NASTRAN SOL 146 을이용한서보공탄성해석방법론에대한연구 한국항공우주연구원백승길 / 책임연구원
AeroServoElastic Triangle Structural Dynamics FLUTTER Structural Coupling Test AeroServoElasticity Unsteady Aerodynamics AeroServoDynamic Flight Control System Dynamics
서보공탄성문제 서보공탄성 (Aeroservoelasticity) 항공기비행조종시스템과구조적진동모드의상호작용임 서보공탄성진동은다음으로구성된폐루프피드백의결과임 유연비행체 비행제어시스템 (Flight Control System, FLCS) 센서 Pitch rate gyro, Normal accelerometer, Angle-of-attack indicator Roll rate gyro, Lateral accelerometer, Angle-of sideslip indicator Yaw rate gyro, EGI 비행조종컴퓨터 (Flight Control Computer, FLCC) 조종면구동기 조종면 에일러론, 엘리베이터, 러더
전형적인 ASE 피드백 ELEVATOR PITCH CHANNEL AILERON RUDDER ROLL CHANNEL YAW CHANNEL ROLL RATE GYRO YAW RATE GYRO PITCH RATE GYRO NORMAL ACCELEROMETER ANGLE-OF-ATTACK SENSOR SIDESLIP SENSOR LATERAL ACCELEROMETER ROLL ATTITUDE INDICATOR AIRPLANE DYNAMICS
기본적인 ASE 피드백매커니즘 항공기진동모드가비행중에가진이됨 난류, 조종입력, 기타 유연한항공기가진동하는동안 FLCS 센서도같이진동함 진동하는센서신호가 FLCC에전송됨. FLCC 내의제어규칙이조종면구동기에진동운동을명령함 FLCC 는항공기강체운동을감쇠시키고있다고생각함. 강체운동과탄성운동의차이를식별할수없음 진동하는조종면이진동하는양력을발생시킴. 탄성모드진동을지속시키는작용을할수있음. 진동하는양력이탄성모드진동을지속시키면 ASE 불안정 이때, 양력은충분한크기와적절한위상을가짐
ASE Example YF-16 ASE Feedback Mechanism 6.5 Hertz Antisymmetric Wingtip Missile Pitch Mode From : Flutter Prevention Handbook : A Preliminary Collection, WL-TR-96-3111 Upward Lift Wingtip Missile Pitched Nose Up Flaperon Deflected Up Wingtip Missile Pitched Nose Down Flaperon Deflected Down Roll rate gy ro Roll rate =. Downward Lift Shape one half cy cle later
전형적 ASE 구조도 Sensor Dynamics Control Law Actuator Dynamics G : 유연항공기 Dynamics 조종면구동기장착점의변위에의한 FLCS 센서위치에서의물리량의전달함수 H : FLCS Dynamics FLCS 센서위치에서의물리량에의한조종면구동기장착점의변위의전달함수
ASE 해석방법 Nyquist Stability Criteria 개루프전달함수 (open loop transfer function) TF = δ output δ input θ δ output : actuator displacement commanded by the FLCS δ input : Unit actuator displacement Closed loop TF GH / ( 1 + GH ) 시스템이안정하기위해서 GH -1 Open Loop TF, GH 가 (-1) 에서얼마나떨어져있는지살펴봄으로써폐루프안정성을판단함. Gain Margin : 음의실수축을지날때의 GH db 1 db GH = db GH Phase Margin : GH 가단위원을지날때음의실수축과이루는각 PM -1 GH
서보공탄성관련요구도 MIL-A-8870C : 3.1.1.1 Aeroservoelastic Stability Interaction of the flight control system with the airplane structural modes shall be controlled to prevent any Aeroservoelastic instability. The stability design requirement of 3.1.1(Aeroelastic Stability) shall be met in all operational states of the flight control system (such as normal and failure states, reversionary modes, and augmentation system on and off (if off is a design condition)) and for the range of operating temperatures of the flight control system. In addition, for any single flight control system feedback loop, the airplane structural modes shall have the stability margins listed below at speeds up to V L /M L. The gain margin shall be not less than 6 db (> 6dB) And separately, the phase margin shall be not less than 60 (> 60 )
서보공탄성해석 서보공탄성해석은피치, 롤, 요우채널에대해각각수행되어야함. 피치채널해석 피치채널만개방, 롤과요우채널은연결 롤채널해석 롤채널만개방, 피치및요우채널은연결 요우채널해석 C 요우채널만개방, 피치와롤채널은연결
전체채널이 open loop 일때 GH α γ G H β ξ η γ = G α β = G a G c α β ξ η = H γ = H a H c γ ξ η = H γ = H G α β = H ag a H a G c α H c G a H c G c β = T aa T ac α T ca T cc β = T 여기서 γ = Sensor Output α = Input Control Actuator Deflection (a channel) β = Input Control Actuator Deflection (c channel) ξ = Output Control Actuator Deflection Commanded (a channel) η = Output Control Actuator Deflection Commanded (c channel) α β
부분적 open loop 일때 GH (1/2) α β γ G H ξ η γ = G ξ η = T α β η = α G a G c β η α β η ξ η = T aa T ac KT ca T ac T ac KT cc α KT ca KT cc β 여기서 γ = Sensor Output α = Input Control Actuator Deflection (open channel) β = Input Control Actuator Deflection (closed channel) ξ = Output Control Actuator Deflection Commanded (open channel) η = Output Control Actuator Deflection Commanded (closed channel)
부분적 open loop 일때 GH (2/2) α β γ G H ξ η Closed channel (β η) 전달함수 KT cc = I + T cc 1 T cc = I + H c G c 1 H c G c Open channel (α ξ) 전달함수 T aa T ac KT ca = H a G a H a G c I + H c G c 1 H c G a
Laplace 영역의 ASE 방정식 [M hh ] = Generalized mass matrix of vibration modes (N h x N h square) [C hh ] = Generalized damping matrix of vibration modes (N h x N h square) [K hh ] = Generalized stiffness matrix of vibration modes (N h x N h square) s q = Laplace variable = Dynamic pressure(=1/2rv 2 ) at the speed and altitude of interest. [Q hh (s) ] = Aerodynamic generalized force matrix - full (N h x N h square) {h} = Generalized coordinate vector of vibration modes (N h x 1 ) 항공기탄성모드 {Q hd (s)} = Control surface aerodynamic forcing function vector (N h x N d ) {M hd } = Control surface inertial forcing function vector (N h x N d ) {d} = Coordinate vector of control surface modes (N d x 1 ) 조종면모드 (Component mode synthesis 의개념 )
서보공탄성해석방법 (1/3) Laplace Domain 해석 참고문헌 : T-50 서보공탄성해석및구조연계필터설계 (2003) 강우영, 김철호, 백승길, 김영익 MSC/NASTRAN 은일반화된공력 / 강성 / 질량행렬추출에만사용 SOL 145 Run with special DMAP code 공력행렬을 Minimum State Approximation 을통해 State Space Equation 형태로변환 일반화된공력은유리함수가아니라특정주파수에대한값으로존재함. Well-known Minimum State Approximation by Karpel
서보공탄성해석방법 (2/3) Laplace Domain 해석 문제점 조종면회전모드입력을위한별도의 DMAP 코드필요. 공력행렬의 Minimum State Approximation 과정에서 Error 발생 ASE 만을위해서는, Laplace domain의방정식으로구성할필요는없음. Real part -4500 Q^Q 12-5000 Tabulated n = 4-5500 n = 6 n = 8 n = 10-6000 0 0.5 1 1.5 2 Real part 0-1000 -2000-3000 -4000 Q 22 ^Q Tabulated n = 4 n = 6 n = 8 n = 10 0 0.5 1 1.5 2 500 0 Imaginary part 0-500 Tabulated -1000 n = 4 n = 6-1500 n = 8 n = 10-2000 0 0.5 1 1.5 2 Reduced frequency (k) Imaginary part -2000 Tabulated n = 4-4000 n = 6 n = 8 n = 10-6000 0 0.5 1 1.5 2 Reduced frequency (k)
서보공탄성해석방법 (3/3) Frequency Domain 해석 MSC/NASTRAN 으로전달함수 G 계산 조종면구동기의변위에의한, FLCS 센서물리량의주파수응답함수 공력행렬의 Minimum Approximation 없음 앞서제시한부분적 open loop 때의 GH 수식이용 MSC/NASTRAN 으로전달함수 G 계산시고려사항 비정상공력을포함해야함. SOL 146 사용필요 Direct method 사용불가. Modal method가필수. 구동기의변위에대한응답해석시 : 구동장치의구조동역학적특성유지필요 대개 spring으로모델링됨 Modal Truncation에대한검토필요 Modal Augmentation Vector의사용 PARAM,RESVEC,YES
강제운동에대한주파수응답 (1/2) MSC/NASTRAN Solution MSC Nastran 2012 Dynamic Analysis User s Guide Chap 7 SPC/SPCD SPC 로변위점을구속해야함 개념적으로다소이해하기어려움. Large Mass Method 와등가한결과를줌. Large Mass Method Recommended for cases with known accelerations at a single point. Lagrange Multiplier 복잡한세팅
강제운동에대한주파수응답 (2/2) 구동장치양단에 Force 를가해주는것이직관적임 조종면상대변위는 spoint를이용하여출력가능 조종면변위에대한 FLCS 센서물리량의주파수응답함수 간접적으로계산가능 Force vs. 조종면변위의 FRF Force vs. FLCS 센서물리량의 FRF f f NASTRAN formulation 상에서는결국 constrained force 로구현 Free (f-set), Constrained (s-set) ω 2 M ff M fs M sf M ss + iω B ff B fs B sf B ss + K ff K fs K sf K ss U f U s = 0 q s ω 2 M ff + iωb ff + K ff U f = ω 2 M fs + iωb fs + K fs U s
Sample Example 모델설명 MSC/NASTRAN Aeroelastic User s Guide 바로적용가능한예제는없음. 8.13 Aeroservoelastic Stability Analysis of a Missile (Example HA145J) 응용 Right half model 조종면은 Flipper로표시된부분임. 절점 4와 5 사이에 rate gyro가있음 절점 45 절점 45의회전 (R2) 의속도가 rate gyro가측정하는 pitch rate가됨. 조종면회전각 (δ) 은절점 24와절점 12의 pitch rotation (R2) 의차이가됨. 절점 1~11, 45 Plunge 와 Pitch 운동만가능 절점 24 와 12 에 Spring 추가 25Hz 의조종면회전모드 45 11
고유모드해석결과 Normal Mode #1 Control Surface Rotation Frequency = 25.0 Hz Normal Mode #2 1 st Fuselage Bending Frequency = 45.2 Hz Normal Mode #3 2 nd Fuselage Bending Frequency = 128 Hz
동적공탄성응답해석 SOL 146 비정상공력계산설정 기준길이 : 30.0 in 기준공기밀도 : 1.1468 10 7 lb sec 2 /in 4 동체를중심으로좌우대칭공력조건 공력격자 조종면 : CAERO1 카드 DLM 격자 10(spanwise) X 15(chordwise) 동체 : CAERO2 카드 Slender Body 요소 (6) 비정상공력행렬데이터세트 M = 0.8, k = 0.001,0.1,0.2,0.5,1.0 동압에따른주파수응답함수 Q = 0.001, 0.01, 0.1, 1.0 등에대해계산 Q = 0.001 : 공력의영향이거의없는조건을상정
주파수응답해석 (SOL 111) (1/2) R2@12 와 R2@24 의상대적인변위필요 SPOINT 와 MPC 를통해설정가능 R 2 24 = R 2 12 S 49 R2@12, R2@24 에서 크기 1 의서로반대방향의모멘트부여 주파수응답함수 45 11 T3@23 R2@45
주파수응답해석 (SOL 111) (2/2) T0@49 FRF R2@45/T0@49 FRF R2@45/T0@49 FRF 는 R2@45 와 T0@49 를이용하여계산가능
동압에따른 FRF 변화 (SOL 146) FRF R2@45/T0@49 FRF R2@45/T0@49 FRF R2@45/T0@49
결론 서보공탄성안정성개념및서보공탄성안정성분석을위한방법론에대해설명하였음. 피치, 요우, 롤채널중특정채널에대한이득여유와위상여유를구하기위하여, 특정채널을제외한나머지채널은폐루프가되어야하는데, 이를위한수식을제시. 구동장치작동에따른비행제어센서응답의개루프전달함수를구하기위해 NASTRAN 을이용하여계산하는방법론을제시함. 항공기탄성모드의유지를위해변위입력에대한 FRF 보다는하중입력에대한 FRF 가개념적으로