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-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 ©2002 CRC Press LLC 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-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 ©2002 CRC Press LLC III Sensors and Actuators 16 Introduction to Sensors and Actuators M. Anjanappa, K. Datta, and T. Song Sensors • Actuators 17 Fundamentals of Time and Frequency Michael A. Lombardi Introduction • Time and Frequency Measurement • Time and Frequency Standards • Time and Frequency Transfer • Closing 18 Sensor and Actuator Characteristics Joey Parker 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 19 Sensors Kevin M. Lynch, Michael A. Peshkin, Halit Eren, M. A. Elbestawi, 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 20 Actuators George T C. Chiu, C. J. Fraser, Ramutis Bansevicius, Rymantas 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 ©2002 CRC Press LLC TABLE 16.1 Type of Sensors for Various Measurement Objectives Sensor Features 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 ( continued ) ©2002 CRC Press LLC 17 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 µ s = 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 (10 3 ) events per second, 1 MHz Michael A. Lombardi National Institute of Standards and Technology ©2002 CRC Press LLC . Breedveld University of Twente 20 02 CRC Press LLC 15 The Physical Basis of Analogies in Physical System Models 15 .1 Introduction 15 .2 History 15 .3 The Force-Current Analogy: Across and. ) 20 02 CRC Press LLC 17 Fundamentals of Time and Frequency 17 .1 Introduction Coordinated Universal Time (UTC) 17 .2 Time and Frequency Measurement Accuracy • Stability 17 .3. milliseconds (1 ms = 10 - 3 s), microseconds (1 µ s = 10 - 6 s), nanoseconds (1 ns = 10 - 9 s), and picoseconds (1 ps = 10 - 12 s). Time