Anthony Lawrence

Vibrating Beam Accelerometers

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.

The Interferometric Fiber-Optic Gyro

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 which make it difficult to build the IFOG at a competitive cost.

An Outline of Inertial Navigation

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.

Gyro and Accelerometer Errors and Their Consequences

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].

The Ring Laser Gyro

In Chapter 11 we defined the ring laser gyroscope (RLG) as a type of active resonator 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.

The Pendulous Accelerometer

The pendulous accelerometer, one with an unconstrained single degree of freedom pendulum operated 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 Sundstrand “Q-Flex” design, and 3. the silicon micromachined accelerometer.

Design Choices for Inertial Instruments

In this chapter we will summarize the trade-offs 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.

The Principles of Mechanical Gyroscopes

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

The Principles of Accelerometers

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 which they can use. We will also mention the principles of two new accelerometers, the surface wave and the fiber optic types.

The Dynamically Tuned Gyroscope

In the 1940s engineers in Scotland designed a gyro which 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 for the strange behavior.