Accelerometers

An accelerometer is essentially a mass on a spring. The mass is released from the substrate and is supported by springs. The released mass m reacts to an external force F according to 

If the mass is supported by springs with spring constant k, the springs supply an elastic restoring force  

And if the mass moves through a viscous medium like air at a velocity v, 

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Fig.l shows the layout of the SPATE 9000 system. It basically consists of a scan unit connected to a signal amplifier. The signals are then correlated with a reference signal derived from a load transducer (e.g. strain gauge, load cell, accelerometer, or function generator). 

The advantages of miniaturization are now being exploited in areas beyond microelectronics. Adaptation of materials and processes originally devised for semiconductor manufacture has allowed fabrication of sensors (for example, pressure meters and accelerometers used in the automotive industry) (6,7), complex optical (8) and micromechanical (6,7,9) assembHes, and devices for medical diagnostics (6,7,10) using Hthographic resists. 

Many of the variations developed to make pressure sensors and accelerometers for a wide variety of appHcations have been reviewed (5). These sensors can be made in very large batches using photoHthographic techniques that keep unit manufacturing costs low and ensure part-to-part uniformity. A pressure differential across these thin diaphragms causes mechanical deformation that can be monitored in several ways piezoresistors implanted on the diaphragm are one way changes in electrical capacitance are another. 

It is advisable in most of these cases to use accelerometers. Displacement probes will not give the high-frequency signals and velocity probes because their mechanical design is very directional and prone to deterioration. Figure 10-64 shows me signal from the various types of probes. 

Passive test The test object is mounted on the shake table and subjected to both horizontal (X and Pj movements or one cumulative orthogonal horizontal and one vertical ground movement simultaneously. Accelerometers are mounted on the shake table to measure its movements and also on the test object at its most vulnerable points. These points may be identified by the manufacturer or the user to monitor the behaviour of the object in such locations. 

The advent of new, more reliable, and sensitive vibration instrumentation such as the eddy-current sensor and the accelerometer coupled with modern... 

The monitoring of turbomachinery mechanical characteristics, such as vibrations, has been applied extensively over the past decade. The advent of the accelerometer and the real-time vibration spectrum analyzer has required a computer to match and utilize the extensive analysis and diagnostic capability of these instruments. 

Characterized by high frequency response, accelerometers are compact and rugged, ideal for mounting on machinery cases, foundations, piping, etc. Applications to gear trains and rolling element bearings are typical. 

The si/e of mass within the accelerometer determines the self-resonant frequency of the sensors. The smaller the mass, the higher the frequency Accelerometers are usually operated in a range below this self-resonant, freqncnc)/. 

Since acceleration is the second derivative of displacement, a piezoelectric accelerometer sensor with an integrator becomes a velocity transducer. This arrangement is gradually superseding the self-generating mo ing-coil velocity sensor (where a coil of wire moves relative to a magnetic field). 

Academic des Sciences, 224 Accelerometers, 349 Accumulators, 317 Acoustic Velocity, 26, 39 Adiabatic, 30 Adiabatic efficiency dry, helical, 101 sliding vane, 126 Adiabatic exponent for air-vapor mixtures, 494 Adiabatic head, 32 Adiabatic head... 

This aspect is not included here, but is related to optical flow diagnostics. It is based again on the principle of the optical Doppler effect. Multifunctional equipment is available for noncontact measurements of flow-induced vibration on surfaces of structural elements, for acoustic measurements, and for calibration of accelerometers and vibration transducers. 

Gas-dichte, /. gas(eous) density, -dichtigkeit, /. impermeability to gas. -druck, m. gas pressure, gaseous pressure, -dnickmesser, m. manometer, pressure gage (MU.) accelerometer. -durchlassigkeit, /. permeability for gas. 

Figure 4-218 shows the arrangement of the sensors used in a steering tool. Three flux-gate-type magnetometers and three accelerometers are positioned... 

Accetefometers. Accelerometers measure the force generated by acceleration according to Newton s law ... 

If the acceleration is variable, as in sinusoidal movement, piezoelectric systems are ideal. In case of a constant acceleration, and hence a force that is also constant, strain gages may be employed. For petroleum applications in boreholes, however, it is better to use servo-controlled accelerometers. Reverse pendular accelerometers and single-axis accelerometers are available. 

Figure 4-219 shows the schematic diagram of a servo-controlled inverted pendular dual-axis accelerometer. A pendulum mounted on a flexible suspension can oscillate in the direction of the arrows. Its position is identified by two detectors acting on feedback windings used to keep the pendulum in the median position. The current required to achieve this is proportional to the force ma, and hence to a. ... 

This system can operate simultaneously along two axes, such as x and y, if another set of detectors and feedback windings is mounted in the plane perpendicular to xO, such as yO. The corresponding accelerometer is called a two-axis accelerometer. 

Figure 4-220 shows the schematic diagram of a servo-controlled single-axis accelerometer. The pendulum is a disk kept in position as in the case of the reverse pendulum. Extremely efficient accelerometers can be built according to this principle in a very limited space. The Sunstrand accelerometer is seen in Figure 4-221. 

Every accelerometer has a response curve of the type shown schematically in Figure 4-222. Instead of having an ideal linear response, a nonlinear response is generally obtained with a skewed acceleration for zero current, a scale factor error and a nonlinearity error. In addition, the skew and the errors vary with temperature. If the skew and all the errors are small or compensated in the accelerometer s electronic circuits, the signal read is an ideal response and can be used directly to calculate the borehole inclination. If not, modeling must be resorted to, i.e., making a correction with a computer, generally placed at the surface, to find the ideal response. This correction takes account of the skew,... 

Figure 4-219. Sketch of principle of a servo-controlled inverted pendular dual-axis accelerometer.

Figure 4-220. Schematic diagram of a servo-controlled single-axis accelerometer.

Figure 4-221. Servo-controlled single-axis Sunstrand accelerometer (a) accelerometer photograph (b) exploded view of the accelerometer. (Courtesy Sunstrand [102].)...

Assume that the accelerometer has the ideal response shown in Figure 4-223, with a measurement range of 2 g (32.2 ft/s ). We want to measure 1 g, but the ambient vibration level is +3 g. In this case, the accelerometer s indications are shaved and the mean value obtained is not 1 g but 0.5 g. The maximum acceleration due to vibrations which are not filtered mechanically, plus the... 

For measurement ranges from 0 to 180°, three accelerometers mounted orthogonally must be used as shown in Figure 4-224. The x and y accelerometers are mounted with their sensitive axis perpendicular to the tool axis. The z accelerometer is mounted with its sensitive axis lined up with the tool axis. 

Figure 4-225 shows the inclination measurement using a triaxial sensor featuring three accelerometers. The three coordinates of the earth s gravitational acceleration vector serve to define this vector in the reference frame of the probe. The earth s acceleration is computed as... 

It must be equal to the 32.2 ft/s otherwise the accelerometers are not working correctly. When the readings are in g units, G must be equal to one. 

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