Transcript Translation.

Mechanical Systems
• Translation
 Point mass concept
 P(t) = F(t)*v(t)
 Newton’s Laws & Free-body diagrams
• Rotation
 Rigid body concept
 P(t) = T(t)*w(t)
 Newton’s laws & Free-body diagrams
• Transducer devices and effects
1
Mechanical translation
• Newton’s Laws
 Every body persists in a state of uniform
motion, except insofar as it may be compelled
by force to change that state.
 The time rate of change of momentum is equal
to the force producing it.
 To every action there is an equal and opposite
reaction.
(Principia Philosophiae, 1686, Isaac Newton)
2
Quantities and SI Units
•
“F-L-T” system




•
Define F: force (Newton [N])
Define L: length (meter [m])
Define T: time (second [s])
Derive v: velocity, m: mass
“M-L-T” system




Define M: mass (kilogram [kg])
Define L: length (meter
[m])
Define T: time (second [s])
Derive v: velocity, F: force
3
Physical effects and engineered
components
•
•
•
•
Inertia effect - rigid body with mass
Compliance (stiffness) effect - spring
Dissipation (friction) effect - damper
System boundary conditions:


motion conditions – velocity specified
force conditions - drivers and loads
4
Translational inertia
• Physical effect: *dV
• Engineered device: rigid body “mass”
• Standard schematic icon (stylized
•
•
picture)
Standard multiport representation
Standard icon equations
5
Inertia in translation: standard forms
v
1
F1
F2
m
m * v  F1  F 2
I
F2
F1
F3
1
0  F1  F 2  F 3
6
Compliance (stiffness)
•
•
•
•
•
Physical effects: =E*
Engineered devices: spring
Standard schematic icon
Standard multiport representation
Standard icon equations
7
Standard translation icons
0
C
F  k * ( L  Lfree)
dL
 v1  v 2
dt
8
Dissipation (resistance)
•
•
•
•
•
Physical effects
Engineered devices: damper
Standard schematic icons
Standard multiport representation
Standard icon equations
9
Standard translation icons
0
F  b * (v1  v2 )
R
10
Free-body diagrams
• Purpose: Develop a systematic method for
generating the equations of a mechanical system.
• Setup method: Separate the mechanical
schematic into standard components and effects
(icons); generate the equation(s) for each icon.
• Standard form of equations: the composite of all
component equations is the initial system set;
select a reduced set of key variables (generalized
coordinates); reduce the initial equation set to a
set in these variables.
11
Multiport modeling of
mechanical translation
• Multiport representations of the standard
•
•
icons: focus on power ports
Equations for the standard icons
Multiport modeling using the free-body
approach
12
Multiport modeling of translation based
on free-body diagrams
• Identify each mass point and rigid connector.
•
• Define an inertial velocity for each.
Use a standard multiport component to represent each
mass point
• Write the standard equation for each component.
13
Suitcase example
Vo
14
Bobsled example
See the file Bobsled report.pdf for a study of this model.
15