Lecture Slides: Lecture Mechanics

1Challenge the future

Mechanics

The Modelling Team Department of Design Engineering

Faculty of Industrial Design EngineeringDelft University of Technology

Contents

• Systems

• Key components of Mechanical Systems

• Spring

• Damper

• Mass-Spring-Damper Systems

• Applications in product design

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

Systems

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

Example of a system

Saddle

Courtesy of http://www.cycle9.com/carrboro-chapel-hill-store/batavus-bicycles-lets-go-dutch/Courtesy of http://www.batavus.nl

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

System response

Boundary

Inputs Outputs

Courtesy of http://www.batavus.nlCourtesy of http://www.utilitycycling.org/2009/08/cycling-services/

System response

Boundary

Inputs Outputs

Courtesy of http://www.batavus.nlCourtesy of http://www.utilitycycling.org/2009/08/cycling-services/

What are components of the bike’s model?

Saddle

Courtesy of http://www.batavus.nl

Components - Spring

Component - Spring

Ref. http://en.wikipedia.org/wiki/Spring_(device)

A spring is an elastic object used to store mechanical energy

Spring

Model a spring

Courtesy of http://en.wikipedia.org/wiki/Spring_(device)

Rehearsal: Bungee jumping

Courtesy of http://www.youtube.com/watch?v=sriUfHuHSXY

Components

Spring

Human.

► Earth Bungee jumping system

Cause-effect

Spring

Inertia force Stretchthe spring

Pull the person back

GravityMass of the person Air friction

Slow down the motion

Effect

Modelling using Maple®

The solution

Displacement

Acceleration

Velocity

The solution

The amplitude is getting smaller,

Displacement

Acceleration

Velocity

Is it different? - Trampoline

Courtesy of http://www.youtube.com/watch?v=pSazagYBCM8

Components

Spring

Human.

► Earth Trampoline system

Cause-effect

Spring

Inertia force Stretchthe spring

Push the person back

GravityMass of the person Air friction

Effect

0 0 0 =0

The solution

Displacement

Acceleration

Velocity

The solutionThe amplitude is also getting smaller. The

same reason?

SpeedDisplacement Acceleration

Bungee jumping vs Trampoline

0 0 0 =0

Bungee jumping

Trampoline

Components - Damper

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.

Model a damper

Case study: The slow closing toilet seat

Courtesy of http://www.youtube.com/watch?v=tBK1rewI8vQ

System components

The toilet seat

Cause-effect

Damper

Inertia moment The lid goes down

Slow downthe motion

GravityMass and

geometry of the lid

Effect

Solving the model

The solution

Angular displacement

Angular acceleration

Angular velocity

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

Courtesy http://www.airliners.net/photo/Airbus-Industrie/Airbus-A380-861/1169635/L/

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

System components

The skateboard

Spring

DamperAir

EarthPerson

NeglectNeglect

Neglect, why?Neglect, why?

System

Damper

Inertia force Drag themass back

SpringMass of the board

Effect

Solution

Displacement

Acceleration

Velocity

The step

DiscussionC=50

K=1000 K=100 K=10

DisplacementDisplacement

VelocityVelocity

AccelerationAcceleration

Discussion

C=200 C=50 C=0.1

DisplacementDisplacement

VelocityVelocity

AccelerationAcceleration

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

The natural frequency

( ) ( ) ( ) 0d x t dx tm c kx tdt dt

( ) ( )2 ( ) 0d x t dx t x tdt dt

The damping ratio

Resonance

Case study: Tacoma Narrow bridge

Courtesy of http://www.youtube.com/watch?v=P0Fi1VcbpAI

Interpret the response of a step function

0 0( ) ( )2 ( ) step

d x t dx t x t fdt dt

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

Damping ratio

Natural frequency21

Maximum overshoot ratio

1.3723

Response

2.686A

Damping ratio0.3

Natural frequency1n

Suppose m=1kg

1 kg/m, 0.6 Ns/mk c

Industrial applications

The pogo-stick

Courtesy of http://connect.in.com/pogo/photos-1-1-1-9ed7a7cecf4cb85de07b7f05697bfe43.html

Question?Where is

the damper?

The suspension systems (ref/auto.howstuffworks.com/)

Courtesy of http://auto.howstuffworks.com/car-suspension4.htmAI

The door closer (ref. /www.usbuildersupply.com)

Courtesy of http://www.usbuildersupply.com/index.php/hardware-basics/door-closer-overview/

Thank You!

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