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Über dieses Buch

Mechanical Engineering, an engineering discipline borne of the needs of the in­ dustrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound issues of pro­ ductivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series features graduate texts and research mono­ graphs intended to address the need for information in contemporary areas of me­ chanical engineering. The series is conceived as a comprehensive one that covers a broad range of concentrations important to mechanical engineering graduate education and re­ search. We are fortunate to have a distinguished roster of consulting editors on the advisory board, each an expert in one of the areas of concentration. The names of the consulting editors are listed on the next page of this volume. The areas of concentration are applied mechanics, biomechanics, computational mechanics, dynamic systems and control, energetics, mechanics of materials, processing, ther­ mal science, and tribology. I am pleased to present this volume in the Series: Modern Inertial Technology: Navigation, Guidance, and Control, Second Edition, by Anthony Lawrence. The selection of this volume underscores again the interest of the Mechanical Engi­ neering series to provide our readers with topical monographs as well as graduate texts in a wide variety of fields.

Inhaltsverzeichnis

Frontmatter

Introduction

Abstract
Automatic navigation makes ocean-going and flying safer and less expensive: Safer because machines are tireless and always vigilant; inexpensive because it does not use human navigators who are, unavoidably, highly trained and thus expensive people. Unmanned deep space travel would be impossible without automatic navigation. Navigation can be automated with the radio systems Loran, Omega, and the Global Positioning System (GPS) of earth satellites. In some circumstances, such as when a submarine is deeply submerged or in a war zone where radio signals may be jammed, these aids are not available. Then we must use a self-contained system called inertial navigation.
Anthony Lawrence

1. An Outline of Inertial Navigation

Abstract
Pioneers returning from their journeys provided travel instructions for those who wished to repeat their journeys. They wrote descriptions of their routes and made charts or maps pointing out landmarks and hazards such as rivers and mountains on land or shoals and rocks at sea. Mapmakers devised a global coordinate system using a grid of latitude and longitude circles, by which the position of any place on earth could be defined.
Anthony Lawrence

2. Gyro and Accelerometer Errors and Their Consequences

Abstract
Inertial navigation is an “initial value” process in which a vehicle’s location is deduced by adding distances moved in known directions to the known position of the starting point. Errors in the deduced location come from imperfect knowledge of the starting conditions, from errors in the strapdown computation, and from errors in the gyros and accelerometers (referred to as sensors). In Chapter 1 we alluded to gyro bias when describing gyrocompassing, without defining it; here we will consider sensor performance more rigorously. For the most part we will follow the terminology used in IEEE Standard 528 [1].
Anthony Lawrence

3. The Principles of Accelerometers

Abstract
In this chapter we consider acceleration measurement and examine the dynamic behavior of a common accelerometer, the mass-spring second-order model, describing its responses to an impulse and to a sustained periodic driving force. We will describe open-and closed-loop (servoed) instruments and the types of servos they can use. We will also mention the principles of two new accelerometers, the surface wave and fiber-optic types.
Anthony Lawrence

4. The Pendulous Accelerometer

Abstract
The pendulous accelerometer, one with an unconstrained single-degree-of-freedom pendulum operated in a closed loop, may well be the most common navigation accelerometer. In this chapter we will consider three types of pendulous accelerometer:
1.
a generic pendulous instrument
 
2.
the “Q-Flex” design, and
 
3.
the silicon micromachined accelerometer.
 
Anthony Lawrence

5. Vibrating Beam Accelerometers

Abstract
In this chapter we will investigate the design of vibratory accelerometers. Their underlying physical principle is that the transverse resonant frequency of a string or bar depends on the tensile stress, and the stress can be made a function of acceleration by fixing a proof mass to the string or bar. We will examine the design of two versions of vibrating beam accelerometers (VBAs) and describe their performance models. We will also consider a recent micromachined silicon version.
Anthony Lawrence

6. The Principles of Mechanical Gyroscopes

Abstract
In this chapter we present the base for describing, in subsequent chapters, different ways of making mechanical gyros. We will derive the Law of Gyroscopics and the expression for the Coriolis acceleration, the phenomena underlying spinning wheel and vibratory gyroscopes.
Anthony Lawrence

7. Single-Degree-of-Freedom Gyroscopes

Abstract
In Chapter 6 we described the Law of Gyroscopics, so now we can see how instruments put this law to work and how they are designed. We begin with the single-axis, or single-degree-of-freedom gyro (SDFG). There are two types to consider, the rate gyro, an open-loop sensor, and the rate-integrating gyro, a closed-loop version. As usual, the closed-loop gyro has higher accuracy, whereas the open-loop gyro is less expensive. The most common SDFGs are filled with a fluid to provide damping and sometimes flotation; why and how this is done will be a subject of this chapter. The SDFG is the most common type in the field; more than a million have been put into service, and even though optical technology will make them obsolete, they will be in the inventory for many years.
Anthony Lawrence

8. Two-Degree-of-Freedom Gyroscopes

Abstract
In the 1950s, when inertial navigation began, there were two schools of thought as to how to make gyros. To generalize somewhat, the East Coast school, led by Draper (at MIT), opted for single-degree-of-freedom floated gyros, which constrain the precession of a gyro wheel to a single rotational axis (the output axis). The West Coast school, however, successfully made two-degree-of-freedom gyros (2DFGs). Some companies (Litton, and East Coast Arma) made floated 2DFGs, while Autonetics made gimbal-less gyros using a ball-and-socket made from a spherical self-acting gas bearing inside the wheel. Others (Autonetics and neither coast Honeywell) made the ball-and-socket the entire gyro, supporting a sphere either electrostatically or magnetically, the latter type using superconducting materials to eliminate power dissipation and heating. Two-degree-of-freedom gyros are sometimes called two axis-gyros, or free gyros.
Anthony Lawrence

9. The Dynamically Tuned Gyroscope

Abstract
In the 1940s engineers in Scotland designed a gyro that used a spinning flywheel on a universal (Hooke’s) joint (Figure 9.1). The gyro was surprisingly unstable, and Arnold and Maunder at the University of Edinburgh showed that the dynamic inertia effects of the gimbal in the universal joint were responsible.
Anthony Lawrence

10. Vibrating Gyroscopes

Abstract
Gyroscopes would be more reliable and less expensive if they had neither spinning wheels nor flotation fluids. Single-degree-of-freedom gyro (SDFG) wheel bearings must be stiff and isoelastic, and for both SDFGs and dynamically tuned gyros (DTGs) the bearings must be noiseless, as low friction as possible, and must start at low temperatures. Gas bearings cost more, and flotation fluids can require temperature control, damping compensation, and scrupulously clean assembly. By the 1960s every reasonable path around these problems had been tried.
Anthony Lawrence

11. The Principles of Optical Rotation Sensing

Abstract
So far, we have considered inertial navigation sensors that use the mechanics of matter described by Newton’s laws of motion, basically concerned with the conservation of momentum in a frame of reference fixed in the stars. In this and the following chapters we will describe gyroscopes based on the inertial property of light. We will begin by defining that property, then we will review the theory of some optics used in gyros.
Anthony Lawrence

12. The Interferometric Fiber-Optic Gyro

Abstract
In this chapter we show how the basic Interferometric Fiber-Optic Gyro (IFOG), the Sagnac interferometer described in Chapter 11, is operated at its maximum sensitivity point, closed-loop. We will describe phase nulling and the serrodyne feedback system, and then we will consider some of the IFOG’s error sources. We will also mention some of the factors that affect the cost of the IFOG.
Anthony Lawrence

13. The Ring Laser Gyro

Abstract
In Chapter 11 we defined the ring laser gyroscope (RLG) as an active resonator optical gyro. Clifford Heer conceived the RLG in 1961 [1]; he saw that the properties of the laser, recently invented by Schawlow and Townes, could be exploited to measure rotation. Heer and Adolph Rosenthal [2] independently developed the theory, and, in 1963, Macek and Davis [3] demonstrated the first RLG, a square gyro, 1 m on a side. Scientists around the world contributed to the field during the 1970s, and Bogdanov’s survey article [4] describes the results.
Anthony Lawrence

14. Passive Resonant Gyros

Abstract
In Chapter 11 we divided resonator gyros into active and passive types, and in Chapter 13 we described active ring laser gyros, RLGs. Now we describe the passive resonator gyros, which can be made from either “free space” optics—lenses, mirrors, and other discrete components—or from guided wave optics—fibers or integrated optics, waveguides, and thin film devices. The free-space type might use an empty RLG-like block with mirrors on it, while the guided wave type can use an optical fiber resonator or an integrated optics resonator in which waveguides are formed into an optical chip. We shall look at each in turn, and then we’ll compare them.
Anthony Lawrence

15. Testing Inertial Sensors

Abstract
In Chapter 2 we described inertial systems error modeling and the generation of specifications for the sensors in an inertial navigator, specifications which could (and should) follow the Institution of Electrical and Electronic Engineers (IEEE) standard formats for inertial sensors. In this chapter we will describe the testing of accelerometers and gyros for conformance to these specifications; we will describe the tests that we would perform for acceptance test procedures (ATPs) on a pendulous accelerometer and on three types of gyro, the single-degree-of-freedom (SDFG), the dynamically tuned gyro (DTG), and the ring laser gyro (RLG). This description is general and takes account of neither specific design issues nor of particular customer needs that would expand the ATP in real life.
Anthony Lawrence

16. Design Choices for Inertial Instruments

Abstract
In this chapter we will summarize the tradeoffs between inertial systems designs and sensors, considering performance, cost, and reliability. The technology appropriate for a particular system depends on the performance and reliability needed and the size available; the cost will always need to be the lowest possible. We will also try to predict where the instrument design field is headed, allowing for the full impact of the Global Positioning System (GPS) satellite radio aid.
Anthony Lawrence

Backmatter

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