Landing Gear Design Analysis David Sandells Lecturer in Aerospace Engineering
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David Sandells (MEng, CEng (MIET) Lecturer in aircraft system design (undergraduate & postgraduate). Landing gear, hydraulics, electrical systems, structural design and industrial project management & sustainable aviation. Industry experience (Chief, Principal & Systems Engineer). 787 Landing Gear valves and uplocks Merlin Electrical primary flight actuation system Fuel systems, hydro-mechanical & electro-mechanical actuation systems Patents in electrical thrust reverser design and actuator design. Aviation enthusiast BGA gliding instructor, NPPL (SLMG), MGIR
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Today s talk Explaination of typical landing gear calculations. Demonstration using SMath software tool Preliminary aircraft design stage Focus on Kinematic Analysis Landing loads
SMath Software Maths software problems: Cannot read equations easily Unit conversions Results rather than method displayed Hard to add comments Printing in a reviewable format SMath Freely available www.smathstudio.com Paper interface Handles Units No affiliation with Coventry University Use at own risk
KINEMATICS
Kinematics Analysis of Mechanism Movement
Finding Mechanism Position φ d l Vary φ until d = l We need a function: d(φ) Find φ where: d φ l =
Finding positions of joints Y How do we find the position of J2 relative to the origin. Given that the mechanism rotates. Whilst avoiding trigonometry! J2
Vector Representation of Positions X Y 3 2 Frame X Y Frame 2 = 4 6 2 T 6 4 Translation Rotations 2 3 = = 2 9 2 3 4 6 Pt F Coordinates of point relative to Frame
Vector Representation of Positions X Y Frame T 2 ( ) ( ) ( ) ( ) = 4 cos sin 6 sin cos 2 T ( ) ( ) ( ) ( ) = 2 3 4 cos sin 6 sin cos y x Rotation about Z
Vector Representation of Positions X Y Frame T 2 ( ) ( ) ( ) ( ) = 2 3 cos sin sin cos 4 6 y x Order is important Translate Rotate Pt
Vector Representation of Positions X Y Z Can translate in x, y and z directions Can rotate around x, y and z axis We can use a 4x4 matrix to define these transforms 2 3
Transformation Matrices Homogeneous Matrices representation ( ) =,, z y x z y x Trl ( ) ( ) ( ) ( ) ( ) = cos sin sin cos R X ( ) ( ) ( ) ( ) ( ) = cos sin sin cos R Y ( ) ( ) ( ) ( ) ( ) = cos sin sin cos R Z
Transform inversions We can go the other way by inverting the matrix (M - ) :- T 2 = cos sin ( ) sin( ) ( ) cos( ) 6 4 Goes from frame to frame 2 T 2 = cos sin ( ) sin( ) ( ) cos( ) 6 4 Inverted - Goes from frame 2 to frame
F F F4 F3 F2
F F F4 F3 F2 T 2 = TTT(ll x, ll y, ) T 23 (φ) = R Z (φ) T 34 = TTT( ll,,) T () = R Z () Position of F4 relative to F7 T 7 = TTT(, ll,) x74 y 74 = T2 T23( ϕ) T34 z 74 T7 T( ) F 7 F 4 = f (, ϕ )
Walkthrough KINEMATIC CALCULATIONS IN SMATH SEE EXAMPLE FILE
LANDING LOADS
m : Mass of aircraft V : Vertical Decent Velocity KE = 2 m v 2
( ) PE = m g S S + S T S s : Shock Compression S T : Tyre Compression
Shock Absorber Modelling Given component characteristics we can predict landing gear response. Most gear have a static and dynamic response Spring F(pppp) Damper F(vvv)
Shock Absorber Modelling Air Springs polytrophic process PP n = C Puuu ggg: n =.35 MMMMM: n =. (typical) Dampers Fluid flow through an orifice P = 2 cc2 ρ v2 Leaf spring Cantilever bending d2 v = BB(x) dx 2 E I(x) v = BB(x) E I(x) dd σ = BB(x) I x Springs, Bungees, Tyres Linear approximation or Lookup table t 2
LANDING LOAD SIMULATIONS
Modelling the response An approximation fixed time step model:- Start at the point of touchdown Position = Vertical Speed = Vertical Sink Speed Deceleration = F M Calculate force from position & vertical speed Calculate deceleration from the force Move forward a time-step Calculate new vertical speed (deceleration over time-step) Calculate position (velocity over time-step)
Walkthrough LANDING LOAD SIMULATIONS IN SMATH SEE EXAMPLE FILE
Coventry University Courses Next Courses 7-7 th April 24 Look out for booking on LAA website (under training) business.ec@coventry.ac.uk Design Courses: Design for Manufacture Aerodynamics theory and practice (wind-tunnel) Aerodynamic Simulation (CFD) Flight Simulation and Performance (Simulators) Landing Gear & System Design Focus on free/open source or inexpensive software Stress Courses: Fundamental Stress Analysis Introduction to the Finite Element Method Composite Material Stress Analysis