Design and system modeling
are complementary activities - "models give insight into design decisions,
and design objectives guide modeling decisions. Yet the two efforts are
distinct." Smith, p.1.
The type of system model
used at each step in the design must be appropriate to that level of the design
effort. That is, the model must have sufficient detail to answer the questions
the designer is considering at that point in the design. On the other hand, the
model should not be so complex that it is difficult to calculate the response
of the system to realistic inputs, or to interpret the results.
Modeling Requirements for Conceptual
Design:
- The model should demonstrate the connectivity of the various
elements of the proposed solution - The model should define how the potential
solution is organized
- The model should show the cause and effect relationships for the design
concept - the model gives insight into how the potential solution might convert
the specified inputs into the desired outputs.
- The concept model should define the disturbances expected from the
environment and the outputs which will be delivered to the environment.
- The model should define which of the inputs can be controlled, and how that
control will be achieved.
- The model should define which of the internal and external outputs can be
measured to illustrate how the system can be monitored.
Modeling Tasks During Preliminary
Design:
- During the preliminary design phase the designer identifies those
hardware options which will provide each of the design functions.
- The preliminary model must establish the design parameters that will affect
the performance and set some limits on their values.
- Finally, the preliminary design model must support the simulation efforts,
creating numerical data that can be compared to the design specifications.
- The goal of the preliminary design model is to provide enough information
about the proposed design that the designer can modify the design parameters,
the architecture and the hardware to meet the specifications.
A machine is a device that
converts energy from one form to another. A heat engine, for example, converts
the chemical energy stored in a fuel to useful mechanical work. In essence, a
power flow model simply represents cause and effect - fuel in, work out. At
this level of abstraction the model is not particularly useful. However, it can
easily be expanded to reveal more detail about how this particular heat engine
is organized.
Using a process called
"Functional Reductionism" we can decompose a high level model into
its constituent parts. For example, if the heat engine is a spark ignited
internal combustion engine then the fuel is probably gasoline. The chemical
energy is converted to heat (and exhaust gases) by a combustion process. The
engine uses the heated gases from the properly synchronized combustion in each
cylinder to turn a crank shaft producing a torque. The speed of the crank shaft
is controlled by the torque, acting as a load on the system, and the amounts of
fuel and air admitted to each cylinder, which in turn are controlled by the
throttle setting determined by the operator.
To be useful, in the design
process, the model should present some of this information. In particular the
model should identify:
Power is the time rate of
doing work, or alternatively it is the first derivative of the energy. Power is
usually calculated as the product of two variables, R, a potential variable and
Q, a flow variable. Electric power is the product of the potential V(t), or voltage, and the flow I(t), which is the current.
P(t) = V(t) I(t)
The units of power are {SI}
1 Watt = 1 Joule/sec. = 1 Newton meter/sec.
{Eng} foot pound/sec. or in pound/sec.
1 Horsepower = 550 ft-lb/sec = 745.7 Watt
The most common modes of
power encountered in engineering design are shown in Table 1.
TABLE 1 - MODES OF POWER
|
MODE |
POTENTIAL
VARIABLE |
FLOW
VARIABLE |
|
Electrical |
Voltage |
Current |
|
Mechanical
Translation |
Force |
Velocity |
|
Mechanical
Rotation |
Torque |
Angular
Velocity |
|
Thermal |
Temperature |
Rate
of Heat Flow |
|
Fluid
Flow |
Pressure |
Volumetric
Flow Rate |
|
Chemical
Reaction |
Specific
Energy |
Mass
Flow Rate |
|
Magnetic |
Magnetomotive Force |
Magnetic
Flux |
The most useful power flow
elements encountered in mechanical engineering applications are listed in Table
2.
TABLE 2 - POWER FLOW
ELEMENTS
|
POWER
SOURCES |
POWER
CONVERTERS |
POWER TRANSMISSIONS |
LOAD |
|
Battery |
IC Engine |
Mechanical |
Dissipation (Heat): |
|
Fuel Cell |
Electric Motor |
- Gears |
- Resistance |
|
Chemical Fuel |
Reciprocating Steam Engine |
- Chains |
- Coulomb (Dry) Friction |
|
Rotating Flywheel |
Steam Turbine |
- Belts |
- Fluid Friction |
|
Raised Weight |
Gas Turbine |
- Friction Drives |
|
|
Deformed Spring |
Water Wheel |
Hydraulic Transmission |
Inertia |
|
Charged Capacitor |
Wind Mill |
Clutch |
|
|
Inductor |
Hydraulic Turbine |
Nozzle/Diffuser |
|
|
Fluid Accumulator |
Pump |
Lever |
|
|
Nuclear Reactor |
Hydraulic Motor |
Heat Exchanger |
|
|
Solar Energy |
Rocket Engine |
Pulley |
|
|
Electric Power Grid |
Electrical Generator |
Electrical Transformer |
|
|
Heated Mass |
Compressor |
Hydraulic Amplifier |
|
|
Wind |
Hydraulic Cylinder |
Electrical Amplifier |
|
|
Tides |
Pneumatic Cylinder |
Mechanical Linkage |
|
|
Geo-thermal Differences |
Boiler |
Cam and Follower |
|
|
Draft Animals |
Combustor |
Indexing Drive |
|
|
Human Effort |
Photovoltaic Cell |
Electrical Inverter |
|
|
|
|
Linear Slide |
|
|
|
|
Crank |
|
This is not a comprehensive
list but it is adequate for most design tasks.
Table 2 is extremely useful
during conceptual design. For any given task, Table 2 can be used to
systematically enumerate the possible methods of powering the machine. For each
appropriate power source the designer can identify one, or more, possible configurations
for utilizing that power source. For example, batteries might be used to power
a DC motor. By putting a solid state inverter into the system, the same
batteries could be used to power an AC induction motor.
Energy Converters:
IC Engine - {mass flow rate of fuel and air in, shaft speed and torque out}
Spark Ignition
Compression Ignition
Electric Motor - {voltage and current in; shaft speed and torque out}
Wound Field DC
* Permanent Magnet Field DC
AC Induction
Stepper
Linear Induction Motors - {voltage and current in, force and velocity out}
Generator - {shaft speed and torque in; current and voltage out}
Hydraulic Motors - {fluid flow and pressure in}
Cylinders - {force and velocity out}
Rotary motors - {shaft speed and torque out}
Pneumatic Actuators - {fluid flow and pressure in}
Cylinders - {force and velocity out}
Rotary motors - {shaft speed and torque out}
Pump, Compressor - {shaft speed and torque in; fluid flow rate and pressure out}
Reciprocating Steam Engine - {fluid pressure and flow rate in; force and velocity out}
Steam Turbine - {fluid pressure and flow rate in; shaft speed and torque out}
Gas Turbine - {mass flow rate of fuel and air in, shaft speed and torque out}
Stirling Cycle Engines {rate of heat flow in, shaft speed and torque out}
Hydraulic Turbine - {fluid pressure and flow rate in; shaft speed and torque out}
Fuel Cell - {reactant flow rate in; voltage and current out}
Solenoid - {current and voltage in; force and velocity out}
Electromagnetic
Shape memory actuator
Chemical Reactor
Nuclear Power Reactor - {reactants in; fluid flow rate and pressure out}
Rocket Motor - {flow rate of reactants in; force and velocity out}
Energy Transformers:
Mechanical Transmissions {mechanical power in; mechanical power out}
Gears
Chain and Sprockets
Belt and Pulleys
Friction Drives
Lever
four-bar linkages
Fluid Transmissions {flow rate and pressure in; flow rate and pressure out}
Hydrostatic
Hydrodynamic
Electrical Transformers {current and voltage in; current and voltage out}
Electrical Amplifiers {current and voltage in; current and voltage out}
Hydraulic Amplifiers {flow rate and pressure in; flow rate and pressure out}
Electrical Filters {current and voltage in; current and voltage out}
Nozzles and Diffusers {flow rate and pressure in; flow rate and pressure out}
Heat Exchanger {flow rate and pressure in; flow rate and pressure out}
Mixing Chamber {flow rate and pressure in; flow rate and pressure out}
Energy Storage Devices:
Flywheel - {kinetic, rotational}
Heated material - {heat}
Spring - {potential, elastic strain}
Battery - {chemical, electric}
Capacitor - {electric field}
Inductor - {magnetic field}
Weight in a gravity field - {potential}
Fluid reservoir - {potential}
Fuel - {chemical}
Energy Sources:
Solar Cell - {radiation to electricity}
Electric Power Grid
Combustor - {chemical to heat}
Solar Collector - {radiation to heat}
Photosynthesis - {radiation to chemical}
Geo or Ocean:
Thermal differences
Wind
Water Flow
Tides
Nuclear fission
Nuclear fusion (?)
Energy Dissipation - {heat}
Coulomb friction
Fluid friction
Electrical Resistance
Energy Distribution
Electrical Conduction
Pipe flow
Thermal Conduction
Thermal Convection
Thermal Radiation
Electromagnetic Radiation
Energy Flow Control
Mechanical Clutch
Ratchet
Fluid Valves
Electric Switches
Electric Relays
Mechanical Positioning
Systems:
Linear
Rails
Ball Screw
Power Screw
Belt
Rollers
Cam and Follower
Rotary
Indexing table
Roll thrusters
Sensors
Temperature
Thermocouples
Thermistors
Linear Position
LVDT
Linear potentiometer
Ultrasonic transceiver
Angular Position
Potentiometer
Digital encoder
Angular Velocity
Tachogenerator
Hall effect tachometer
Strobotach
Digital encoder
Acceleration
Accelerometer
Strain
Resistance Strain Gauge
Force
Spring scale
Strain gauge load cell
Piezoelectric crystal
Pressure
Manometer
Strain gauge membrane
Piezoelectric crystal
REFERENCES:
Ira Cochin, Harold J. Plass, Jr., Analysis and Design of Dynamic Systems, 2nd
Edition, Harper & Row Publishers Inc., NY, 1990.
C. Nelson Dorny, Understanding Dynamic Systems: Approaches to
Modeling, Analysis, and Design, Prentice-Hall Inc., Englewood Cliffs, NJ, 1993.
David L. Smith,
Introduction to Dynamic Systems Modeling for Design, Prentice-Hall Inc.,
Englewood Cliffs, NJ, 1994.