lecture slides: lecture mechanics
DESCRIPTION
The lecture slides of lecture Mechanics of the Modelling Course of Industrial Design of the TU DelftTRANSCRIPT
1Challenge the future
P-L-3
Mechanics
The Modelling Team Department of Design Engineering
Faculty of Industrial Design EngineeringDelft University of Technology
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Contents
• Systems
• Key components of Mechanical Systems
• Spring
• Damper
• Mass-Spring-Damper Systems
• Applications in product design
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Aim
KnowledgeKnowledge
InsightInsight
CommunicationCommunication
To develop a basic understanding of the properties of mass-spring-damper system and its applications in product designs
To demonstrate that such a system might be modeled so as to provide useful data for designs
To communicate with experts in their professional languages
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2
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Systems
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Repetition: What is a system?
System consists of a set of interacting or interdependent system components (or sub-systems)
System
-Structure & interconnectivity-Boundary-Input & Output-Surroundings
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Example of a system
Tyre
Saddle
Tyre
…
Courtesy of http://www.cycle9.com/carrboro-chapel-hill-store/batavus-bicycles-lets-go-dutch/Courtesy of http://www.batavus.nl
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System response
Boundary
Inputs Outputs
Courtesy of http://www.batavus.nlCourtesy of http://reviews.mtbr.com/blog/tag/Cycle-Solutions/
Velocity in the vertical direction
Displacement in the vertical direction
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System response
Boundary
Inputs Outputs
Courtesy of http://www.batavus.nlCourtesy of http://www.utilitycycling.org/2009/08/cycling-services/
Velocity in the vertical direction
Displacement in the vertical direction
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System response
Boundary
Inputs Outputs
Courtesy of http://www.batavus.nlCourtesy of http://www.utilitycycling.org/2009/08/cycling-services/
Velocity in the vertical direction
Displacement in the vertical direction
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What are components of the bike’s model?
Tyre
Saddle
Tyre
Courtesy of http://www.batavus.nl
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Components - Spring
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Component - Spring
Ref. http://en.wikipedia.org/wiki/Spring_(device)
A spring is an elastic object used to store mechanical energy
Spring
2 m
eter
s 40
0 N
2 m
eter
s 40
0 N
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Model a spring
Courtesy of http://en.wikipedia.org/wiki/Spring_(device)
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Rehearsal: Bungee jumping
Courtesy of http://www.youtube.com/watch?v=sriUfHuHSXY
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Components
Spring
Human.
Air.
► Earth Bungee jumping system
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Cause-effect
Spring
Inertia force Stretchthe spring
Pull the person back
GravityMass of the person Air friction
Slow down the motion
Effect
Cause
0 =0
101
000
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Modelling using Maple®
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The solution
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The solution
Displacement
Acceleration
Velocity
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The solution
The amplitude is getting smaller,
Why?
Displacement
Acceleration
Velocity
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Is it different? - Trampoline
Courtesy of http://www.youtube.com/watch?v=pSazagYBCM8
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Components
Spring
Human.
Air.
► Earth Trampoline system
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Cause-effect
Spring
Inertia force Stretchthe spring
Push the person back
GravityMass of the person Air friction
Slow down the motion
Effect
Cause
0 0 0 =0
101
000
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Modelling using Maple®
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The solution
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The solution
Displacement
Acceleration
Velocity
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The solutionThe amplitude is also getting smaller. The
same reason?
SpeedDisplacement Acceleration
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Bungee jumping vs Trampoline
0 =0
0 0 0 =0
Bungee jumping
Trampoline
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Components - Damper
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Component - Damper
A damping elements resists relative velocity across them
Damper
Courtesy of http://en.wikipedia.org/wiki/Shock_absorber
Shock absorber with internal reservoir.
The components are:A - rod,B - the piston with seals,C - the cylinder,D - oil reservoir,E - floating piston,F - air chamber.
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Model a damper
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Case study: The slow closing toilet seat
Courtesy of http://www.youtube.com/watch?v=tBK1rewI8vQ
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System components
The toilet seat
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Cause-effect
Damper
Inertia moment The lid goes down
Slow downthe motion
GravityMass and
geometry of the lid
Effect
Cause
/2=0
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Modelling using Maple®
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Solving the model
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The solution
/2/2
Angular displacement
Angular acceleration
Angular velocity
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The mass-spring-damper system
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The mass-spring-damper system
Courtesy of http://www.taiwan-bicycle.com.tw/Pd_Detail.asp?FKindNO=F000004&SKindNO=S000671&ItemNo=I00002896
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The mass-spring-damper system
Courtesy of http://www.taiwan-bicycle.com.tw/Pd_Detail.asp?FKindNO=F000004&SKindNO=S000671&ItemNo=I00002896
ElasticityYoung's ModulusPoisson's RatioAnisotropy
Damping Coefficient
Spring Damper
Regarding material
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The mass-spring-damper system
Courtesy http://www.airliners.net/photo/Airbus-Industrie/Airbus-A380-861/1169635/L/
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Case study: The skateboardThe movement in the vertical direction
Courtesy of http://skateboardingmagazine.com/blog/2009/02/01/the-worlds-largest-skateboard/
Designer:
Rob Dyrde
The World largest skateboard
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System components
The skateboard
Spring
DamperAir
EarthPerson
NeglectNeglect
Neglect, why?Neglect, why?
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System
Damper
Inertia force Drag themass back
Slow down the motion
SpringMass of the board
Effect
Cause
=0
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Modelling using Maple®
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Solution
Displacement
Acceleration
Velocity
The step
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DiscussionC=50
K=1000 K=100 K=10
DisplacementDisplacement
VelocityVelocity
AccelerationAcceleration
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Discussion
K=100
C=200 C=50 C=0.1
DisplacementDisplacement
VelocityVelocity
AccelerationAcceleration
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Consider human also as a spring and a damper, can we model the shock to the head?
21 1 2
1 1 1 2 12
( ) ( ) ( )( ( ) ( )) ( ) 0d x t dx t dx tm k x t x t cdt dt dt
22 1 2 2
2 1 1 2 1 2 2 22
( ) ( ) ( ) ( ) ( )( ( ) ( )) ( ) ( ( ) ( )) ( ) 0d x t dx t dx t dx t dy tm k x t x t c k x t y t cdt dt dt dt dt
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The natural frequency
2
2
( ) ( ) ( ) 0d x t dx tm c kx tdt dt
0km
2cmk
22
0 02
( ) ( )2 ( ) 0d x t dx t x tdt dt
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The damping ratio
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Resonance
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Case study: Tacoma Narrow bridge
Courtesy of http://www.youtube.com/watch?v=P0Fi1VcbpAI
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Interpret the response of a step function
Sett
ling
time
band
Mp St
eady
-sta
te
erro
r
22
0 0( ) ( )2 ( ) step
d x t dx t x t fdt dt
max
ss
ss
xAx x
22
ln
ln
A
A
21n
pt
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Interpret the response - 2Example: If we know the response of a mass-spring-damper system regarding a step function F(t), can we extract parameter c and k from the response?
From definitions
Maximum overshoot ratio
max
ss
ss
xAx x
Damping ratio
22
ln
ln
A
A
Natural frequency21
n
pt
Maximum overshoot ratio
max
13.28
1.3723
ss
p
xt
x
Response
2.686A
Damping ratio0.3
Natural frequency1n
0km
2
cmk
Suppose m=1kg
1 kg/m, 0.6 Ns/mk c
m
k
c
x(t)
F(t)
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Industrial applications
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The pogo-stick
Courtesy of http://connect.in.com/pogo/photos-1-1-1-9ed7a7cecf4cb85de07b7f05697bfe43.html
Question?Where is
the damper?
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The suspension systems (ref/auto.howstuffworks.com/)
Courtesy of http://auto.howstuffworks.com/car-suspension4.htmAI
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The door closer (ref. /www.usbuildersupply.com)
Courtesy of http://www.usbuildersupply.com/index.php/hardware-basics/door-closer-overview/
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Thank You!