metal VTotal = VCasting + VSprue required.] 1.2 (VCasting + VSprue) × ρm Yield of casting:

A1v1 A2

Fig. 2. Sectional view of sprue with dam

S l é vá re ns t v í . L X V . k v ě te n – č e r v e n 2017 . 5 – 6

Calculated Filling Time

Experimented Filling Time Fig. 3. Schematic diagram of experi4 mental set up (top) experimental glass set up (bottom) 3 5

Filling Time (s)

v1  gz1 

Area Area

Calculated Filling Time Experimented Filling Time

g Time (s)

PŘESNÉ LITÍ

0 0.0

0.2

0.4

0.6

Percentage of Volume

0.8

1.0

v f  [v g 

P

liq