An Analysis of the Stress Relief Process of
Drum Rotors
John Moran
Conduction Heat Transfer
MEAE6630H01
April 6, 2000
Abstract
In the manufacture of jet engine compressors, the disks which hold the airfoil blades
are welded together to form drum rotors. As a result of the welding process the newly
formed drum must subsequently be heat treated to relieve residual stress. This project is an
analysis of that heat treating process. A representative part has been chosen and analyzed in
order to gain insight into the heat treating process.
Background
A jet engine axial compressor is typically composed of six to eleven stages. Each
stage is made up of a set of moving blades mounted to a rotating disk and a stationary set of
vanes. The blades force the air to move axially along the compressor, while the vanes
redirect the airflow to optimize it for use by the next stage. At the end of each stage, the
pressure of the air increases.
Based on criteria such as serviceability, expected engine environment and
requirements for manufacturing, several stages of the disks are welded into what is referred
to as a drum rotor. It is desirable to weld them together because it saves weight and
eliminates the need for bolts, which can come loose during engine operation.
Consider now the task of manufacturing a drum rotor. The manufacturing process
begins with rotors that are referred to as being in “detail”. They are easiest to work with
while they are in this state and are machined as close to their finished form as possible. The
drums are then joined into an “assembly” using a process known as electron beam welding.
The welding process causes a variable amount of upset between the rotors and introduces
residual stress at the weld joints, so some final dimensions can not be machined until after
the drum has been welded. In order to relieve the residual stress the drum must be heat
treated. It is this heat treating process will be the focus of this analysis.
Process Description
Heat treat is done using an Abar Ipsen furnace. This is a cylindrical vacuum furnace
with a 6’ x 8’ hot zone chamber designed to accommodate parts up to 48” wide by 54” high.
The hot zone is composed of three banks of wide band sheet molybdenum heating
elements. There is one set of heaters across the top of the cylinder, one set across the bottom,
and the third set around the wall of the cylinder. The percentage of total power applied to
each bank may be varied initially, but can not be adjust on the fly during a heat treat cycle.
Since various combinations of part types and loads are treated in the furnace, it is considered
impractical to attempt to optimize the power distribution for any specific part or load of parts.
Protection and control of the heating elements are provided by a control and an over
temperature thermocouple located near the elements.
The furnace walls are water cooled and protected by heat shields. The heat shields
are made up of layers of molybdenum and kaowool and are located between the heaters and
the furnace walls. The furnace is equipped with a gas blower so that forced convection
cooling is possible.
The furnace is set above the floor so that the bottom can be lowered for part loading.
There is a grate between the bottom heater bank and the hot zone to hold the load. Steel
fixtures are used to protect the parts from damage. The part and fixture are placed onto the
grate, the furnace is sealed and the process begins.
To study the process in detail, a representative part was chosen. This particular part,
part number 56H306-01, is an assembly of four disks. The treatment of this part begins by
loading the part and fixture onto the grate. Two pairs thermocouples (TC), staggered 90
apart, are attached to the part as shown in figure 1. The part is then placed into the furnace
and heated to 1100 F 15 F at a rate of 15 F/min. Full power is applied to the heating
elements. The heat up rate is controlled by the part TC or the control TC, whichever is most
limiting. Whenever the prescribed heat up rate is exceeded the power is cut back. This is
significant because it means that the actual heat up rate is not smooth and continuous.
When the control TC reaches 1100 F the power is scaled back to maintain this
temperature. When the last part TC reaches 1085 F the clock is started for a two hour soak
period. Cooling of the part is initially accomplished by pure radiation to a temperature of
900F. The next stage of cooling is by free convection using Argon gas to a temperature of
500F at a rate not to exceed 400 F per hour. The final stage is cooling by forced
convection to 200 F. All of the cool down transitions are signaled when the last part TC
reaches the prescribed temperature. When the part has reached 200 F, it is removed and the
stress relief process is complete.
Analysis
In order to summarize this report, the raw data, calculations and results have been
presented in two appendices. Appendix I is provided at the end of this document and is
intended to contain enough data so that this report can stand alone. Appendix II is provided
in the form of an Excel spreadsheet (apndx2.xls) and contains raw data, plots and detailed
calculations. It is not necessary to refer to this appendix to get the gist of this analysis, but it
has been provided as a reference.
The process was analyzed using a 2D axisymmetric model with the MARC finite
element code. A cross section of the geometry was created using Unigraphics CAD
software. MSC PATRAN software was used for pre and post processing. The choice of
software was based on availability and the authors knowledge of the software. The
PROCAST finite element code has exceptional ability to model radiation and would have
been preferred, however it was not available.
The choice to use an axisymmetric model was made for three reasons:
1. Because the part is still early in the process, the are few 3D features that need to
be neglected in order to use the axisymmetric approach.
2. Little information was available with regard to furnace parameters such as heater
and wall temperatures, emmisivity values and so forth. Additionally the accuracy
of the solution is limited by the poor ability of the MARC code to deal with
radiation heat transfer. Since the accuracy is limited, there is little point in
reaching for a high level of detail.
3. The run time required for a 2D model would be much smaller than it would be for
a full 3D model. The run time was an important consideration since the heat flux
parameters would need to be estimated and then matched to the provided TC data
through trial and error.
TC 13, 14
25
28
212
Weld Joint 3
477
133
Weld Joint 2
731
Web (4 plcs)
Weld Joint 1
1092
CL
TC 19, 20
1182
X
Y
490 Bore (4 plcs)
885
Fixture
Z
Figure 1 – Finite element model of drum rotor and fixture
The drum rotor and fixture were modeled using four noded quadrilateral elements.
The drum rotor is made of titanium while the fixture is made from steel. The details of the
material properties are given in appendix II. Thermal contact resistance between the fixture
and the drum has been neglected. The locations of the part TC’s are shown in figure 1 along
with the nodes, which were used to simulate them. Additionally, the locations of nodes used
to monitor other areas of interest have been labeled.
Radiation fluxes were applied to the edges of the elements though the use of a
subroutine. For the heat up portion of the cycle, the flux application was broken into three
parts, the top, the side and the bottom. As a matter of practicality, the internal radiation in
the cavities was neglected as a simplifying assumption. This assumption resulted in
significant error, however it was necessary to limit the number of variables in order to arrive
at a solution. Based on the TC data, the flux was then estimated by assuming that the
element temperature was offset by some initial amount from the part temperature and that it
increased linearly with time. In estimating the initial offset temperature it must be
recognized that the temperature of the elements would be higher than the temperature read by
the control and over temp TCs which reflect the entire environment. Trial runs were made
by iterating on the value of the initial offset and the ramp rate to arrive at an equivalent flux
function. The iteration was carried out until a reasonably close match was made to the TC 13
and 14 data. The view factor and the emmisivity were assumed to be lumped into this
equivalent flux function. The side and bottom fluxes were then assumed proportional to the
top flux and further iteration was done until the data for TC 19 and 20 was matched. It was
found here, as expected, that the bottom flux reaching the part would be considerably less
than side and top fluxes since the view to the bottom heating elements is obstructed by the
grate and the fixture. The mass of the fixture also slowed the response of temperature to the
flux. For the soak condition, the constants of the radiation were kept the same and an
element temperature of 1100 F was assumed. Plots of TC data versus the nodal
temperatures calculated for the same locations are presented in appendix II.
Before proceeding with the rest of the analysis, the heat up portion was checked
against some rough hand calculations using the Heisler charts. Since no fluxes were applied
to the top or bottom surfaces of the inner two disks they were effectively insulated on these
surfaces as far as the finite element analysis was concerned. This means that they could be
expected to behave similarly to an infinitely long cylinder. An equivalent convection
coefficient for radiation was calculated based on the fluxes applied by the subroutine. The
Heisler chart calculations were hot on the bore area by about 150 F (30% off) and cool at the
surface by about 300 F or 40%. This is adequate to confirm that the analysis is accurate to
the correct order of magnitude. The top disk was considered as the product of a 1” thick
infinite slab and an infinite cylinder. Since the top disk is effectively insulated on the
bottom, the slab used for the Heisler chart was taken as 2” thick where the center temperature
(x/L = 0) would then correspond to the temperature on the insulated surface. These
calculations were very close to the analysis results and were taken as a validation of the finite
element model. These calculations are presented in detail in appendix II.
Because there was error involved in the heat up calculation, the part temperatures for
the cool down portion of the analysis were reset to a uniform value of 1100 F to be in
agreement with the TC data. The radiation cool down portion was matched to the data in the
same manner as the heat up portion. The cool down by convection was done in a similar
manner by making educated guesses at a convection coefficient and Tinf. The effects of
radiation heat transfer were neglected to simplify the analysis. Since the gas is stagnant in
the cavities, it seemed reasonable to assume that the convection coefficient there would be
some small fraction of the convection around the outside of the part. As a simplifying
assumption, Tinf was assumed constant. It is known that the cooling water temperature in the
furnace walls is somewhere in the neighborhood of 100 F. Based on the cooling of the
furnace walls and absorption of heat from the part and environment, the guess made at Tinf
assumed a value that was somewhat greater than 100 F. For the free convection, this value
was assumed higher than that of the forced convection, since the environment had cooled
more before the forced convection was used.
All of the calculations described above were carried out using British units of BTU,
lbm, inches and seconds. Time steps were chosen automatically by the program. The
specific equations used to apply the fluxes described above can be found in the
”SUBROUTINE FLUX". This is a FORTRAN subroutine and includes comments. The
regions of flux application and the proportions of the flux are determined by the array
variable N(4). The regions are defined in the cooldown.dat file by the " DIST FLUXES"
cards. These files can be found in the appendix I.
Results
In this section, the results will be considered in five parts, heat up, soak, radiation
cool, free convection cool and forced convection cool. When viewing figures 2 though 6 it is
suggested that the zoom be increased to 400 or even 500%. Doing this will display some of
the lighter pink color contours which appear to be lost at normal magnification. Raw data
and additional results in the form of plots and tables are presented in appendix II.
1132.
1075.
1018.
1132.
960.
903.
846.
788.
731.
673.
616.
559.
272.
501.
444.
387.
Y
Z
329.
X
Time = 3894.6
272.
default_Fringe :
Max 1132. @Nd 212
Min 272. @Nd 100
Figure 2 – Temperature profile after heat up period
Figure 2 shows the temperature profile at the end of the heat up period. Because
internal radiation had to be neglected, it is expected that the interior of drum is somewhat
hotter than predicted. Although it is not reasonable to expect the predicted temperatures in
the interior to be accurate, it is reasonable to conclude that the interior bores of the part will
have the greatest lag in heat up. If a maximum differential temperature throughout the part is
to be a limiting factor, a TC should be placed on at least one of these bores. It is believed
that this analysis does show with a reasonable amount of accuracy that the weld joints and
the top corner of the part heat up fastest and reach the highest maximum temperatures during
the heat up process. This result makes sense because these areas have direct line of sight to
the heating elements, a relatively large surface area and small amount of mass. It is also of
interest to note that the area directly under the fixture is not as cold as might be expected. It
is thought that the fixture may behave as a fin and that this behavior might offset the effect of
its extra mass.
Referring to figure 3, the analysis shows that the part is indeed essentially at a
uniform temperature of 1100 F as expected, except for the bottom and the interior bores.
Because internal radiation heat transfer had to be neglected, it is believed that this area is also
in fact at uniform temperature. In order to compensate for this error, the initial temperatures
for the entire part were reset to 1100 F for the cool down portion of the analysis. The fact
that this error is significant indicates that conduction is not the dominant means of heat
transfer for the inner web and bore areas.
1100.
1093.
1087.
1080.
1074.
1067.
1061.
1054.
1048.
1041.
1034.
1028.
1002.
1100.
1021.
1015.
Y
Z
1008.
X
Time = 15360
1002.
default_Fringe :
Max 1100. @Nd 1
Min 1002. @Nd 439
Figure 3 – Temperature profile after soak period
1024.
1006.
988.
757.
970.
953.
935.
917.
899.
881.
864.
846.
828.
1024.
810.
792.
Y
Z
775.
X
Time = 3780
757.
Max
1024. @Nd
default_Fringe
:100
Min 757. @Nd
212
Figure 4 – Temperature profile after radiation cool down period
The radiation portion of the cool down cycle has the same modeling limitations as the
heat up cycle. As before, it is thought that the results for the top bore and side regions of the
drum are reasonable and these indicate a max differential temperature of roughly 120 F
across the part. The interior bores are likely cooler than shown, but are still believed to be
the hot spots. This suggests that the actual temperature difference is greater than 120 F but
less than the value of 267 F indicated in the figure. This overestimation's of the inner bore
temperature will necessarily be carried forward in the analysis of cool down by convection.
646.
626.
605.
585.
341.
564.
544.
524.
503.
483.
463.
442.
422.
646.
402.
381.
Y
Z
361.
X
Time = 8820
341.
Max
646. @Nd
default_Fringe
Min
341.
@Nd
437
:212
Figure 5 – Temperature profile after free convection cool down period
The analysis of the free convection cool down shows a differential temperature of 305
F across the part. Although convection was estimated and applied to the entire part there is
still some error carried forward from the radiation cool down. It is believed that the actual
temperature difference across the part is less than 305 F, but that the temperature difference
is indeed larger that that of the radiation cool down.
307.
295.
283.
126.
271.
259.
247.
234.
222.
210.
198.
186.
174.
307.
162.
150.
Y
Z
138.
X
Time = 10020 sec
126.
default_Fringe :
Max 307. @Nd 474
Min 126. @Nd 212
Figure 6 – Temperature profile after forced convection cool down period
The final differential temperature across the part is now estimated to be
approximately 181 F. It had been expected that this number would be higher due to the
drastic increase in the cool down rate and the expectation that forced convection would
further exastrabate the difference between the convection rates across the part. It would
appear that the higher bore temperature might have created a higher differential temperature
for convection heat transfer in that area. It is noted that the change in temperature at the
lower bore was 339 F during this phase of cool down.
Conclusions
The process of attempting to match a flux function to the known TC data indicates
that the power distribution to the bottom bank of heaters heat should be increased. The
furnace is calibrated using TCs that are placed on a fixture that resembles a coat rack. It is
believed that this allows the lower TC sight to side and upper heating elements that the part
doesn't see.
In general, the inner bore areas are the most limiting. The present location of TCs
does not reflect the maximum temperature difference across the part. As a minimum, the
lower bore temperature should be monitored.
Considering the overall results of cool down, an important result is the temperature
difference across any given disk. The two inner disks show a much greater temperature
difference from inner to outer diameter. This is import because historically, the inner disks
of these types of drum rotors (particularly the lower ones in larger drums) are prone to a
condition known as dishing. Dishing is a condition where the web of the disk wraps later in
the process. In the past, this has been attributed to abusive machining in detail or the forging
process of the vendor. Blocks have been inserted between the bores in this heat treat process
as an attempt to prevent this. While this analysis is too coarse to reach a conclusion, it
strongly suggests that a thermo-mechancal analysis with detailed modeling of radiation be
done to evaluate any residual stresses that may actually be created in the web areas due to
this "stress relief" process.
Appendix I
Heat Up Subroutine
SUBROUTINE FLUX(F,TS,N,TIME)
IMPLICIT REAL*8 (A-H, O-Z)
DIMENSION TS(6),N(7)
C VFE is view factor, not used
VFE = 1.0
C SIG is boltzmans constant in english units
SIG=0.330E-14
C TT is user defined surface temperature in degrees R
TT=TS(3)+460.0
C TS(3) is element surface temperature at time = TIME
C TENV is user defined temperature at infinity in degrees R
C This is the heat up portion
TENV=0.195*TIME+400.0+460.0
IF (TIME .GE. 3900.0) THEN
C This is the soak portion
TENV=1100.0+460.0
ENDIF
C F is the value of flux returned, 1.0 represents the emmisivity
F=1.0*VFE*SIG*((TENV**4)-(TT**4))
C This scales the flux for the bottom of the part
IF (N(4) .EQ. 1) THEN
F=0.06*F
ENDIF
RETURN
END
Cool Down Subroutine
SUBROUTINE FLUX(F,TS,N,TIME)
IMPLICIT REAL*8 (A-H, O-Z)
DIMENSION TS(6),N(7)
VFE = 1.0
SIG=0.330E-14
TT=TS(3)+460.0
C Radiate to cooled walls of the furnace
TENV=100.0+460.0
C Define equiv. Flux
F=0.1*VFE*SIG*((TENV**4)-(TT**4))
C Scale flux on bottom surface
IF (N(4) .EQ. 1) THEN
F=0.68*F
ENDIF
C Neglect radiation heat transfer in cavities
IF (N(4) .EQ. 2) THEN
F=0.0
ENDIF
C Skip this block until free convection heat transfer begins
C Redefine flux when free convection heat transfer begins
IF (TIME .LE. 3780.0) GOTO 10
F=-3.0E-6*(TS(3) - 175.0)
IF (N(4) .EQ. 2) THEN
F=0.1*F
ENDIF
C Skip until forced convection heat transfer begins
C Redefine flux when forced convection heat transfer begins
IF (TIME .LE. 8820.0) GOTO 10
F=-4.0E-5*(TS(3) - 125.0)
IF (N(4) .EQ. 2) THEN
F=0.1*F
ENDIF
10 RETURN
END
Main Program
TITLE MARC K6 job created on 15-Mar-00 at 08:21:16
TITLE Cool down
$
$ The heat up deck is essentially identical and has not been included to save space
$
SIZING,0,1046,1414,0,90,
ELEMENTS,40,
FLUXES,12,90,
HEAT,0,0,2,
THERMAL
$ Used lumped mass approximation
LUMP
END
OPTIMIZE,2,
5,0,0,0.,0,
POST
1,16,17,0,0,19,20,0,1,0,6,
9,
NO PRINT
CONNECTIVITY
1046,5,0,
1,40,7,8,2,1,
2,40,2,8,9,3,
.
$ List of elements and the nodes which define them, abridged to save space
.
1045,40,1271,1255,1254,1258,
1046,40,1257,1256,1255,1271,
COORDINATES
3,1414,5,0,
1,117.7342,3.85,0.,
.
$ List of nodes and their coordinates, abridged to save space
.
1413,105.977,11.26628,0.,
1414,105.9813,11.29761,0.,
ISOTROPIC
$ Conductivity, specific heat and density for steel at 70F
1,
1.659E-04,0.1055,0.286,0.,0.,
929 TO 1046
$ Conductivity, specific heat and density for titanium at 70F
2,
1.08E-04,0.1280,0.164,0.,0.,
1 TO 928
$
TEMPERATURE EFFECTS DATA
$ List of conductivity and specific heat vs. temperature for steel
16,16,,,,,1,
1.6590E-04,70.,
1.69753E-04,100.,
1.82677E-04,200.,
1.95602E-04,300.,
2.08333E-04,400.,
2.20872E-04,500.,
2.33410E-04,600.,
2.45756E-04,700.,
2.58488E-04,800.,
2.72762E-04,900.,
2.87423E-04,1000.,
3.00733E-04,1100.,
3.14429E-04,1200.,
3.29668E-04,1300.,
3.45293E-04,1400.,
3.60725E-04,1500.,
0.1055,70.,
0.1073,100.,
0.1137,200.,
0.1920,300.,
0.1238,400.,
0.1273,500.,
0.1297,600.,
0.1321,700.,
0.1343,800.,
0.1362,900.,
0.1383,1000.,
0.1404,1100.,
0.1427,1200.,
0.1456,1300.,
0.1490,1400.,
0.1531,1500.,
TEMPERATURE EFFECTS DATA
$ List of conductivity and specific heat vs. temperature for titanium
11,18,,,,,2,
1.08E-04,70.,
1.08025E-04,200.,
1.15741E-04,300.,
1.23457E-04,400.,
1.31366E-04,500.,
1.39468E-04,600.,
1.47569E-04,700.,
1.56636E-04,800.,
1.66667E-04,900.,
1.77469E-04,1000.,
1.80E-04,1500.,
0.12800,100.0,
0.12820,250.0,
0.12840,300.0,
0.12870,350.0,
0.12920,400.0,
0.13000,450.0,
0.13190,500.0,
0.13490,550.0,
0.13940,600.0,
0.14450,650.0,
0.14980,700.0,
0.15440,750.0,
0.15840,800.0,
0.16180,850.0,
0.16470,900.0,
0.16730,950.0,
0.16980,1000.0,
0.17000,1200.0,
INITIAL TEMP
$ define all nodes to be at 1100F (this would be 89F for heat up)
1100.0,
1 TO 1414
CONTROL
500,20,0,
20.,10.,0.,
DIST FLUXES
$ Define element edges for flux application
$Distributed fluxes from load set named "bottom"
$ for the card below field 1 indicates the face of the element and that flux is supplied by subroutine
$ field 2 would be the flux value, but is ignored because a subroutine has been specified
$ field 3 is the value of N(4) referenced by the subroutine. Different values were used for heat up
3,1.,1,
$the card below is a list of elements
701 704 707 710 713 721 729 735 824 833 843 854 AND 865 TO 869 890 892
$ this pattern of cards is repeated until all fluxes are defined
7,1.,1,
742 757 758 866 891
9,1.,1,
567 756 810
11,1.,1,
584 599 616 632 651 668 682 691 695 698 810 AND 929 TO 937
$Distributed fluxes from load set named "side"
3,1.,
149 150 217 237 239 242 255 259 268 272 280 289 298 306 310 316 318 322 326 C
327 347 AND 350 TO 353 356 378 389 402 409 AND 421 TO 423 443 445 460 501 503 C
505 507 508 519 524 528 AND 530 TO 533 536 561 AND 572 TO 576 578 579 593 610 C
625 699 702 705 708 711 AND 715 TO 719 737 738 AND 748 TO 751 770 776 781 785 C
789 793 797 801 877 894 905 913 920 925
7,1.,
156 164 218 315 337 355 419 420 506 535 570 571 714 736 927 928
9,1.,
386 400 412 555 557 559 560 568 569 585 600 617 862 914 921 926
11,1.,
150 239 550 553 579 730
$Distributed fluxes from load set named "top"
3,1.,
65 69 73 77 81 86 96 105 114 122 132 136 140 144 145 151 159 164 168 173 176 C
AND 181 TO 183 186 191 196 AND 201 TO 204 208 212 AND 227 TO 230
7,1.,
61 201
9,1.,
53 57 128
11,1.,
1 6 11 16 21 26 31 36 41 48
$
$Distributed fluxes from load set named "cav_front"
3,1.,2,
454 468 482 490 495 498 500 502 504 509 517 523 527 537 545 551 554 556 558 C
563 580 595 612 628 647 664 678 687 703 706 709 712 720 727 728 AND 732 TO 734 C
739 740 752 753 764 765 772 773 778 782 786 790 794 798 802 AND 805 TO 807 818
7,1.,2,
693 700 777
9,1.,2,
334 564 565 689 696 697 699 702 705 708 711 718 781 785 789 793 797 801 808 C
948 960 990 998
11,1.,2,
345 361 373 385 396 408 418 438 564 566 567 581 596 613 629 648 665 679 694 C
809 819 951 962 967 969 AND 973 TO 975 978 979 981 982 984 985 987 991 993 994 C
1000 1001 1006 1007 1010 1014 1016 1019 AND 1027 TO 1029
$Distributed fluxes from load set named "cav_aft"
3,1.,2,
58 62 66 70 74 78 83 93 102 111 115 123 130 134 138 142 143 147 148 154 155 C
162 163 171 172 179 180 189 190 199 200 215 216 233 234 250 251 264 265 275 C
276 284 285 292 293 301 302 308 309 313 314 320 321 329 330 340 341 349 357 C
362 369 374 379 380 390 392 405 406 416 417 436 437 452 453 466 467 AND 477 C
AND 478 TO 481
7,1.,2,
131 135
9,1.,2,
1 5 10 125
11,1.,2,
2 TO 5 15 20 25 30 35 40 45 50 87 97 106 107 117 139
$Distributed fluxes from load set named "cav_mid"
3,1.,2,
489 494 497 516 522 526 529 538 547 552 555 557 559 568 585 600 617 618 645 C
646 661 663
7,1.,2,
139 418 438 499 636
9,1.,2,
82 87 143 148 155 163 172 180 190 200 216 234 251 265 276 285 293 302 309 314 C
321 AND 330 TO 332 341 357 369 380 392 406 407 417 437 453 454 467 468 480 482 C
490 495 498 AND 500 TO 504 507 509 517 523 527 537 545 551 554 556 558 563 580 C
595 612 628 647 664
11,1.,2,
82 AND 88 TO 91 101 110 119 126 131 135 331 333 334 342 358 370 381 382 394
$
END OPTION
The card below specifies automatic time steping and criteria for termination
TRANSIENT
0.50,10020.0,200,0,1,1,200.,
CONTINUE