This transient induction heating problem demonstrates a solution sequence alternating between an electromagnetic harmonic analysis and a transient heat transfer analysis with restarting:
The element PLANE13 used in this example has been archived. For more information, see Feature Archive.
A very long steel billet undergoes surface heat treating by rapidly raising the temperature of the billet surface by means of an induction coil. The coil is placed in close proximity to the billet surface and is excited by a large alternating current at high frequency. The AC current induces heat in the billet, most notably at the surface, which quickly raises the surface temperature.
A simplified geometry considers only a finite length strip of the long billet, essentially reducing the problem to a one-dimensional study as shown in Figure 3.6: Axisymmetric 1D Slice of the Induction Heating Domain.
The billet will heat up to over 700°C. This temperature dependency of the material properties must be considered for both the thermal problem and the electromagnetic problem. You must solve the problem sequentially, first doing an AC harmonic electromagnetic analysis and then a transient thermal analysis. In addition, you must repeat the electromagnetic analysis at various time intervals to correct for temperature dependent properties which will affect the solution and hence the heating load to the billet. Figure 3.7: Solution Flow Diagram shows the solution flow diagram.
Procedure:
Set up the electromagnetic analysis as follows:
Define the electromagnetic element types, material properties, and real constants as shown below. Note that the billet surface will be used to define a surface effect element for thermal radiation, and it is handled differently than the solid regions.
Assign boundary conditions and loads as shown below.
Set up the thermal analysis as follows:
Cycle between a harmonic electromagnetic analysis and a transient thermal analysis in a *DO loop:
Resume the electromagnetic database and parameters.
Read in the temperatures and body-force loads for material property evaluation via LDREAD from the results of the thermal analysis.
Solve the electromagnetic harmonic analysis.
Save the electromagnetic database.
Change the element types from electromagnetic to thermal as well as KEYOPT options. Specify the null element type in the air and coil region (assume the heat transfer analysis only considers the billet).
Read in the Joule heat generation rate via LDREAD from the results of the electromagnetic analysis.
Solve the thermal transient for a preset time increment (Δt).
Post-process the problem results.
The following figure shows the temperature results obtained in this analysis.
All text prefaced with an explanation point (!) is a comment.
/batch /prep7 shpp,off /title, Induction heating of a solid cylinder billet /com, et,1,13,,,1 ! PLANE13, axisymmetric, AZ degree of freedom et,2,13,,,1 et,3,151,,,1,1,1 ! SURF151, thermal, radiation r,3,0 ! Real constant set for SURF151 row=.015 ! outer radius of workpiece ric=.0175 ! inner radius of coil roc=.0200 ! outer radius of coil ro=.05 ! outer radius of model t=.001 ! model thickness freq=150000 ! frequency (Hz.) pi=4*atan(1) ! pi cond=.392e7 ! maximum conductivity muzero=4e-7*pi ! free-space permeability mur=200 ! maximum relative permeability skind=sqrt(1/(pi*freq*cond*muzero*mur)) ! skin depth ftime=3.0 ! final time tinc=.05 ! time increment for harmonic analysis time=0 ! initialize time delt=.01 ! maximum delta time step emunit,mks ! set magnetic units ! electromagnetic material properties mp,murx,1,1 ! air relative permeability mp,murx,3,1 ! coil relative permeability mptemp,1,25.5,160,291.5,477.6,635,698 ! temps for relative permeability mptemp,7,709,720.3,742,761,1000 mpdata,murx,2,1,200,190,182,161,135,104 ! steel relative permeability mpdata,murx,2,7,84,35,17,1,1 mptemp mptemp,1,0,125,250,375,500,625 ! temps for resistivity mptemp,7,750,875,1000 mpdata,rsvx,2,1,.184e-6,.272e-6,.384e-6,.512e-6,.656e-6,.824e-6 mpdata,rsvx,2,7,1.032e-6,1.152e-6,1.2e-6 ! steel resistivity ! thermal material properties mptemp mptemp,1,0,730,930,1000 ! temps for conductivity mpdata,kxx,2,1,60.64,29.5,28,28 mptemp mptemp,1,0,27,127,327,527,727 ! temps for enthalpy mptemp,7,765,765.001,927 mpdata,enth,2,1,0,91609056,453285756,1.2748e9,2.2519e9,3.3396e9 mpdata,enth,2,7,3.548547e9,3.548556e9,4.3520e9 mp,emis,2,.68 ! emissivity ! finite element mesh rectng,0,row,0,t ! billet rectng,row,ric,0,t ! air-gap rectng,ric,roc,0,t ! coil rectng,roc,ro,0,t ! outer air aglue,all numcmp,area ksel,s,loc,x,row ! select keypoints at outer radius of workpiece kesize,all,skind/2 ! set meshing size to 1/2 skin depth ksel,s,loc,x,0 ! select keypoints at center kesize,all,40*skind ! set meshing size lsel,s,loc,y,t/2 ! select vertical lines lesize,all,,,1 ! set 1 division through thickness lsel,all asel,s,area,,1 aatt,2,1,1 ! set attributes for billet region asel,s,area,,3 aatt,3,1,2 ! set attributes for coil region asel,s,area,,2,4,2 aatt,1,1,2 ! set attributes for air region asel,all mshape,0,2d mshk,1 amesh,1 ! mesh billet area lsel,s,loc,y,0 lsel,a,loc,y,t lsel,u,loc,x,row/2 lesize,all,.001 lsel,all amesh,all ! mesh remaining areas n ! create space node for SURF151 *get,nmax,node,,num,max lsel,s,loc,x,row type,3 real,3 mat,2 lmesh,all ! mesh billet outer radius with SURF151 *get,emax,elem,,num,max emodif,emax,3,nmax ! modify element to add space node for radiation et,3,0 ! reset type 3 to null element ! magnetic boundary conditions nsel,s,loc,x d,all,az,0 ! apply flux-normal b.c. nsel,all esel,s,mat,,3 bfe,all,js,,,,15e6 ! apply current density to coil esel,all finish nsteps=ftime/tinc *do,i,1,nsteps ! solution *do loop time=time+tinc ! increment time /filnam,induc *if,i,ne,1,then parsav,scalar resume parres,new *endif /solu antyp,harm harfrq,150000 *if,i,eq,1,then tunif,100 ! initial temperature *else ldread,temp,last,,,,therm,rth ! read thermal analysis temps *endif nsub,1 kbc,1 solve ! solve harmonic analysis finish save,induc,db /filnam,therm /prep7 et,1,55,,,1 ! PLANE55 thermal element, axisymmetric et,2,0 ! null element type for coil and air region et,3,151,,,1,1,1 ! SURF151 element for radiation keyopt,3,9,1 r,3,1,5.67e-8 ! form factor, Stefan-Boltzmann constant finish /solu antype,trans toffst,273 tunif,100 ! initial uniform temperature d,nmax,temp,25 ! ambient temperature cnvtol,heat,1 ! convergence tolerance kbc,1 ! step loads trnopt,full autos,on ! auto time-stepping deltim,1e-5,1e-6,delt,on ! time step control outres,basic,all ! save all load step information finish /solu parsav,scalar ! save parameters before multiframe restart *if,i,gt,1,then antype,trans,rest ! thermal restart *endif parres,new ! restore parameters after multiframe restart time,time ! time at end of thermal run esel,s,mat,,2 ! select billet region ldread,hgen,,,,2,induc,rmg ! apply Joule heating load from emag solve finish *enddo ! end of solution looping finish /post26 ! time-history postprocessor nsol,2,1,temp,,tempcl ! store temp at billet centerline nsol,3,2,temp,,tempsurf ! store temp at billet outer diameter prvar,2,3 /axlab,x,Time (s) /axlab,y,Temperature (deg.C) plvar,2,3 ! plot temperature rise over time fini