Method of Optimization of Three Dimensional Stress
Concentration Features in a Rotor Using Two Dimensional
Plate Models for Thermo-Mechanical Fatigue
by
Nicholas D. Aiello
A Thesis Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF MECHANICAL ENGINEERING
Approved:
_________________________________________
Prof. Ernesto Gutierrez-Miravete, Thesis Adviser
Rensselaer Polytechnic Institute
Troy, New York
April, 2012
© Copyright 2012
by
Nicholas D. Aiello
All Rights Reserved
ii
CONTENTS
LIST OF TABLES .......................................................................................................... ivv
LIST OF FIGURES ........................................................................................................... v
LIST OF SYMBOLS ........................................................................................................ vi
ACKNOWLEDGMENT ................................................................................................. vii
ABSTRACT ................................................................................................................... viii
iii
LIST OF TABLES
iv
LIST OF FIGURES
Figure 1: Load, Lock, and Shield Slot Configuration ....................................................... 3
Figure 2: NX CAD Model of 3D Sector ............................................................................ 4
Figure 3: Meshed 3D Sector Model................................................................................... 5
Figure 4: Element Types in 3D Model .............................................................................. 5
Figure 5: Node Files for Boundary Condition Mapping ................................................... 6
Figure 6: 3D Detail of Blade-Disk Interface Area............................................................. 8
Figure 7: 2D Slot Configuration in Strip Model .............................................................. 10
Figure 8: 4 identical 2D Strip Models, 1 for Each Mission Point ................................... 10
Figure 9: Sections Cut into 2D Strip Model .................................................................... 11
Figure 10: DOE Input Variables on Forward Rail........................................................... 12
Figure 11: DOE Input Variables on Aft Rail ................................................................... 13
Figure 12: Schematic View of iSight DOE Loop ............................................................ 14
v
LIST OF SYMBOLS
R = radial coordinate of cylindrical system, goes from rotor centerline outward in
3D finite element model
θ = circumferential coordinate of cylindrical system, follows “right hand rule” with
Z axis in 3D finite element model
Z = axial coordinate of cylindrical system, goes from forward to aft of rotor in 3D
finite element model
vi
ACKNOWLEDGMENT
Type the text of your acknowledgment here.
vii
ABSTRACT
Thermo-mechanical fatigue has become a significant concern with respect to rotor life in
turbine engines as maximum metal temperatures have increased in newer designs. Stress
concentration features, such as those present in a tangentially bladed rotor, tend to be the
primary areas of concern for this type of fatigue. This paper will explore a method of
optimizing of a set of three dimensional stress concentration features using two
dimensional plate models that are correlated to three dimensional finite element analysis
by adjusting the plate thickness, and are subject to the realistic design constraints of a
functional
tangentially
bladed
rotor
viii
in
a
turbine
engine.
1. Introduction
Thermo-mechanical fatigue (TMF) is a mechanism that causes damage to parts
subjected to transient thermal loading in their within the operational envelope. This
failure mechanism is of concern in several industries including both automotive and
aerospace (3). In the aerospace industry, parts subjected to this type of fatigue include
blades/airfoils and disks/rotors (henceforth used interchangeably) in the high
temperature sections of gas turbine engines. This becomes even more of a concern as
new products push temperatures even higher to help meet industry demands for higher
efficiency propulsion systems.
Focusing on gas turbine engine rotors, the means by which thermo-mechanical
fatigue is introduced deals mainly with the mission profile of the engine. In commercial
aircraft engines, for example, a typical mission includes take-off, climb, cruise, descent,
and landing. The points of the mission in which thermal large thermal transients exist are
at the beginning of the mission (take-off/climb) and the end of the mission
(descent/landing). These are the primary points of interest in the analysis of rotor parts
for thermo-mechanical fatigue.
During the take-off portion of a commercial turbine engine mission, the gas path
of the engine heats up, while the portions of the engine inside the gas path annulus
remain cool. Since a typical rotor consists of a radially outboard and fairly thin rim
directly exposed to the gas path, a massive bore at the most radially inboard point, and
thin web connecting them, this sudden heating up of the gas path heats the rim of the
disk rapidly, but the disk’s massive bore takes much longer to heat up. This causes a
thermal fight in the disk as the rim wants to thermally expand, while the bore holds it
back. What results is a compressive hoop stress field in the rim of the disk that increases
to a maximum during the portion of take-off with largest transient thermals, and then
dissipates as the bore of the disk begins to respond to the increase in flow path
temperatures.
During the descent portion of this typical mission, the opposite of this
phenomenon is in effect. Going from a cruise condition, where the entire engine is
essentially at a thermal equilibrium, to descent, the engine’s gas path suddenly takes on
cooler air. This cools the rim of the disk rapidly, while the bore remains hot. This time
1
the thermal fight in the rotor occurs in the opposite direction. The disk rim wants to
contract due to the decrease in gas path temperature, while the hot bore will not let it.
This results in a tensile hoop stress field at the rim of the disk that behaves in the
opposite manner as compared to the takeoff cycle, meaning the thermally induced hoop
stresses decrease as the bore cools after reaching a maximum transient point during the
descent.
The thermo-mechanical stresses introduced on the rim of a rotor throughout a
mission become particularly problematic when the rotor has some sort of stress
concentrating feature, such as a slot, in the rim of the disk. In the case of a tangentially
bladed rotor, stress concentrating feature generally consist of locking and loading slots.
Loading slots serve as a means of installing blades into a tangential disk. Locking slots
accept locks that are loaded intermittently between blades. These locks serve as a means
of transmitting load between the blades and disk at low power (until friction takes over)
such that the blades don’t freewheel in the disk as well as a means of ensuring the blades
cannot escape through the loading slot. The shape and orientation of these stress
concentrating features to one another is dictated by several design considerations, but
also can have an impact on how large of a stress concentration (or Kt) each feature
actually imposes upon the disk rim. This paper will focus on optimizing the shape and
location of these stress concentrating features, subject to constraints of design
considerations, in order to maximize TMF life for the rotor part.
2
2. Methodology
The objective of this thesis project is to create a method of optimizing three
dimensional features, in this particular case a load, lock, and shielding slot configuration
(See Figure 1) for a tangentially bladed rotor, such as that of a turbine engine. The
optimization routine explores the design space of the problem, given a set of inputs, and
chooses an optimal solution based on output parameters/targets. Inputs to the
optimization routine account for the shape of the whole rotor, the thermal profile for the
rotor (considered a constant during the optimization), the underlying mission that the
part is subjected to (which is typical commercial turbofan engine mission, considered a
“given” in for the purposes of this project and will not be discussed in detail), a
parameterized shape of each slot, and the shape of the blade root that must fit in the
loading slot; and output parameters are stresses in each feature and in corresponding farfield locations of the rotor at several mission points, the corresponding temperatures at
which these stresses occur, and a calculated TMF life using these outputs. The optimal
solution maximizes TMF life by adjusting the stress concentrations in these features
within pre-set boundaries by balancing their lives with one another while still allowing
for installation of a tangential blade into the rotor.
Figure 1: Load, Lock, and Shield Slot Configuration
3
The project can be thought of as three distinct parts. The purpose of the first part
of the project is to establish a baseline for comparison with the results of optimization.
This is done by first creating a 3D model, in this particular case the load, lock, and
shielding slot configuration in the tangentially bladed rotor mentioned above, is created
in a CAD system (NX Unigraphics). This 3D CAD model is then imported into a finite
element program where it is meshed, boundary conditions are applied, and the model is
solved. The output from this step is the peak stresses in each three dimensional feature at
the prescribed mission points.
The second part of the project is the optimization step. A model is again created,
but this time in two dimensions, and it represents the three dimensional features in
relation to one another in a hoop stress field (i.e. a plate model with the stress
concentrating features that is pulled on the ends). This model is then brought into a FEA
program where it is meshed, boundary conditions are applied, and the model is solved,
but this time the through thicknesses of different sections of the plate model are adjusted
to match the stress concentration factors (Kt’s for the purposes of this paper) calculated
using the peak stresses calculated in the first step and the nominal disk stresses
(calculated previously, details are not discussed in this paper). Once plate models have
been created that match the Kt’s calculated using the information from part 1 of the
project, the model is run through a design of experiments (DOE) routine to map the
response surfaces created by the effect that changing various dimensions has on the
fatigue life (in this case TMF life) . The output of this step is a more optimal
dimensioning scheme and a set of stress concentration factors for each slot as predicted
by the 2D model.
The third and final part of this project is the verification step. This step mirrors the
first step, but uses the geometry chosen as optimal by the 2D analysis instead of the
baseline geometry. This step is considered successful if the peak stress predicted by this
set of 3D analysis is similar to the predicted stress concentration in the 2D analysis
multiplied by the nominal disk stresses.
4
Part 1: Establish a Three-Dimensional Baseline
The first step in this project is to evaluate a baseline design for the rotor. The
analysis is conducted on a three dimensional (3D) sector model of a bladed disk and is
run for a complete mission (using ANSYS as a finite element solver). More specifically,
the model is of the area surrounding the tangential groove of disk, from the upper web to
the disk rim (see Figure 2). This was made by first creating a CAD (computer aided
design, NX Unigraphics used) model of the geometry to be analyzed in 3D, then creating
a finite element mesh representation of that model (meshed using ANSYS, see Figure 3).
The mesh consists primarily of 3 types of elements: 10 node tetrahedron elements for the
complex geometry of the area surrounding the 3D slot features, 8 node brick elements
for the axi-symmetric portions of the disk to help keep the element count down and
increase run speed, and 20 node brick elements that collapse to form the pyramid shaped
elements that connect the other 2 element types (see Figure 4). The blades in the model
are represented as a finite element mesh of the portion of the blade root below the neck
(also called the blade stump) with a mass point at the center-of-gravity of the upper
portion of the blade connected to the blade stump by high stiffness spring elements.
Figure 2: NX CAD Model of 3D Sector
5
Figure 3: Meshed 3D Sector Model
Figure 4: Element Types in 3D Model
6
The effect of the rest of the disk is simulated by mapping deflections from a
previously created two dimensional (2D) model onto the corresponding cut boundaries
of the 3D model for each mission point analyzed with that model. This was done by first
exporting the nodes of the 3D finite element model into a separate file. These nodes,
representing the shape of the 3D model, were then all rotated to the mid-plane of the
model (i.e. θ=0), after ensuring their nodal coordinate systems were set to the cylindrical
system being used in the rest of the model. The completed model, containing all of the
nodes of the 3D model compressed into a 2D format (see Figure 5), was saved as another
separate file for use in mapping the thermal response of the rotor. Continuing work on
the node file for mapping of deflection boundary conditions, compressed nodes now in
2D that are not located on the model’s cut boundaries were deleted, leaving only the
nodes residing directly on the boundaries (see Figure 5). The deflections from the 2D
model were then mapped onto these nodes for each mission point that the 3D model will
analyze, ensuring that compensation was made for any differences in coordinate
assignments, and degree-of-freedom boundary conditions files were created for each
point. Similarly, the node file containing all of the 3D model nodes compressed into a
2D format is used to map temperatures on each node for each 3D mission point and
creating thermal boundary condition files for each point. These boundary condition files
are later loaded into the 3D finite element model when the analysis is run.
Figure 5: Node Files for Boundary Condition Mapping
7
Before the model can be run, though, there are a few more boundaries in the 3D
finite element model that need to be resolve, those being the free sides of the disk sector
and the interface of the blade stumps to the disk. The free sides of the disk sector were
given the boundary condition of not allowing movement in the circumferential (θ)
direction. This still allows the disk model to move radially and axially at the boundaries,
but the lack of circumferential motion simulates the existence of the rest of the axisymmetric portion of the rotor. Doing this does not allow for any three dimensional
effects to transfer through the end of the 3D rotor section, so it is important that model
sector is chosen such that the behavior near the sector edges is indicative of the axisymmetric behavior of the rotor. That resolved, the last issue is the interface of blade
stumps to the disk’s bearing surface in the tangential groove (see Figure 6). This
interface was resolved using contact elements between the corresponding sets of faces.
The contact elements used were set to frictionless contact with no separation of face,
which allows the blade to slide along the disk’s bearing surface but not separate from it.
This contact behavior was chosen as an approximation of the actual blade/disk interface
behavior because it helps simplify the model in a way that increases run speed and
decreases likelihood of non-convergence of the finite element solution. The final step in
completing boundary resolution of the 3D model was to constrain the airfoils so that
they, too, could not move in the circumferential direction. This resolves the
circumferential movement still possible with no-separation contacts, and is a fairly
accurate approximation of blade behavior in a tangential disk as the friction force on the
blade bearing surface due to radial blade pull generally keeps a blade in place
circumferentially at most engine operational speeds.
8
Figure 6: 3D Detail of Blade-Disk Interface Area
With the boundary conditions of the 3D model now resolved, the model is ready
to run. A run file was created that loads the various inputs (finite element model with
internal boundary conditions, deflection cut boundary conditions, and thermal
conditions), and applies the correct set of inputs and rotational speeds for each mission
point in the set. Upon successful completion of the run, the peak stress at each slot for
each mission point is extracted and saved for the second part of the project.
Part 2: Two-Dimensional Optimization
The second part of this project begins with the creation of a two dimensional
plate models. These start as CAD models of long thin rectangles and then have the three
dimensional features, analyzed in part 1, cut out of them in the proper orientation
relative to one another to preserve the effect of inter-relation of the stress fields
surrounding them (see figure 7). The limits of the strip model extend far beyond the area
of the slots in order to allow any stress field created by the slots to completely die out
well before the ends of the model. This is important, since the stress concentration factor
9
(Kt) will be calculated using the peak stress prediction at each slot in the strip model
divided by the nominal, or far-field, stress. The height of each strip is determined by the
minimum through-thickness of each 3D rail in the area of each set of slots, or an average
thereof in the case of multiple slots with varying through-thicknesses. The 2 strip models
created, one for each rail, are then copied 3 times, as there were 4 mission points run in
the 3D analysis in part 1 of the project, with the slot geometries all directly linked to the
first set of strip models via parametric modeling in NX (see figure 8). This model will be
used to calculate all 4 mission point sets of slot Kt’s simultaneously.
Figure 7: 2D Slot Configuration in Strip Model
Figure 8: 4 identical 2D Strip Models, 1 for Each Mission Point
10
The next step in this part of the project is to match the results determined by this
2D model with the 2D-to-3D stress concentration factors (Kt’s) calculated using the
peak stresses at each slot location for each mission point calculated in the 3D model
from part 1 of this project divided by the nominal disk stress mentioned in the beginning
of the Methodology section (again, these are considered inputs for the purposes of this
paper). The first step in doing this is creating an FE model of the 2D plate models
described in the previous paragraph and assigning thickness parameters to each section
of the plate. There is a section of the plate model created for each slot as well as a nonslot, or nominal section (see figure 9). The means by which the 2D models are
manipulated to match these Kt’s is by varying the through thickness parameter assigned
to each slot section of the plate model until the desired set of 2D Kt’s is achieved. The
2D Kt’s are calculated by dividing the peak stress at each slot determined by the FE
analysis by the far-field stress taken at a partition in the nominal section of the 2D plate
model. Since this analysis is conducted with elastic properties and compressive and
tensile loading was shown to produce the same Kt’s for a given geometry, the loading
applied to each plate model was and arbitrary tensile displacement (the same for each
plate). The determination of the various plate thickness combinations is done via
manually running an FE model for a given set of through thicknesses, then adjusting
these through thicknesses based on the results. After doing this a few times, the data was
plotted and trend lines were created to more quickly converge on the desired plate
thickness for each slot.
Figure 9: Sections Cut into 2D Strip Model
11
Once the plate thicknesses are adjusted in the 2D FE model such that the 2D Kt’s
match the 2D-to-3D Kt’s determined in the beginning of this step, the automated
exploration of the design space can begin. This exploration is conducted using iSight
Multidisciplinary Design Optimization Software. This software automates adjustment of
variables based on user defined limits and feeding of initial and consequent inputs (i.e.
outputs of one program/step that become inputs to the next) to various programs in series
or parallel steps set up by the user. The software also has built in routines to conduct
various optimizations, DOE’s, etc. based on the inputs and outputs on the system set up
by the user. In this case, a DOE is set up with CAD software (UG) as the first process,
with input variables set to be the various slot dimensions that are to be changed during
the run (see figures 10 and 11). Figures 10 and 11 also show the means by which the
depth of the aft load slot is adjusted, that being a simulated “blade stub” that must fit into
the pair of load slots. This simulated blade stub serves to couple the forward and aft load
slots (and therefore reduce the amount of variables in the DOE) in a way that is a
functional restriction on the geometry of the slots, being that they must accept a blade at
installation.
Figure 10: DOE Input Variables on Forward Rail
12
Figure 11: DOE Input Variables on Aft Rail
Once the input variables and therefore the initial step in the DOE are defined in
iSight, a FEA step is inserted into the loop. This FEA step uses ANSYS to apply loads
and boundary conditions to the geometry created previously in the CAD step. The
geometry is constrained in what would equate to the circumferential direction on an
actual rotor on the left side of each plate model and an arbitrary displacement (the same
for each iteration) is applied on the right side. As this analysis is conducted using only
elastic properties, the magnitude of the displacement is unimportant. The model is also
constrained in the 3D-equivalent axial direction along the non-slot side of each plate.
This prevents bending of the plate about its thinner sections at slot locations, which does
not occur to any significant degree in an actual rotor. Once the boundary conditions and
loads are applied to the plate geometry, the FE model is solved. The ANSYS control file
(see appendix 1) is set up to then automatically calculate the 2D Kt’s of each slot by
searching for the max stress along each slot, then dividing it by the corresponding
nominal (or far field) stress taken at the non-slot section of the plate model (see figure
9). These 2D Kt’s are the output variables of the FEA step in the DOE.
The 2D Kt output obtained in the FEA step is then fed into the next step in the
DOE loop, that being the lifing section. In the lifing section, these 2D Kt’s are applied as
multipliers to the axi-symmetric stresses (calculated outside of this project, treated as a
given input) at each of the four mission points modeled in the previous steps. This
creates a concentrated stress value each of these mission points that equate to the stress
13
state of the slot itself (as opposed to the non-slot or axi-symmetric stress at that location
on the rotor). The concentrated stress is then interpolated for the rest of the mission by
averaging the concentrated stresses in the two points ahead of and behind each mission
point that is not calculated directly (the beginning and end mission points are assumed to
have a 2D Kt of one). The calculated mission concentrated stresses, as well as the
temperatures which are assumed to not change for the types pf relatively small geometric
variations studied in this project, are then run through a TMF lifing system and a mision
TMF life is calculated for each slot. This TMF life is the approximation of what the 3D
model of each set of slot geometry would give, but using Kt’s from the 2D-to-3D
correlated model described previously.
This process is performed for multiple iterations automatically (see figure 12 for
an iteration schematic), with iSight driving the variations in geometry based on the
number of DOE points it is allowed to run and the range of variability for each
parameter allowed (both are set by the user). The output from this, the second part of this
project, is a set of geometries and the life at each slot corresponding to each geometry,
from which the highest life set of slots (that with the highest minimum slot life) is
chosen to be analyzed in 3D to verify the Kt’s and ultimately life predicted by the 2D
geometry.
Figure 12: Schematic View of iSight DOE Loop
14
Part 3: Verify Optimization in Three-Dimensions
The objective of the third and final part of this project is to verify the results of
the two-dimensional optimization part of the project. This boils down to getting peak
stresses in each slot that match the concentrated stress calculated using 2D plate model
for each mission point in the previous step. This is conducted in the same fashion as the
first part of this project with a few changes incorporated to save time.
Similar to part 1, the new slot geometry is modeled using NX Unigraphics, but
instead of bringing the whole model into ANSYS, only the sections of the model that
contain parts of the slots are brought in. The elements (as well as nodes, areas, lines and
volumes) that make up the baseline geometry are deleted (the tetrahedron and pyramid
elements, shown in purple and red in figures 3 and 4), and the new volumes are used to
create and FE mesh that is combined with the remaining baseline mesh (the axisymmetric portion of the rotor and the blade stumps). As this creates new elements and
areas, with different numbers assigned to them, the contact elements must be recreated
between the blade stumps that touch parts of the slot volumes and the new areas they
interface. This is done using the same method described in part 1. Similarly, the new
node numbers in the slot volumes require the 3D nodes to be compressed to 2D again for
the mapping of thermals. The boundary nodes do not need to be recreated as none of
those nodes reside in/on the slot volumes.
Excluding these minor changes, part 1 of the project is essentially redone for
using the new slot geometry, the model is run, and the peak stress at each slot for each
mission point is extracted and saved for comparison to the 2D optimization results.
15
3. References
1. Determination of stress concentration factors of a steam turbine rotor using FEA
Nagendra Babu, R.; Ramana, K.V.; Rao, K. Mallikarjuna Source: Proceedings of the 2nd
WSEAS International Conference on Engineering Mechanics, Structures and Engineering
Geology, EMESEG '09, p 56-59, 2009, Proceedings of the 2nd WSEAS International
Conference on Engineering Mechanics, Structures and Engineering Geology, EMESEG
'09
2. Overview of High Temperature and Thermo-mechanical Fatigue (TMF)
Sehitoglu, H. Source: University of Illinois Mechanical and Industrial Engineering
3. Simulation of complex thermomechanical fatigue
Bardenheier, R.; Rogers, G. Source: Acta Metallurgica Sinica (English Letters), v 17, n 4,
p 400-406, August 2004
4. Thermo-Mechanical Fatigue Life Prediction: A critical Review
Zhuang, W.Z.; Swansson, N.S. Source: DSTO Aeronautical and Maritime Research
Laboratory, January 1998
5. Turbine blade fir-tree root design optimisation using intelligent CAD and finite
element analysis
Song, Wenbin; Keane, Andy; Rees, Janet; Bhaskar, Atul; Bagnall, Steven Source:
Computers and Structures, v 80, n 24, p 1853-1867, September 2002
16
4. Appendices
Appendix 1: 2D ANSYS Control File
pwautom !!Runs automatic mesher/label creator based on parameters coded into
UG model
!!This section applies arbitrary displacements to the ends of each plate model (all
names p\"pull_1")
/solu
cmsel,s,pull_1
nsll,s,1
d,all,uy,0.005
allsel
!
solve !!solves model with applied boundary conditions
!!This section post processes maximum stress at each slot for each timepoint, then
divides it by the nominal stress to calculate a 2D Kt
allsel,all
/post1
set,first
*cfopen,results,out
!!Calculate max stress at forward load slot for first timepoint
allsel
cmsel,s,F_Load_1
nsll,s,1
esln
nsort,s,1
*get,fls1,sort,0,max
!
!!Calculate max stress at lock slot for first timepoint
cmsel,s,Lock_1
nsll,s,1
esln
17
nsort,s,1
*get,ls1,sort,0,max
!
!!Calculate max stress at shield slot for first timepoint
cmsel,s,Shield_1
nsll,s,1
esln
nsort,s,1
*get,ss1,sort,0,max
!
!!Calculate max stress at aft/rear load slot for first timepoint
cmsel,s,R_Load_1
nsll,s,1
esln
nsort,s,1
*get,rls1,sort,0,max
!
!!Calculate nominal stress at foward nominal section for first timepoint
cmsel,s,fnom_1
nsll,s,1
esln
nsort,s,1
*get,fnoms1,sort,0,max
!
!!Calculate nominal stress at aft/rear nominal section for first timepoint
cmsel,s,rnom_1
nsll,s,1
esln
nsort,s,1
*get,rnoms1,sort,0,max
!
18
!!Calculates 2D Kt's for each slot for first timepoint
flkt1=fls1/fnoms1
lkt1=ls1/fnoms1
skt1=ss1/fnoms1
rlkt1=rls1/rnoms1
!
!!Repeats calculations for second through fourth timepoints
cmsel,s,F_Load_2
nsll,s,1
esln
nsort,s,1
*get,fls2,sort,0,max
!
cmsel,s,Lock_2
nsll,s,1
esln
nsort,s,1
*get,ls2,sort,0,max
!
cmsel,s,Shield_2
nsll,s,1
esln
nsort,s,1
*get,ss2,sort,0,max
!
cmsel,s,R_Load_2
nsll,s,1
esln
nsort,s,1
*get,rls2,sort,0,max
!
19
cmsel,s,fnom_2
nsll,s,1
esln
nsort,s,1
*get,fnoms2,sort,0,max
!
cmsel,s,rnom_2
nsll,s,1
esln
nsort,s,1
*get,rnoms2,sort,0,max
!
flkt2=fls2/fnoms2
lkt2=ls2/fnoms2
skt2=ss2/fnoms2
rlkt2=rls2/rnoms2
!
cmsel,s,F_Load_3
nsll,s,1
esln
nsort,s,1
*get,fls3,sort,0,max
!
cmsel,s,Lock_3
nsll,s,1
esln
nsort,s,1
*get,ls3,sort,0,max
!
cmsel,s,Shield_3
nsll,s,1
20
esln
nsort,s,1
*get,ss3,sort,0,max
!
cmsel,s,R_Load_3
nsll,s,1
esln
nsort,s,1
*get,rls3,sort,0,max
!
cmsel,s,fnom_3
nsll,s,1
esln
nsort,s,1
*get,fnoms3,sort,0,max
!
cmsel,s,rnom_3
nsll,s,1
esln
nsort,s,1
*get,rnoms3,sort,0,max
!
flkt3=fls3/fnoms3
lkt3=ls3/fnoms3
skt3=ss3/fnoms3
rlkt3=rls3/rnoms3
!
cmsel,s,F_Load_4
nsll,s,1
esln
nsort,s,1
21
*get,fls4,sort,0,max
!
cmsel,s,Lock_4
nsll,s,1
esln
nsort,s,1
*get,ls4,sort,0,max
!
cmsel,s,Shield_4
nsll,s,1
esln
nsort,s,1
*get,ss4,sort,0,max
!
cmsel,s,R_Load_4
nsll,s,1
esln
nsort,s,1
*get,rls4,sort,0,max
!
cmsel,s,fnom_4
nsll,s,1
esln
nsort,s,1
*get,fnoms4,sort,0,max
!
cmsel,s,rnom_4
nsll,s,1
esln
nsort,s,1
*get,rnoms4,sort,0,max
22
!
flkt4=fls4/fnoms4
lkt4=ls4/fnoms4
skt4=ss4/fnoms4
rlkt4=rls4/rnoms4
!
!!Writes calculated Kt's above to a text file that can be read in the iSight DOE
*vlen,1,1
*vwrite,'fload1','=',flkt1
(a12,a5,f7.3,)
*vwrite,'lock1','=',lkt1
(a12,a5,f7.3,)
*vwrite,'shield1','=',skt1
(a12,a5,f7.3,)
*vwrite,'rload1','=',rlkt1
(a12,a5,f7.3,)
*vlen,1,1
*vwrite,'fload2','=',flkt2
(a12,a5,f7.3,)
*vwrite,'lock2','=',lkt2
(a12,a5,f7.3,)
*vwrite,'shield2','=',skt2
(a12,a5,f7.3,)
*vwrite,'rload2','=',rlkt2
(a12,a5,f7.3,)
*vlen,1,1
*vwrite,'fload3','=',flkt3
(a12,a5,f7.3,)
*vwrite,'lock3','=',lkt3
(a12,a5,f7.3,)
*vwrite,'shield3','=',skt3
23
(a12,a5,f7.3,)
*vwrite,'rload3','=',rlkt3
(a12,a5,f7.3,)
*vlen,1,1
*vwrite,'fload4','=',flkt4
(a12,a5,f7.3,)
*vwrite,'lock4','=',lkt4
(a12,a5,f7.3,)
*vwrite,'shield4','=',skt4
(a12,a5,f7.3,)
*vwrite,'rload4','=',rlkt4
(a12,a5,f7.3,)
*cfclose
fini
/exit,nosa
24