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Helicopter vibration reduction in forward flight using blade integral twist actuation

  • Sang Joon Shin
  • Carlos E. S. Cesnik
Article

Abstract

An analytical framework has been developed to examine integrally-twisted helicopter blades and their aeroelastic behavior during forward flight. This is accomplished by modifying an existing multi-body dynamics code, DYMORE, with active material constitutive relations. An integral twist-actuated rotor blade was designed within this framework. A four-bladed fully-articulated active rotor system was built and tested to demonstrate the present concept in forward flight. The impact of integral twist actuation on fixed and rotating system loads during forward flight is evaluated by the proposed analysis. While discrepancies are found in the amplitude of the loads under actuation, the predicted trend of load variation with respect to its control phase correlates well with the experiments. Factors affecting the accuracy of the present analysis against the experimental results are described in detail. Based on the present discussion, an improved analysis is planned to be conducted.

Key Words

Helicopter Vibration Integral Twist-actuated Blades Geometrcially-exact Beam Formulation Multi-body Dynamics Individual Blade Control 

Nomenclature

a

Global frame attached to the hub

b

Undeformed reference frame of the blade

B

Deformed reference frame of the blade

Cba

Transformation matrix froma tob

CBa

Transformation matrix froma toB

CT

Non-dimensionalized rotor thrust coefficient

F1

Beam axial force

F1(a)

actuation component of beam axial force

FB

Internal force column vector in theB frame

FB(a)

Actuation column vector for internal force

g1(s),g2(s),g3(s)

Warping due to axial strain (1) and bending strains (2, 3)

G(s)

Torsion related warping

HB

Angular momentum vector in theB frame

k

Sectional elastic curvature vector

K

Total kinetic energy of the blade

Kij

Beam stiffness components

M1, M2, M3

Beam torsional moment (1) and bending moments (2, 3)

M1(a), M2(a), M3(a)

Actuation component of beam torsional moment (1) and bending moments (2, 3)

MB

Internal moment column vector in theB frame

MB(a)

Actuation column vector for internal moment

N

Number of blades

Nact

Sine dwell actuation frequency in/rev

rn

Projection of the position vectorr to the vectorn normal to the blade surface

PB

Linear momentum vector in the B frame

S

Coordinate with respect to the middle surface point along the blade

u1, u2, u3

Displacement field of the cross-section reference point in the blade

uo

Position vector of a point on the beam reference line before deformation

u

Position vector of a point on the beam reference line after deformation

U

Total potential energy of the blade

V1, V2, V3

Displacement of an arbitrary point in the blade

V1(a) (s)

Actuation to the out-of-plane displacement

V(t)

High voltage applied to integral actuators

Vamplitude

Amplitude of high voltage signal in volts

VB

Linear velocity column vector in theB frame

W

External loads, such as aerodynamic force

y, z

Cartesian coordinates with respect to the reference point in the cross section

αs

Rotor shaft tilt angle

Γ11

Beam axial strain at the reference point

k2, k2, k3

Beam curvature due to torsion (1), and bending (2, 3) at the reference point

γB,KB

Components of sectional strain vector, measured in theB frame

ϕ (x)

Elastic twist angle of the cross section

ϕblade i

Phase difference for eachi-th blade

ϕincontrol phase

Control phase for each azimuthal division

μ

Advance ratio

ω

Sectional angular velocity vector

ωinactuation

Sine dwell actuation frequency in rad/sec

Ω

Rotor rotational frequency

ΩB

Angular velocity column vector in theB frame

ψ

Blade azimuth angle

(′), () °

Derivative with respect to time

() ′

Derivative with respect to the beam spanwise coordinate,x 1

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Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2007

Authors and Affiliations

  1. 1.School of Mechanical and Aerospace EngineeringSeoul National UniversitySeoulKorea
  2. 2.Department of Aersopace EngineeringUniversity of MichiganAnn ArborUSA

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