15 The Physical Basis of Analogies in Physical System Models 15.1 Introduction 15.2 History 15.3 The Force-Current Analogy: Across and Through Variables Drawbacks of the Across-Thr
Trang 115 The Physical Basis
of Analogies in Physical
System Models 15.1 Introduction
15.2 History
15.3 The Force-Current Analogy: Across and Through Variables
Drawbacks of the Across-Through Classification • Measurement as a Basis for Analogies • Beyond One-Dimensional Mechanical Systems • Physical Intuition 15.4 Maxwell’s Force-Voltage Analogy:
Effort and Flow Variables
Systems of Particles • Physical Intuition • Dependence
on Reference Frames 15.5 A Thermodynamic Basis for Analogies
Extensive and Intensive Variables • Equilibrium and Steady State • Analogies, Not Identities • Nodicity 15.6 Graphical Representations
15.7 Concluding Remarks
15.1 Introduction
One of the fascinating aspects of mechatronic systems is that their function depends on interactions between electrical and mechanical behavior and often magnetic, fluid, thermal, chemical, or other effects
as well At the same time, this can present a challenge as these phenomena are normally associated with different disciplines of engineering and physics One useful approach to this multidisciplinary or “multi-physics” problem is to establish analogies between behavior in different domains—for example, resonance due to interaction between inertia and elasticity in a mechanical system is analogous to resonance due to interaction between capacitance and inductance in an electrical circuit Analogies can provide valuable insight about how a design works, identify equivalent ways a particular function might be achieved, and facilitate detailed quantitative analysis They are especially useful in studying dynamic behavior, which often arises from interactions between domains; for example, even in the absence of elastic effects, a mass moving in a magnetic field may exhibit resonant oscillation However, there are many ways that analogies may be established and, unfortunately, the most appropriate analogy between electrical circuits, mechan-ical and fluid systems remains unresolved: is force like current, or is force more like voltage? In this contribution we examine the physical basis of the analogies in common use and how they may be extended beyond mechanical and electrical systems
Neville Hogan
Massachusetts Institute
of Technology
Peter C Breedveld
University of Twente
Trang 215 The Physical Basis
of Analogies in Physical
System Models 15.1 Introduction
15.2 History
15.3 The Force-Current Analogy: Across and Through Variables
Drawbacks of the Across-Through Classification • Measurement as a Basis for Analogies • Beyond One-Dimensional Mechanical Systems • Physical Intuition 15.4 Maxwell’s Force-Voltage Analogy:
Effort and Flow Variables
Systems of Particles • Physical Intuition • Dependence
on Reference Frames 15.5 A Thermodynamic Basis for Analogies
Extensive and Intensive Variables • Equilibrium and Steady State • Analogies, Not Identities • Nodicity 15.6 Graphical Representations
15.7 Concluding Remarks
15.1 Introduction
One of the fascinating aspects of mechatronic systems is that their function depends on interactions between electrical and mechanical behavior and often magnetic, fluid, thermal, chemical, or other effects
as well At the same time, this can present a challenge as these phenomena are normally associated with different disciplines of engineering and physics One useful approach to this multidisciplinary or “multi-physics” problem is to establish analogies between behavior in different domains—for example, resonance due to interaction between inertia and elasticity in a mechanical system is analogous to resonance due to interaction between capacitance and inductance in an electrical circuit Analogies can provide valuable insight about how a design works, identify equivalent ways a particular function might be achieved, and facilitate detailed quantitative analysis They are especially useful in studying dynamic behavior, which often arises from interactions between domains; for example, even in the absence of elastic effects, a mass moving in a magnetic field may exhibit resonant oscillation However, there are many ways that analogies may be established and, unfortunately, the most appropriate analogy between electrical circuits, mechan-ical and fluid systems remains unresolved: is force like current, or is force more like voltage? In this contribution we examine the physical basis of the analogies in common use and how they may be extended beyond mechanical and electrical systems
Neville Hogan
Massachusetts Institute
of Technology
Peter C Breedveld
University of Twente
Trang 3Sensors and Actuators
Sensors • Actuators
Introduction • Time and Frequency Measurement • Time and Frequency Standards • Time and Frequency Transfer • Closing
Range • Resolution • Sensitivity • Error • Repeatability • Linearity and Accuracy • Impedance • Nonlinearities • Static and Coulomb Friction • Eccentricity • Backlash • Saturation • Deadband • System Response • First-Order System Response • Underdamped Second-Order System Response • Frequency Response
Ivan J Garshelis, Richard Thorn, Pamela M Norris, Bouvard Hosticka, Jorge Fernando Figueroa, H R (Bart) Everett, Stanley S Ipson, and Chang Liu
Linear and Rotational Sensors • Acceleration Sensors • Force Measurement • Torque and Power Measurement • Flow Measurement • Temperature Measurements • Distance Measuring and Proximity Sensors • Light Detection, Image, and Vision
Systems • Integrated Microsensors
Tadas Tolocka, Massimo Sorli, Stefano Pastorelli, and Sergey Edward Lyshevski
Electromechanical Actuators • Electrical Machines • Piezoelectric Actuators • Hydraulic and Pneumatic Actuation Systems • MEMS: Microtransducers Analysis, Design, and Fabrication
Trang 4TABLE 16.1 Type of Sensors for Various Measurement Objectives
Linear/Rotational sensors Linear/Rotational variable differential
transducer (LVDT/RVDT)
High resolution with wide range capability Very stable in static and quasi-static applications Optical encoder Simple, reliable, and low-cost solution
Good for both absolute and incremental measurements Electrical tachometer Resolution depends on type such as generator or magnetic pickups Hall effect sensor High accuracy over a small to medium range
Capacitive transducer Very high resolution with high sensitivity
Low power requirements Good for high frequency dynamic measurements Strain gauge elements Very high accuracy in small ranges
Provides high resolution at low noise levels Interferometer Laser systems provide extremely high resolution in large ranges
Very reliable and expensive Magnetic pickup Output is sinusoidal Gyroscope
Inductosyn Very high resolution over small ranges
Acceleration sensors Seismic accelerometer Good for measuring frequencies up to 40% of its natural frequency Piezoelectric accelerometer High sensitivity, compact, and rugged
Very high natural frequency (100 kHz typical) Force, torque, and pressure sensor
Strain gauge Dynamometers/load cells
Good for both static and dynamic measurements They are also available as micro- and nanosensors Piezoelectric load cells Good for high precision dynamic force measurements Tactile sensor Compact, has wide dynamic range, and high Ultrasonic stress sensor Good for small force measurements
Flow sensors Pitot tube Widely used as a flow rate sensor to determine speed in aircrafts Orifice plate Least expensive with limited range
Flow nozzle, venturi tubes Accurate on wide range of flow
More complex and expensive Rotameter Good for upstream flow measurements
Used in conjunction with variable inductance sensor Ultrasonic type Good for very high flow rates
Can be used for both upstream and downstream flow measurements Turbine flow meter Not suited for fluids containing abrasive particles
Relationship between flow rate and angular velocity is linear Electromagnetic flow meter Least intrusive as it is noncontact type
Can be used with fluids that are corrosive, contaminated, etc The fluid has to be electrically conductive
Temperature sensors Thermocouples This is the cheapest and the most versatile sensor
Applicable over wide temperature ranges ( - 200 ∞ C to 1200 ∞ C typical) Thermistors Very high sensitivity in medium ranges (up to 100 ∞ C typical)
Compact but nonlinear in nature Thermodiodes, thermo transistors Ideally suited for chip temperature measurements
Minimized self heating RTD—resistance temperature detector More stable over a long period of time compared to thermocouple
Linear over a wide range
Trang 517 Fundamentals of Time
and Frequency 17.1 Introduction
Coordinated Universal Time (UTC) 17.2 Time and Frequency Measurement
Accuracy • Stability 17.3 Time and Frequency Standards
Quartz Oscillators • Rubidium Oscillators
• Cesium Oscillators 17.4 Time and Frequency Transfer
Fundamentals of Time and Frequency Transfer
• Radio Time and Frequency Transfer Signals 17.5 Closing
17.1 Introduction
Time and frequency standards supply three basic types of information: time-of-day, time interval, and
frequency Time-of-day information is provided in hours, minutes, and seconds, but often also includes the date (month, day, and year) A device that displays or records time-of-day information is called a
clock If a clock is used to label when an event happened, this label is sometimes called a time tag or time stamp Date and time-of-day can also be used to ensure that events are synchronized, or happen at the same time
Time interval is the duration or elapsed time between two events The standard unit of time interval
is the second(s) However, many engineering applications require the measurement of shorter time intervals, such as milliseconds (1 ms = 10-3 s), microseconds (1 µs = 10-6 s), nanoseconds (1 ns = 10-9 s), and picoseconds (1 ps = 10-12 s) Time is one of the seven base physical quantities, and the second is one
of seven base units defined in the International System of Units (SI) The definitions of many other physical quantities rely upon the definition of the second The second was once defined based on the earth’s rotational rate or as a fraction of the tropical year That changed in 1967 when the era of atomic time keeping formally began The current definition of the SI second is:
The duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom
Frequency is the rate of a repetitive event If T is the period of a repetitive event, then the frequency
f is its reciprocal, 1/T Conversely, the period is the reciprocal of the frequency, T= 1/f Since the period
is a time interval expressed in seconds (s), it is easy to see the close relationship between time interval and frequency The standard unit for frequency is the hertz (Hz), defined as events or cycles per second The frequency of electrical signals is often measured in multiples of hertz, including kilohertz (kHz), megahertz (MHz), or gigahertz (GHz), where 1 kHz equals one thousand (103) events per second, 1 MHz
Michael A Lombardi
National Institute of Standards and Technology