ANALYTICAL MODELS FOR DESIGN (Notes prepared for Sr. Design by Ken Halliday)

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.

The "Power Flow" Model For Design Concepts:

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.

APPENDIX 2A - SOME USEFUL DESIGN ELEMENTS:

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.