Landing Gear Design Analysis

David Sandells Lecturer in Aerospace Engineering

Mission Statement 2010-2015

“We aspire to be a dynamic, global, enterprising university. We will work in partnership with external organisations through our research

and engage our students as partners in a community of learning.”

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

University Profile

The Guardian League Table

Key Facts

Origins rooted in industry - Founded 1843, well-known and highly respected as Lanchester Poly from 1970s, became Coventry University 1992 as one of the ‘modern universities’

Modern City Centre campus on single 33-acre site London campus opened 2010 International Offices in China, Nigeria, Pakistan and Kenya Over 17,000 students (15% International) Approximately 2,500 staff New £55m Engineering & Computing building opened September 2012 World-leading and internationally excellent research in every Faculty - 7 out of 16

areas receiving the highest rating in overall quality profile in the RAE 2008 A Top 25 UK Higher Education Institution (Working with business and supporting the

economy). £11.4m HEIF5 Investment 2011-2015. Entrepreneurial University of the Year (Times Higher

Education Awards, November 2011) Coventry University risen to 46th overall

(Sunday Times University Guide 2014, September 2013)

Key Facts

• Modern City Centre campus on single 33-acre site • Over 17,000 students (15% International) • Approx. 2,500 staff • World-leading and internationally excellent research in every

Faculty - 7 out of 16 areas receiving the highest rating in overall quality profile in the RAE 2008

• A Top 25 UK Higher Education Institution (Working with business and supporting the economy). £11.4m HEIF5 Investment 2011-2015.

World Class Facilities

• £55m Engineering and Computing building (2012) • £32m Students “Hub” (2011) • 20-acre £20m Technology Park (2003)

– Innovation Centre (for new enterprises), Design Cluster, Enterprise Centre and state-of-the-art conference facilities

• Bugatti Building (housing digital/modeling labs) opened (2002), sports complex (2004)

• £16m Library (2000)

The Faculty of Engineering & Computing

300 Academic Staff 3500 Undergraduate Students 800 Postgraduate Students (MSc/MBA) 150 Research Students (PhD/MPhil/MSc) Activity Led Learning (ALL) Applied research - relevant to today’s challenges Providing real business impact Mitigating risk through technical solutions Delivering value for money Empowerment through expert advice Creating and maintaining effective and rewarding relationships

“The students we educate and the companies we serve demand the same: responsive expertise delivered when it is required and followed up by advice

and value for money support.”

Our Aerospace Teaching

Undergraduate • Aerospace Systems Engineering

– Royal Aeronautical Society (CEng) – Overall Satisfaction 97%

• Aerospace Technology – Royal Aeronautical Society (“Exemplar” IEng) – Overall Satisfaction 89%

Postgraduate • Aerospace Engineering • Aerospace Manufacturing Engineering

Key Research Activities

• COGENT Research centre – World-leading applied research centre – Dedicated to analysis and development of sensing-based

sociotechnical systems. – Dual focus: robust, deployable pervasive sensing systems for

real-life applications at scale; and effective packages for empowering users to maximise the benefits of those systems.

– HEAT - Highly Efficient Autonomous Thermocouple system • Wireless temperature sensing and health monitoring • Partnered with Vibro-Meter UK

Capabilities

Disciplines Structural Engineering Software Engineering Rehabilitation Engineering Motorsport Engineering Mechanical Engineering Mathematics Materials Engineering Electronics Engineering Electrical Engineering Digital Security & Forensics Computer Networking Computer Hardware &

Software Engineering Communications Engineering Control Engineering Civil Engineering &

Architecture Automotive Engineering Aerospace Engineering

Application Sectors Transport & Logistics Manufacturing Health Finance Environment Energy Digital Security Digital Media Defence ICT Built Environment Automotive Aerospace

Technologies Vehicle Structural

Optimisation Stress Analysis Rapid Prototyping Mobile Applications Low Carbon Vehicle

Technologies Games Technology Digital Forensics Control Systems Computer Visualisation Composite Materials

Multidisciplinary Capabilities Product Design &

Engineering Metrology Lean Manufacturing Design & Ergonomics Sustainability Supply Chain Management Simulation & Modelling Marketing Knowledge Management Business Management

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

• Vary 𝜑 until 𝑑 = 𝑙

• We need a function: 𝑑(𝜑)

• Find 𝜑 where: 𝑑 𝜑 − 𝑙 = 0

θ 𝑑

𝑙

𝜑

Finding positions of joints

Y How do we find the position of J2 relative to the origin.

J2

Given that the mechanism rotates. Whilst avoiding trigonometry!

Vector Representation of Positions

X

Y

32

Frame 1

X

Y Frame 2

−

=

100001004010

6001

12T 6−4

Translation

Rotations

1023

−

=

⋅

−

=

102

9

1023

100001004010

6001

1FPt

Coordinates of point relative to Frame 1

Vector Representation of Positions

X

Y Frame 1

𝑇12

( ) ( )( ) ( )

−

−

=

1000010040cossin

60sincos

12

θθθθ

T

( ) ( )( ) ( )

=

⋅

−

−

10

1023

1000010040cossin

60sincosyx

θθθθ

Rotation about Z

Vector Representation of Positions

X

Y Frame 1

𝑇12

( ) ( )( ) ( )

=

⋅

−

−

⋅

−

10

1023

1000010000cossin00sincos

100001004010

6001yx

θθθθ

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

1023

Transformation Matrices

• Homogeneous Matrices representation

( )

=

1000100010001

,,zyx

zyxTrl

( ) ( ) ( )( ) ( )

−

=

10000cossin00sincos00001

θθθθ

θXR

( )

( ) ( )

( ) ( )

−

=

10000cos0sin00100sin0cos

θθ

θθ

θYR

( )

( ) ( )( ) ( )

−

=

1000010000cossin00sincos

θθθθ

θZR

Transform inversions

• We can go the other way by inverting the matrix (M-1) :-

( ) ( )( ) ( )

−

−

=

1000010040cossin

60sincos

12

θθθθ

T

( ) ( )( ) ( )

−

−=

1000010040cossin

60sincos1

21

θθθθ

T

Goes from frame 1 to frame 2

Inverted - Goes from frame 2 to frame 1

F1

F0 F2

F3 F4

F1

F0 F2

F3 F4

𝑇17 = 𝑇𝑇𝑙(0,−𝑙𝑙,0)

𝑇01(𝜃) = 𝑅𝑍(𝜃)

𝑇34 = 𝑇𝑇𝑙(−𝑙𝑙,0,0)

𝑇23(𝜑) = 𝑅𝑍(𝜑)

𝑇02 = 𝑇𝑇𝑙(𝑙𝑙𝑥, 𝑙𝑙𝑦 , 0)

Position of F4 relative to F7

( )ϕθϕθ

,

1000

)()(

11

1 4

3423020117

7

74

74

74

fTTTTTz

yx

FF

=

⋅⋅⋅⋅⋅=

KINEMATIC CALCULATIONS IN SMATH – SEE EXAMPLE FILE

Walkthrough

LANDING LOADS

V : Vertical Decent Velocity

m : Mass of aircraft

2

21 vmKE ⋅=

Ss : Shock Compression

ST : Tyre Compression

( )TS SSgmPE +⋅⋅=∆

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(𝑣𝑣𝑙)

Shock Absorber Modelling

• Air Springs – polytrophic process 𝑃𝑃𝑛 = 𝐶 𝑃𝑢𝑇𝑣 𝑔𝑔𝑝: 𝑝 = 𝑙.35

𝑀𝑀𝑀𝑣𝑑: 𝑝 = 𝑙.𝑙 (typical)

• Dampers – Fluid flow through an orifice

– ∆𝑃 = 12∙𝑐𝑐2

𝜌 𝑣2

• Leaf spring – Cantilever bending

– 𝑐2𝑣𝑐𝑥2

= 𝐵𝐵(𝑥)𝐸∙𝐼(𝑥)

𝑣 = ∬𝐵𝐵(𝑥)𝐸∙𝐼(𝑥)

𝑑𝑀 𝜎 = 𝐵𝐵(𝑥)𝐼 𝑥

𝑡2

• Springs, Bungees, Tyres

– Linear approximation or Lookup table

LANDING LOAD SIMULATIONS

Modelling the response

• An approximation fixed time step model:-

• Start at the point of touchdown – Position = 0 – Vertical Speed = Vertical Sink Speed – Deceleration = 𝐹

𝐵

• 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)

LANDING LOAD SIMULATIONS IN SMATH – SEE EXAMPLE FILE

Walkthrough

Coventry University Courses

• Next Courses 7-17th April 2014 – 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

Stress Courses: • Fundamental Stress Analysis • Introduction to the Finite Element Method • Composite Material Stress Analysis

Focus on free/open source or inexpensive software