Rotating Shake Test and Modal Analysis of a Model Helicopter Rotor Blade

Table 1. Properties of Model Rotor Blade (a) Structural properties Section mass Center of mass Inboard Chordwise area Torsional area moment offset forward Flapwise area moment of moment of moment of Section mass, of inertia, of elastic axis, section radius, Section spar in-lb2/in. in.

in. area, in 2 inertia, in 4 inertia, in 4 inertia, in 4 lb/in.

3.00 5.50 0.5000 0.5000 0.2632 0.4251 0.2200 0.0 6.87 0.371 0.1500 0.0500 0.1316 0.1938 0.04826 0.0 8.87 0.371 0.0250 0.0040 0.0105 0.04086 0.02505 0.0 0.0250 0.0 10.625 0.371 0.0040 0.0105 0.15113 0.05671 12.50 0.377 0.0355 0.00394 0.0394 0.14048 0.05559 0.0 13.00 0.386 0.0252 0.00249 0.00976 0.03134 0.02779 0.0 15.375 0.339 0.0252 0.00249 0.00976 0.04376 0.02961 0.0 17.85 0.278 0.03040 0.00231 0.00674 0.04123 0.02888 0.0 23.75 0.249 0.02636 0.00181 0.00565 0.0400 0.02810 0.0 28.25 0.224 0.02447 0.00151 0.00485 0.03903 0.02756 0.0 51.00 0.247 0.02447 0.00151 0.(X)485 0.03903 0.02756 0.0 52.75 0.279 0.02448 0.00160 0.00502 0.04125 0.02826 0.0 53.00 0.305 0.0500 0.00500 0.01435 0.07867 0.03984 -0.106 54.00 0.099 0.0400 0.00400 0.01148 0.0607 0.03563 -0.170 54.25 0.05 0.0050 0.00050 0.01435 0.01101 0.004401 -0.940 (b) Assumed material properties Modulus of elasticity, lb/in 2 Poisson's ratio 1.0 x 107 0.3 rotation is effectively out of ground effect (15 ft, or I- Flapping and lead-lag approximately 1.6 times the rotor diameter). All hover hinge location Pitch axis (e/4) 7 testing in the HHF is conducted at sea level atmospheric [ Strain gauges / conditions.

3 0 I_ (0.179, 0.539, 0.749) / Center-- +_-- ]. _ ..... .L .... [ /--x Model Description of ; A four-bladed articulated rotor hub, with coincident r°tati°n-_l LI [4.24 lead-lag and flapping hinges, was used in this experi-

6.a7-- I I

ment. The structural and inertial properties of the model blades are listed in table 1. The blades were rectangular ._-12.5---I 55 0 in planform and possessed no built-in twist. A standard Figure 2. Rotor blade geometry. R is blade radius, and c is chord; NACA 0012 airfoil contour was used over the aerody- all dimensions in inches.

namic portions of the blade. One blade was instrumented with flapwise, chordwise, and torsional-direction strain gauges mounted at three radial locations. The blade plan- 47-hp output at 12000 rpm) that is connected to the rotor form geometry, with strain-gauge locations indicated, is shaft through a belt-driven, two-stage, speed-reduction illustrated in figure 2.

system. Collective pitch and cyclic pitch inputs are pro- vided through a conventional swashplate arrangement.

The testbed for this experiment was the NASA/U.S.

The swashplate is positioned by three electrically Army Aeroelastic Rotor Experimental System (ARES) controlled hydraulic actuators, which are controlled model shown in figure 3. The ARES model has a stream- remotely from the HHF control room. Signals from the lined fuselage shell that encloses the rotor controls and blade strain gauge, as well as the signal from a strain- drive system. The fuselage shell, which is not usually gauge-instrumented pitch link signal, are transferred installed when testing the ARES model in the HI-IF, was from the rotating system to the fixed system through a omitted during this test. The model rotor is powered by a 30-channel slip-ring assembly.

variable-frequency, synchronous electric motor (rated at L-86-11,726 Figure 3. ARES model mounted in HHF.

Test Procedure electronic signal analyzer. Output signals from the blade- mounted strain gauges were used as a measure of the The experimental portion of this test was designed to blade modal deflection, while the pitch-link-mounted provide accurate measurements of elastic blade mode strain-gauge signal was used as a measure of the force frequencies over a range of rotor operating speeds. The input to the blade structure. From these two measure- experimental procedures described below are not neces- ments, a frequency-response function could be generated sarily the ideal techniques for experimentally measuring using the signal analyzer. The frequency of the excited rotating blade frequencies, but are the best use of the blade mode was then identified by looking for an ampli- existing ARES hardware and instrumentation for this tude peak in the frequency-response function.

purpose. For this experiment, only elastic blade modes with frequencies up to and including the first torsion Nonrotating modal frequencies were determined mode were measured. Because of the limited blade with a different procedure. For these measurements, the instrumentation, no attempt was made to measure blade hub assembly, with a single attached blade, was removed mode shapes during this test.

from the ARES model and suspended so that the blade hung vertically. This method permitted measurements to Rotating-frequency measurements for each mode be made without the blade resting on the hub flapping were made at rotor speeds that ranged from 150 rpm to stops. A conventional impact-response test using a blade- 660 rpm at approximately 100-rpm intervals. The mounted accelerometer, a signal analyzer, and an impact nonoscillatory collective pitch of the blades was fixed at hammer was then performed. Nonrotating blade mode 0 °. At each rpm increment, the blades were excited by frequencies in this case were identified by looking for the sinusoidally oscillating the collective pitch of the rotor amplitude peaks in the spectral-response function gener- with the ARES hydraulic control system. This collective ated with the accelerometer signal.

pitch oscillation frequency was varied over a 10- to 20-Hz frequency band in the vicinity of each modal fre- quency. The amplitude of vibratory loads caused by the NASTRAN Analysis movement of the swashplate together with the small amount of aerodynamic excitation present from the col- Blade Analytical Model lective pitch oscillation was sufficient to excite all of the blade modes of interest.

Analysis of the articulated rotor blade was per- Blade mode frequencies were determined by pro- formed using several versions of the MSC/NASTRAN cessing blade and pitch-link strain-gauge signals with an finite-element-analysis computer code. The original, pretest runs wereperformed using MSC/NASTRAN and only forces acting on the blade as a result of rotation were considered. The MSC/NASTRAN executive con- version 66b. Subsequent runs using version 67 and, more trol cards, case control cards, and bulk data used for a recently, version 68 were made to verify that procedures used with previous versions were still applicable and that sample solution 66 run are included in the listing in the results had not changed. appendix A.

The blade analytical model was constructed using Once the smile analysis of the blade had been com- standard finite-element-modeling techniques. A list of pleted, a modified normal modes analysis (solution 63) the complete input data deck is provided in appendix A. was performed as a "restart" job using the MSC/ All material and structural property values for the blade NASTRAN database files generated and saved from the model were taken from values shown in table 1. The solution 66 run. Two modifications were made in the blade structure was modeled entirely with CBEAM solution 63 DMAP code to obtain the correct rotating- one-dimensional beam elements, with sectional masses blade mode shapes and frequencies of the structure.

and mass moments of inertia for all elements modeled as The first modification was the inclusion of a standard nonstructural mass.

MSC/NASTRAN rigid format DMAP alter (RF63D89) into the solution 63 source code. This DMAP alter The blade-root boundary conditions were approxi- allowed the stiffness matrix generated and saved from mated by allowing rotations only about the Y- and Z-axes the solution 66 run, which included the differential stiff- of the global coordinate system, which represented ening effects of the radial forces acting on the rotor motion about the flapping and lead-lag hinges. The blade, to be used instead of the stiffness matrix normally blade-root lead-lag damper was modeled using a generated in the solution 63 run. A second DMAP modi- CELAS2 scalar spring dement with an appropriate fication (NLGYRO.ALT) was made to include addi- damping value and a small linear spring rate. Rotation tional centrifugal softening terms in the stiffness matrix.

about the X-axis (blade pitching degree of freedom) was NLGYRO.ALT also adds Coriolis terms to the damping constrained to be zero, representing in essence an infi- matrix; however, for the normal modes analysis nitely stiff control system.

described here, damping and Coriolis terms can be ignored. This modified solution 63 DMAP source code, Rotating System Analysis Procedure with the RF63D89 and NLGYRO.ALT DMAP alters included, was then recompiled and executed as a restart MSC/NASTRAN and COSMIC/NASTRAN have job using the previously generated solution 66 database both been used to analyze the rotating modal behavior of files.

compressor and turboprop blades (refs. 5 and 6). In these studies, plate, shell, and solid elements were used to The nonrotating (0-rpm) case required no initial non- model the blades. The computational procedure used in linear statics run and was performed using the unmodi- these studies required that two MSC/NASTRAN runs be fied solution 63 normal-modes solution sequence.

made for each condition. First, a large-displacement The executive control cards and case control cards analysis was made using MSC/NASTRAN solution 64.

necessary to execute the solution 63 runs are shown This solution sequence performs a large-displacement in appendix B. Changes required between MSC/ analysis on the rotating blade, computes steady-state NASTRAN version 68 and earlier versions (66 and 67) displacements and stresses, and then stores the blade final stiffness and mass matrices of the blade model in a are noted. The RF63D89 alter code, provided in the gen- eral distribution of MSC/NASTRAN, has not been database. The frequencies and mode shapes were then shown here. The NLGYRO.ALT alter code, which was computed with solution 63, using the saved matrices from the solution 64 run. written originally for use with version 66b and is not usu- ally provided in the general distribution, was obtained The current study also used a two-step process to independently from MSC. Several modifications to this obtain the blade frequencies and mode shapes although, DMAP alter are necessary for it to be used with MSC/ as mentioned previously, beam elements are used here NASTRAN version 68. These modifications are noted in to model the rotor blade. At each desired rotor speed con- appendix C.

dition, the blade model was first analyzed using the nonlinear statics (database) MSC/NASTRAN solution Presentation of Results sequence 66, which is the updated version of solution 64.

This run calculated the deflections of the blade structure A comparison of the experimental and analytical fre- caused by a radial force field defined with the RFORCE quency results is shown graphically in figure 4. This plot card in the bulk data deck. Gravity forces and aerody- shows blade mode frequencies (Hz) versus rotor speed namic forces were neglected throughout this analysis, (rpm) for the first five elastic blade modes. The solid wise and torsion modes. Variations in the rotor rpm Experiment settings were very small, typically less than :t2 rpm.

o First flap r_ Second flap First chord Discussion of Results o Third flap • First torsion The correlation of the MSC/NASTRAN-computed, rotating-blade frequencies with the experimentally mea- -- Analysis sured frequencies was, overall, very good, with the best results being obtained for the lower flapping and chord- wise modal frequencies. With the exception of blade torsion, trends in mode frequency with rotor speed were J Jo adequately predicted by the analysis. The largest discrep- Jo ancies between the analytical and experimental results N J o -1- o occurred with the third elastic flap mode results and the >_ 75 o o o first torsion mode results.

The discrepancies with the third flapping mode were thought to be due to inaccurate flapping stiffness data LL used in defining the analytical model. MSC/NASTRAN, [] jl when given accurate structural modeling information, 25 J generally does an excellent job of predicting the non- Z rotating modes and frequencies of a structure. As the I I I I I nonrotating-frequency calculation for this mode was still 0 150 300 450 600 750 significantly in error with the experimental value, the Rotor speed, rpm difference is thought to be due to the structural modeling of the blade and not a fundamental error with the MSC/ Figure 4. Comparison of experimental and analytical frequencies NASTRAN procedures used in this study.

vs rotor speed. Rigid body flap and lead-lag modes not shown.

The discrepancies in the torsional frequency magni- tude are thought to be due primarily to the "infinitely stiff" control system approximation used for the blade lines represent the analytical predictions of the blade root boundary conditions. A finite stiffness associated mode frequencies made by MSC/NASTRAN. The symbols denote experimental frequency values measured with the pitching degree of freedom at the root would in the HHF. A comparison of these experimental and move the frequency magnitudes upward toward the analytical frequency values is also provided in table 2. experimentally measured values. The slight upward trend Analytical calculations of the flapping and lead-lag rigid- of the measured frequency with rotor speed was also not body mode frequencies have been omitted. Repeatability predicted in the analytical results. This trend is thought to be caused by the absence of a propeller-moment-type in the frequency measurements was within +l Hz for the term in the NLGYRO.ALT alter code.

three flapping modes measured, and _+2 Hz for the chord- Table 2. Comparison of Experimental and Analytical Blade Frequencies Frequency, Hz at rotor speed of--- 0 rpm 150 rpm 250 rpm 350 rpm 450 rpm 550 rpm 660 rpm Exper- Exper- Exper- Exper- Exper- Exper- Exper- Mode iment Analysis iment Analysis iment Analysis iment Analysis iment Analysis iment Analysis iment Analysis 1st flap 10.7 11.53 12.2 13.10 14.7 15.51 17.6 18.52 21.2 21.91 24.9 25.51 28.8 29.62 2nd flap 32.6 36.38 33.1 37.64 35.8 39.78 39.0 42.77 42.7 46.44 46.7 50.63 51.75 55.69 1st chord 41.0 42.44 41.1 42.82 42.8 43.49 44.4 44.48 43.0 45.75 45.2 47.30 49.1 49.29 3rd flap 67.8 76.80 70.0 77.97 72.5 80.01 75.3 82.95 80.4 86.70 85.3 91.11 91.5 96.52 1st torsion 110.3 102.05 1i 1.0 102.06 110.0 102.09 112.0 102.12 113.0 102.18 114.5 102.28 115.0 102.53 articulated helicopter rotor blade structure. Accurate

Concluding Remarks

prediction of torsional frequencies and trends will most The rotating frequencies of a model articulated heli- likely require some additional modifications to the MSC/ copter rotor blade were measured and compared to NASTRAN DMAP source code.

analytical frequency calculations performed using the MSC/NASTRAN finite-element structural analysis com- puter code. These results show that MSC/NASTRAN NASA Langley Research Center can, with slight modifications, adequately predict flap- Hampton, VA 23681-0001 ping and chordwise rotating modal characteristics of an January 22, 1997

Appendix A

MSC/NASTRAN Solution 66 Input Data Deck

The material in this appendix constitutes the complete input data deck used to construct the blade analytical model.

SSS$$$S$$$SSSSSSS$$$SS$SSSSSS$$SSSSSSSSSSSSSSSSSS$S$$SS$$$SS$SS$$SSSSSSSSSSS $$ EXECUTIVE CONTROL CARDS $$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ ID ART-L, WKW SOL 66 $ NONLINEAR STATICS (MSC/NASTRAN VERSIONS 66, 67 OR 68) TIME 20 CEND $ $$$$$$$$$$$$SSSS$SSS$S$SS$$S$SSS$SS$SS$SSSSS$$SSSSSSS$SSS$SSS$SSS$SSSSSSSSS$ $$ CASE CONTROL CARDS $$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$S$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$S$$$ $ TITLE-FRB (LIGHT BALLAST) ON ARTICULATED HUB LABEL-(CF LOAD II HZ ROTATION) SUBTITLE- NONLINEAR STATICS SOL 66 $ ECHO-BOTH DISP-ALL OLOAD=ALL $ SEALL-ALL $ LOAD-I S NLPARM-100 S BEGIN BULK $ $$$$$$$$$$$$$$S$$SSSSS$$S$$S$SS$$S$$SSS$SSS$$SSS$SS$SSSS$SSSSSSSSS$$$$$$$$$$ $$ BULK DATA CARDS 55 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $ MISCELLANEOUS PARAMETERS $$SSSSSSSSSSSSSSSSS$SSSSSSSS S PARAM,TINY, 0.999 PARAM,GRDPNT,0 PARAM,MAXRATIO,I.*I3 PARAM,COUPMASS,I PARAM,WTMASS,0.00259 PARAM,AUTOSPC,YES $ $ PARAMETERS FOR SOL 66 SSSSSSSSSSSSSSSSS$SSSSSS$ $ PARAM,LGDISP, I NLPARM,100,2,,ITER, I S PARAM,TESTNEG,I $ $ CENTRIFUGAL LOAD $SSSSSSSSSSSSSSSSSS$ $ RFORCE, 1,0, ,11.,0.,0.,1.,2 $ $$SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS$SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS$ $$ ARTICULATED HUB CUFF AND BLADE ROOT: 4-8-92 $$ $$$$$$SSSS$SSSSSSSSSSS$SSSSSSS$$SSSSSSSSSSSSSSSS$SSSSSSSSSSSSS$SSS$$$$$$$$$$ $ $ .............................................

$ GEOMETRY: $ ...........................................................

$ ..................................................................

$ GRID ID CP Xl X2 X3 CD PS SEID $ ....... 2 ....... 3 ....... 4 ....... 5 ....... 6 ...... 7 ....... 8 ....... 9 ....... A .......

GRID, 200,, 3.00, 0.0, 0.0,, 1234 GRID, 201,, 6.87, 0.0, 0.0 GRID, 202,, 8.87, 0.0, 0.0 GRID, 203,, 10.625, 0.0, 0.0 GRID, 204,, 3.00, 0.0, 0.0,, 123456 S $ ..............................................................................

$ CONNECTIVITY: $ ..............................................................................

$ BLADE CUFF AND ROOT (RS 3.0 TO 12.5) $ ............................................................................

$ CBEAM EID PID GA GB Xl X2 X3 $ ....... 2 ....... 3 ....... 4 ....... 5 ....... 6 ....... 7 ....... 8 ....... 9 ...... A CBEAM 200 200 200 201 0.0 1.0 0.0 CBEAM 201 201 201 202 0.0 1.0 0.0 CBEAM 202 202 202 203 0.0 1.0 0.0 CBEAM 203 203 203 i000 0.0 1.0 0.0 $ $ LEAD-LAG DAMPER ELEMENT $ ............................................................................

$ CELAS2 EID K G] C1 G2 C2 GE S $ ....... 2 ....... 3 ....... 4 ....... 5 ....... 6 ....... 7 ...... 8 ....... 9 ..... A .......

CELAS2, 204, 464.0, 204, 6, 200, 6, 980.0 $ $ ...................................................................

$ PROPERTY CARDS: S ....................................................................

$ ...............................................................

$ PBEAM PID MID A Ii I2 I12 J NSM $ ....... 2 ....... 3 ....... 4 ....... 5 ....... 6 ....... 7 ....... 8 ....... 9 ....... A .......

PBEAM, 200, i000, 5.500, 0.5000, 0.5000, , 0.2632, 0.42511, +P2001 +P2001 ......... +P2002 +P2002 ..... 2.200-1 $ PBEAM, 201, i000, 0.371, 0.1500, 0.0500, , 0.1316, 0.19380, +P2011 +P2011 ......... +P2012 +P2012 ..... 4.826-2 S PBEAM, 202, i000, 0.371, 0.0250, 0.0040, , 0.0105, 0.04086, +P2021 +P2021 ......... +P2022 +P2022 ..... 2.505-2 $ PBEAM, 203, i000, 0.371, 0.0250, 0.0040, , 0.0105, 0.15113, +P2031 +P2031 ......... +P2032 +P2032 ..... 5.671-2 S 555S5$555555555555$$$5555$555555555555555555555555555$$$55555555555555555555 $5 FREON RESEARCH BLADE, LIGHTLY BALLASTED ( RS 12.5 TO 55.0 ) 4-9-92 $5 5SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS555555$SSSSSSSSSSSS5555$5 S S ..................................................................

$ GEOMETRY: $ ..........................................................................

5 .......................................................................

5 GRID ID CP Xl X2 X3 CD PS SEID 5 ....... 2 ...... 3 ....... 4 ..... 5-- - 6 ..... 7 ....... 8 .... 9 --A -- GRID i000 12.500 0.000 0 000 GRID i001 13.000 0.000 0 000 GRID 1002 14.000 0.000 0 000 GRID 1003 15.000 0.000 0 000 GRID 1004 15.375 0.000 0 000 GRID 1005 15.600 0.000 0 000 GRID 1006 16.000 0.000 0 000 GRID 1007 17.000 0.000 0 000 GRID 1008 17.850 0.000 0 000 GRID 1009 18.000 0.000 0 000 GRID i010 19.000 0.000 0.000 GRID I011 20.000 0.000 0.000 GRID ]012 21.000 0.000 0.000 GRID 1013 22.000 0.000 0.000

GRID 1014 23.000 0.000 0.000

GRID 1015 23.750 0.000 0.000

GRID 1016 24.000 0.000 0.000

GRID 1017 25.000 0.000 0.000

GRID 1018 26.000 0.000 0.000

GRID 1019 27.000 0.000 0.000

GRID 1020 28.000 0.000 0.000

GRID 1021 28.250 0.000 0.000

GRID 1022 29.000 0.000 0.000

GRID 1023 29.150 0.000 0.000

GRID 1024 30.000 0.000 0.000

GRID 1025 31.000 0.000 0.000

GRID 1026 32.000 0.000 0.000

GRID 1027 33.000 0.000 0.000

GRID 1028 34.000 0.000 0.000

GRID 1029 35.000 0.000 0.000

GRID 1030 36.000 0.000 0.000

GRID 1031 37.000 0.000 0.000

GRID 1032 38.000 0.000 0.000

GRID 1033 39.000 0.000 0.000

GRID 1034 40.000 0.000 0.000

GRID 1035 41.000 0.000 0.000

GRID 1036 41.250 0.000 0.000

GRID 1037 42.000 0.000 0.000

GRID 1038 43.000 0.000 0.000

GRID 1039 44.000 0.000 0.000

GRID 1040 45.000 0.000 0.000

GRID 1041 46.000 0.000 0.000

GRID 1042 47.000 0.000 0.000

GRID 1043 48.000 0.000 0.000

GRID 1044 49.000 0.000 0.000

GRID 1045 50.000 0.000 0.000

GRID 1046 51.000 0.000 0.000

GRID 1047 52.750 0.000 0.000

GRID 1048 53.000 0.000 0.000

GRID 1049 54.000 0.000 0.000

GRID 1050 54.250 0.000 0.000

GRID 1051 55.000 0.000 0.000

S

GB X1 X2 X3

$ CBEAM EID PID GA

--6....... 7 - 8 ...... 9....... A -

CBEAM 1000 i000 i000 I001 0.0 1.0 0.0

CBEAM I001 I001 i001 1002 0.0 1.0 0.0

CBEAM 1002 1001 1002 1003 0.0 1.0 0.0

CBEAM 1003 i001 1003 1004 0.0 1.0 0.0

CBEAM 1004 1004 1004 1005 0.0 1.0 0.0

CBEAM 1005 1004 1005 1006 0.0 1.0 0.0

CBEAM 1006 1004 1006 1007 0.0 1.0 0.0

CBEAM 1007 1004 1007 1008 0.0 1.0 0.0

CBEAM 1008 1008 1008 1009 0.0 1.0 0.0

CBEAM 1009 1008 1009 I010 0.0 1.0 0.0

CBEAM i010 1008 i010 I011 0.0 1.0 0.0

CBEAM i011 1008 i011 1012 0.0 1.0 0.0

CBEAM 1012 1008 1012 1013 0.0 1.0 0.0

CBEAM 1013 1008 1013 1014 0.0 1.0 0.0

CBEAM 1014 1008 1014 1015 0.0 1.0 0.0

CBEAM 1015 1015 1015 1016 0.0 1.0 0.0

CBEAM 1016 1015 1016 1017 0.0 1.0 0.0

CBEAM 1017 1015 1017 1018 0.0 1.0 0.0

CBEAM 1018 1015 1018 1019 0.0 1.0 0.0

CBEAM 1019 1015 1019 1020 0.0 1.0 0.0

CBEAM 1020 1015 1020 1021 0.0 1.0 0.0

CBEAM 1021 1021 1021 1022 0.0 1.0 0.0

CBEAM 1022 ]021 1022 1023 0.0 1.0 0.0

CBEAM 1023 1021 1023 1024 0.0 1.0 0.0

CBEAM 1024 1021 1024 1025 0.0 1.0 0.0

CBEAM 1025 1021 1025 1026 0.0 1.0 0.0

CBEAM 1026 1021 1026 1027 0.0 1.0 0.0

CBEAM 1027 1021 1027 1028 0.0 1.0 0.0

CBEAM 1028 1021 1028 1029 0.0 1.0 0.0 CBEAM 1029 1021 1029 1030 0.0 1.0 0.0 CBEAM 1030 1021 1030 1031 0.0 1.0 0.0 CBEAM 1031 1021 1031 1032 0.0 1.0 0.0 CBEAM 1032 1021 1032 1033 0.0 1.0 0 0 CBEAM 1033 1021 1033 1034 0.0 1.0 0 0 CBEAM 1034 1021 1034 1035 0.0 1.0 0 0 CBEAM 1035 1021 1035 1036 0.0 1.0 0 0 CBEAM 1036 1021 1036 1037 0.0 1.0 0 0 CBEAM 1037 1021 1037 1038 0.0 1.0 0 0 CBEAM 1038 1021 1038 1039 0.0 1.0 0 0 CBEAM 1039 1021 1039 1040 0.0 1.0 0 0 CBEAM 1040 1021 1040 1041 0.0 1.0 0 0 CBEAM 1041 1021 1041 1042 0.0 1.0 0 0 CBEAM 1042 1021 1042 1043 0.0 1.0 0 0 CBEAM 1043 1021 1043 1044 0.0 1.0 0 0 CBEAM 1044 1021 1044 1045 0.0 1.0 0 0 CBEAM 1045 1021 1045 1046 0.0 1.0 0 0 CBEAM 1046 1046 1046 1047 0.0 1.0 0 0 CBEAM 1047 1047 1047 1048 0.0 1.0 0 0 CBEAM 1048 1048 1048 1049 0.0 1.0 0 0 CBEAM 1049 1049 1049 1050 0.0 1.0 0 0 CBEAM 1050 1050 1050 1051 0.0 1.0 0 0 S $ ..............................................................................

$ PROPERTY CARDS: S ......................................................................

S ..............................................................................

S PBEAM PID MID A Ii I2 I12 J NSM S ....... 2 ....... 3 ...... 4 - --5 ...... 6 ....... 7 ....... 8 ....... 9 ...... A .......

PBEAM, 1000,1000,0.377,0 03550,0.00394 ,0.03940,0.14048,+P001 +P001 ......... +P002 +P002 ..... 5.559-2 .... ÷P003 +P003, 0.00, 0.0, 0.00, 0 0 $ PBEAM, 1001,1000,0.386,0 02520 0.00249 ,0.00976,0.3134-I,+P011 +P011 ......... +P012 +P012 ..... 2.779-2 .... +P013 +P013, 0.00, 0.0, 0.00, 0 0 S PBEAM,1004,1000,0.339,0 02520 0 00249 ,0.00976,0.4376-I,+P041 +P041 ......... +P042 +P042 ..... 2.961-2 .... +P043 +P043, 0.00, 0.0, 0.00, 0 0 $ PBEAM, 1008,1000,0.278,0 03040 0 00231 ,0.00674,0.4123-I,+P081 +P081 ......... +P082 +P082 ..... 2.888 2 .... +P083 +P083, 0.00, 0.0, 0.00, 0 0 S PBEAM,1015,1000,0.249,0 02636 0 00181 ,0.00565,0.400-I,+P151 +PI51 ......... +P152 +P152 ..... 2.810-2 .... +P153 +P153, 0.00, 0.0, 0.00, 0 0 S PBEAM, 1021,1000,0.224,0 02447 0 00151 ,0.00485,0.3903 I,+P211 +P211 ......... +P212 +P212 ..... 2.756 2 .... +P213 +P213, 0.00, 0.0, 0.00, 0 0 $ PBEAM, 1046,1000,0.247,0.02447,0 00151,,0.00485,0.3903-I,+P461 +P461 ......... +P462 +P462 ..... 2.756-2 .... +P463 +P463, 0.00, 0.0, 0.00, 0 0 $ PBEAM, 1047,1000,0.279,0.02448 0 00160,,0.00502,0.4125-I,+P471 +P471 ......... +P472 +P472 ..... 2.826-2 .... +P473 +P473, 0.00, 0.0, 0.00, 0.0 S PBEAM, 1048,1000,0.305,0.05000,0.00500,,0.OI435,0.7867-1,+P481 ÷P481 ......... +P482 +P482 ..... 3.984-2 .... +P483 +P483, -0.106, 0.0, -0.106, 0.0 $ PBEAM,1049,1000,0.099,0.04000,0.00400,,O.01148,0.607-1,+P491 +P491 ......... +P492 +P492 ..... 3.563-2 .... +P493 +P493, -0.17, 0.0, -0.17, 0.0 S PBEAM, 1050,1000,0.05,0.00500,0.00050,,0.01435,0.1101 I,+P50] +P501 ......... +P502 +P502 ..... 4.401-3 .... +P503 +P503, -0.940, 0.0, -0.940, 0.0 $ $ ......................................................................

$ MATERIAL PROPERTY CARDS: $ .........................................................................

$ i000: FIBERGLASS BLADE (ASSUMED PROPERTIES) $ ........................................................................

$ MID E G NU RHO $ ....... 2 ....... 3 ...... 4 ..... 5 ....... 6 ....... 7 ....... 8--- 9- -A ....

MAT1 i000 1.0+7 0.3 S $ ENDDATA II

Appendix B

MSC/NASTRAN Solution 63 Restart Data Deck

This appendix presents the executive control cards and the case control cards required to execute the solution 63 runs.

RESTART

(use this executive control section for MSC/NASTRAN version 66 or 67:)

S $$SSSSSSSSSSSSSS$$S$$SSSSSSSSSSSSSS$S$$SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS$ $$ EXECUTIVE CONTROL CARDS 55 $SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS$$$$$$$$$ $ ID ATR-L, WKW SOL 63 $ NORMAL MODES DATABASE V. 66B TIME 20 S $ RECOMPILE SOL 63 TO INCLUDE ALTERS (MSC/NASTRAN VERSIONS 66 AND 67) SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS$ $ COMPILE SOL63 SOUIN=MSCSOU NOLIST NOREF $ S ALTER 193 $ FILE EST=OVRWRT/GEI=OVRWRT/GPECT:OVRWRT/KELM=OVRWRT/KDICT=OVRWRT $ S RFALTER RF63D89 S $ INCLUDE GYRO TERMS SSSSSSSSSSSSSSSSSSS$$$ S INCLUDE 'NLGYRO.ALT' S CEND

(use this executive control section for MSC/NASTRAN version 68:)

SSSSSSSSSSSSSSSSSSSSS$SSSSSSSSSSSSSSSSSSSSSSSSSSSSS$SSSS$$$SSSSSSSSSSSSSSSS$ S$ EXECUTIVE CONTROL CARDS 55 $$$SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS$SSSSSSSSSSSSSSSSSSSSSSSS$ S ID ATR-L, WKW SOL 63 $ NORMAL MODES DATABASE V. 66B TIME 20 $ $ RECOMPILE SOL 63 TO INCLUDE ALTERS (MSC/NASTRAN VERSION 68) $$$$$$$SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS $ COMPILE SOL63 SOUIN:MSCSOU NOLIST NOREF $ NOLIST NOREF $ $ RFALTER RF63D89 $ $ INCLUDE GYRO TERMS $SSSSSSSSSSSS$SSSSSSS$ S INCLUDE 'NLGYRO.ALT' $ CEND S

(remaining sections are the same for all versions of MSC/NASTRAN)

$ SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS$SSSSSSSSSSSSSSSSSSSSSSSSSS$ $$ CASE CONTROL CARDS $$ $$$SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS$ $ TITLE=FRB (LIGHT BALLAST) ON ARTICULATED HUB LABEL:(CF LOAD ii HZ ROTATION) SUBTITLE- NORMAL MODES RESTART SOL 63 $ ECHO=BOTH DISPLACEMENT=ALL OLOAD=ALL s SEALL=ALL $ LOAD-I S METHOD-10 S BEGIN BULK S S $SSSSSSSSSSSS$$SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSsss$ $$ BULK DATA CARDS S$ $$$$$$$SSSSS$$$$$$$$$$$$SSSSSSSSSSSSSSSSSSS$SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS$ $ $ MISCELLANEOUS PARAMETERS SSSSSSSSSSSSSSSSS$SSSSSSSSSS $ PARAM TINY,0.999 PARAM GRDPNT,0 PARAM MAXRATIO, I.+I3 PARAM COUPMASS,I PARAM WTMASS,0.00259 PARAM AUTOSPC,YES $ $ PARAMETERS FOR SOL 63 $SSSSSSSSSSSSSSSSSSSSS$$$ S PARAM,LGDISP, Z PARAM,LOOPID, 2 $ PARAM,TESTNEG,I $ $ EIGENVALUE EXTRACTION METHOD FOR SOL 63 RESTART sssassssssssssssssssssssssssssssssssssssssssssssss$ S EIGR, Z0,SINV,0.,100.

S S CENTRIFUGAL LOAD $SSSSSSSSSSSSSSSSSSS $ RFORCE, Z,0,,11.,0.,0.,1.,2 S

(model definition bulk data omitted; same as solution 66 deck)

$ ENDDATA

Appendix C Modifications to NLGYRO.ALT for Use With MSC/NASTRAN Version 68 Much of the DMAP language was changed between MSC/NASTRAN Version 68 and earlier versions. Because of this change, two minor changes in the original version 66b NLGYRO.ALT DMAP source code (obtained from MSC) are required for it to execute properly under MSC/NASTRAN version 68. These modifications follow.

1. In line 1 (ignoring comments), change ALTER 492 $ to ALTER 504 $ 2. In line 23, change VECPLOT , ,BGPDT, EQEXIN, CSTM, 'RBGLOBAL///4/ $ to VZCPLOT ,,BGPDT,EQZX_N,CSTM,, ,/RBCr.OSAL///4/ S (i.e., add two commas after CSTM.)

4. Lee, Sang H., ed.: Preliminary MSC/NASTRAN Handbook for References Nonlinear Analysis. MacNeal-Schwendler Corp., 1991.

1. Anon.: MSC/NASTRAN User's ManuaI--MSC/NASTRAN Ver- sion 66. MacNeai-Schwendler Corp., 1988.

5. Lawrence, Charles; Aiello, Robert A.; Ernst, Michael A.; and 2. Joseph, Jerrard A., ed.: MSC/NASTRANApplication Manual-- McGee, Oliver G.: A NASTRAN Primer for the Analysis of MSC/NASTRAN Version 66A. MacNeal-Schwendler Corp., Rotating Flexible Blades. NASA TM-89861, 1987.

1991.

6. McGee, Oliver G.: Finite Element Analysis of Flexible, Rotat- 3. Mack, Wayne V., ed.: MSC/DYNA Theoretical Manual--MSC/ DYNA Version 1. MacNeal-Schwendler Corp., 1989. ing Blades. NASA TM-89906, 1987.

Form Approved REPORT DOCUMENTATION PAGE OMB No.0704-0188 Publicreporting burden forthis colleoticn of information is estimatedto average1 hour per response, includingthe time for revlew4ng instructions, searchinge0dsting data sources, gathetlngand maintainingthedata needed,and completing and reviewing the collectionof information. Send comments regardingthisburdenestimateor any otheraspectof this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, D_'ectorete for Information Operations and Reports,1215 Jeff_son DavisHighway,Suite1204, Arlington, 'CA22202-4302, and to the Officeof Managementand Budget, PaperworkReduction Project (0704-0188), Washington, DC 20503.

1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED June 1997 Technical Memorandum 4. TITLE AND SUBTITLE 5. FUNDING NUMBERS Rotating Shake Test and Modal Analysis of a Model Helicopter Rotor Blade WU 505-63-36-02 A5008 6. AUTHOR(S) W. Keats Wilkie, Paul H. Mirick, and Chester W. Langston 7. PERFORMING ORGANIZATION NAME(S) ANDADDRESS{ES) 8. PERFORMING ORGANIZATION REPORT NUMBER NASA Langley Research Center Vehicle Technology Center Hampton, VA 23681-0001 U.S. Army Research Laboratory L-17352 NASA Langley Research Center Hampton, VA 23681-0001 10. SPONSORING/MONITORING 9. SPONSORING/MONITORING AGENCY NAME(S) ANDADDRESS(ES) AGENCY REPORT NUMBER National Aeronautics and Space Administration Washington, DC 20546-0001 NASA TM-4760 and U.S. Army Research Laboratory ARL-TR-1389 Adelphi, MD 20783-1145 11. SUPPLEMENTARY NOTES Wilkie, Mirick, and Langston: Vehicle Technology Center, ARL, Langley Research Center, Hampton, VA.

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Unclassified-Unlimited Subject Category 05 Availability: NASA CASI (301) 621-0390 13. ABSTRACT (Maximum 200 words) Rotating blade frequencies for a model generic helicopter rotor blade mounted on an articulated hub were experi- mentally determined. Testing was conducted using the Aeroetastic Rotor Experimental System (ARES) testhed in the Helicopter Hover Facility (HHF) at Langley Research Center. The measured data were compared to pretest ana- lytical predictions of the rotating blade frequencies made using the MSC/NASTRAN finite-element computer code. The MSC/NASTRAN solution sequences used to analyze the model were modified to account for differential stiffening effects caused by the centrifugal force acting on the blade and rotating system dynamic effects. The cor- relation of the MSC/NASTRAN-derived frequencies with the experimental data is, in general, very good although discrepancies in the blade torsional frequency trends and magnitudes were observed. The procedures necessary to perform a rotating system modal analysis of a helicopter rotor blade with MSC/NASTRAN are outlined, and com- plete sample data deck listings are provided.

14. SUBJECT TERMS 15. NUMBER OF PAGES Helicopters; Model rotor testing; Rotor analysis; NASTRAN; Structural dynamics 16. PRICE CODE A03 17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF REPORT OF THIS PAGE OF ABSTRACT OF ABSTRACT Unclassified Unclassified Unclassified NSN 7540-0%280-5500 Standard Form 298 (Rev. 2-89) Prescribedby ANSI Std. 7--39-18 298-102