COMPUTER SIMULATION OF CONTINUOUS ELECTROMAGNETIC STIRRING FOR MAKING RHEOLOGIC SEMI-SOLID SLURRY OF

CHINESE JOURNAL OF MECHANICAL ENGINEERING●108●Vol. 21, No. 6, 2008 .DOI: 10.3901/CJME.2008.06.108, available online at www.cjmenet.com; www.cjmenet.com.cnCOMPUTER SIMULATION OFCONTINUOUS EL ECTROMAGNETICSTIRRING FOR MAKING RHEOLOGIC，SEMI-SOLID SLURRY OF ZL112YLIU ChangmingALUMINUM ALLOYYANG LingAbstract: To realize the technology of fabricating the theologic semi-solid slurry of ZL112Yalumioum alloy via continues electromagnetic stiming process, ANSYS software was used to simulateZU0 Hongzhiclectromagnetic force field and fluid velocity field in the alloy melt in a crucible tube in three coils. InCollege of Material Scencethe first section of the paper, eletromagnetic force field and fluid velocity field caused by single coilwere simulated. The result of this simulation gives an average velocity of 3.2 cm/s and it is calledand Engineering,critical velocity because a fluid velocity over it will cause a fine and spherical structure of solidChongqing Universityprimary a in a semi-solid melt. And, from this result, a reasonable temperature of semi-solid of theChongqing 40044 Chinaalloy and an electrical curent intensity were etablished. The electrical current intensity of the resultof this simulation corresponded to the curent intensity used in a practice experimeat, in which theprimary a was obviously refined and sphericized. Based on this simulation of single coilelectromagnetic stiring, in the second section of the paper, eletromagnetic force field and fluidvelocity field caused by three coils were simulated. The resut of the simulation shows that, 1) there isa semisolid zone of 32 mm from bottom of the crucible tube to the upper; 2) the elecrical currentintensties of three coils of 400 A, 600 A, and 400 A, which were set to top range, middle range andbottom range of the tube, respectively, were the optimum parameters of electromagnetic curentintensity under the condition of this investigation; and 3) under effect of these electromagnetic curtentintensity, the fuid velocities of the melt in the tube were 6.3 cm/s in top range, 3.75 cm/s in middlerange, and 3.9 cm/s in bottom range of it, respectively.Key words: Electromagnetic siring Electromagnetic force field Fluid velocity fieldRheologic semi-solid sury Compuer simulationYURKO in MIT in America'), this method has no problem of0 INTRODUCTIONatrition wear because of no mechanical string. And comparedComparing with thixoforming, rheoforming simplifed thewith the methods of cooling slopeln and low super-heatb, moreglobaand fine dendritic structure will be obtained becauseprocess of semi-solid metalworking, improved the efficiency, andelectromagnetic field made an intensive stirring.made the indutrialization easier to come true. And rheoformingIn order to enhance the efficiency of making semi-solidshows a series of caceritie.s sch as high efcve low slumry, this topic makes a computer simulatio of elcomageieenergy conservation, sbort procedures, and so on!". At theforce field in a melt and fluid velocity field of a melt on abegining, the mechanical stiring process was used in thecondition of electromagnetic stirming with three coils. There aretheofoming to preparing suryy Stiring paddle was bee heavily two steps in this computer simulaion. First, computerworm to break, because it worked at a bigh temperature for a longsimulation of electromagnetic force field in a melt and fluidtime. This is the reason rheofoming was quickly been instead bythixoforming. However, in thixoforming, there is a remelt processout and the processing parameters were selected and optimized toother than in rheofoming, so researchers, Fan， in Brunelobtain the suitable semi-solid slurry, then the processingUniversity in Britain gave an innovation of contioues twin-screwparameters of continuous strring with three coils were simulated.stirring rheocasting to prepare semi-solid slurry4.Anyway, there is a vital shortage of damage by corrosion ofThe purpose of these researches is to find a rtheoformingmelt to screws, so the service life of twin screws is very short.technological process that is a reasonable, highly effective andUnder these conditions, this paper put forward a proposal ofalso satisfies the indusrialization production.continues electromagenetic strring to make rheologic slury,by 1 COMPUTER SIMULATION METHODwhich primarygrains were refined and sphericized underelectromagnetic force. In this technology, superheated melt ispoured into a tube from its top and flows from top to bottom1.1 Computer simulation software used and modelingcontinues electromagnetic stiring process was; simulatedunder effects of an electromagnetic stiring force given by threeby the ANSYS sofware. This software is with capabilities ofelectromagnetic coils fixed outside the tube. By controllinghandling problems of finite element analysis and can be used toelectrical current intensity, a state of liquid of a melt is kept at thecalculate many physical fields. In the electromagnetism,upper of the tube and a state of semi-solid is kept at the lower. Thepaper about the lecromagnetic string for making theologice ecromagnetic force feld on a fuid and a: vlocity field of asemisolid slumry of the aluminum alloy was seldom reportedfluid (Simulation processesThis paper introduces the continuous electromagnetic string forinclude中国煤化工scomeae fimaking semi-solid slurmy. Compared with twin-screw BeneraiYHC N M H Gng physical parameter,rbeocasting'" and a new mechanical stirring method innovated byThe model of electromagnetic force field used in thissimulation is as followseccived June 20, 2007; received in revised form October 20, 2008; acceptedf=JxB(1)October 24, 2008CHINESE JOURNAL OF MECHANICAL ENGINEERING●109.where-Electromagnetic force3 Experimental of electromagnetic stirring with single-Electromagnetic curent intensityinduction coil.The alloy used in the experiment_ is ZL112Y. TheB一-Electromagnetic induction intensitycomposition of the alloyis as fllows Si 8.86%, Cu 3.44%, FeThe model of fluid velocity of a melt field used in this1.29%，and aluminum the rest. The temperature of ZL112Y'ssimulation is as followsliquidus is 594 C and solidus is 540 CFirstly, the melting alloy in the resistance fumace was poured-Vp+4V2+f(2) into the crucible, and the situation of the alloy's temperature atthis time was real-time monitored by a temperature measurementwhere ρ--Fluid densitysystem. Three different strring powers, concussive current were500 A, 800 A and 1 000 A, are used respectively for electrom--Fluid velocityagnetic sirring in meling alloy when the temperature is belowp一-Pressure590 C, and, the changing situation of temperature was recorded.The appearances of surface of the melting alloy at different.2 Simulation of the flowing velocitles in the melting alloystiring powers were observed when temperature reached to 590of electromagnetic stirring with single induction coilC, and a ltle melt was poured into a mould and quickly cooled. .The related data and parameters in simulation process are asFinally, samples of three kinds of strring powers were made forfllows: the concussion frequency of induction heating equipment microstrucure observation.is 90 kHz curant deasity 5.8x10 A/m? ;elativ pemebiliyof 1.4 Slmulation ofthe course of cntiouous trringaluminum, A=pμuo=8; electrical resistivity of Al-Si alloy,2.1x10-7 2●m; density of ZLII2Y aloy, 2 740 kg/m'. Because vertical was descending in the course of continuous stiring. The .viscosity data of Al-Si alloy can not be found as the temperature istemperature of the alloy at the top of tbe tube is 660 C, under thelower than that of the liquidus of this aloy, a curve, which isbottom it is 590 C. Separating the liquid alumioum in verticalshown in Fig. 1, by regression analysis method was made with theinto eight different temperature areas, and the viscosities atgiven data above the liquidusSr and the viscosity data under diferent temperature area are listed in Fig. 1.liquidus were obtained in this curve. From Fig. 1 it is seen that theInduced curent intensity being correspondence to differentviscosity number is4.12x10-N .m'.s' at 590 c (the volume induction crrent are lsed in Table 101. The rest parameters werefraction of solid of the alloy is 20% at this temperature).as the same with the simulation of electromagnetic stirring withsingle induction coil.0.045-Table 1 Current density at dfferent induction current; 0.040-Induction200 300 400 500 600 800 1000 1100 1200curtent 1IACurrent intensity2.323.48 4.64 5.8 6.96 9.28 11.6 12.76 13.92J(10'A-m”)The dimensions of high-alumina tube used for bolding the0.030-melting metal in the contiouous stiring unit were 56 mm indiameter, 8 mm in thickness, and 490 mm in length. The process0.025of this electomagnetism stiming is a issue about axial symmetry,so it can be transformed and solved by the two _dimensionalmethod model. One half of the axis section, that is a rectangle020500 5600 550with dimensions of 28 mmx460 mm of melting alloy, can beTemperature 77Cselected as the two dimensional method model. The distanceFig 1 Graph of viscosities vs temperatues of L112Y alybetween each induction coil is 5 mm, and between the center ofthe induction coil and the side surface of the melting metal areaFig. 2 is a schematic ilustration showing the relationship is 10 mm. In order to reduce the reciprocity of each groupbetween cylindrical crucible and the electromagnetic coil when induction coil, the distance between each group can be set be 50electromagnetic stirring with a single induction coil. The distance mm. The model of the continuous electromagnetic stirring isbetween each induction coil is 5 mm, and between the center of shown in Fig. 3, and, the green part means the area of meltingthe induction coil and the side surface of the meling metal area is alloy and the red part means the area of air.10 mm.By dividing this rectangle into 14 meshes in the horizontaldirection and 230 meshes in the vertical direction with mappedmeshing in the area of melting alloy, square meshes were obtainedwith 2 mm length for each side.Firstly, three groups of coils were assigned to differentcurrent intensity and concussion frequency, respectively. ThenMelting metalelectromagnetic physical environment was set up. Secondly,different viscosity was appointed to diftrent area in the modeland a physics environment of fluid field was set up. Thirdly, themodel was solved using electromagnetic physical environment,and, a distribution of the electromagnetic field was obtained.Fourthlyvas obtained by acoupling中国煤化工d and the fluid feld.一were designed in thesimulatiMHCNM HGring. In a technology,Al2O, cnucibleeach of three coils in vertical was given a different inductionFig. 2 Scbematic ilustration of electomagncticcurrent. Three different stirring technologies designed forstiring with single induction coilsimulation are as follows.LIU Changming, et a: Computer simulation of continvous eletromagnetic stiring for making rheologic●110.semi-solid slurry of ZL112Y aluminum alloy(1) The induction current at the top of the coil is I 00 A, at gain finer grains with circle fluxions in melting aloy. Therefore,the middle is 800 A, at the bottom is 500 Ahe suitable semi-solid microstructure can be received at the(2) The induction current at the top of the coil is 800 A, at condition of 590 c and 3.2 cm/s. This velocity is considered asthe middle is 600 A, at the bttom is 4000A.a criterion of flow rate.(3) The induction current at the top of the coil is 600 A, atthe middle is 400 A, at the bottom is 200 A.50 mm-5mmFig. 5 Distribution of the flowing velocitiesin the meling ZL112Y aloy at590 c, 500 AFig. 3 Model of the course of continuous stiring.2 Experimental results and discussfons of the electro-2 SIMULATION RESULTS AND ANALYSISmagnetic stirring with single induction coilAppearances of surfaces and the changes of temperature2.1 Simulation analysis of the fnowing veloctty In the meltingof the melt treated at three stiring powersalloy strred with single induction coilTable 2 shows the appearances of surfaces and the changes ofThe vector graph of lorentz fore in the melting metal area is temperature of the melt aly treated at three stiring powers. Itsbowa in Fig, 4.can be seen from this table that the largest hunch size of thesurface of the meling aloy is 1.8 cm when the currentis I 00 A,Nthe medium size is 1.2 cm when the current is 800 A, and the咖128smallest size is 0.8 cm when the curent is 500 A. Comparing withthe current of 500 A, the temperature changes rapidly and is noteasy to be contolled when the current is I 000 A. The control oftemperature is very important for the processing of semi-solid, soit is necessary to find a suitable power that has well effects bothon electromagnetic stiring and contolling easily for a changingtemperature.Table2 Appearance of surfaces and the changes of temperstureof the met AI aly treated at three sirring powersInductionChange of the surfacesChange of temperaurecurrent DAof the melting aloywith timeThe hunch size of the central The change of temperaturesuface of the melting alay is is etemely slow, and ascend-00 0.8 em, and fne material motion ing I C once a minuteFig.4 Vector graph of electromagnetic forcein it because of the stiring ofin the meling metal areaelectromagneticThe bunch size of tbe ceouml The change of temperatureFig. 5 shows the distribution of the flowing velocities in thesurface of the melting aly is is slow, and ascending 18 cmelt of ZL112Y alloy at 590 C with a induction current of 5008001.2 cm, and material motion oce a minute. A. It can be seen that two equal swirls are distributed in theobviouslymelting area in lengthways under the effect of the electromagneticfield. These two equal swirls are formned owing to a driving forceThe hunch size of the ceotral The change of temperatureof motion tendency caused by electromagnetic force toward the1 000surface of the meling alloy is is fast, and ascending 40 Cside surface of the melt. Moreover, the maximal velocity, 43 cm/s,1.8cm, and material motion ooCe 8 minuteoccurs at the top right comer and under right corner of the meltingquite obviouslyalloy, and, the minimum velocity, 1.4 cm/s, occurs at the centerswirl of the melting aloy, The average velocity of3.2 cm/s in the 22.2 Semisoid micotuctures at same temperature andmelting alloy area was calculated by calculating velocity at everydifferent stirring Dowersnode in melting aloy.M< |中国煤化工undeunder three kind ofIt is known that two equal swirls distributed in the meltingdifferenllographie microstruc-area by an analysis of the flowing velocities in the melting area tures W|Y片C N M H Gietures of the ZL12Ywith ectromagnetic sriring The average veocties in the melt aly at anerer sumng powers a C Itcan be see that thealloy with 20% solid phase particles is 3.2 cm/s, comparing with structure presents a nondendritic morphology at dfferent powers,one-way fluxion, dendrite crystals are more easily to be brokento in which the bright white is a phase, and, the primary a phase isCHINESE JOURNAL OF MECHANICAL ENGINEERING●111.●more finer, the higher the sirring powers is. It is known that the top of the alloy is greater than that at the others, and, at the middlehigher the concussive current is, the more strength the and underside of the aloy, velocities have no great different.electromagnetic power isthe greater the velocity of the meltingalloy is, and under a intensive fushing and impioging, the fioerprimary a phase ist50μm()590 C()500A50um()600 c(b)800AS0μm(2)610 CFig. 7 Microstructures of the AI-Si aly at diferenot temperaturesand the same strring powers(500 A) at 590 C(100x)(C)1000A .Fig. 6 Microstructures of the Al-Si alloy at diftrent stiringpowerst590 c (100x)2.2.3 Semi-solid microstructures at different temperatures andthe same stiring powerFig. 7 shows the microstructures of the alloy at differenttemperatures (590 C, 600 C, 610 C) and same strring powerof 500 A. Fig. 7a sbows the global primary a phase distributeduniformly on the matrix. However, in Fig. Tb and Fig. 7c, themicrostructures are a dendritic structure. It can be seen from thisfigure that the global primary a phase dstributed unifomly onmatrix only at the condition of 590 C and 500 A. Themicrostructure of the primary a pbase keeps the shape ofu 1.1 .中1.里1.国dendretic stucture when the temperatures are 600 C and 610(a) Al the top of the alyC, owing to a higher temperature than liquidus. It is known that,590 C is the suitable temperature for making semi-solid slurry.E品.2.3 Simulation results of the course of continuous stirring2.3.1 Distributions of flowing velocitis at dfferent currentsFig. 8 is the distibutions of the flowing velocities at eacharea in the melting alloy with the first technology(The inductionthe bottom is 500 A). Fig. 8a is the distribution of the flowing中国煤化工velocities at the area of tbe top of the alloy, and its averagevelocity is 11.3 cm/s. Fig. 8b is the velocities distribution at theHCNMH Garea of the middle, and its average velocity is 6.62 cm/s. Fig. 8c isthe velocities distribution at the area of the underside, and its(6) AI the middle of the alayaverage velocity is 6.3 cm/s. It is shown that the velocity at theLIU Changming. et al: Computer simulation of continuous electromagnetic sirring for making rheologic.112.semi-solid slurry of zL1 12Y aluminum aloyANCFig. 10 shows the distribution of the flowing velocities ateach area in the melting alloy with the third technology (TheE.induction current at the top of the coil is 600 A, at the middle is400 A, at the bottom is 200 A). The average velocities in the threeareas were calculated respectively, and the avernage velocity at thetop of the alloy is 4.6 cm/s, at the middle of the alloy is 2.1 cm/s,and at the underside of the alloy is 2.45 cm/s.lt can be known from the simulation of electromagneticsirring with single induction coil, the stiring average velocitycan't be lower than 3.2 cm/s if suitable semi-solid slury at 590C is expected. After the simulation of the flowing velocities withthree technologies, It is found that the sirring velocity is exced3.2 cm/s with the first and the second technologies, and, tbe(C) Underside of the alyvelocity with the first technology is 6.3 cm/s, with the secondFig. 8 Distribution of the flowing velocities at cach arcatechnology is 3.9 cm/s, and the third is 2.45 cm/s. The secondin the meling ZL112Y alay with the furst tchnologytechnology is a suitable process from the considerations ofFig. 9 shows the distribution of the flowing velocities at each microstructure cotrol and the enengy conservation.area in the melting alloy with the second technology (Theinduction current at the top of the coil is 800 A, at the middle is600 A, at the bottorm is 400 A). Tbe average velocities io the threeareas were calculated respectively, and the average velocity at thetop of the alloy is 7.8 cm/s, at the middle of the alloy is 4.3 cm/s,and at the underside of the alloy is 4.1 cm/s.N1.制(2) AI the top of the alolyAN(旧) Al the top of the aly三。(6) At the middle of the alayA(b) At the middle of tbe lloy.中国煤化工-也Jallyy(C)Underside ofthe lloyMYHCNMHGFig. 9 Distribution of the flowing velocities at each arcaFig. 10 Distribution of the flowingoe fowing vlocitiesatcech areain the melting ZL112Y aloy with the second technologyin the melting ZL112Y alloy with the third technologyCHINESE JOURNAL OF MECHANICAL ENGINEERING●113●2.3.2 Distribution of the flowing velocities at each area with the control and the energy conservation.amended currentsThe tiring velocity is 7.8 cm/s at the top of the alywi 3 CONCLUSIONSthe second technology and has an obvious discrepancy with thevelocity at the middle and underside of the alloy. Tbeo, the second(1) It is known from the simulation analysis in the meltingtchnolgoy is amended to a technology of400 A 600 A 400 A lly siring with single indution coil (S00 A 590 C) that theprocess. Fig. 11 is the dstributio of the flowing vlocities ateach average velocity is 3.2 cm/s. The global and uniform semisoidarea in the melting alloy with the amended technology.microstructure can be obtained by electromagnetic stiring with aflow velocity over this value. Therefore, this velocity isconsidered as a criterion velocity whether the alloy can gaiANTglobal and uniform semi-solid microstructure. And this criterion isa basis for the simulation of the continuous course ofEelectromagnetic strring with three coils.(2) It can be observed from the microstructures, which wereobtainedat590Cand500A,800Aand1000A,that1)thetemperature was easy to be controlled at 500 A; 2) thetemperature changing was only 1 c per a minute; and 3) the agrains distributed in the alloy and the average diameter of a grainsis as small as 20 μum. It is concluded that 500 A is the perfectparameter. By making an analysis to the microstructure of thisalloy at diferent termperaure (590 C, 600 C, 610 C) in theparameter of 500 A, it is seen that, at 590 C, global a grainshomogenously distributed in the microstructure of alloy. It is(间) At the top of he aloyconcluded that 590 C is the suitable semi-solid temperature.These results accorded with the result of experimeat of tbeM.. |electromagnetic stiring with a single coil.(3) A continuous stirring unit for experiment was desigped色anddistributionfluid field of continuouselectromagnetic strring with three coils in the whole melt areawas obtained by modcling and simulation. Many swirls of flow inwhole alloy in the vertical direction were found, Tbe range of thetemperatures was 590 C to 594 C in the arca from the bottomof tbe tube to tbe beight of 32 mm. Because these temperatureswere below the liquidus of this alloy, solid phase appeared in thisarea. But above this area there exist no solid phase because thetemperature in the area was higher than the liquidus of this alloy.The second technology was better than the others. Furthermore,this technology was amended to the process of 400 A-600 A-400(b) At the middle of the alyA, and tbe velocity at the top of the alloy was 6.3 cm/s, at themiddle of the alloy was 3.75 cm/s, and at the underside of thealloy was 3.9 cm/s. This velocity distribution was comparativelyperfect and it is meaningful to guide experimental research of tbe|5mcontinuous electomagnetic stiring of alloys.References[1] PAN Hogping, DING hiyong. vrifiatio and oumerical simuation forthe thixoforming process of semi-solid AISi7Mg aly[C/Proceedings ofthe 2th National Conference on Semi-Solid Metal Process, GeneralInstitute of Noferrous Mctals, Bejing, China July 20 _23, 2002: 60 -66.[2] FAN z, J s, BEVIS M J. Twin-screw rtheompocessing tchologlgyocdiogiRoyal TurinPolytechnic. Turin. Italy. September27- -29, 2000: 61-66.(C) Underside of the aloy[3] YURKO」A, MARTINEZ R A Developmeot of the semi-solidtbeocasting (SSR) process[C)/Proceedings of the 7h IntemationalConference on Semi-solid Processing of Alloys and Composites. NationalFig. 11 Distribution of the flowing velocitis at cach artaInstitute of Advanced Industrial Science aod Technology, Japan Societyin the melting ZL112Y aloy with the aumended technologyfor Tecbnology of Pasticit, Tsukube, Japan, Sepiember 25 -27; 2002:659-664.The average velocity in the three areas was calculated [4] JA Fei Tecbnical opimization and stucure propety of cectromagnetierespectively and average velocities were obtained at each area incontinuous casting[DV/Dulian: Dalian University of Techology, 20the melting alloy with the amended technology. Tbe average(in Chince)velocity at the top of the alloy is 6.3 cn/s, at the middle of the[5] KEIST 了， APELIAN D. Inductio Heating of SSM Bllets[C]ce o Sermisolid of Aloyalloy is 3.75 cm/s, and at underside of the alloy is 3.9 cm/s.nd |中国煤化工in iay, Sebr27-2,2Compared with tbe second technology, the sirring velocity at the20top of the aloy becomes loower with the amended technology, but 6] WYHfoecment mecbhanismC NM H Gaaemo mochenism。still exceeds the criterion velocity of 3.2 cm/s. Obviously, theLiaoning Technical Universiy, 2000, 19(4): 430- 434. (in Chinese)amended tecbnology is the most suitable process for the[7] TOSHIO Hag, KAPRANOS P, KIRKWOOD D H Rhcocasting processclectromagnetic stirring ftom the considerations of microstructureusing a cooling slope low super heat casting [C/Proceedings of the 7thLU Changming, et a: Computer simulation of continuous electromagnetic stiming for making rheologic●114.semi-solid slurry of ZL112Y aluminum alloyIntermational Conference on Semi-solid Alloys and Composites. NationalInstiute of Advanced Industial Science and Jechnology, Jepan Society Biographlcal notesfor Technology of Plasticity, Tsukuba, Jepan, Sepember 25 -27, 2002:LIU Changming is a professor in College of Material Science and Engineering,801-806.[8] LIU Dan, cu Jianzhog, XIA K N. Microstructure of liquidus castingChongqing Universiy, China. His researcb interests include new light alloyaluminum aly 2618[]. Joural of Northeasterm Universiy, 1999 20(2;:nateial and metal composite materal, semisoid metal forming tectnique,; GEIGER G H, POIRIER D R. Transport Pbenomena in Metalurgy[MVeMTel: +86- 1-65111670; E-mai: cdcmliu@x263.netMenlo Park, Califrnia London Don Mills. Ontario: Addisop-WYANG Ling is curently a master ceandidate in College of Mterial Science and[10] ZHU Mingyuan, SHI Wen. Influence of electromagnetie stiring onEngineering, Chongqing University, China. Her Tresearch project includesaluninum alloy microstnucture[]. Chin. J. Noferrous Met, 1999, 9(1):studying on semi-solid casting, aluminum marix composites and advanced29- -34. (in Chineselight alloy material and processing engineering.(1] WANG Kai, LIU Changming. Strucural evoluions of ZL112Y alyy in Tel: +86 10611170; E-mail: yling9410@sobu.comprocedures of semisolid die casting[]. Chin. J. Nonferrous Met, 2003,ZUO Honghi is a master candidate in College of Mechanical Engineering,13(4): 956 362 (in Chince)[12] YANG Bicheng, DU Dongchao. Effects of electomagnetic siriog on Chongqing University China. His research interets include advanced lightmicrostructure of Mg-Al-Si lly Special Casting and Nonierous maierial and poessig egineing, semi-solid forming, ecAlloys, 2004(3): 26 -28. (in Chincse)Tel: +86- 10-65111670; E mail: zhihongz@sobu.com中国煤化工MYHCNMHG