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NASA / TM--2001-210901
High Temperature, Slow Strain Rate Forging
of Adwanced Disk Alloy ME3
Timothy P. Gabb and Kenneth O'Connor
Glenn Research Center, Cleveland, Ohio
National Aeronautics and
Space Administration
Glenn Research Center
August 2001
https://ntrs.nasa.gov/search.jsp?R=20010098771 2020-05-07T09:50:09+00:00Z
Acknowledgments
The authors wish to acknowledge the many helpful discussions with David Mourer at General electric Aircraft
Engines. The tests were performed at Wyman-Gordon Forgings, Houston R&D lab, by mike Powell, while the
subsequent heat treatments were performed by Jim Smith, under the direction of William Konkel.
NASA Center for Aerospace Information7121 Standard Drive
Hanover, MD 21076
Available from
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22100
Available electronically at ht_://gltrs.grc.nasa.gov/GLTRS
High Temperature, Slow Strain Rate Forging ofAdvanced Disk Alloy ME3
Timothy P. Gabb and Kenneth O'Connor
National Aeronautics and Space AdministrationGlenn Research Center
Cleveland, Ohio 44135
Introduction
The advanced disk alloy ME3 was designed in the HSR/EPM disk program to
have extended durability at 1150-1250F in large disks. This was achieved by designing
a disk alloy and process producing balanced monotonic, cyclic, and time-dependent
mechanical properties, combined with robust processing and manufacturing character-
istics. The resulting baseline alloy, processing, and supersolvus heat treatment produces
a uniform, relatively fine mean grain size of about ASTM 7, with as-large-as (ALA) grain
size of about ASTM 3 (ref. 1 ).
There is a long term need for disks with higher rim temperature capabilities than
1250F. This would allow higher compressor exit (T3) temperatures and allow the full
utilization of advanced combustor and airfoil concepts under development. Several
approaches are being studied that modify the processing and chemistry of ME3, to
possibly improve high temperature properties. Promising approaches would be applied
to subscale material, for screening the resulting mechanical properties at these high
temperatures. An obvious path traditionally employed to improve the high temperature
and time-dependent capabilities of disk alloys is to coarsen the grain size (ref. 2, 3). A
coarser grain size than ASTM 7 could potentially be achieved by varying the forging
conditions and supersolvus heat treatment (ref. 4).
The objective of this study was to perform forging and heat treatment experiments
("thermomechanical processing experiments") on small compression test specimens of
the baseline ME3 composition, to identify a viable forging process allowing significantly
coarser grain size targeted at ASTM 3-5, than that of the baseline, ASTM 7.
Material and Procedure
Specimen machining, testing, and heat treatments were performed by Wyman-
Gordon Forgings, Houston, Texas. A 1.1" thick cross-section of extrusion SMK05398
was removed using an abrasive disk saw. Specimen blanks were then electrodischarge
machined along a 4.5" diameter circle centered in the cross section. Twenty right circular
cylinder (RCC) specimens having a diameter of 0.50" and length of 0.75" were then
machined. Six double cone (DC) specimens were also machined according to Fig. 1 (ref.
5). The matrix of test conditions for the RCC and DC specimens is shown in Table 1.
RCC specimens were tested at 3 temperatures 2025, 2050, and 2075F using 3 strain rates
of 0.0001, 0.0003, and 0.001 sec L, after being pre-soaked at the test temperature for
times of either 1 or 10 h. This represented a 3x3x2 full factorial statistical test matrix.
Additional RCC tests were performed at the mid temperature 2050F and strain rate
0.003 sec-_: after a pre-soak of 5h to represent the centerpoint of the test matrix, and after
NASA/TM--2001-210901 1
an extended pre-soak of 24h. All RCC tests were continued to an upset of at least 50%,
and true strain of 0.70. DC specimens were tested at the 2 extreme temperatures of 2025
and 2075F and 2 extreme strain rates of 0.0001 and 0.001 sec -1 after a 10h presoak,
giving a 2x2 test matrix. Additional DC tests were performed at the mid temperature
2050F and strain rate 0.003 sec -I after a pre-soak of 5h as for the RCC matrix centerpoint,
and after an extended pre-soak of 24h. All DC tests were continued to an upset of 50%.
After the tests, all specimens were sliced into four quarters. Single quarters of
each specimen were heat treated together on a tray in a resistance heated furnace using a
"direct heatup'" (DH) supersolvus heat treatment of 2140F/lh and then air cooled. Other
quarters were given a "pre-annealed" (PA) supersolvus heat treatment consisting of a
subsolvus pre-anneal of 2075F/lh, followed by an extended supersolvus treatment of
2140F/3h. Heat treated and as-forged quarters were then sectioned, metallographically
prepared, and swab etched for 3 minutes using Kallings reagent. Five fields near the
center of the forging specimen were measured to determine mean grain size in each case,
using a circular overlay grid according to ASTM El 12. The largest grain observed on
each metallographic section was measured for as-large-as (ALA) grain size according to
ASTM E930. Statistical evaluations of flow stress and grain sizes were then performed.The test datum of 2050F/0.0003s-l/24h presoak was not used in the statistical evaluations,
as it would unbalance the statistical matrix designed around presoak times of I and 10h.
Controlled variables were orthogonally scaled to standardized form in all cases using the
relationship Vi'=(Vi-Vme,_)/(0.5*(Vn_x-V_n)). This produced a range for each standardized
variable of-I to +1. This gave standardized variables for temperature (T'), presoak time
(P'), and log strain rate (log(R)') of:
T'=(T-2050)/25 P'=(P-5.5)/4.5 log(R)'=(log(R)+3.5)/0.5
After regression model equations were selected, major effects, residuals, and predicted
confidence intervals were examined for each response.
Results and Discussion
Forging Stress-Strain Response
Typical engineering stress-strain curves are shown for RCC tests, and load-
displacement curves for DC tests are shown in Fig. 2. Flow stress at a true strain of 0.5
for each RCC test was employed in detailed analyses. Scatter plots of this flow stress (S)
vs. temperature (T), pre-soak time (P) and strain rate (R) are shown in Fig. 3. Strong
dependencies of flow stress on temperature and strain rate are obvious. Reverse stepwise
selection linear regression of log(stress) on log(strain rate), temperature, pre-soak time,
and their interactive products were performed, using an F-to-enter=4. The resulting
linear regression equation was:
log(stress)=-.240553+0.041239T'+0.018252P'+0.554102log(R) ' (1)
with a correlation coefficient R2adj =.984 and rms error=O.03434. The complete statistical
output is included in Appendix A- 1. Plots of the resulting predicted and observed
log(stress) vs. pre-soak time and vs. log(strain rate) showed only random error. A plot
NASA/TM--2001-210901 2
of predicted and observed log(stress) vs. temperature is also shown in A-1. A systematic
divergence at intermediate temperature is obvious, suggesting a non-linear dependence
of log(stress) on temperature. Therefore, reverse stepwise selection regressions were
performed including the squares of each variable. The resulting nonlinear regression
equation was:
log(stress)=381.044539-0.371578T'+0.000091T'2+0.019031P'+0.5639071og(R)' (2)
with a higher correlation coefficient R2adj =.995 and lower rms error=0.0194. The plot of
predicted and observed log(stresst vs. temperature showed improved agreement (A-2).
This equation indicated flow stress generally increased with presoak time and strain rate,
but the dependence varied with temperature. In the temperature range of 2025 to 2050F,
flow stress only slightly increased with temperature. Such a temperature response would
be preferable in a production process. But at higher temperatures, flow stress increased
more sharply with temperature.
It is highly preferable that the alloy exhibit superplastic flow during a forging
process. This allows complete flow of the material into all forging die cavities with
uniform strain and strain rates in the disk alloy, and minimizes the buildup of stresses in
the dies. Superplastic flow is present when a material exhibits high strain rate sensitivity
(m), as usually defined by the relationship _=K(dv_Jdt) n_. A material is considered
superplastic in deformation conditions where a strain rate sensitivity m of at least 0.3 is
observed. The strain rate sensitivity m was determined by fitting a second order
polynomial to the log(stress) data as a function of log(strain rate) for each temperature
and pre-soaks of 1 and 10h. The first derivative was then taken and evaluated at each
tested strain rate. It should be cautioned that only three strain rates were tested for each
temperature and pre-soak. Therefore, the second order polynomial fit used three data
points to estimate 3 constants, resulting in 0 degrees of freedom and a perfect fit through
the data. This did not allow an estimate of the remaining rms standard deviation between
the experimental data and the curve fit. The resulting equation constants are in Table 2,
and strain rate sensitivities are included in Table 1. The material exhibited superplastic
flow for all conditions evaluated.
Grain Size Response
1. As-For_;ed
Images of the typical microstructures observed in all specimens in the as-forged
state are compared in Fig. 4-9. Macrostructures appeared uniform in all cases. Scatter
plots of as-forged mean grain size (AFG) versus temperature (T), pre-soak time (P), and
log(strain rate) (R) are shown in Fig. 3. Dependencies of grain size on temperature and
strain rate are obvious. Reverse stepwise linear regression of mean ASTM grain size
number on temperature, pre-soak time, log(strain rate), and their interactive products
were performed, using an F-to-enter--4. The resulting linear regression equation was:
AFG= l 1.294737-0.416667T'
with a correlation coefficient R2adi =0.6598 and rms error=0.2408. The complete
statistical output is given in Appendix B. Plots of the resulting predicted and observed
NASA/TM--2001-210901 3
meangrain sizevs.pre-soaktimeandvs.log(strainrate)showedonly randomerror(A-3). Theaccompanyingplot of predictedandobservedmeangrainsizevs.tempera-tureshoweda systematicdivergenceatintermediatetemperature,suggestinga non-lineardependenceof meangrainsizeon temperatureasobservedfor flow stress.Therefore,additionalreversestepwiseregressionswereperformedincludingthe squaresof eachvariable. Theresultingnonlinearregressionequationwas:
AFG=11.486292-0.415313T'-0.0772181"+0.091960R'-0.100000T'P'+0.088773T'R'-0.301556(T')2 (3)
with ahighercorrelationcoefficientR-'._dj=0.9072andlowerrmserror=0.1258.Theplotof predictedandobservedgrainsizevs.temperatureshowedimprovedagreementwithrandomremainingerror. Theseresultsmirroredtheflow stressanalysisin therespectthatwithin atemperaturerangeof 2025-2050F,as-forgedgrainsizedid not stronglyincreasewith temperature.This wouldbea favorabletemperatureresponserangeforproductionconsiderations.
2. Direct Heatup (DH) vs. Pre-Annealed (PA) Heat Treatment Response
Images of the typical macrostructures and microstructures observed in all
specimens after DH and PA heat treatments are compared in Fig. 10-29. During forging,
disks could have significant localized variations in strain rate, based on forging shape and
material flow characteristics. During solution heat treatment, disks could have significant
localized variations in solution time at temperature and subsequent cooling rate based on
forging section thickness and mass, along with production practices. The microstructures
are therefore compared at constant forging temperature and pre-soak time, to inspect the
variations in grain size due to forging strain rate and solutioning time. Macroscopic
variations of grain size with location are obvious for long presoaks, slow strain rates, and
higher temperatures, especially at 2075F. Some of the variations in grain size were
localized near the surface and might be machined away from a disk forging. However,
the grain size variations for higher temperatures extended nearly across the entire
specimen cross section. The RCC and DC specimens tested at 2075F often had over
100% larger grains in the center of the specimen, than near the sides. This excessive
grain growth, while not classifiable as true critical grain growth at high strain rates
(ref. 5), was definitely not conducive to a uniform supersolvus heat treatment grain size
response desired in this study.
Grain sizes were consistently measured near the center of the cross section of
each specimen. Scatter plots of averaged DH and PA mean grain size and ALA grain
size are shown versus temperature (T), pre-soak time (P), and log(strain rate) (R) are
shown in Fig. 30. Dependencies of grain size on temperature and strain rate are obvious.
Regression analyses were therefore employed.
Two approaches were used to analyze this data. The first approach C evaluated
the stability of grain size response with the Constraint that the two solution heat treat
types DH and PA could be used to simulate expected random cause heat treatment
process variations. The average and standard deviation between DH and PA mean grain
sizes and the average between DH and PA ALA grain sizes were first analyzed in
NASA/TM--2001-210901 4
approach C. The C analyses therefore had 19 data points for each of averaged grain size,
standard deviation of grain size, and averaged ALA grain size.
The second approach U used solution time as a fourth Unconstrained process
variable. From a practical standpoint, solution time variations could be due to furnace
run-to-run dwell time variations, material location in a disk, and location of a disk on a
tray of multiple disks within a furnace. Note that approach U ignored the contribution of
the pre-anneal step of the PA heat treatment on resulting grain size. Approach U
assumed that the grain size differences between DH and PA heat treatments were
primarily due to only solution time, which for a disk can be measured with embedded
thermocouples and modeled as a function of location for any disk shape. The U analyses
therefore had 38 data points for each of mean grain size, standard deviation of grain size,
and ALA grain size. The evaluations below indicated solution time did not significantly
affect mean grain size, ALA grain size, and standard deviation of grain size.
Reverse stepwise selection linear regression of mean grain size (G) on the
standardized variables and their interactive products were performed, using an F-to-
remove=3.9. The resulting linear regression equations (A-4C and A-4U) were:
G=3.577042-1.008333T'-0.325844P'
G=3.550790-1.000000T'-0.314903P'
R2adj =0.8251, rms error=0.403 (4C)
R2adj =0.7394, rms error=0.5077 (4U)
These equations both indicated ASTM grain size number decreased (grain size increased)
with increasing temperature and presoak time.
Linear regression of ALA grain size on the standardized variables and their interactive
products were also performed, using an F-to-remove=3.9. The resulting linear regression
equations were:
ALA=-0.499171 - 1.066667T'-0.428152P'+0.197674R" R2adj =0. 87O0, (5C )mas error--0.3756
ALA=-0.496379-1.062500T'-0.425361 P'+0.206261R'-0.179167 T'P' (5U)
R-'adj =0.8467, rms error=0.4122
The complete statistical output is given in Appendix A-5C and A-5U. Plots of the
resulting predicted and observed mean and ALA grain size vs. temperature, pre-soak time
and vs. log(strain rate) showed only random error. The equations both indicated that
ALA grain size coarsened with increasing temperature, presoak time, and decreasing
strain rate. Equation 5U indicated an additional interactive contribution of combining
high temperature and long presoak times gave coarser ALA grain sizes.
The regressions of standard deviation of supersolvus grain size (SDG) gave mixed
results:
9
SDG=-.357895 R-adj =0.0000, rms error=-0.2969 (6C)
Log(SDG)=- 1.172359+0.394899T'-0.192353R'-0.259390T'R' R2,_dj=0.4186 (6U)nns error=0.4417
NASA/TM--2001-210901 5
The complete statistical output is given in Appendix A-6C and A-6U. Plots of the
resulting predicted and observed standard deviation of grain size vs. temperature, pre-
soak time and vs. log(strain rate) showed only random error. While the rms error was
larger using approach 6U, this equation did provide guidance in what variables controlled
SDG. The standard deviation of grain size increased with temperature and decreased
with strain rate, with their additional interactive contribution decreasing standarddeviation.
Selection of Modified Forging Conditions
The equations generated to describe flow stress, mean as-forged grain size, as
well as supersolvus heat treated mean, standard deviation, and ALA grain sizes could
now be used to allow selection of modified forging conditions. It was clear that the target
grain size of ASTM 3-5 could easily be attained using various combinations of
temperature, presoak, and strain rate. The flow stresses were all acceptably low, and the
material remained superplastic in all conditions evaluated. However, the uniformity goal
was a key discriminator. The variation in grain size observed across the TMP specimens
and across specimens with varied strain rates and presoaks clearly increased with
temperature. Further, the ALA grain size coarsened unacceptably at high temperatures.
These trends all pointed to the lower temperature of near 2025F as preferable. Flow
stress and as-forged grain size was relatively stable between 2025 and 2050F. Heat
treated grain size and ALA grain size only moderately increased with increasing presoak
time at 2025F, as opposed to the larger changes at 2050 and 2075F. ALA grain size
became finer with increasing strain rate.
The statistical software was used to determine optimal conditions for minimized
ALA grain size in equ. 5C and 5U, and for minimized standard deviation of heat treated
grain size in equ. 6U. The optimal conditions were 2025F/lh presoak/0.001 s -_ strain
rate. However, a constant presoak time of lh would not be possible in a section greater
than 1" thick, due to variations in heat up time in a furnace. Heat up times can vary by
1 hour between a surface and midsection. So a longer presoak time would be necessary
to allow for such heat up effects. An intermediate presoak of 5h was selected for several
reasons. This time should minimize the effects of the above heat up time variations
according to the regressions, and therefore be practical to use as an aim in a variety of
forging shapes. A 5 h presoak time would also fit best into the statistical test matrix
design, giving a tightened full factorial of two temperatures 2025 and 2050F by 3 presoak
times of 1, 5, and 10h. The conditions of 2025F/5h presoak/0.001 s-_ were therefore
entered into the above equations.
The resulting regression equation predictions of flow stress, as-forged grain size,
mean supersolvus grain size, standard deviation of supersolvus grain size, and ALA
supersolvus grain size are listed for the selected conditions of 2025F/5h presoak/0.001 s-j
with 95% confidence intervals in Table 3. The predictions and confidence intervals were
all judged acceptable and will be compared to experimental results when these conditions
are employed to forge and heat treat 20 pound subscale pancakes.
NASA/TM--2001-210901 6
Summary and Conclusions
A series of forging experiments were performed with subsequent supersolvus heat
treatments, in search of suitable forging conditions producing ASTM 3-5 supersolvus
grain size. High forging temperatures of 2025F to 2075F and slow strain rates of 0.0001
to 0.00Is -_ were used, after presoaks of lh to 24h. Two supersolvus heat treatments were
then used having solution times of lh or 3h. The findings can be summarized as follows:
1) The material displayed superplastic response under all tested conditions.
2) Forging flow stress increased with strain rate, but did not significantly increase
with temperature from 2025-2050F.
3) As-forged grain size coarsened with decreasing strain rate and increasing presoak
time, but did not significantly vary with temperature from 2025 to 2050F.
4) Heat treated mean and ALA grain size coarsened with increasing temperature,
presoak time, and decreasing strain rate.
5) The forging temperature of 2075F gave very nonuniform supersolvus grain sizes.
6) The forging conditions of 2025F/5h presoak/0.001 s_ strain rate were selected,
based on grain size uniformity, standard deviation, ALA, and processing window,
for evaluations on subscale pancakes.
It can be concluded from this work that:
1) Forging at high temperatures of 2025-2050F at moderately slow strain rates can
produce consistent supersolvus grain sizes of ASTM 4-5 in ME3 disk alloy.
2) The supersolvus grain sizes do not significantly vary with solution times of 1 to
3h or with the introduction of a subsolvus pre-anneal before solutioning.
3) The forging temperature of 2075F should be avoided for this alloy if uniform
grain size is desired.
References
1. Enabling Propulsion Materials Program Final Technical Report, Vol. 5: Task K -
Long Life Compressor/Turbine Disk Material, Contract NAS3-26385, NASAGlenn Research Center, May 2000.
2. K.R. Bain, "Development of Damage Tolerant Microstructures in Udimet 720",Superalloys 1984, ed. M. Gell, et. al., The Minerals, Metals, and Materials
Society, Warrendale, PA, 1984, pp. 13-22.3. J. Gayda, R. V. Miner, T. P. Gabb, "On the Fatigue Crack Propagation Behavior
of Superalloys at Intermediate Temperatures", Superallo_s 1984, ed. M. Gell, C.S. Kortovich, R. H. Bricknell, W. B. Kent, J. F. Radavich, The Minerals, Metals,
and Materials Society, Warrendale, PA, 1984, pp. 733-742.
4. M. Soucail, M. Harry, H. Octor, "The Effect of High Temperature Deformationon Grain Growth in a P/M Nickel-Base Superalloy", Superalloys 1996, ed. R. D.
Kissinger, et. al., The Minerals, Metals, and Materials Society, Warrendale, PA,
1996, pp.663-666.
5. E.Huron, S. Srivatsa, E. Raymond, "Control of Grain Size Via Forging Strain
Rate Limits for R'88DT", Superalloys 2000, ed. T. M. Pollock, R. D. Kissinger,R. R. Bowman, K. A. Green, M. McLean, S. L. Olson, J. J. Schirra, The
Minerals, Metals, and Materials Society, Warrendale, PA, 2000, pp. 49-58.
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NASAJTM--2001-210901 38
Appendix A- 1
Least Squares Coefficients, Response LS, Model DESIGN__AUTO__J.S
0 Term 1 coeff. 2 Std. Error 3 T-value 4 signif, 5 Transformed Term
1 1 0.240553 0.0078802 ~T O. 041239 0.009913 4.16 0. 0008 ((T-2.05e+03)/2.5e+01)3 ~P 0.082134 0.008091 10.15 0.0001 ((P-5.5)/4.5)4 -LSR O. 277051 0.009909 27.96 0.0001 ((LSR+3.5)/5e-01)
NO. cases - 19 R-sq. - 0.9836Resid. df - 15 R-sq-adj. = 0.9804- indicates factors are transformed.
RMS Error - 0.03434Cond. No. - 1.022
Least Squares Summary ANOVA, Response LS Model DESIGN__AUTO_LS
0 Source 1 df 2 Sum Sq. 3 Mean Sq. 4 F-Ratio S Signif.
i Total(Corr.) 18 1.0815452 Regression 3 1.063857 0.354619 300.70 0.00003 Residual 1S 0.017689 0.001179
R-sq. = 0.9836R-sq-adj. _ 0.9804
Model obeys h_erarchy. The sum of squares for each termis computed assuming higher order terms are first removed.
Least Squares Components ANOVA, Response LS Model DESIGN_AUTO__LS
0 Source 1 df 2 sum Sq. 3 Mean sq, 4 F-Ratio 5 Stgnif. 6 Transformed Term
1 Constant I 1,0528702 ~T I 0.020408 0.020408 17.31 0.0008 ((T-2.05e+03)/Z.Se÷O1)3 ~P 1 0,12150S 0.121505 103.00 0.0000 ((P-S.S)/4.S)4 -LSR 1 0.921797 0.921797 781.70 0.0000 ((LSR+3.5)/Se-OI_5 Restdual 15 0.017689 0.001179
~ indicates factors R-sq. - 0.9B36are transformed. R-sq-adj. - 0.9804
Default sum of squares.Model obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.
NASA/TM--2001-210901 39
Appendix A-1 (cont.)
Nul reg _ExFrMPONULREG, Model DESIGN_UTO__LSMain Effects on Response LOGSTRESS
(w_th 95% confidence Znterva]s)
T: 2025 to 2075
P: I to 10
LSR; -4 to -3
L....... D-.... _;
i '- -i
I ' _
0.0 0.1 0.2 0.3 0.4 0.5 0-6
Increase in LS
LOGSTRE$S vs TFJ4P, Adjusted for Remaining Predictorsusing Mulreg GEX_ULREG, Mode] DESIGN___TO_S
0.35-
AL
do 0.30jGu ss T 0.25t R
• E 0.20_'dsS b
2030 2035 2040 2045 2050 2055 2060 2065
TEMP
_J Adjusted Data ValuesAdjusted Fitted Curve
p, • |
2070 2075
0.4"
ALdO
JGo. 3-uS
STtReE0.2-
dS
0. I_1
LOGSTRESS vS PRESOAK, Adjusted for Re_tnfng PredictorsUsing Nu]reg _EXPTMP_NULREG, Mode] DESIGN__AUTO_LS
2 3 4 5 6 7 8 9
PRESOAK
i.: Adjusted Data ValuesAdjusted Fitted Curve
i
10
NASA/TM--2001-210901 40
Appendix A- 1 (cont.)
LOGSTRES$ vS LOGSTRART, Adjusted for Remaining Predictorsusi no _ulreg eEXFrTMPi_MULREG, Mode] DES_GN_.__UTO__LS
AL j_-_
dO 0.4jG
ST 0.2 __._-_'tR
eEdS 0.
4.2 t _--- _- -_ _ _ ..... l --) ) .......... 4-4.0 -3.9 -3.8 -3,7 -3.6 -3.5 -3.4 -3.3 -3.1 -3.1 -3.O
..-J
LOGSTRART
Adjusted Data valuesAdjusted Fitted Curve
.
e
s 0idu -1-a
-2"
Case Order Graph of Residuals of LSusing Studentized Residuals in wodel DESIGN_..AUTOjLS
÷ + +
+
+
+ 1.
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Case Number
17
÷ 1.
18I, I
lg 2O
Re$i
Residuals of LS vs Fitted V_luesusing studentized Residuals in _odel DESIGN._AUTO__LS
+ 4"
+ ÷
4-+ 4-
',F
aU]__.i0!
$ -
-- r
2
I-
÷
-4-
,' ; "r I t I t t
-O.l 0.0 0.1 0.2 0.3 0.4 0.5
Fitted Values
0.6 0.7
NASA/TM--2001-210901 41
O, 99-
C O.95-u 0._
m 0.8-
HPro O. 2=
b 0.1_0.05
O. O_
Appendix A-1 (cont.)
No_a] Probability Plot of Residuals of LSUsing studentized Residuals in Model DESZGN___UTOmLS
Csample size = 19)
_____..... .-._r--¸
÷
: _ F I tS -2.0 -1.5 -1.0 -0.5 0.0
÷
4. + 4.
0.5 1.0 1.5
Residuals of Ls
,
Fre4-quen 2-cY
H_stogr_ of Residuals of LSusing student_zed Residuals in Model DESZGN.__UTO_LS
(Sample size = 19)
Residuals of LS
m_
t
, !i t
I , _, s [ t '; '10.6 0.8 1.0 1.2 1.4 1.6
0 Factor, Response 1 Range 2 Zn_tta] 3 Optima1or Formula Setti ng Value
1 Factors2 TEMP3 PRESOAK4 LOGSTRART56 Responses7 LOGSTRESS
2025 to 2075 2050 20251 to 10 5.5 1.0004-4 to -3 -3.5 -3.9974
N_N -0.15841
converged to a, tolerance of 0.000077 after 109 Steps.
NASA/TM--2001-210901 42
O, 99
C 0.95u 0.9
m 0.8-
1PPo 0.2-b 0.1-
0.OS-
0.0__2
Appendix A- 1 (cont.)
Normal Probability Plot of Res_duaTs of LSUsing studentized Residuals in Model DESIGN___UTO__L$
CSamp]e size = 19)
÷
÷
.--_@
+
S -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Residuals of LS
.
Fr
e 4'qU
en 2"¢Y
Histogra_ of Res_dua]s of LSusing Student_zed Residuals _n Node] DESIGN_.AUTO__LS
(sample s_ze = 19)
1
I
r ........................ i - ........I,J
I.......... i , , t ,1 I _ !
Residuals of LS
0 Factor. Response 1 Range 2 In_¢tal 3 Optimalor Formula Se_cing Value
1 Factors2 TEMP 2025 to 2075 2050 20253 PRESOAK 1 to 10 5.5 1.00044 LOGSTRART -4 to -3 -3.5 -3.9974S6 Responses7 LOGSTRESS M_N -0,1$841
converged to a _olerance of 0.000077 after 109 steps.
NASA/TM--2001-210901 43
Appendix A- 1 (cont.)
LOGSTRESSPRESOAK = 1.0004
-3.0'
LOGST -3.5,RART
-4,C2025
' ' ' ......... U 4_...... 0,35 .............. - ........................... 0.4 ............ _ .... " :_------
................... 0.3 ........... - .....................................--o.25 .......... ........................ 0.3..................:-.................... 0.35 .......... 0 2 ---0, 25 ..............
_ _'_.............................. 0 2 .......................... 0.25 ........... U" L_ ............ " ............. . ......................
r_....... _ ....................... O. 15_ ....... - ........................--o ._s.i_i_...__i._................................... o.z--Z.:i-±-.i_................. ,o.15........
• -........... o.o5.................. -.............--S'-_L- ........... 0 ................................... 0 ........ ' .................... _). 05 ....---o.o_ .......................................... 0.05 .......... "........
........................ ,0 1 ........ ........ 0.05--.--..... ," : ------:-_-. ......... - :-.- .-------._-r, -9__ .1 .... ,,..... i 4 --- ,
2030 2035 2040 2045 2050 2055 2060 2065 2070 2075
TEMP
....... LS
1C"
P 8-R
E 6"SOA 4"K
LOGSTRF_RSLOGST_ ,, - 3.9974
r _ .......... : : .-rb. 04 ¢ I
__.__0 , 02 .2_ .......... _ ................ 0 " 0_ .......
:--°.°6,_ -......o.o -0.04_
................. ' ............... 0. 1 .._ --'- --0o 0_,
2 .......... 01.14. _ _ ..........:.._..... -0.12 .... . ............ T--0,1 .... "---0.08 ..
2025 2030 2035 2040 2045 2050 2055 2060 2065 2070
................ --'0.04 .......
-_-_0.02 ............
2075
TEMP
......... LS
LOGSTRESSTE_ ,- 2025
-3.0' " ......... b, 4._L.:_. : t _ I i _ f .......... ,L .................................. -0.4 ...... ' ................... " ..... -' -----'-0.5 -'------
O ................... -0,3 .......... - .............. "............... '.................. 0.4 .....
G ........................ 0.3
S .................. _). 2 ,. '............................................ O. 3 .....T -3.5,_ ...... - ...................................... 0.2 ............. -
R , -.............. _3,1 .... ........... ' ................................... 0.2 ......A .................... 0.1 ........R ..................... 0 ...... "--................. ............................ 0.1T ......... .....
-4.o,-...._.........._......i........_--o._t....., , , , , . .... ...... , , _.....,..o.__z.o 1.s 2.0 2.s 3.0 3.s 4.0 4.5 5.0 5.5 6.0 _.5 7.0 7.s 8.0 8.s 9.0 9.5 10.0
PRESOAK
....... LS
NAS A/TM--2001-210901 44
Appendix A-2
Bisquare coeffScients, Response L5, model DESIG_UTO_S
0 Term 1 coeff. 2 Std. Error 3 T-value 4 Signif, 5 Transformed Term
1 1 0.207982 0.0073352 ~r 0.046337 0.005602 ((T-2.05e÷03)/2.Se+01)3 _P 0.085639 0.004572 18.73 0.0001 ((P-5.5)/4.5)4 -LSR 0.281954 0,005600 50.35 0,0001 ((LSR+3.S)/Se-01)5 ~T**2 0.056926 0.009229 6.17 0.0001 ((T-Z.05e+03)/2.Se+01)**
No. cases = 19 R-sq, _ 0.9953Resid. df m 14 R-sq-adj, = 0.9940~ indicates factors are transformed.
RMS ErrOr - 0.0194cond. No. _ 2.958
Bisquare Summary ANOVA, Response LS Model DESIGlq_UTO_LS
0 Source 1 df 2 SUm Sq. 3 Mean Sq, 4 F-Ratio 5 sign_f.
1 TotalCcorr.) 18 1,1336312 Regression 4 1.128359 0.282090 749.20 0.00003 Linear 3 1.114033 0.371344 986.20 0.00004 Non-linear 1 0.014326 0.014326 38.04 0.00005 Residual 14 0,005272 0.000377
R-Sq. - 0.9953R-sq-adj, = 0.9940
Node1 obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.
0 Source
Bisquar_Compor_nts ANOVA, Response LS Model DESIGN_.AUTO_LS
1 df 2 sum Sq, 3 Mean sq, 4 F-Ratio 5 Signif. 6 Transformed Term
1 Constant 1 1,0824062 ~T 1 0.025765 0.025765 68.43 0.0000 ((T-2.0Se+03)/2.Se+0I)3 ~P 1 0.132090 0.132090 350.80 0.0000 ((P-5.5)/4.5)4--LSR 1 0.954705 0,954705 2535.00 0.0000 ((LSR+3,5)/Se-01)5 -T**2 1 0.014326 0.014326 38.04 0,0000 ((T-2.05e+03)/Z.Se+01_**6 Residual 14 0.005272 0.000377
~ indicates factors R-sq, - 0.9953are transformed. R-sq-ad_. = 0.9940
Defmult sum of squ_res.Model obeys hierarchy, The sum of squares for each termis computed assuwing higher order terms are f_rst removed.
NASA/TM--2001-210901 45
Appendix A-2 (cont.)
Mulreg gEXPTMP_AtULREG, Model DESIGN__AUTO.__LSMain Effects on Response LOGSTRESS
(with 95% Confidence Intervals)
T: 2040 to 2075
P: 1 to 10
LSR: -4 to -3
I ! I t :
; t I0.0 0.1 0.2 0.3 0.4
Zncrease in LS
O.S 0.6
ALdoJGu ssTt R• Eds
S
O. 35_
O. 30
O.25
I
0.20_'_--_'----
_S02 ........ :O. 5 2030
LOGSTRESS vs TEMP, Adjusted for Remaining PredictorsUsing Mulreg _-XPTMP_IULREG, Mode] DESIGN._AUTO__LS
2035 2040I .I t ...... t
2045 2050 2055 2060
TEMP
'_ Adjusted D_ta ValuesAdjusted Fitted curve
.....I " I2065 2070 207S
ALdO
jGuSs TtReEdS
$
LOGSTRESS vs PRESOAK, Adjusted for Remaining PredictorsUsing blulreg 8EXFTMI_tULREG, Model DESIGN__AUTO_.L5
0.35
0.30
0.25
0.20
0.10 2 3 4I I I _ t I5 6 7 8 g I0
PRESOAK
Adjusted oata valuesAdjusted F_tted Curve
NASAITM--2001- 210901 46
Appendix A-2 (cont.)
LOGSTRESS VS LOGSTRART, Adjusted for Remaining Predictors
USing Mul reg _EXPTMPgNULREG, Model O_SIGN_..AU_LS
~
J
AL 0"iIdO 0.jG
°' tsT 0.2-
dS O. -_-_
S-0.2-L I J
-4.0 -3.9 -3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3.2
LOGSTRART
iZ Adjusted Data values---- Adjusted Fitted Curve
• -L ........ I-3.1 -3.O
Case order Graph of Residuals of LSUsing Studentized Residuals in Mode] DESIGN__AUTO__LS
2TR ÷
d
a -2
1
_.- P I _0 1 2 3
÷ +
+ 4- ÷ +
+ ÷
4 5 6 7 8 9 10 11 ].2 13 14 15 16 17 18 1.9 ZO
Case Number
2T
R 1-
es Oid -iua -2-1
s _}
÷
Residuals of LS vs Fitted values
using studentized Residuals in Model DESIGN__AUTO_LS
+ ÷
÷
÷
++
t
÷ q-
4-
I t t
2 -0.1 0.0 0.1 0.2 0.3
Fitted values
0,4 0.5 0.6 0.7
NASA/TM--2001-210901 47
0.99'
¢ 0.95-u 0.9.
m 0.8.
Hro 0.2,b 0.1
0.05
0.01
Appendix A-2 (cont.)
Normal Probability Plot of Residuals of LSUsing studentized Residuals in _odel DESIGN__AUTO_L$
(Sample size = 19)
+
j"
f_
,/
', : _ : : ;-3 -2 -I 0 1
/ +/
Residuals of LS
B
1.0 isqu
r
.S •
et
g
3.0 h2
s
.
Fr_equ 4-enc 2,Y
0"; " :-4.0 -3.5
Histogram of ResSduals of LSUsing studentized Residuals _n Model DESIGN__AUTO_LS
(sample size - lg)
Ft
; .......... _........... i t-3.0 -2.5 -2.0 -1.5
F ....................
ii
I
i
-1.0 -0.5 0.0
Residuals of LS
I ..... _ - I :0.5 1.0 1.S 2_0
0 Factor, Response 1 Range 2 Initial 30p_imalor Formula Setting Value
1 Factors2 TEWP 2025 to 2075 2050 2039.33 PRESOAK 1 to 10 5.5 1.05124 LOGSTRART -4 to -3 -3.5 -3,99995
6 Responses7 LOGSTRESS _N -0.16798
Converged to a tolerance of 0.000077 after 71 steps.
NASA/TM--2001-210901 48
0.00-
LO -0.O5-GST -0.10-
RES -0.15-S
-0.20
Appendix A-2 (cont.)
Predictions and 95% simultaneous confidence intervalsfor mean responses of LOGSTRESS using model DESIGN_..AUTO__LS
P - 1.0512, LSR = -3.9999
Lr 4 b i
2025 2030 2035 2040
r-
-F
I
J
2045 2050 2055 2060 2065 2070 207_
TEMP
------- Curve I
0_1"
L
o 0.0GST -0.1-RE
S -0.2-5
-0.3
Predictions and 95% simultaneous confidence intervalsfor mean responses of LOGSTRESS usin9 model DESIGN__AUTO_LS
LSR = -3.9999, T = 2039.3
.... _ .... L
}1 2 3 4 5 6 7 8 9 10
PRESOAK
----F_-- Curve ]L
0-6"
L 0.4"O
GS 0.2-T
R O.O-
SS -0.2-
Predictions and 95% simultaneous confidence intervals
for mean responses of LOGSTRESS using model DESIGN__AUTO__LST = 2039.3, P = 1.0512
. ...
_-- ---_
_ _----
-0.4 -4,0 -3_,9 -3.8 -3'.7 -3,6 -3.5 -3.4 -3.3 -3.2 -3.1 -3.0
LOGSTRART
--r_ _.... Curve 1
NAS A/TM--2001- 210901 49
Appendix A-2 (cont.)LOGSTRESS
LOGsTRART = -3.9999
P
R
E
S
0
A
K
10'
8
6-
2-
2025
............................................... o ............. ............_ ........oo4.- .i- ............-0.06..........................-0.°6?......-.-i............-I"-Co.o2."....
......... 0,12 ........................... - ........... . -0,04 "-
2030 2035 2040 2045 2050 2055 2060 2065 2070 Z075
TEMP
.... L5
LOGSTRESS
PRESOAK - 1.0512
-3.O
L
0
G
S
T -3.5,R
A
R
T
-4.C2025
...... _, f .... I ,, _, - -0_ ............::: -_.i i.......O._S__ :
......... O. 35 ........................................................... _ .... _. "'_-----.
7_o-7_¢:_-7---TL---7_--Z---.---.--7.-_--Z.o_i-CT_" "..........--o._s.....'_-:
............o.i........ _" •............ --o.ls......"-0.05 ................................ 0,0S ................. ....
................ -o ............................. o ............... _................. o o5 "--o.o5...........................................o.os...............-.................." ........
.... -_'_ ........ _-,,'--T-------r ............._, __7-/ ....... ::7"-° z :?7 7 .os......zo_ 203s 2040 204s zo50 20s5 2060 206s 2070 zon
TEMP
....... LS
LOGSTRESSTEMP - 2039.3
-3.0
LO
G
S
T -3.R
A
RT
_4 ..... ( U _ " _ • I l t t I t_L_.:.. I I I I ! J
....... - ...................................0.4 ........ - " - - 0.5 .... |I........... -u . :_...................... ................... -.0.4 .... [
.................-0.3...... 0................O.Z......................................-0.2-.
:................ -0.1 .................... ................... 0.2 ..................... -0.1 ......
......................0 ..... "....................._--0. I....
............. i-7i .....:,:,::_--0. a....... : . _...... ,...... T.... -r-°--.'--4. _L40 ; ....• z.s _.0 2.s 3.0 3.s 4.0 4.s s'.o s:s 610 6:.s ,'.0 ,.s 8.0 s.s 9.0 _.s zo.o
PRESOAK
.......... LS
Predictions and 95_ stmult&neous confidence intervals
for r_n responses of LOGSTRF_S using mode] DESIGN__AUTO._.J.S
LSR - -3
P T-2025
Lower 0.4534585 Predicted 0.491009
Upper 0.528560
NASA/TM--2001-210901 50
Appendix A-3C
Least Squares Coefficients, Response A_GS, Model DESIGN._.AUTO__AFGS
O Term l coeff. 2 std. Error 3 T-Value 4 Signif. 5 TransFormed Tern
1 1 11.294737 0.0552552 -T -0.416667 0.069527
No. cases = _9 R-sq. = 0.6787Resid. df _ 17 R-sq-adj, = 0.6598~ indicates factors are transformed.
-5.99 0.0001
RM5 Error = 0.2408cond. No. = 1
((T-2.05e÷03)/2.Se+01)
Least Squares Summary ANOVA, Response AFGS Mode] DESIGN__AUTO_FGS
0 Source I df 2 Sum Sq. 3 Mean Sq. 4 F-Ratio 5 signif,
I Total(Corr,) 18 3.0694742 Regression 1 2.083333 2.083333 35.91 0.00003 Residual 17 0.986140 0.058008
R-Sq. = 0.6787R-sq-adj, = 0.6598
Model obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.
Least Squares Components ANOYA, Respoltse AFGS Model DESZG_O_FGS
0 Source 1 df 2 Sum Sq. 3 Mean Sq. 4 F-Ratio S Signif. 6 Transformed Term
1 Constant 1 24242 ~T 1 2.083333 2.083333 35.91 0.0000 ((T-2.0Se+O3)/2.Se+O1)3 Residual 17 0.986140 0.058008
~ indicates factors R-sq. = 0.6787are transformed. R-sq-adj. = 0.6598
DefauIt sum of squares.t4odel obeys hierarchy. The sum of squares for each termis computed &ssuming higher order terms are first removed.
NASA/TM--2001-210901 51
Appendix A-3C (cont.)Mulreg _IEXPT_MULREG, Model DESIGN_UTO__AFGS
Main E_fects on Response ASFORGEDGS(w_th 95% confidence Intervals)
Ii
ttrt
-0.5
Xncrease in AFGS
A _'°T
flF ij o lz.sJ_uR [
tE II,eo
dG j
S i0 5 2030
ASFORGEDGS vs TEMP, Adjusted for Remaining Predictorsusing Nulreg @EXPT_I_ULREG, Model DESZGN_UTO_.J_FGS
....( _ ....2035 2040
r-'
t '- I , I J2045 2050 2055 2060
TEMP
i;:! Adjus%ed Data values_, Adjusted Fitted curve
.p , f2065 2070 2075
Case Order Graph of Residuals of AFGSusing student_zed Residuals _n Model DESIGW___UTO._AFGS
+ +
÷
+
+
2TJ
l
° la
1I
-2!0
÷ ÷
+ +
-Ih ÷
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 _8 19 20
Case Number
NASA/TM--2001-210901 52
2TI
Rle +
s
id 0 + ....u I +
1 -1
i.- _ e - io_,9
Appendix A-3C (cont.)Residuals of AFGS VS Fitted Values
Using 5tudentized Residuals in Model DESIG___AUTO__AFGS
-t-
÷
4-
11.0 11.1 11.2 11.3 11,4 11, S 11.6 ll.l 11.8
Fitted values
Normal Probability Plot of Residuals of AFGSUsing Studentized Residuals in Node] DESIGN._.AUTO___AFGS
(Sample size = 19)
0.ggT0.95
m
"!:_i._ J_--_ _...........p ._ .__¢_.... ;k _'- ""
o _T --b ....._.- -"
0+
-2.0 -1.S -1.0 -0.S O.0 O. S
Residuals of AFGS
1.0 1.5 2.0
Histogram of Residuals of AFGSUsing Studentized Residuals in Model DESIGN.,_AUTO_.A_GS
(Sample size - 19)
r I
• 41tq
n - ..................
c ! i i
1.o"-_. ' ' ' _ '_.'_ .... _....... i _ ; ' _ ; i I • _ ,-t _ 2 1.4 1.6 1.8 2"0-2.0-1.8-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.8
Resiclua]s of AFGS
NAS A/TM--2001-210901 53
Appendix A-3C (cont.)
0 Factor, Response 1 Range 2 Initial 3 Optima]or Formula setting Value
1 FaCtOrS2 TENP 2025 TO 2075 2050 20253 PRESOAK 1 TO 10 5.5 7,7S4S Responses6 ASFORGEOGS MAX 11. 7117 AVGS_ALA 3.969g
converged to a tolerance of 0.00012 after 46 steps.
Predictions and 95% simu]taneous confidence _nterva)sfor mean responses ot= ASFORGEDGS using mode] DESIGN.__UTO__AFG5
_"°T T
A ._ .....S i ----
F 11.5 t ± " -O
R 1G FDE li. O_-
GS
I0.5 _ _ '.2025 2030 2035 2040 204S 2050
L
2055 2060 2065 2070 2075
TEMP
NASA/TM--2001-210901 54
Appendix A-3U
Least squares coefficients, Response AFGS, Model DES_GN___UTO_..AFG5
0 Term 1 coeff. 2 Std. Error 3 Tovalue 4 SSgnif. 5 Transformed Term
1 1 11,486292 0.0475562 -T -0,415313 0-0363223 _o -0.077218 0.0295434 --LSR 0,091960 0.0363015 -T*P -0._00000 0.0363156 -TWLSR 0.088773 0.0444627 -'1"*'2 -0,301556 0.059832
NO. cases = 19 R-sq. = 0.9381Resid, df = 12 R-sq-adj. = 0.9072~ indicates factors are transformed.
-2.75 0.01752.00 0.0691
-5.04 0.0003
((T-Z.05e+03)/2,$e'_ll._
((_-5.s)/4.s)((LSR+3.5)/Se-01)((T-2.05e+03)/Z.5e+01_*(((T-2.05e+O3)/2.Se+01)*(((T-2.05e_03)/Z.Se+01_**
t_5 Error = 0.1258cond. No, - 2.958
Least Squares sun_nary/U_OVA, Response AFGS Model DESIGN__AUTO__AFGS
0 source 1 df 2 sum Sq. 3 Mean Sq. 4 F-R_tio 5 s_gnif.
1 Total(corr.) 18 3.0694742 Regression 6 2.879564 0.479927 _0.33 0.00003 Linear 3 2.294470 0.764823 48,33 0,00004 Non-_inear 3 0.585094 0.195031 12.32 0,0006
5 Residual 12 0.189909 0.015826
R-sq. = 0.9381R-sq-adj. _ 0.9072
Model obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.
Least Squares Components ANOVA, Response AFGS Model DESIGtC_AUTO___APGS
0 Source t df 2 sum sq. 3 Mean sq, 4 F-Ratio 5 Stgn_f. 6 Transformed Term
1 constant 1 24242 ~T 1 2.083333 2.083333 I31.60 0.00003 ~P I 0.107391 0.107391 6.79 0,02304 ~LSR 1 0.101557 0.101557 6.42 0.02635 ~T*P 1 0.120000 0.120000 7,58 0.01756 -T*LSR 1 0.063089 0.063089 3.99 0.06917 -T**2 1 0.402005 0.402005 25.40 0.00038 Residual 12 0.189909 0.015826
(O'-2.05e._3)/Z.Se+0_((p-5. s)/4, 5)CCLSR÷3.5)/5e-0 I)((T-2.05e+03)/2.5e+01)*(C(T-2.05e+03)/2.5e+.Ol)* C((T-2.05e+0 3)/2.5t+O_**
~ indicates factors e-sq. - 0.9381are transformed. R-sq-adj, = 0.9072
Default sum of squares.Mode_ obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are f_rst removed.
NASA/TM--2001-210901 55
Appendix A-3U (cont.)
_u]reg @EXPT_4ULREG, Mode] DES_GN_AUTO__AFG5Main Effects On Response AS_OllGEDGS
{w_th 95_ Confidence Intervals)
T: 2033 ¢o 2075
P: lto20
LSR: -4 ¢o -3
-1.2
,_ ', ; _
-1.0 -0.8 -0.6 -0.4 -0.2 0.O
Increase in AFG5
0.2 0.4
Mu]reg _EXPT_LREG, Model DESZGN__AUTO_.AFGS2nteraction Effeccs of TEMPwith LOGSTRART
on Respoflse ASFORGEDGS
LS_ = -3 t- _ _ ' I
LSR: -4 1:O -T 2025T = 2050
T = 2075 _ 4 _ :. a-1.5 -1.0 -O.S 0,0 0.5
95% confidence IntervalsFor Increase in ASFOP_EDGS
1.O
Mu]reg OEXFrT_MULREG, Model DESIGN___AFGSInteraction Effects of TEMPwtth PRESOAK
On Response ASFORGEDGS
T. zo2s } !T = 2050 _ ,_-
T - 2075 ! !
-Z.4 -1.2 -1.O -0.8 -0.6 -0.4 -0.2 O.O 0.2 0.4
gs_ Confidence IntervalsFOr Zncrease in ASFORGEDGS
NASA/TM--2001-210901 56
A 12._A SdF --j o ii.S-uRs G
t E li._• Dd_
$i0°5 -;
202 2030
Appendix A-3U (cont.)
ASgORGEDGS vs TEMP, Adjusted for Remaining Predlctorsu,:i ng Mul reg OEX_ULREG, Model DESTGN.__U_FGS
2040 2045 2050 2055 2060 2065 2070 2075
TEMP
Adjusted Data ValuesAdjusted F_tted Curve
AASdFjouRsGtEeDdG
S
ASFORGEDGS vs PRESOAK, Adjusted for Remaining Predictorsusing Mulreg _EXPT_IULREG, _odel DESIGN__AUTO__AFGS
11.6_,
zz.
11.2-
11.0-
_0. g2
_D
3 4 5 G 7 8 ,9 10
PRESOAK
Adjusted Data valuesAdjusted Fitted curve
ASdF .jo
sG 1.1..2
eD 11.
S 10.
ASFORGEDGS vs LOGSTRART, Adjusted for Remaining predic_corsusing Mulreg _F.XPTO_JLREG, Mode] DESTGN._AUTQ__AFGS
H
-3.9 -3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3,2 -3.1 -$.0
LOGSTRART
:-2 Adjusted Data va]uesAdjusted Fitted Curve
NASA/TM--2001-210901 57
2-
R 1e
s Oidu -1-a1
--2"
-3 o
Appendix A-3U (cont.)
Case order Graph of Resiflua]s of AF_using studencized Residuals in Mode] OESIGN_UTO___FGS
+ ++
+ + +
÷ ÷ +
+ +
÷ ÷ ++
+
i 2 3 4 s 6 7 s 9 zo lz lz z3 z4 is 16
Case Number
! -I'- ! -
17 18 I9 Z0
.
R
S
i 0d
u_ 1 +a
1s -2,
_.o.4 .0.6
Residuals of AFGS vs Fitted ValuesUsing studentized Residuals in Mode] DESTGN__AUTO__AFGS
÷
÷
+
÷
ar
', ; I I10.8 11.0 11.2 11.4
Fitted Values
+
q11.6
|11.8
0.99"
c 0.9_u 0,9m 0.
r
0 O.b 0.1"
O.OS"
o._
Nomal Probability Plot of Residua]s of AFGSUsing Studentized Residuals in Model _ESZGN__UTO__AFGS
(Sample size _ 19)
f ..----
_._ *--- Jr
J
+
,5 -2.0 -1.5 -1.0 -0.5 0,0
Aesiduals of AFGS
4-
/
+ : : :O.S 1.0 1.$ Z.O
NASA/TM--2001-210901 58
Appendix A-3U (cont.)
Histogram of Residuals of AFG$Using Studertt_zed Residuals in Model DESZGN__AUTO.._AFGS
(sample size = 19)
Fr• 4-quen 2-c
Y ,- ....... 7I
-2.5 -2.O
I
-1'.5 -I.0 --O.5
i ! ! 'o_o o.5 1_o z.s 2.0
Resi dual s of AFGS
0 Factor, Response 1 Range 2 Initial 3 optimalor Formula Setting Value
1 FaCtOrS2 TEMP 202S to 207S 2050 2040.33 PRESOAK i to 10 5.5 1.0024 LOGSTRART -4 to -3 -3.5 -3.001S6 Responses7 ASFORGEDGS MAX 11.6988 LOGSTRESS O. 39439
converged to a tolerance of 0.00012 after 4S steps.
1_°0"
ASF
11. S"ORG
E 11.ODGS
Predictions and 95_ s_multaneous confidence intervals
for mean responses of ASFORGEDG5 using model DESZGN_TO__AFGSP _ 1,002, LSR - -3.001
T
i
•- ,' t ] I ,I t -2025 2030 2035 2040 2045 2050 20SS
TEMP
2O6O
.4.
2065 2070 2075
-- iS---curve ].
NASA/TM--2001-210901 59
Appendix A-3U (cont.)
Predictions and 95% simultaneous confidence intervalsfor mean responses of A_FORGEDGS using model DESIGN__AUTO_.AFGS
LSR _ -3.001, T - 2040.3
5 12.0F
° 11.87 ;_R ............ :.................
°°fE ll.
D
sG 11.4_ .k
ii 2 .... _ ' '1 2 3 4 5 6
', : I , i,,7 g 9 10
PRESOAK
---C_--- Curve I
12.2-
AS 12.0
F
0 ll.&R
GE 11.6-
0
G 11.4-S
11.2
predictions and 95_ simultaneous confidence intervalsfor mean responses of ASFDRGEDGS using model DESIGN_AUTO_.AFGS
T = 2040.3, P _ 1.O02
Td
i/
1
|
!
/ I" I-4.0 -3.9 -3.8
1-
I
I I : - _ I ,' ,' - I'-"-3.7 -3.G -3,5 -3.4 -3.3 -3.2 -3.1 -3.0
LOGSTRART
-,- .--C---- Curve 1
PRESOAK
10"
8-
6
4-
\
2025 2030L t .
2035 Z040
ASFORGEDGSLOGb"TRART - -3.001
.... i .......
\• ,...
x
_1.6
i ab
2045 2050
%
" % il
% ", N "\
\ "a. _ \,.. ,. 11.I
\
1"1.5 11.4 11.3 X ".,'x• \
- _!-,! 12-., "_.2055 2060 2065 2070
TEMP
.........AFGS
2075
NASAffM--2001-210901 60
-3.0"
L IO
GS
T -3,5,R
ART
2025
Appendix A-3U (cont.)
ASFORGEi_S
PRESOAK - 1.002
1
If.st
; .... !.... i • I $
\ x1,6\
20_0 Z035 204O
- o-_, ++
: / -'--./ ,./(
2045 2050 2055
TEMP
/
/ /
; / /,/ ]"
e " •
• -" /," .1 /f :
• / • , .
:: /.'" ,/ / /"
/" " J t " "/ ..I"
II._ II.} ll.'i 1£"" I0.!
/ l" f _/'1• _ -" l-'-" " : /"
2060 2065 2070 2075
....... AFGS
ASFORGEDGS
TEMP - 2040.3
-3.0
L
0
G
S
x -3.5.R
A
R
T
........................ ..Ii. 6 .........
_- ---- ii.58 -
"" ..... II.6 .... --""- "
.......... il. 5S .... zz. 56- iil. 6
I1, 52 .......... :
-4"_L_0 1.5 2.0 2.5 3.0 3:5 4.0 415 $:0 5:5 6+.O-+25 710 7:5 6:0 B.5 9.0 9.$ 10.0
PRESOAK
........ AFGS
Predictions and g5_ simultaneous confidence intervals
for mean responses of _FORGEOGS using model DESI_TO._.AFGSLSR _ -3
P 1--2025
SLower 11.249138
Predicted 11.600705Upper 11.952272
NASA/TM--2001 -210901 61
Appendix A-4C
Least Squares coefficients, Response AVG, Model DESZGN___UTO_VG
0 Term 1 coeff. 2 std. Error 3 T-Value 4 Signif. 5 Transformed Term
1 1 3.577042 0.0924532 ~T -1,008333 0.116332 -8.67 0.00013 -P -0.325844 0.094954 -3.43 0.0034
NO. cases - 19 R-sq. - 0.8445 RNS Error - 0.403Resid. df - 16 R-sq-adj. = 0.8251 Cond. No. - 1.006~ indicates factors are transformed.
CCT-Z.05e+03)/2.Se+01)CCP-5.S)/4.S)
TABLE:49296 3R x 5C
Least squares Summary ANOVA, Response AVG Node1DESIGN__AUTO__AVG
0 source 1 df 2 SUm sq. 3 Mean Sq. 4 F-Ratio 5 Signif.
1 Total (Corr.) 18 16.711582 Regression 2 14.11321 7.05661 43.45 0,00003 Residua] 16 2.59836 0.16240
A-sq. - 0.8445R-sq-adj. - 0.8251
Nodel obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.
16-SEP-ZO00 21:12 Page 1
Least Squares Components ANOVA, Response AVG Nodel OESIG_O__J_VG
0 Source i df 2 Sum Sq. 3 Mean sq. 4 F-Ratio 5 Signtf. 6 Transformed Term
1 Constant 1 243.36B422 ~T 1 12.20083 12.20083 75.13 0.00003 ~P 1 1.91238 1._123B 11.78 0.00344 Residual 16 2.59836 0.16240
~ indicates factors R-s;. = 0.8445are transformed. R-sq-adj. - 0.B251
Default sum of squares.Model obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.
((r-2.05e-_.O3)/2.Se-t.O1.)(Cp-s.s)/4.s)
NASA/TM--2001-210901 62
Appendix A-4C (cont.)Mulreg @EXPT_MULREG, Wodel DESIGN__AUTO_j_VG
Main Effects on Response AVGS(with 95% confidence Intervals)
T: 2025 to 2075
P: 1 to 10I
-3.0
¢ t ) i I
+ ............. • .............. !
42.5 -2.0 -1.5
Increase in AVG
I°1.0
I-0.S 0,0
d
uvsGtSed
2030
AVGS VS TEMP, Adjusted for Remaining Predictorsusing Mulreg OEXPTt_NULREG, Model DESIGN__AUTO__AVG
2035 2040 2045 2050 2055 2060
TEMP
_: Adjusted Data Values---- Adjusted Fitted Curve
2065 2070 2075
4.s
j A _'u v l:s G 3.5_
de 3,50_,
AVGS vs PMESOAK, Adjusted for Remaining PredictorsUsing Mu|reg @EXPTQMULREG, Model DESIGN__AUTO_.AVG
1 2 3 4 5 6 7 8
PRESOAK
_: Adjusted Oata ValuesAdjusted F_tted Curve
NASA/TM--2001-210901 63
3
2
1-
0
-20
Appendix A-4C (cont.)case order Graph of Residuals of AVG
Using studentized Residua]s in _lodel DESIGN_UTO__AVG
+
+ +
÷
++ +
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Case Number
++
16 17 18
+
19 2O
R 2"e
s
i 1"d
u 0a
1s -1.
Residuals of AVG v$ F_tted Valuesusing student_zed Residuals in Mode] D£SIG_I_AUTO_J_VG
++
+
+J.
+
t-
•4- + +
+ 4-+
I f t ,_ I 1
2.5 3.0 3.5 4.0 4.5 S.O
Fitted values
o.99T
m 0.8-1-
0 " -
b O.1-O.OS-
0.01
Normal Probability Plot of Residuals of AVGusing Student_zed Residua]s in Mode] DESZGhL_AUTO__AVG
(sample s4ze - 19)
.0
i
Jf
+
t I- . f t-1.5 -1.0 -0.5 0.0
_..,.-. .,Ib. "-"
0.5 1.0 1.5 2.0 2.5
Residuals of AVG
NASA/TM--2001-210901 64
Appendix A-4C (cont.)
Histogram of ResSduals of AVGUsing Studentized Restdua)s in Node1DESZGN__AUTO_._VG
Csamp]e s_ze - 19)
Fr
• 2-
qUenc
Y
IJ
-O.
I
I
I;
-0_2.0 -1,5 -I.0 5 0.0 0.5 1.0 I_5I
2.0 2.5
Residuals of AVG
0 Factor, Response 1 Range 2 Initial 3 optimalor FOrmula setting Value
I Factors2 TE_P 2025 to 2075 2050 20253 PRESOAK 1 tO 10 5.5 1.006545 Responses6 AVGS MAX 4.9106
Converged t_ a to]erance of 0.0OO36 after 39 steps.
Predictions and 95_ simultaneous confidence intervalsfor mean responses of AVGS using model DESIGN___UTO_._AVG
P _ 1.OO65
..... ,-..
. - : --% .....2 2025 2030 2035
4..
2040 2045 2050 2055 2060 206S 2070 2075
TEMP
.... -: .... Curve i
NASA/TM--2001-210901 65
AVGs
Appendix A-4C (cont.)
Pred_ ctions and 95% simultaneous confidence _ ntervals
for mean responses of AVGS us1 ng mode] DESZGN._.AUTO_.AVGT ,, 2025
5-5
5,0"
4,_"
4.0-
T
_i.
3.5 _ " - _ - -; .... _ ' "q1 2 3 4 S
-- ....... i
r t I I I6 7 8 9 10
PRESOAK
--E--_ Curve 1
AVGS
PRES0AK
10'
8-
6-
2-
2025
_.6 4.4
2030
\.
4z
2035 2040
! _ . .I
2055
"4 3.8
2045 2050
TEMP
..... AVG
--,,%
_.6
i
- %
3.4
"" ''""" I "_""",I2060 2065
... , ;_.
_ 2.6
3.2 3_ _'_.
[
2070 2075
Predictions and 95_ simultaneous confidence interval s
for mean responses of AVGS ustng model DESIGN_.AUTO__AVG
p T-2025
Lower 4.1573425 Predicted 4,621580
upper 5,085819
NASA/TM--2001-210901 66
Appendix A-4U
Least Squares Coefficients, Response AVG, Mode] DESIGN_AUTO_VG
0 Term I Coeff. 2 std. Error 3 T-value 4 Signif. 5 Transformed Term
1 1 3.550790 0.082366
2 ~T -1.000000 0.103639 -9.65 0.0001 ((T-2.05e+03)/2.Se+01)3 ~P -0.314903 0.084594 -3.72 0.0007 ((p-5.5)/4.5)
NO. cases = 38 R-sq. - 0.7534Resid. df - 35 R-sq-ad_. = 0.7394~ indicates factors are transformed.
RMS Error - 0.5077Cond. No. - 1.006
Least Squares Summary ANOVA, Response AVG Model DESIGN___UTO__AVG
0 SOurce 1 df 2 Sum Sq. 3 Mean Sq. 4 F-Ratio 5 Signif.
1 Total(Corr.) 37 36.594742 Regression 2 27.57221 13.78611 53.48 0.00003 Residual 35 9.02253 0.25779
R-sq. = 0.7534R-sq-adj. = 0.7394
Model obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.
Least Squares Components ANOVA, Response AVG Model DESIGN__AUTO_YG
0 Source 1 df 2 sum $q. 3 Mean sq. 4 F-Ratio 5 signif. 6 Transformed Term
1 Constant 1 479.60526
2 ~T 1 24.00000 24.00000 93.10 0.0000 ((T-2.05e+03)/Z.Se+01)3 _ 1 3.57221 3.57221 13.86 0.0007 (CP-5.S)/4.S)4 Residual 35 9.02253 0.25779
~ indicates factors R-sq, _ 0.7534are transformed. R-sq-adj. - 0.7394
Default sum of squares.Model obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.
NASA/TM--2001-210901 67
Appendix A-4U (cont.)blulreg _EXPT_MULREG, Model DESIGN__AUTO_VG
Nain Effects on Response AVG5(w_th 95% confidence Intervals)
!
T: 2025 to 2075 l/
P: 1 tO I0
I _ .......
I-2.5
.... i
-2.0 -1. S -1.0 -0.S
Increase in AVG
0.0
AVGS vs TEMP, Adjusted for Remaining Predictorsusing Nulreg _EXPT_MULREG, Model DESIGN___UTO__.AVG
6TJ
A S_d
jA4_-----------_
SGt$ 3
'td 2
5 2030 203S 2040 2045
:.-%
2050 20S 5 2060 2065
"I'EMP
Adjusted Data Values-- Adjusted Fitted Curve
2070 2075
ST_
dA4-_
u v !:
AVGS vs PRESOAK. Adjusted for Remaining PredictorsUsing Nulreg @EXPT_ULREG, wodel DESIGN__AUTO_AVG
sG
etS 3,id
1.0 1.5
L.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
PRESOAK
Z_
6.5 7.0 7.5 8-0 8.5 9.0 9.5 1.0.0
Adjusted Data values-- Adjusted Fitted Curve
NASA/TM--2001-210901 68
3T
1 -2_
-310
Appendix A-4U (cont.)
Case order Graph of Residuals of AVGUsing Studentized Residuals in Mode] DESZGN_UTO_JWG
+
+
2 4 6
+
4-
__+__.
+
.I- +
I0 12 14
+
+
+
+
+ +
+
+
+
+
+
+
+
'1 '- t 't' t _ I J , _ i "-I-- _ I -
16 18 20 22 24 26 28 30 32 34 36 38
Case Number
3-
R 2'e
s 1.
i
d 0U
a -1
I
s -2-
-I!o
Residuals of AVG vs Fitted values
using studentized Residuals in Model DESIGN__JWTO__AVG
+
÷
++ +
+ ÷ :1:,+ _ + ;
÷ +
+
. t+
+
+
2.5 3.0 3.5 4.0 4.5
Fitted Values
l1
S,O
C 0.9
uiII1
P .
t
o 0.2
b
0.% o
Normal Probability Plot of Residuals of AVGUsing studentized Residuals in _I DESIGt4,..AUTO,__VG
(sample size- 38)
/•w f
-2.5 -2,0
° _ _-r-f ¢
1+.-t%
I I | I I t I ' I .... _,
-1,5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2,5
Residuals of AVG
NASA/TM--2001-210901 69
15-
Fr
• I_clU
e
c
y
Appendix A-4U (cont.)HiStogram of Residuals of AVG
using S_udeN1;_zed Residuals in Node1 DESZGN__AUTO___AVG(Samp]e size = 38)
_
r---_ !
-3.0 -2.5 -2.0 -1.5 -1.0
, i
, !i !
;
, _ • , .-0.5 0.0 0.5 Z.0
Resi duals of AVG
1
1.5 2.0 Z.$
0 FaCtOr, Response 1 Rangeor Formula
2 Initial 3 OptimalSett-i ng Value
1 Factors2 TEMP 2025 to 2075 20503 PRESOAK 1 to 10 S. S45 Responses6 AVGS K_X
2025.11.0088
4. 8616
converged to a tolerance of 0.00046 after 29 steps.
predtcttons and 95_; simultaneous conf_ dence interval sfor mean responses of AVGS using model DESIGN__AUTO_.AW;
P - 1.0088
6T
V ..... _ ._
-_,- ! I2025 2030 2035 2040 20'45 20'50 20:55 2060 2065 2070 2075
TEMP
.... V_._-- Curve I
NASA/TM--2001-210901 70
Appendix A-4U (cont.)Predictions and 95_ simultaneous confidence intervals
for mean responses of AVGS using model OESIGhI__AtrrO.._AVGT I, 2025.1
S. ST
.°lik .... _ .... _ ......... _
V 4 . S * _ .................................
G I
4.
13.51 - _ -_- , : --_-- _ --_-
1 2 3 4 $ 6 7
T
8 9 10
PRESOAK
-_--- Curve I.
AVGS
4.4
2030 2035 2040
'4 ,_
2045
3.8
\
2050
-- _ --,'-
• \
%
3,6
"k\
*x. 2.6
"x
2055
2.8
3.4 3.2 "3 ""
-_, "" P "" -- I2060 2065 2070
TEMP
.......... AVG
2075
NASA/TM--2001-210901 71
Appendix A-5C
0 Term
LeaSt Squares coefficients, Response AVA, Node1 DESIG___AUTO__VA
I coeff. 2 Std. Error 3 T-Value 4 sign_f. 5 Transformed Term
1 1 -0.499171 0.0861902 -1 -1.066667 0,108427 -9,84 0,0001 ((T-2.0Se+03)/2.Se+01)3 ~P -0,428152 0.088S01 -4.84 0.0002 ((P-5.5)/4.5)4 ~LSR 0.197674 0.108385 1.82 0.0882 ((LSR+3.S)/Se-01)
NO. cases - 19 R-sq. - 0.8917Resid. df - lS R-sq-adj. = 0.8700- indicates factors are transformed,
RMS Error - 0.3756cond. No. = 1.022
Least squares Sunuary ANOVA, Response AVA Model DESZGN__AUTO_VA
0 Source I df 2 Sum Sq. 3 Mean Sq. 4 r-Ratio 5 S_gnif.
I xotalCcorr.) t8 19.540002 Regression 3 17.42385 5.80795 41.17 0.00003 Residual 15 2.11815 0,14108
R-sq. - 0.8917R-sq-adj. = 0.8700
14odel obeys hierarchy, The sum of squares for each term_s computed assuming higher order terms are first renoved.
Least squares Components ANOVA, Response AVA M4odel DESIGIq_AUTO_VA
0 Source i df 2 Sum sq. 3 Mean Sq. 4 F-RatiO S signif. 6 Transformed Term
i Constant 1 4.75000
2 ~T 1 13.65333 13,65333 96.78 0.00_ ((T-2.0Se+O3)/2.Se+O1)3 _P 1 3.30180 3,30180 23.40 0.0002 ((P-5.$)/4.5)4 --LSR 1 0.46926 0.46926 3.33 0.0882 ((LSR+3.S)/$e-01)$ Residual 15 2.11615 0.14108
- tnd4cates factors R-sq. - 0.8917are transformed. R-sq-adj. - 0,8700
Default sum of squares.Model obeys h_erarchy. The sum of squares for each term_s ,computed assunring higher order terms are first removed.
NASA/TM--2001-210901 72
Appendix A-5C (cont.)Mulreg _q_Xlrl_LREG, Node_ DESIGH__A_VA
Ma4n Effects on Response AVALA(With 95X confi dence Interval s)
T: 2025 to 2075
P: 1 to 10
LSR: -4 tO -3
4
J . . ., lI
+ _ _, 4 +-___-___-3.0 -2.5 -2.0 -1.S -1.0 -0.5 0.0 0.5 1.0
Increase in AVA
o.s]
dA O.
jv
u A -0.5_s L
tA
• -I._d
-1,5a-4.0
AVALA vs LOGSTRART, Adjusted for Remaining PredictorsUsing Mu]reg _EXPT_IMULREG, Model DESIGN_UTO__AVA
2
;5;
-3.9 -3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3.2 -3.1 -3.0
LOGSTRART
_ljusted Data Values--- Adjusted Fitted Curve
AdAjvu As LtAed
AVALA VS TEMP, Adjusted for Remaining Predictorsusing Mulreg OEXPTOMULREG, Model DESIGN__AUTO._JWA
1T
O
-1
--2-
_I
2025p - I
2030 2035
i-_,
' - I - - _ _ t : " I r2040 2045 2050 2055 2060 2065 2070 2075
TEMP
Adjusted Data Values---- Adjusted Fitted curve
NASA/TM--2001-210901 73
Appendix A-5C (cont.)
AVALA vs PRESOAK, Adjusted for Remaining Predictors
Using Nulreg _EXPT(_ULREG, Mode] DESIGN__AUTO_VA
A 1TdA !"
uA _SL L
t A -i[d
I-t.o 2 d'z .5 3J5
,.&__
4.0 4.5 5.0 5.5 6.0 6_5 7.0 7.S 8.O
PRESOAK
Adjusted Data values
-- Adjusted F_tted Curve
0
: ..T : :8.5 9.0 9.5 I0.0
2-
R _e
s (>id
U -1]
0
÷
3. 2 3
Case order Graph of Residualsof AVA '
Using studentized Residuals in Model DESIGN._AUTO._.AVA
÷
÷
4-
4 S 6 7 B 9 10 11 12 13 14 15 16 17
Case Number
,, pI8
÷
!19
!
2O
e
si Od
U -]La
1S -2
Residuals of AVA vs Fttted V_lues
Vstng studenttzed Residuals in Node1 OESZGN...AUTO__AVA
÷4-
÷
<.
4- ÷ 4"
4- 4-
+ 4- ÷ ++
4-
- .5 -2.0 -1.S_. I ! I
-1.0 -O.5 O.0 O.5
Fitted Values
÷
1.0 1.S
NASA/TM--2001-210901 74
C09
m 018+
0 * '
b 0.1-0.05-
0.0_ -- ,0 -2.5
Appendix A-5C (cont.)Normal probability Plot of Residuals of AVA
using 5tuclentized Residuals in Model DESIGN_._AUTO__.AVA(sample size = _Ig)
.J
t4
._...
-2.0 -1.5 -i,0 -0,5 0.0 0,S 1.0
Residuals of AVA
f
f
t1.5
I2.O
Histogram of Residuals of AVAUs4 ng studen_i zed Residuals i n Flodel DESIGN.._UTO_AVA
(sample s_ze - 19)
r
e
qu 4-e
n
c 2_.-
Y :I
...................... s
o.o 0.5
i..................
• i
1.0 1.5 2.0
Residuals of AVA
0 Factor, Response 1 Range 2 Initial 3 _i_1or Fornmla Setttng Value
1 Factors
2 TEWP 2025 TO 2075 2050 20253 PRESOAK 1 TO 10 5.5 1. 0001
4 LOGSTRART -4 TO -3 -3.5 -3.001556 Responses7 AVALA MAX 1.1916
converged _o a tolerance of 0.0004 after 65 steps.
NASA/TM--2001-210901 75
A
V
A
L
A
Appendix A-5C (cont.)
Predictions and 95% simultaneous confidence intervalsfor mean responses of AVALA using model DESZGN__.AUTO_..AVA
P - 1.0001, LSR = -3.0015
2TT
0
202S 2030 2035 20_ 204S 2050 2_5 2060 2065 2070 207S
-......
W _|
TEMP
---_ Curve 1
A
V
A
k
Predictions and 9_ sfmultaneous confidence _r_ervalsfor mean responses of AVALA using model OESTGN.._AUTO_._AVA
LSR m --3.0015, T = 2025
°11 2
I --I _ I I I3 4 S 6 7 8
T
II
i
9 I0
PRESOAK
_--- Curve I
2.0 T
It 5 N "_"
A
V
A 1.0-
L
A
0.S-
0,_ ,' I
-4.0
Predictions and 95% simultaneous confidence _ntervals
for mean responses of AVALA using model DESIGN__AUTO_..AVAT = 2025, P- 1.0001
TI
!t
i!
i
l .... I ' I I '" I - t !-3.9 -3.8 -3.7 -3,6 -3.S -3,4 -3,3 -3.2
LOGSTRART
-3.I -3.0
.... ?::--*-curve I
NASA/TM--2001- 210901 76
Appendix A-5C (cont.)AVALA
LOGSTRART ,, -3,0015
10_' 0. _._, '- - 0 .1
p 8_ "- .........
E 6 - "--• ", ,,S "" , ,
A 4_ " .......K
2-" '1. "0.8
2025 2030
" -,, ....... " " " . '1.4
..... '" " "" L1 "
"1_1. _ .... '0.. -_1 Z --0.4 --0.6 --0 o8 """,.
. - _ ".
2040 2045 2050 2055 2060 2065 2070 2075
"'0",6 0.4
, I2035
TEMP
....... AVA
AVALA
PRESOAK - 1.0001
L - 3" Oil .'/I /O
GS
TR -3.5 IA ,,
R i 'T "/
-4. o_,-:2025
I I
O.8
/:
/"
0.6
/
-i2030
q p ,
/ / I ¢
:: .., //
.-: ./. .,,"
. ..1
: / /
/ '" .
J / 1/ I ,,
•" o.2 /' -o.20.4 , O
i ,/
/'t / i .J ik
2035 2040 2045 2050
; 3
s . /.. .¢
, i i /::': : I /
,'., /; i /
,: ,' : ,
i /
: /
-o.'4 -o.'6 -o.s -z :'1• " . j . -" /..
/ ' / ,•
2055 2060 2065 2070 2075
TEMP
...... AVA
AVALATEMP = 2025
-3 .-, . / _ .l- .... _ t _ _ r- .... "" 0.4.L 1 ' 0.9 0,8" 0.7 0.6 0.S 0.3"
• ..- .."" ,..
GO If "" "" ........... " "'" " ""'-" "'"'"J ....... "" "-" ""'- ,_-" " " """'. " " " "- "" ""
T -3.5_(" ,.'/'" "'" -..... -'"'"' - . ' i" ...."" .--'"_" '
TAR il " " '"'" ": '"'" ....' 0.3"" 0.2 "'" 0.1 """,.0.8 "' 0.7" " 0.6" 0.5"" 0,4"
-4.0, . , I ,,, _ _ i . - , ,--'"_ _ .-_ t, -4 I .<" ,I.1,0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.S 8.0 8.5 9.0 9.5 10.0
PRESOAK
....... AVA
Predict-ions and 95_ simultaneous confidence intervals•For mean responses Of AVALA uslng mode] DESZGN__AUTO...AVA
LSR = -3
P 1"-2025
Lower O.lg3091S Predicted 0.812742
upper 1.432393
NASAfl'M--2001-210901 77
Appendix A-5U
Least Squares coefficients, Response AVA, Model DESIGN_.AUTO..J_VA
0 Term 1 coeff. 2 std. Error 3 T-value 4 Signif. 5 Transformed Term
I 1 -0. 496379 0.0668842 ~T -1.062500 0.084141 ((T-Z. 05e+03)/2. Se+01)3 ~P -0. 425361 0.068678 ((P- 5.5)/4.5)4 ~LSR 0.206261 0,084108 2.45 0.0197 ((LSR+3,5)/Se-01)5 ~T*P -0.179167 0.084141 -2.13 0.0408 ((T-2.05e+03)/2.Se+01)*(
No. cases - 38 R-sq. = 0.8633Restd. df = 33 R-sq-adj. x 0.8467~ indicates factors are transformed.
RMS Error = 0.4122cond. No. = 1.022
LeaSt Squares sur_maryANoVA, Response AVA Mode] DESIGN__AUTO_VA
0 Source 1 df 2 sum Sq. 3 Mean Sq. 4 F-Ra_io 5 Signif.
1 Total(Corr.) 37 41.009742 Regression 4 35.40267 8.85067 52.09 0.00003 Linear 3 34.63225 11,54408 67.94 0.00004 Non-linear 1 0.77042 0.77042 4,53 0.04085 Residual 33 5.60707 0.16991
R-sq. - 0.8633R-sq-ad_. = 0.8467
Node1 obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.
Least Squares Components ANOVA, R_porlSe AVA Model DESZGN__AUTO._AVA
0 source I df 2 Sum Sq. 3 Mean $q. 4 F-RatiO 5 Signif. 6 Transformed Term
1 Constant 1 9.400262 ~T 1 27.09375 27.09375 159.50 0.0000 ((T-2,0$e+03)/Z.5e+01_3 -P 1 6.51780 6.51780 38.36 0.0000 ((P-5,5)/4.5)4 ~LSR 1 1.02183 1.02183 6.01 0.0197 ((LSR+3.5)/Se-O1)5 -T*P 1 0.77042 0.77042 4.53 0.0408 ((T-2.05e÷O3)/2.Se+01)*(6 Residual 33 5.60707 0.16991
- _nd|cates f&ctors R-sq. = 0.8633are transformed. R-sq-adj, = 0.8467
Def&ul¢ sum of squares.Model obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.
NASA/TM--2001-210901 78
Appendix A-5U (cont.)
Mulreg _EXPT_IMULREG, Mode] DES_GN,._AUT'O.._AVAMain Effects on Response AVALA
(with 95_ Confidence Intervals)
T: 2025 to 2075
P: 1 to 10
LSR: -4 _O -3
t t I '
L
-2.5 -2.0 -1.5 -1.0 -O.S O.O 0.5 1.O
Increase in AVA
Mulreg @EXPTOMULREG, Mode] DESIGN__AUTO_VAInteraction Effects of TERP with PRESOAK
on Response AVALA
T: 2025 to 2075iP-1 tP =' 10 I
P: i to I0
T = 2025T ,,, 2075
-3.0
I .f , • i
I: I
-2.5 -2.0 -1.5
! t
--- . ...... !
It J J
-1.0 -0.5
95_ confidence InteevalsFor Increase in AVALA
0.0
AdA
jvuAs LtAed
0-
-1
--2'
2030
AVALAvS TEMP, Adjusted for Remaiaing Pred_c¢orsusing Mulreg _qEXPT_b4ULREG, Mode] DESIC4_L_.AUTO_._AVA
• i
2035 2040 2045 2050 2055 2060
TEMP
_ Adjusced Data Values-- Adjusted Fitted Curve
2065 207'0 Z075
NASA/TM--2001-210901 79
A 0.dA
jvu A -0.5 -_s L
t A -1.O_ed -I.5
-2. !1 2
Appendix A-5U (cont.)
AVALA vs PRESOAK, Adjusted for Remaining Predictorsusing Mulreg @EXPT_ULREG, Model DESIGN_._AUTO_..AVA
Et
I b I ÷ _
3 4 S 6 7 8
PRESOAK
Adjusted Data values_- Adjusted Fitted Curve
5
: I9 IO
AdA . kjvu A 5-_s L -0.
"id
-4.0
AVALA vs LOGSTRART, Adjusted for Reclining Predictorsusing Mulreg_EXPT_LREG, Model DESZGN_J_JTO___VA
LJ
'ii.
-3.9
G
El I -_ ...... l,,, I , _ - I
-3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3.2
LOGSTI_RT
Adjusted Data Va]ues_- Adjuszed Fitted Curve
•, !-3.1 -3.0
3-
2-
R
e 1-S
idU
a "zL1
--2
0 2
4-
+
Case O_der Graph of Restdua]s of AVAUsing Student_zed Residuals _n Mode] DESZGN__AUTO__AVA
4- +
÷ + +
T
t I r q t4 6 8 10 12
+ ÷ ÷
.f.
÷
÷÷
÷ -F +
+ 4.+ + 4- +
4,
+ 4- ÷
_ - _ _ .... _ t ' I' ' " _ : " : : I
14. 16 18 20 22 24 26 28 30 3,?. 34 36 38
C_se Number
NASA/TM--2001-210901 80
3 ^
R 2e
S 1id 0tl
a -1 _] ÷
s -2 +
--2.s
÷ ,F
++
Appendix A-5U (cont.)
Residuals of AVA VS Fitted ValuesUsing student_zed Residua]s in Model DESIGN__AUTO___AVA
"4- +
÷ ÷
+ % + ÷
÷ + ÷-F
+ +
++
-2.0 -1.5 -1.0 -0.5 0.0 0.5
Fi tted Values
+
q-
÷
t
1.0I
1.5
Normal probabiIfty Plot of Residuals of AVAUsing studentized Residuals in _odel DESIGN___UTO__AVA
(sample size _ 38)
0.99-
C 0.95-u 0._m 0.8-
o 0._b 0.1"
0.05-
0.01_ ''_-f-2.5 -2,0
j,p-'
-1.5 -1.0 -0.5 0.0 0,S 1.0 1.5
I. j +f
- _ : -I2.0 2.5 3.0
Residuals of AVA
10'
Histogram of Residuals of AVAusing studentized Residuals in Node1 DESZGN...AUTO...AVA
(sasmple size = 38)
,m .........
t
S.
f
• i
-,_5 -2.0 -I, 5 -I,0 -0.5 0.0
.......... i
1 ; i
r
...... _
0'5 l_O Z._ 2.0 2.5 3.0
Residuals of AVA
NASA/TM--2001-210901 81
Appendix A-5U (cont.)
0 Factor, Response 1 Range 2 Initial 3 Optimalor Formula Setting Value
1 Factors
2 TEMP 2025 to 2075 2050 20253 PRESOAK 1 to 10 5.5 1,00164 LOGSTI_.RT -4 to -3 -3.5 -3.000356 Responses7 AVALA MAX 1.0176
converged to a tolerance of 0.00043 after 69 steps.
AVALA
Predictions and 95% s_multaneous confidence interv_]sfor mean responses of AVALA using mode] DESZG_UTO_..AVA
P - 1.0016, LSR - -3.0003
-1
T
±
I 2
2025 2030 2035 2040 2045 2050 2055 2060 2065 2070 2075
TENP
--_ Curve 1
AVALA
Predictions and 95% simultaneous confidence intervalsfor mean responses of AVALA using mode] DESIGN_AUTO.._AVA
LSR - -3.0003, T - 2025
2°I1.5 !
1.0 -_ ..................
o.sI L0.0
O5-- o ,,i 2 I - _ - ) ; ' '1 t ___ l
3 4 5 6 7 8 9
PRESOAK
T
1
10
.... U.- Curve 1
NASA/TM--2001-210901 82
Appendix A-5U (cont.)Predictions and 95_ simultaneous confidence intervals
for mean responses of AVAI.A USirlg mode] DESIGN___AUTO...AVAT = 2025, P - 1.0016
Z.O
1.5"
Av 1.0-
A
L 0.5-A
O°0"
T"
!
....................... .........
[
F.... ........ _,_-t. _- --
i
4.
-0,5 t I ' - I I .F. _ _ 1 I • ; :-4.0 -3.9 -3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3.2 -3,1 -3.0
LOGSTRART
.... _ ..... Curve I
-3.0'
LO 0.8"
S .//
T -3.5:R
/A "
R 0.6T /
/
-4.0 "2025
AVALAPRESOAK = 1.0016
//
j_
/
/
/
,../
0.4 O. 0
I t z_ I -- :"2030 2035 2040
,. .."
, .e
7 / . ./": 7 •-"
,e :k ./ .." ;/
" -o, _ -o. a -o. g/ / •
/. s .,
." * / p . :l (.2045 2050 2055 2060 2065
//
jr
• .t
-O.g -1
, i I ,2070 2075
TEMP
........ AVA
i0 _ : _ m ,_.- .
:If2025
0.6 o. 4\I " 4 ,, t "',
2030 2035 2040
AVALALOGSTRART ,, -3.0003
. F
-0.4
0.2 '0 -0.2
I _ ,_ ' '2045 2050 2055
' _" i _ ...... : .
" ", .... . ', "_ -1.2 '"
"'-0.8 "'
-0.4 ~0.6 .........._ : "'-_.: "_. "_
2_0 2065 20_ 2075
TEIaP
....AVA
NASA/TM--2001-210901 83
Appendix A-5U (cont.)
AVALATEMP = 2025
-3.0-" f : ', ', _'-- t t I _ 4 _ _ 1._ i _ i 0 6 t_ I 4 "P'
°[ Is 3 5 .....'" ....... " ...... -- 0,6 .......... 0.5 ........ 0.4 .... "'_
T-.,, m..... ..0.7.... .....-.... ,.... ._ ........... j.._.Tm
R ....0,6 ".......... -...... "...... "..... "J'"T .... yn. 5 '- ".... 0.4""" "" . .0.3...... '- 0.2 ....-4.0_-.":F-_...._ , ,_ , _ _ -"i _ .', ',_ , _- -.- _"_ , • , ,
1,0 1.5 2,0 2.5 3.0 3.5 4,0 4.5 5,0 5.5 6,0 6.S 7.0 7.5 8.0 8,5 9.0 9.5 10.0
PRESOAK
............ AVA
Predictions and 95_ simultaneous confidence intervalsfor mean responses of AVALA u$i no model DESIGN__AUTO__AVA
LSR = "3
P T=2025
Lower O. 312069S Predicted 0.799737
Upper 1.287406
NAS A/TM--2001-210901 84
Appendix A-6C
Least squares Coefficients, Response SDG, Model DESIGN__AUTO__SDG
0 Term 1 Coe_. 2 Std. Error 3 T-value 4 signif.
1 i 0,35789S 0,068105 5,26 0,0001
No. cases - 19 R-sq. = 0.0000 RMS Error = 0.2969Resid. df = /8 R-sq-adj. = 0.0000 Cond. No. = 1
Least Squares Summary ANOVA, Response SDG Model DESIGN__AUTO__SDG
0 source 1 df 2 Sum Sq. 3 _ean Sq. 4 F-Ratio 5 signif.
1 Total Ccorr.) 18 1, 58631E2 Regression 0 0.0000003 Residual 18 1, 586316 0,088129
R-sq. - O.0Q00R-sq-adj, = 0,0000
Nodel obeys hqerarchy. The sum of squares for each termis computed assuming higher order terms are first removed.
Least Squares coefficients, Response SDA, _de] DESIGN__AUTO_DA
0 Term 1 coeff. 2 std. Error 3 T-value 4 Signif.
I 1 0.247368 0.042830 5.78 0.0001
No. cases - 19 R-sq. - 0.O000 R4_S Error - 0.1867Resid. df - 18 R-sq-adj. = 0.0000 Cond. No. - 1
Least Squares summary ANOVA, Response 5DA Model DESIGN_AUTO_DA
0 Source i df 2 sum sq. 3 Mean Sq. 4 F-Ratio 5 signif.
1 Total(Corr.) 18 0.62736842 Regression O 0.00000003 R.sldual 18 0.6273684 0,0348535
R-sq. - 0.0000R-sq-adj. - 0.0000
Model obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.
NASA/TM--2001-210901 85
Appendix A-6U
0 Term
Bisqu_re coefficients, Response $log_SDG, Model DESIGN__AUTO__SDG
1 coeff. 2 std. Error 3 T-value 4 Signif. S Transformed Term
1 1 -1.172359 0.0716772 ~T 0.394899 0.0901873 ~LSR -0.192353 0.0901374 -T*LSR -0.259390 0.110399
No. cases . 38 R-sq. = 0.4657Resid, df = 34 R-sq-adJ. - 0.4186~ indicates factors are transformed.
-2.35 0.0247
RMS Error = 0.4417Cord. No. - 1.021
((T-2.05e+03)/Z.Se+01)((LSR+3.S)/Se-0_)((T-2.05e÷03)/Z.Se+01)*(
Bisquare summary ANOVA, Response $1og_SDG Model DESIGN_UTO_SDG
0 source 1 df 2 Sum Sq. 3 Mean Sq. 4 F-Ratio 5 signtf.
1 TotalCcorr.) 37 12.418842 Regression 3 5.78402 1.92801 9.88 0.00013 Linear 2 4.70673 2.3S337 12.06 0.00014 Non-llnear 1 1.07729 1.07729 5.52 0.0247$ Residual 34 6.63482 0.19S14
R-sq. - 0.46S7R-sq-ad_. - 0.4186
Mode_ obeys hierarchy. The sum of squares for each termis computed &ssuming higher order terms are first removed.
Sisquare Components ANOVAo Response $]og_SDG Model DESZGN_.AUTO__SDG
0 Source 1 df 2 Sum $q. 3 Mean Sq. 4 F-Ratio S Sign-if. 6 Transformed Terra
1Constant 1 51.939612 ~T 1 3.81805 3.81805 19.57 0.000I3 -LSR 1 0.88868 0.88868 4.55 0.04014 -T*LSR 1 1.07729 1.07729 5,52 0,02475 Restdual 34 6,63482 0.19514
~ indicates factors R-sq. - 0.4657are transformed. R-sq-adj. - 0.4186
Defau]t sum of squares.Model obeys hierarchy. The sum of squares for each termis computed assuming higher order terms are first removed.
(CT-2.05 e+03)/2.5e+01)(CLSR+3. S)/5e-01)((T-2.05e_03)/2. Se+0!)* (
NASA/TM--2001-210901 86
Appendix A-6U (cont.)
Mulreg _EXPT_MULREG, Model DESIGN_AUTO__SDG_ain Effects on Transformed Response SDGS
(with 95% confidence Intervals)
T: 2025 to 2075
LSR: -4 to -3
-1.0
I t
F" -- ............. _ ...........
-0.5 0.0 0.5 1.0
Increase in Transformed SDG
1.5
Mulreg eEXPT_LREG, Model DESIGN__AUTO_._SDGZnteraction Effects of TEMP with LOGSTRART
on Transformed Response SDGS
/
T: 2025 tO 2075rLSR = -4LSR - -3
LSR, -4 to -3T - 2025T ,= 2075
-2.0
I
.t-1.5
t ? _ '- :
F I , I
, I', _ I T I
-1o0 -0,5 0.0 0,5 l,O _..5
95% Confidence IntervalsFor Increase in Transformed SDGS
2,0
TA rdajnu ssft o• rdm
ed
0"
S _1-'
DG
S -24
"2_z5 2030
SDGS vs TEMP, Adjusted for Remaining PredictorsUs|n 0 Mu]reg QEXPTtlMULREG, Mode] DESIGN_.AUTO__SDG
I=
, ,_ , ,
2035 2040 2045 2050 2055 2060
TEMP
Adjusted Data Values-- Adjusted Fitted Curve
2065 2070
J
2075
NASA/TM--2001-210901 87
Appendix A-6U (cont,)SOGS vs LOGSTRART, Adjusted for Remaining Predictors
using leulreg _EXPT_IMULREG. Model DESIGN__AUTO_SDG
rTj nS-" _i
u s D -1.0_ _s fG _.t o s -1. S_
d m -2.e
d -2 .- ' -:-4.0 -3.9
l
7
c
I t t .,. I.,- I I I ..... ! q-3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3.2 -3.1 -3.0
LOGSTRART
',j Adjusted Data V_luesAdjusted g_tted Curve
Case order Graph of Residuals of Transformed SO,;Using studenttzed Residuals in Model DESIGN_AUTO___SDG
2*
1-
R
e 0$id -1ua -21
-3
4-
+ +÷
+ ++ 4-
+
+ + + + _ ¢-" -":k -+
+ 4- + ÷
4-
0 2 4 6 8 10 12 1'4 16 18 20 22 2'4 26 2'8 30 32 34 36 38
case Number
2-
R 1-
es 0id-l"
Ua-2-]s -3"
Reslduals of Transformed SO(; vs Fitted Values
Using studenttzed Residuals in Model RSZGN__UTO_SOG
4-
÷ 4- ÷
+ ++ 4-+÷ +
÷ • -I"+ "P
+ + 4"
÷÷
-1.6 :1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2
Transformed Fitted values
NASA/TM--2001-210901 88
0.99-
C 0.95-u 0,9-m 0.8"
PP0 " "
b 0,1-0.05-
0.01"-'_.5
-+i-3.0
Appendix A-6U (cont)
Normal Probability Ploc of Residuals of Transformed SDGUsing 5tudentized Residuals in Model DESIGN__AUTO_SDG
(sample size = 38)
I/
/" +
/
_" _1-" 4"÷
/
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0,5 1.0 I,S
Residuals of Transformed SOG
B
-1.0 iS
qU
a
r
0.$ •
We
i
g
218.0 ths
lelO,quenc
Y
Histogram of Residuals of Transformed SDGUsing studentized Residuals in Model DESIGN__AUTO__SDG
Csample size - 38)
' t . . , ; "
03_ . - 1 .......... . , ' - , ;-3.0 -2.5 -2.0 -1,5 -1.0 -0.5 0.0
' I
0'.5 110 1.5
Residuals of Transformed SDG
2.0
0 Factor, Response 1 Range 2 Initial 3 olrcim_lor Formula Setting value
I Factors2 TEMP 2025 to 20753 LOGSTRART -4 to -345 Responses6 SDGS kiN
2050 2025-3.5 -3.9999
0.19518
Converged to a tolerance of 0.00009 after 43 steps.
NASA/TM--2001- 210901 89
1.5"
1.0"SDG
S0.5
0.1
0°5"
0.4 !
sD
0,3GS
o.z!
0.1
Appendix A-6U (cont.)Predictions and 95% simultaneous confidence intervals
for mean responses of SDG$ using mode] DESIGN_UTO_SDGLSR = -3.999g
T
2025 2030 2035 2040 2045 2050 2055 2060 2065 2070 2075
TEMP
Predictions and 95_ simultaneous confidence intervalsfor mean responses of SDGS using model DESZGN_AUTO__SDG
T = 2025
(
T ti!
i
k
-3r
: I
F + I I .' t..... i _ 4- 4 -; ',-4.0 -3,9 -3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3.2 -3.1 -3.0
LOGSTRART
SDGs
---__"..'-- Curve I
--_---- Curve I
-3,0'_
L0GST -3.5RART
-4,02025
--j .... : +
/
:
0._s:
/
I ') t /2030 2035 2040
+
0.3
_..i; _ _ l + "- -- ;- ---
+_0.3 ............t + ....... __0.35 ......
.... 0.4 .....
0.35 +_-+_+ .... +_ -"o.+"'G 7.1....0.4 0.55 ..-
• ]
+ '+'_ '+' '+ _,, + + I "-++ ' 'I *°+ " " i -"' "_2045 2050 2055 2060 2065 2070 2075
TEMP
$DG
Predictions and 95_Q simultaneous confidence intervals
1:or mea_ respol_ses of SINS using mo(_)l DE$IGN__AUTO__SOG
LSR T=2025
Lower 0.122143-3 Predicted 0.2230B1
Upper 0.407435
NASA/TM--2001- 210901 90
REPORT DOCUMENTATION PAGE FormApprovedOMB No. 0704-0188
Public reporting burden for this collectionof information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources.gathering and maintaining the data needed, and completing and reviewing the collection of information, Send comments regarding this burden estimate or any other aspect of thiscollection of information, including suggestions for reducing this burden to Washington Headquarters Services, Directorate for Information Operations and Reports 1215 JeffersonDavis Highway, Suite 1204. Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503
1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED
August 2001 Technical Memorandum
4. TITLE AND SUBTITLE
High Temperature, Slow Strain Rate Forging of Advanced Disk Alloy ME3
6. AUTHOR(S)
Timothy P. Gabb and Kenneth O'Connor
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
National Aeronautics and Space Administration
John H. Glenn Research Center at Lewis Field
Cleveland, Ohio 44135-3191
9, SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
National Aeronautics and Space Administration
Washington, DC 20546-0001
11. SUPPLEMENTARY NOTES
5, FUNDING NUMBERS
WU-714-04-10-00
8. PERFORMING ORGANIZATIONREPORT NUMBER
E-12778
10. SPONSORING/MONITORINGAGENCY REPORT NUMBER
NASA TM--2001-210901
Responsible person. Timothy E Gabb, organization code 5120,. 16-43.-3.7_.
12a.
13.
DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE
Unclassified - Unlimited
Subject Category: 26 Distribution: Nonstandard
Available electronically at http://_ltrs.grc.nasa.gov/GLTRS
This publication is available from the NASA Center for AeroSpace Information. 301 _o21 _)390.
ABSTRACT (Maximum 200 words)
The advanced disk alloy ME3 was designed in the HSR/EPM disk program to have extended durability at 1150 to 1250 °F in large
disks. This was achieved by designing a disk alloy and process producing balanced monotonic, cyclic, and time-dependent mechanical
properties, combined with robust processing and manufacturing characteristics. The resulting baseline alloy, processing, and
supersoh, us heat treatment produces a uniform, relatively fine mean grain size of about ASTM 7, with as-large-as (ALA) grain size of
about ASTM 3. There is a long term need for disks with higher rim temperature capabilities than 1250 °E This would allow higher
compressor exit (T3) temperatm-es and allow the full utilization of advanced combustor and airfoil concepts under development. Several
approaches are being studied that modify the processing and chemistry of ME3, to possibly improve high temperature properties.
Promising approaches would be applied to subscale material, for screening the resulting mechanical properties at these high tempera-
tures, n obvious path traditionally employed to improve the high temperature and time-dependent capabilities of disk alloys is to
coarsen the grain size. A coarser grain size than ASTM 7 could potentially be achieved by varying the forging conditions and
supersolvus heat treatment. The objective of this study was to perform forging and heat treatment experiments ("thermomechanical
processing experiments") on small compression test specimens of the baseline ME3 composition, to identify a viable forging process
allowing significantly coarser grain size targeted at ASTM 3-5, than that of the baseline, ASTM 7.
14. SUBJECT TERMS
Forging; Superalloy; Disk; Grain size: Thermomechanical processing
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