ISIJ Internationa Vo 54 (2014) No 2 pp 254 258 Numerica Simuation for Optimizing Temperature Gradients during Singe Crysta Casting Process Aeksandr Aeksandrovich INOZEMTSEV 1) Aeksandra Sergeevna DUBROVSKAYA 2) * Konstantin Aeksandrovich DONGAUZER 3) and Nikoay Aeksandrovich TRUFANOV 4) 1) Aviadvigate OJSC 614990 93 Komsomosky Prospect Perm Russia 2) PhD Student Appied Mathematics and Mechanics Department of PNRPU 614990 29 Komsomosky Prospect Perm Russia 3) Casting Simuation Department Aviadvigate OJSC 614990 93 Komsomosky Prospect Perm Russia 4) Department Computation Mathematics and Mechanics Department of PNRPU 614990 29 Komsomosky Prospect Perm Russia (Received on June 24 2013; accepted on November 7 2013) This artice describes appication of computationa simuation for manufacturing of castings using investment casting technique A mathematica mode was created describing the process of meted meta pouring into the ceramic she with its further soidification Using this mode the process of manufacturing singe-crysta patterns from heat-resistant nicke superaoy was simuated The obtained computationa mode was verified by the temperature measuring of the rea-ife production experiment Using mathematica simuation the speed of the patterns moving out was optimized to increase temperature gradient on the casting KEY WORDS: mathematica simuation; computationa simuation; investment casting; soidification 1 Introduction One of the techniques used for manufacturing high-quaity machines components is investment casting which aows in one operation to manufacture compex geometry castings (incuding thin-was bades) for expensive heat-resistant aoys which are not very machinabe 1) But due to the production process compexity and arge number of factors infuencing on the resuted product quaity soidification shoud be checked especiay stricty Mathematica simuation of processes associated with components manufacture by investment castings aows to reduce costs because gating system design and temperature-time parameters of the technoogica process are exercised in mathematica mode virtua space instead of rea-ife expensive casts Low cost and short time of computationa experiment execution as we as arge voume and visuaization of the obtained information about the technoogica process progress and quaity of the future casting make computationa simuation an important research too 2) This topic is novety and scantiy investigated Earier this probem was considered in 3) This work studies the process of manufacturing singe-crysta patterns from heatresistant nicke aoys A mathematica mode is buit which describes this process The mode is verified by comparing the data obtained by computationa experiment with temperature measuring resuts Mathematica mode appication is examined in terms of optimizing the speed of the casting moving out of shes preheating furnace * Corresponding author: E-mai: dubrovskaya-as@avidru DOI: http://dxdoiorg/102355/isijinternationa54254 2 Mathematica Mode Buiding Let us study the process of manufacturing singe-crysta patterns from heat-resistant nicke aoys The partners are casted in a specia-purpose machine of direct soidification Soidification is proceeding simutaneousy in two shes obtained by investment casting and poured with ceramics as per Shaw technique 4) Each she consists of three patterns Before the pouring the meted materia the shes are heated in a furnace during 4 200 seconds up to process-oriented temperature Then the meted nicke aoy is poured in From the moment of pouring up to shes moving out the patterns are conditioned within ten minutes Inside the machine during the whoe process the temperature is maintained at the eve higher than the aoy iquidus point Soidification and singe-crysta structure perfection are defined by the speed of shes moving out of the heating modue Now we wi describe the mathematica process Figure 1 shows the circuit of the casting manufacturing incuding the ceramic she Shaw ceramics and the region of the casting formation Non-stationary therma profies in computationa area whie pouring meta and soidification is studied using differentia equation of heat conductivity H ρ ρ λ + U gradt = ( T ) x T t V where the casting materia enthapy 1 1 1 1 T H ( T ) = c ( T ) dt + L 1 g ( T ) 1 0 p1 [ ] s 2014 ISIJ 254
ISIJ Internationa Vo 54 (2014) No 2 Fig 1 Scheme of castings manufacturing process where V 1 area of casting body V 2 Shaw ceramics VS 3 she S 1 boundary for meta pouring S 2 boundary of meta and she interference S 3 boundary of Shaw ceramics and she interference S 4 meta free surface S 5 Shaw ceramics free surface S 6 she free surface for the she materia and Shaw ceramics the heat conductivity differentia equation ooks as foows: Hi ρ λ i i T x Vi t = ( ) T Hi( T) = cpi( T) dt 0 where indices: 1 2 and 3 refer to areas V 1 V 2 and V 3 respectivey T temperature; t time; ρ materia density; с p specific heat capacity; L specific heat of phase transition; λ = λ (T) heat conductivity factor; U = ( u effective meting rate vector cacuated through iquid phase 1 u2 u3) actua speed U 1 as foows: U = g ; g iquid phase U1 portion; g s soid phase portion g s = 1 g ; x = ( x1 x 2 x3) radius-vector in Cartesian coordinate system Heat conductivity equation additionay is competed with boundary conditions on the surface of the she-casting contact: λ = λ T = α 3 1 13( T1 T3 ) x S2 n n On the boundaries of heat conductivity with environment the conditions are as foows: ( ) λ α T T εσ T T n = ( ) 4 4 i ic i c i c 1 S4 i = 2 S 5 3 S6 where α(t) heat reease coefficient determined as per 3) index с is for environment parameters ε emissivity factor σ Stefan Botzmann constant Heat transfer conditions between the Shaw ceramics and the she are considered to be idea T 2 = T 3 S 3 Initia conditions are transferred to the pored meta temperature and the she with Shaw ceramics Ti( x 0) = T0 i( x) i = 123 ; V i To mode the process of meted meta pouring into the ceramic she and to cacuate heat and mass transfer the motion differentia equation is appied In computationa area we consider non-isotherma aminar fow of non-compressed Newtonian viscous iquid Phase interface is not ceary distinguished U ρ1 2 ρ1 2ρ1 τ + grad( U ) 2 + ( rotu U ) μ = ρ 1g + grad( p) + grad μdiv( U )+ U K V 1 g gravitationa acceeration; p pressure; μ viscosity ratio; K dendrite frame structure permeabiity g3 cacuated as per Karman-Kozeny equation: K = where 2 ksv 61 ( g ) S specific surface of soid-iquid phase D V = D dendrite typica size k Karman constant vaue k = 5 The motion equation is additionay competed with the evoutionary equation of compressibe medium continuity in iquid phase area to meet the mass conservation aw: ρ0 + div( ρ0u )= 0 x V1 t The motion equation is additionay competed with the foowing boundary conditions: σˆ n = p at S 4 the condition of tangent ines absence ( p τ = 0 ) and simpe stress equity with gas pressure at free c surface ( p ) n unit norma eement at the casting n = p n free surface Free surface geometry S 4 is defined as reated to time through reationship of simpe stress and meta surface tension S according to the procedure described in 5) 4 At the boundary S 2 for the soidified meta the speed U is automaticay becoming 0 because U = g and g = 0 U1 It is assumed that at initia point at surface S 1 there is a meted meta source with the known initia speed distribution: U 00 u = ( ) 0 0 3 Mathematica Mode Verification Considering the abovementioned mathematica reations the finite-eement mode of singe-crysta patterns manufacture was buit Soution area incuded casting body she and Shaw ceramics 4) Cooing conditions were specified using specia boundary conditions (Fig 2) To simuate the process of pouring and soidification of the air ceaner case we used the muti-purpose software soution and in particuar ProCAST system of casting process computer simuation (Fig 3) To verify the proposed mathematica mode an experiment was conducted at Aviadvigate s deveopment pant for manufacturing singe-crysta patterns from nicke superaoy During the work a specia-purpose vacuum furnace was used for the preheating of the shes Two modues were poured in the preiminary heated shes After certain time 255 2014 ISIJ
ISIJ Internationa Vo 54 (2014) No 2 Fig 2 Finite-eement mode of (a) casting (b) she (c) the whoe computationa area Fig 3 Resuts of computationa simuation of pouring heat-resistant nicke super-aoy and its further soidification the patterns were sowy moved out of the furnace to achieve fat therma gradient opposite to crystas growth direction At carrying out fu-scae experiment the ceramic she and the casting cavity were fitted with specia-purpose therma sensors with numbers 7 12 (thermocoupes arrangement is given in Fig 4) Thermocoupes with odd numbers showed the temperature in the ceramic she and the thermocoupes with even numbers in the casting The obtained thermocoupes readings were interpoated into the temperature-time reationship curves These curves were compared with computationa cacuation resuts in points corresponding to sensors arrangement Figure 5 show comparison of computationa cacuations with the thermocoupes data in the she and in the casting correspondingy Absoute accuracy for mathematica mode didn t exceed 10 С that is ess than 1% in soidification temperature intervas Therefore correspondence between numerica simuation resuts and experimenta data was proved It confirms the possibiity of numerica modes wide appication in production process Fig 4 Thermocoupes arrangement in the ceramic she (geometrica sizes are given in 10 3 m) 4 Optimization of the Patterns Moving Out Speed Having proved that numerica mode truy refects therma processes in a casting assemby et us modify the production process to improve the patterns structure 2014 ISIJ 256
ISIJ Internationa Vo 54 (2014) No 2 Fig 5 Comparison of the thermocoupes data with the temperature evoution in the reative component using computationa simuation Cacuation resuts are shown in grey and the thermocoupe data in back The Figure eft side refers to the shes and the right side to the castings Fig 6 The patterns moving out speed (the ight dashed ine shows the speed before optimization the dark dotted ine shows the speed mode cacuated using the optimization the soid ine shows the piecewise inear approximation of the optimized speed mode) One of the quaity parameters is the therma gradient width which is infuence by the she moving out speed Therefore we wi optimize the speed of the she moving out of the furnace to achieve maximum temperature gradient As an optimized function et us chose the width of soidification front-ine and et it tend to a minimum For optimization we use gradient descend method with a constant step D = f( ω) min where ω 00 ωz the speed of the patterns moving out and D the width of soidification front-ine tending to a minimum = ( ) D = D D 1 2 ω ω 2 1 Tabe 1 Therma gradient in the casting Casting part At the beginning of the starting cone At the end of the starting cone At the beginning of the casting body In the midde of the casting body At the end of the casting body Before optimization 34 10 3 K/m 23 10 3 K/m 15 10 3 K/m 13 10 3 K/m 14 10 3 K/m After optimization 50 10 3 K/m 42 10 3 K/m 37 10 3 K/m 34 10 3 K/m 47 10 3 K/m 257 2014 ISIJ
ISIJ Internationa Vo 54 (2014) No 2 Where λ = 05 the seected step for the gradient descend method Criteria for breaking the process of minimum definition: As a resut for speed a temporary reationship was obtained (Fig 4) For convenient appication of the optimized speed function in the production process it was approximated by the straight ine (Fig 6) It can be emphasized that on pattern castings the soid-iquid area width reduced sufficienty after optimization Therefore the change of the patterns moving out speed ed to the gradient increase in the castings Tabe 1 specifies therma gradient aong the casting ength before and after optimization of the moving out speed 5 Concusions [ k+ 1] [ k] [ k] ω = ω λ D( ω ) [ k+ ] [ k] ω ω εwhereε = 10 1 3 Hence computationa anaysis appication aows not ony to study singe-crysta structure formation from inside but aso provides a possibiity of carrying out numerica experiments for investigating process and design parameters infuence on manufacturing singe-crysta castings of gas turbine engine parts which is probematic and unreasonaby expensive if it is done at rea-ife patterns It aows to increase the quaity of manufactured castings sufficienty and to minimize the risk of possibe defects occurrence REFERENCES 1) J A Dantzig and M Rappaz: Soidification EPFL Press Lausanne (2009) 9 2) А В А V Моnastyrsky V P Моnastyrsky and Е М Levitan: Casting Process Deveopment for Industria Gas Turbine Large Bades Using Poygon and ProCAST Systems Casting Production No 9 (2007) 29 3) А А S Dubrovskaya and К А Dongauze: Numerica Study of Process and Design Parameters Infuence on Manufacturing Singe- Crysta Castings of Gas Turbine Engine Parts PSTU Newsetter Appied Mathematics and Mechanics No 9 Pubishing office of Perm State Poytechnic University Perm Russia (2011) 102 4) E P Degarmo J T Back and R A Kohser: A Materias and Processes in Manufacturing 9th ed Wiey New York (2003) 315 5) J U Brackbi D B Kothe and C Zemach: J Comput Phys 100 (1992) 335 2014 ISIJ 258