jwuivi^rti w cv ^,,^Z & TECHNOLOGY * No 79B - 2010 I N F L U E N C E O F R U D D E R A E R O D Y N A M I C L O A D ON T H E STABILITY O F F L I G H T M E C H A N I C S A N D T H E STABILITY O F C O N T R O L H Y D R A U L I C CIRCUIT ANH H U ' N G CUA LU'C Kl ll' D Q N G T R L N CANH LAl H U ' N G T I O N D I N H B A Y V A O N D I N H M A C H fl lUY LUC DILU KHILN Hoang Thi Bich Ngoc, Nguyen Manh Hung Hcmoi I'll ivers ity ofScience and Techindogy ABSTRACT The paper shows the influence of the aerodynamic load on the rudder of airplane on the stability of flight mechanics and the stability of rudder control hydraulic system Based on solving differential motion equations of flight mechanics and solving transfer functions of control hydraulic system, the report presents results about influences of the variation of rudder control angle and the variation of airplane velocity on the airplane stability and the rudder control system stability The aerodynamic force on rudder having control winglet turned at different angles is calculated by built program using a tridimensional singularity method The transfer equation of hydraulic circuit controlling the rudder is written for a servo-mechanism of elements as servo-valve and power cylinder engine transmitting translational movement to rotational movement of rudder pivot with crank The differential equation system of flight mechanics is solved and programmed by small disturbance method in which considered angle variations of control areas TOM TAT Bdi bdo tnnh bay anh hwdng Iwc ddng tdc ddng len cdnh Idi hwdng cua mdy bay ddi vdi sw 6n dmh bay vd mach thuy Iwc diiu khiin cdnh Idi hwdng Tren ca sd gidi phwang trinh vi phdn chuyin dong ca hoc bay vd phwang tnnh ham truyin mach thuy Iwc diiu khiin, bdo cdo trinh bdy kit qud danh gid anh hwdng cua sw thay ddi gdc diiu khiin cdnh lai hwdng vd van tic bay tdi in dinh cua may bay vd he thing diiu khiin thuy Iwc cdnh Idi Lwc ddng tdc dung len cdnh lai hwdng cd cdnh diiu khiin quay dwgc a cdc gdc khdc dwgc lap tnnh tinh todn bdng phwang phdp ki di 3D Phwang tnnh ham truyin ciia mach thuy Iwc diiu khiin cdnh Idi hwdng^ dwgc viit ddi vdi mach trg dong gdm cdc phin tir Id van phdn phii vd ddng ca piston truyin chuyin ddng thing din true quay canh hwdng nhd ca ciu tay quay He phwang trinh vi phdn chuyin ddng ca hoc bay cua mdy bay dwgc lap tnnh giai theo phwang phdp nhiiu ddng nhd xet din sw thay ddi gdc quay ciia cdc mat diiu khiin rudder; Calculating the transfer function of control hydraulic circuit for investigation system stability with different aerodynamic Calculating the flight stability with the control I INTRODUCTION For an airplane with the rudder controlled by a hydraulic system, aerodynamic forces on the rudder are basic to calculating the hydrostatics of control circuit The hydrodynamics of the circuit is investigated through transfer function of the system Based on the built transfer function, we can study the influence of aerodynamic force variations on stability quality of control hydraulic system rudder of the forces; rudder II RESOLUTION 2.1 Calculation of aerodynamic force on the rudder In the straight movement, the rudder is symmetric along movement direction, so the lift is equal to zero When carrying out a change of direction, the rudder control part turns a certain angle that leads to the appearance of lift (pushing it to the left or to the right) In this case, the aerodynamic force is determined for wings having turned winglet The lift is produced by rudder angle, but the incidence being null In this report Under the view of flight mechanics, the aerodynamic force acting on the rudder changes the flight direction of airplane, therefore, this one concerns the lateral stability of airplane For evaluating the influence of rudder aerodynamic force on the stability of control circuit and the stability of flight, it is necessary to solve three problems: Calculating aerodynamic load on the 159 .IOtlKNALOKS( ll.N( I, &TECIINGi.»jv,i ^ MU ,, I'iguie 2.1 shows the grid of trapezium wing having root and tip chords of 4.9m and 2.1m; rudder height is 5,4m; pivot distance is 30% of chord; control angle is 10" Ihe variation of lift coefficients with control angles is shown in figure 2.2 at free Mach numbers M=0.1; M 0.3; VI 0.5 With these numerical results, we can see that the aerodynamic lorce on thc rudder increases after thc control angle At small control angles, thc relation between lift coefficient and control angle is quasi linear At higher speeds, thc aerodynamic force more increases acrodv namic rmccs arc calculated by a 31) sin!J,iilaritv' method (promammcd by iisinsj, Fortran), Singiilaritv elements of sinircc (slicngth rr, ), rinti vorlcx (strength I", ), and horseshoe vorlcx (slieiiL^lh y ), arc used [I] The index "i" is taken alonjj, thc profile contour, and "j'" along thc span Ihe induced vclocitv of sinmilarilies tor a panel n is determined bv: = L + r-(.V) 4-1 (/) + r.' (2.1) where I ' ' " ' , ]"'•0) I " ' ' are velocities induced from source, ring vorlcx and horseshoe vortex • • ' •(.V) V r I.Vl I Cp PRESURE COEFCENT, Naca2418.1 = -IO* Mtfp \: yr;^v=y^-|-,rT„; ,-\ (D^y, j y /-I 1-1 (/ ,:(/.! ^ \ ^ , - I / (-1 ,2.2) ; ' The boundai^ condition on thc wall al a panel a| Incidence -10 Contro' angie IC' n is wriuen: ' II /i,,n = r " - ' ) j i =-V /i (vr' + y ; -< for ;/ = U ( A x \ / ) ] —»— Present cjiculation - E x p e r i n e n t j l result (2.3) The Joukovski condition at the trailing edge is taken on the bisector just behind the trailing edge (J.6 O.S \C Cp PRESURE COEFiCIENT, Naca2413,1 = 6" 0=10= as a slip condition: I „./!/.,„ = for /;/ = I H- ,V with m is the index along the span at trailing edge (TE) The resolution of the equation (2.1) has been presented in [1] and [2] N3ca0012 Ct/cn-1) 1:1 311% bl Incidence: 5' Control ang> I O 1l)(1r() Present calculation ExperinentJl result TE "o 0.2 O.-l 0.6 xC ij Comparison of Fig 2.3 Pressure coefficient resent calculation and experiment f3] Fig 2.1 Grid of trapezium wing C.l = 10" Lift coetdcleni In figure 2.3 are presented comparisons of nuinerical results of the established program for calculation of 3D aerodynamic forces of wing having control winglet and those of experiments [3] (sub-figure a: Naca 2412, incidence: -10°, control angle: 10°; sub-figure b: Naca 2412, incidence: 6°, control angle: 10°) Figure 2.4 shows results calculated for a rectangular wing having the ratio b/c=4 (span and chord), profile Naca 2312, M=0.5 Three-dimensional distribution of pressure coefficient Cp of present calculation is compared O 051- 10 Fig 2.2 Ci 12 control angle 160 JOURNAL OF SCIENCE & TECHNOLOGY * No 79B - 2010 with one calculated by CFX software, and Cp at demi-span section is compared between three methods (present calculation, CFX software and Fluent software) function of system is determined from motion equations of these components [4, 5] Motion ecjuaticm of the rudder: Pressure coefficient 3D Naca 2312 b/c=4 dt ' ' F.I, (2.1) where: J is thc inertia moment of rudder; F' is the force transmitted from power ram to rudder; F is the aerodynamic load on rudder; f and f, are cranks corresponding to F' and F Assume that the aerodynamic load and the rudder control angle d have a quasi-linear relation, F = K,.S Span Governing control.^ Da«l-SPAN SECTION Naca2312,AOA=0deg.M=0 Servo valve ' Present cai 5D Sing CFX Fluent Fig 2.5 Control hydraulic system Motion equation of the power ram: 92 c- O.S ce d-y m—^ dt' = Pressure coefficient 3D Naca 2312 b/c=4 dy p.F,^.-b.— dt (2.2) F^ where, m is the mass of power piston and power ram; F,^, is the effective area of piston; b is the viscous friction coefficient; F is the force on power ram, F^ = F^ ; with a small control angle, y = l^ S CFX at OS Equation of fluid flow rate into servo valve: \3 Span n-K r ^ r n-F ^^ ^ ^° ^P dt Fig 2.4 3D distribution ofCp and Cp at demispan section Comparison between present resuhs and CFX Fluent results (2.3) 2E dt where, K^,^ is the rate coefficient depending on the displacement x; K^^^ is the rate coefficient 2.2 Analysis of control hydraulic system depending on the pressure; V^ is the initial volume of power cylinder chamber; E is the elastic module of fluid; p is the pressure of fluid The control hydraulic system of rudder consists of servo valve and power cylinder transmitting translational movement to rotational one of thc rudder The transfer 161