landing gear design analysis - royal aeronautical society3) david... · • landing gear,...
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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
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
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
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
=
⋅⋅⋅⋅⋅=
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
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)
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
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