An aeroelastic model suitable for the study of aeroelastic and structural dynamic effects in multirotor vehicles simulating a hybrid heavy lift vehicle was developed and applied to the study of a number of diverse problems. The analytical model developed proved capable of modeling a number of aeroelastic problems, namely: (1) isolated blade aeroelastic stability in hover and forward flight, (2) coupled rotor/fuselage aeromechanical problem in air or ground resonance, (3) tandem rotor coupled rotor/fuselage problems, and (4) the aeromechanical stability of a multirotor vehicle model representing a hybrid heavy lift airship (HHLA). The model was used to simulate the ground resonance boundaries of a three bladed hingeless rotor model, including the effect of aerodynamic loads, and the theoretical predictions compared well with experimental results. Subsequently the model was used to study the aeromechanical stability of a vehicle representing a hybrid heavy lift airship, and potential instabilities which could occur for this type of vehicle were identified. The coupling between various blade, supporting structure and rigid body modes was identified

Friedmann, P. P.

English

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SUMMARY OF ACCOMPLISHMENTS - FINAL REPORT
1981-1983
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NASA Research Grant NAG 2-116
(NASA-CR-1735U5) A STUDY OF AEROELASTIC AND
	 N84-23620
STRUCTURAL LYNAMIL ""FELTS IN MULTI-RUTUR
SYSTEMS WITH APPLICATIUh Tu HYBRID HEAVY
LIFT VBdICLES Final Report, 1981 - 1983
	 ULclas(CdLi.tOrLid ULiv.)	 12 p HC A02/hF AU1
	 G3/05 19134
A Study of Aeroelastic and Structural
Dynamic Effects in Multi-Rotor Systems with Application
to Hybrid Heavy Lift Vehicles
Peretz P. Friedmann, Professor
Mechanical, Aerospace and Nuclear Engineering'Department
School of Engineering and Applied Science
University of California
Los Angeles, California 90024
April 1984
Table of Contents
1. Introduction and Overview
2. General Mathematical Model for Coupled Rotor/Fuselage Aeromechanical
Problems in Multirotor Vehicles
3. Validation of the General Mathematical Model
4. Aeromechanical Stability Analysis of a Multirotor Vehicle Model
Representing a Hybrid Heavy Lift Airship (HHLA)
5. Concluding Remarks
References (List of Publications which have Originated or are in
Preparation under NASA NAG 2-116
Appendix A: AIAA Paper No. 84-0987-CP
I,
Summary of Accomplishments for the Period 1981-1983
Under NASA Research Grant NAG 2-116, Title: "A Study
of Aeroelastic and Structural DXnamic Effects in Multi-Rotor
Systems With Application to Hybrid Heavy Lift Vehicles"
1.	 Introduction and Overview
Under NASA Research Grant NAG 2-116, which was initially funded on May 1, 1981
and expired on December 31, 1983 an aeroelastic model suitable for the study of
aeroelastic and structural dynamic effects in multirotor vehicles simulating a
hybrid heavy lift vehicle was developed and applied to the study of a number
of diverse problems. The analytical model developed proved itself vo be quite
reliable and flexible and it is capable of modeling a number of aeroelastic
problems, namely:
(a) isolated blade aeroelastic stability in hover and forward flight
(b) coupled rotor/fuselage aeromechanical problem in air or ground resonance
(c) tandem rotor coupled rotor/fuselage problems and
(d) the aeromechanical stability of a multirotor vehicle model representing a
hybrid heavy lift airship (HHLA).
The model was used to simulate the ground resonance boundaries of a three
bladed hingeless rotor model, including the effect of aerodynamic loads, and the
theoretical predictions compared well with experimental results. Subsequently
the model was used to study the aeromechanical stability of a vehicle representing
a hybrid heavy lift airship, and potential instabilities which could occur for
this type of vehicle were identified. The coupling between various blade,
supporting structure and rigid body modes was identified. This research which
represents the first fundamental study of aeroelastic behavior of a hybrid heavy
lift vehicle in the technical literature, indicates that dynamic effects are of
considerable importance in the design of such vehicles.
1
DThe various aspects of this research have been documented in a series of
publication, Refs. 1 through Ref 4 (see list of references at the end of this
report). It should be noted that for the sake of convenience Ref. 4 is attached
as Appendix A of this report. The major thrust of this research was concentrated
on the three topics which are listed below:
1. Derivation of a general mathematical model capable of modeling coupled
rotor/fuselage aeromechanical problems in multirotor vehicles including
hybrid heavy lift airships (Ref. 1)
2. Validation of the general mathematical model by applying it to obtain the
aeromechanical stability boundaries of a three bladed hingeless rotor and
comparison of the theoretical results with experimental data (Refs. 2 and 3)
3. Fundamental study of the aeromechanical stability of a multirotor vehicle
model representing a hybrid heavy lift airship (HHLA), (Refs. 2 and 4).
The major accomplishments in these three subject areas are briefly sum-
marized in the following sections. Finally some additional information is provided
in the concluding section.
2.	 General Mathematical Model for Coupled Rotor/Fuselage Aeromechanical
Problems in Multirotor Vehicles
A detailed description of this Study can be found in REf. L. The Hybrid Heavy
Lift Airsr,ip (HHLA) or Hybrid Heavy Lift Helicopter (MILA) is a candidate vehicle
for providing heavy lift capability. Potentia'k applications of this vehicle are
for logging, construction, coast guard surveil'ance and military heavy lift.
This vehicle consists of a buoyant envelope attached to a supporting structure
to which fou,- rotor systems, taken from existing helicopters are attached. This
configuration is described in a schematic manner in Fig. 1 of Appendix A of this
report. To be able to model the structural dynamic and aeroelastic behavior of
2
wmulti-rotor system a set of governing differential equations of motion, capable
of modeling the dynamics of this hybrid aircraft was developed. The principal
goal of the first portion of this study was to develop a simple, yet accurate,
mathematical model for such a vehicle consiting of multiple rotor systems connected
by an elastic interconnecting structure, thrusters, a buoyant hull, and an
underslung weight. To study the basic aeroelastic problems which could be
encountered in an HHLA type configuration, a typical simplified model of such a
configuration, shown in Fig.2 of Appendix A was selected. The essential features
of this configuration are (Ref. 1):
(a) A flexible supporting structure, connecting the two rotors, with bending
stiffness in the vertical and horizontal plane, combined with torsional
stiffness along its longitudinal axis.
(b) Two rotor systems capable of providing lift, each having an arbitrary
number of blades, are attached rigidly to the ends of the flexible structure
(c) Two masses are attached to the ends of the flexible structure. These
masses represent helicpoter fuselages.
(d) A slung load W un is attached to the structure. This weight can move or can
be locked in a fixed position with respect to the flexible structure.
(e) An envelope providing the buoyant lift, acting at its center of pressure, is
attached to the structure
(f) Concentrated axial loads 
P
TFI' PTF2 simulate thrusters.
Using this mcdel, the dynamic equations of motion for the combined system
consisting of two rotors, flexible structure, buoyant envelope and load Wun
were derived. The derivation consists of four basic ingredients: blade equations
including the effects of support motions, equations for the flexible structure
connecting the rotors, equations representing the forces and moments introduced by
3	 ;
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the envelope and finally a representation of the dynamics of the load Wun.
A detailed derivation of these equations and the related assumptions
are described in detail in Ref. 1, and their treatment is beyond the scope of
this report. However a few important aspects of this mathematical model are
briefly described below.
The blades are modeled by a rigid, offset hinged, spring restrained equivalent
blade model; thus both articulated and hingeless rotors can be modeled. Each
blade has flap, lead-lag and torsional degrees of freedom geometrically nonlinear
terms due to moderate deflections, are included in the blade equations of motion.
Aerodynamic loads are represented by quasisteady aerodynamics, and each rotor
is assumed to .-onsist of three blades or more. The hub is assumed k.o have
pitch and roll degrees of freedom combined with two translatioril degrees of
freedom in a plane parallel to the plane of rotation. The interconnecting, flexible,
supporting structure (Fig. 2, Appendix A) has three elastic degrees of freedom.
The final equations are obtained using an ordering scheme. As stated in Section 1
these equations can be used to represent four problems, namely: (a) isolated blade
aeroelastic stability in hover or forward flight (b) aeromechanical porblems such
as air or ground resonance of a single rotor system coupled to a fuselage
(c) aeromechanical problems of tandem rotor helicopters and (d) aeromechanical
stability problems of multirotor hybrid heavy lift airships or vehicles
3.	 Validation of the General Mathematical Model
The validity of the equations of motion described in the previous section
was verified by applying them to the aeromechanical stability problem of a single
rotor helicopter in ground resonance. The theoretical results from the analytical
model were compared with high quality experimental data obtained by W. Bousman
at NASA Ames (see Section 4 of Appendix A). The analytical results were in good
4
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agreement with the experimental results indicating that the equations of motion
for the coupled rotor/vehicle system are reliable. Sample results from this
validation study (Ref. 3) are presented in Figs.5 and 6 of Appendix A. Figure 5
presents the variation of the rotor and body frequencies with rotor speed of
rotation Q. Figure 6 presents the variation of damping in the lead-lag regressing
mode, which exhibits an instability, as a function of the rotor speed Q. These
figures show that the analytical predictions are in good agreement with the
experimental results. Finally it should be noted that many additional comparisons
between theoretical and experimental data can be found in Ref. ?.
4.	 Aeromechanical Stability Analysis of a Multirotor Vehicle Model Representing
a Hybrid Heavy Lift Airship (HHLA)
A typical hybrid heavy lift vehicle is shown in Fig. 1 of Appendix A.
Clearly such a vehicle is quite different from conventional rotorcraft. It
is well known that aeroelastic and structural dynamic considerations are of
primary importance in the successful design of rotary-wing vehicles. 'The
aeroelastic and structural dynamic behavior of HHLA type vehicles has not been
considered in the technical literature to date. The main objectives of this
research grant were aimed at developing a fundamental understanding of the
aeroelastic and aeromechanical problems which can be encountered in a HHLA
type vehicle.
The nonlinear equations of motion capable of modeling the dynamics of
this coupled multi-rotor/support frame/vehicle system, described in Section
2 and Ref. 1, were used to study the aeromechanical stability of an HHLA type
vehicle. Results of this study are presented in Ref. 2 and in Ref. 4,which is
also attached as Appendix A of this report. The coupling between various blade,
supporting structure and rigid body modes is identified. Furthermore, the effects
5
of changes in buoyancy ratio (i.e., buoyant lift/total weight) on the dynamic
characteristics of the vehicle are studied. Some of the salient features of
this analysis and a concise summary of the major conclusions is also provided
in this section.
The total number of physical degrees of freedom representing an HHLA type
vehicle was 31. These consisted of 24 blade degrees of freedom, 4 rigid body
degrees of freedom and 3 elastic degrees of freedom of the supporting structure.
The details of the solution and the results are presented in Appendix A. The most
important conclusions obtained in this study were
1. The rotor cyclic lead-lag modes couple strongly with the bending mode!, and
the torsion mode of the supporting structure, as a consequence, the stability
of the lead-lag modes is sensitive to changes in stiffness (or the natural
frequencies) of the supporting structure in bending and torsion. Therefore
the natural frequencies of the supporting structure must be designed so as
to be well separated from the frequencies of the rotor lead-lag modes.
This also emphasizes the importance of mcdelling the supporting structure
with an adequate number of elastic modes.
2. The low frequency and high frequency lead-lag modes of the rotor and the
torsion mode of the supporting structure undergo a change in their basic
characteristics, as the torsional stiffness of the supporting structure
is increased from a low value to a high value.
3. The lead-lag modes of the rotor are stable only when the torsional
stiffness of the supporting structure has low or high value% for intermediate
values of the torsional stiffness one of the lead-lag modes is unstable.
4. The body pitch mode is a pure damped mode.
6
77.
5. The body roll mode is a damped oscillatory mode. However, as the buoyancy
ratio is decreased, this mode becomes unstable.
6. The stability analysis of the coupled rotor/vehicle dynamics clearly
illustrates the fundamental features of the aeroelastic stability of the
rotor, coupled rotor/support system aeromechanical stability and the vehicle
dynamic stability in longitudinal and lateral planes.
Furthermore, it should be mentioned that the analytical model developed in
this study, for the aeromechanical stability study of an HHLA type vehicle,
can be also applied to various other types of vehicles as indicated in Section 1
of this report. Finally it should be noted that the analytical model is capable
of representing not only aeroelastic and aeromechanical problems but it is also
suitable for investigating rigid boiy stability and control problems associated
with these types of vehicles.
5.	 Concluding Remarks
During the course of this research very useful analytical models were developed
which will enhance the design tools available to engineers working in the rotary-wing
field. A version of the computer programs used to generate the results was provided
to Dr. H. li;ura from NASA Ames Research Center.
During the course of this research one M.S. student (Paul Blelloch) and one
postdoctoral research scholar (Dr. C. Venkatesan) have received full or partial
financial support from the grant. Paul Blelloch's, M.S. thesis (Ref. 5), was
partially funded by the grant. Presently Mr. Blelloch is a Ph.D student, at UCLA,
working in the dynamics and controls area. Dr. Venkatesan is still associated with
UCLA. It is believed that this training of scientific personnel to supply the
manpower needs of the U.S. research establishment and helicopter industry represents
a significant additional benefit from the research which has been conducted under
the grant.
7 J
With the conclusion of the research program on "A Study of Aeroelas.tic
and Structural Dynamic Effects in Multi-Rotor System with Application to Hybrid
Heavy Lift Vehicles", it is apparent from the foregoing that the.past two and a
half years have been fruitful. In addition to the measurable productivity re-
presented by published research results, this program has helped pruvide intelectual
stimulation and educational enrichment for the graduate student and postdoctoral
scholar affiliated with the program. It is our hope that the analytical tools
developed by this research activity will influence future analysis and design
practices in the field of rotary-wing aeroelasticity and structural dynamics.
Acknowledgement
The extremely valuable advice and support of the grant monitor Dr. H. Miura
are gratefully acknowledged.
J
References (List of Publications which have originated
or are in Preparation under NASA 2-116
1. Venkatesan, C. and Friedmann, P., "Aeroelastic Effects in Multirotor Vehicles
with Application to Hybrid Heavy Lift Systems, Part I: Formulation of Equations
of Motion", Low Number NASA CR in press.
2. Venkatesan, C. and Friedmann, P., "Aeroleastic Effects in Multirotcr Vehicles,
Part II: Method of Solution and Results Illustrating Coupled Rotor/Body
Aeromechanical Stability", NASA CR report under review.
3. Friedmann, P.P. and Venkatesan, C., "Comparison of Experimental Coupled
Helicopter Rotor/Body Stability Results with a Simple Analytical Model",
Paper presented at the Integrated Techn p logy Rotor (ITR) Methodology
Workshop, !''+SA Ames Research Center, Moffett Field, California, June 20-21,
1983, (accepted for publication in the Journal of Aircraft)
4. Venkatesan, C. and Friedmann, P., "Aeromechanical Stability Analysis of a
Multirotor Vehicle Model Represerting a Hybrid Heavy Lift Airship (HHLA)",
AIAA Paper No. 84-0987-CP, presented at the 25th AIAA/ASME/ASCE/AHS
Structures, Structural Dynamics and Materials Conference, May 14-16, 1984,
Palm Springs, California.
5. Blelloch, P., "Coupled Rotor/Fuselage Aeromechanical Stability of a
Hingeless Rotor Helicopter in Hover", M.S. Thesis, University of
California, Los Angeles, Mechanical, Aerospace and Nuclear Engineering
Department, May 1984.
V
APPENDIX A: AIAA Pa Der 84-0987-CP


A study of aeroelastic and structural dynamic effects in multi-rotor systems with application to hybrid heavy lift vehicles

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