Transcript WD013-013.7_DU Engineering of Extreme Sports_Mountain Bike

Engineering of Extreme Sports:
Mountain Biking
University of Denver
Department of Engineering
June 2008
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Mountain Biking
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Mountain Bike Components
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Bike Gear Box!
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Smart Gearing
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What is a simple machine??
A device that helps you to
perform a specific task
• Usually performs work
• Involves transformation
of energy
• multiplies force
• multiplies speed
• changes direction
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Force
• Units of force
• Newtons (N = kg*m/s2)
• Pounds (lb = lb*ft/s2)
SI system
US system
• Force = mass * acceleration
• Weight = mass*g
• Mass (kg), g = 9.81 m/s2
• Mass (slugs), g = 32.2 ft/s2
SI system
US system
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Torque
A torque or moment is equal to a force x
distance at which it acts
  
T  r F

F

r = perpendicular distance
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Sir Isaac Newton
(1642-1727)
Three Laws of Mechanics
1. A body continues in its state
of rest or motion until a force
is applied
2. The change of motion is proportional to the
force applied
3. For every action there is an equal and opposite
reaction
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Static Equilibrium
• Newton’s First Law
• The sum of the forces and moments acting on a
body are zero (0)

F  0
 Fx  0
 Fy  0
 Mo  0
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Levers
• Consist of 3 parts
• Effort
• Resistance
• Fulcrum (pivot point)
Effort Force
W
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Levers
• First class lever – fulcrum between the weight and the
effort
Effort Force
W
• What happens to the effort
• if the fulcrum moves to the left?
• if the fulcrum moves to the right?
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Levers
• Second class lever
W
Effort Force
• Third class lever
W
Effort Force
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Force and Energy Transmission: (Wheel
Axel Lever system)
din
dout
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Mechanical Advantage
• Measure of the ability of a machine to
amplify force
Resistance (Force)
M.A. =
Effort (Force)
Effort Arm
M.A. =
Resistance Arm
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Gears
• Some examples include
•
•
•
•
Can opener
Cork screw
Transmission on your car
Bicycle
• Gears are used to
• Change the direction of motion
• Increase or decrease speed
• Increase of decrease torque
• Gears are commonly used in power transmission
applications because of their high efficiency (~98%)
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Gears Configurations
• Spur gears
• Wheels with mating teeth
• Rack and pinion gears
• Changes rotational motion to linear
motion
• Worm gears
• Bevel gears
• Connects shafts lying at angles
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Gear Ratio
• A gear will rotate with an angular velocity (w)
with units of radians/second
• Gears have teeth that must mesh
• Same pitch = same distance between teeth
• There is a fixed ratio between the teeth and the gear
radius
N1 r1

N2 r2
N = Number of teeth (defined as T in your reading)
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Gear Ratio - Velocity
• Velocity of pitch point C on both bodies must be
equal
w2
w1
Vc  r1  w1  r2  w 2
w2
w1

r1
r2

C
N1
N2
Driver or
Pinion
Driven
w = angular velocity (defined as s in your reading)
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Gear Ratio - Torque
• Force of gear 1 on gear 2 is equal and opposite
to force of gear 2 on gear 1
F
w2
w1
T1
r1

r1
r2


w1 T1
T2
r2
N1
N2
T2
w2
C

T1
T2
Driver or
Pinion
Driven
w = angular velocity (defined as s in your reading)
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Bike Transmission and Shifting
Gears connected with chains
obey the same rules
Addition of the chain can
change the output direction
Higher Gear
Lower Gear
8 Teeth
20 Teeth
12 Teeth
20 Teeth
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Force and Energy Transmission: Gears
& Chains
Lower Gear
Higher Gear
Ratio = 20/12
= 1.67
Ratio = 20/8
= 2.5
8 Teeth
20 Teeth
12 Teeth
20 Teeth
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Bike Transmission and Shifting
12 Teeth
20 Teeth
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Vibration: An Engineering
Nightmare
Understanding Spring Mass Systems
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Simple Harmonic Motion
• In order for mechanical oscillation to occur, a system must possess
two quantities: elasticity and inertia.
• When the system is displaced from its equilibrium position,
• Elasticity provides a restoring force such that the system tries to
return to equilibrium.
• The inertia property causes the system to overshoot equilibrium.
• This constant play between the elastic and inertia properties is what
allows oscillatory motion to occur.
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Natural or Resonant Frequency
• The behavior is characterized by the
• Frequency or period
• Amplitude of vibration
• The natural frequency of the oscillation is related to the elastic and
inertia properties by:
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Spring Mass simplest example
• The simplest example of an oscillating system is a mass connected
to a rigid foundation by way of a spring.
•
•
The spring constant k provides the elastic restoring force, and
the inertia of the mass m provides the overshoot.
• By applying Newton's second law F=ma to the mass, one can
obtain the equation of motion for the system:
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So why vibrations occur?
• Perturbation of the environment and the mass
and spring constant create a different response
http://www.kettering.edu/~drussell/Demos/SHO/mass.html
http://www.kettering.edu/~drussell/Demos/basemotion/BaseMotion.html
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Damped Harmonic Oscillation
• If friction is present the system will not oscillate for ever it is
considered damped:
• The vibration frequency of unforced spring-mass-damper systems
depends on their mass, stiffness, and damping values.
• The ensuing time-behavior of such systems also depends on their
initial velocities and displacements.
http://www.kettering.edu/~drussell/Demos/SHO/damp.html
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Under, Over and Critically Damped
• This equation of motion of this new system is a
2nd order ODE.
• If mass, spring stiffness, and viscous damping
are constants
• The solution is:
• This has 2 independent roots. The roots to the
characteristic equation fall into one of the
following 3 cases:
• 1.If z< 0, the system is termed under damped.
oscillatory motion with an exponential decay in
amplitude.
• 2.If z = 0, the system is termed critically-damped.
simple decaying motion with at most one
overshoot of the system's resting position.
• 3.If z > 0, the system is termed over damped.
simple exponentially decaying motion.
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Practical applications
• Mountain bikes (today)
• Alpine skies (next week)
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Mountain Bike Components: Shocks
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