Accelerometers

Type of physical science: Classical physics

Field of study: Mechanics

An accelerometer is an electromechanical transducer that measures the rate of change of an object's velocity over time. Accelerometers have found diverse application in a wide variety of scientific and engineering disciplines.

Overview

An accelerometer is a device that measures the acceleration of an object to which it is attached. Acceleration is a common experience in everyday life. When a car accelerates from forty to forty-five miles per hour in one second, this represents an acceleration of five miles per hour per second. When a driver applies the brakes to a moving vehicle, the result is a deceleration, or negative acceleration. Although accelerations are experienced often, they are difficult to measure directly.

In order to understand the operating principle of an accelerometer, consider the behavior of a weight suspended by a string from the ceiling of an airplane. When the airplane is at rest on the runway, the weight hangs straight down. When the airplane accelerates on takeoff, the weight swings toward the rear; when the plane decelerates while landing, the weight swings forward. The angle to which the weight swings is a measure of the acceleration: the greater is the angle, the greater is the acceleration. If the length of the string and the distance of the swing are known, then the actual acceleration of the airplane can be calculated. Furthermore, if the duration of a constant acceleration is known, then the velocity and the total displacement may be computed for any point in time.

For greater accuracy, or for nonconstant accelerations, indirect methods must be used to measure acceleration. This is accomplished by calibrating the force exerted on a reference mass by restraints. The inertia of the mass maintains its position as the object to which it is attached accelerates. Since, according to Newton's second law, the force exerted on the mass is proportional to its acceleration, this allows the acceleration to be calculated.

A simple mechanical accelerometer consists of a small mass with an attached pointer suspended by several precisely designed and matched springs. The movement of the mass is restrained somewhat by several dampers, and the entire assembly is mounted in a small housing. When the housing is attached to an accelerating object, inertia causes the suspended mass to lag behind as the housing moves with the object. The pointer will indicate the relative displacement of the mass, which is proportional to the acceleration of the object.

Any refinement that greatly increases the sensitivity of an accelerometer can upgrade the simple device into an electromechanical transducer. One such modification would be to cause the end of the pointer to move over the surface of a potentiometer attached to the housing as the mass moves. When a fixed current exists in the potentiometer, the voltage between one end and a sliding pointer varies directly in proportion to the distance from the pointer to the end of the potentiometer. Since the pointer displacement is proportional to acceleration, the output voltage is an indirect measurement of the acceleration.

Transducing mechanical motion into an electrical parameter can also be accomplished by means of a moving capacitor plate, causing the output voltage to vary with the plate separation, or by electromagnetic means. One of the most useful methods, however, has proved to be the use of piezoelectric materials, because of their large electrical output relative to their size. With accelerometers of this type, the piezoelectric crystal is attached to the mass and takes the place of the spring, becoming, in effect, a very stiff spring. As the accelerating mass compresses the crystal, an electrical output proportional to the acceleration is produced. Like all other mass-spring systems, this device is sensitive along only one axis because the mass is constrained to move along one axis. Additional accelerometers, or a specially designed multi-axis accelerometer, are required in order to measure accelerations along more than one axis.

The sensitivity of an accelerometer is defined as the ratio of its electrical output to its mechanical input—that is, as voltage per unit of acceleration. The unit of acceleration usually employed is the acceleration due to gravity at the earth's surface, designated one g. This measurement is also known as g-force. The output of an accelerometer would be calibrated as having a certain number of millivolts per g.

In addition to their operating principles, accelerometers may be distinguished by their functions and by the types of motion that they measure. Three types of acceleration that can be measured are linear acceleration, rotational acceleration, and vibrational acceleration. A simple mechanical or electromechanical device can be used to measure linear acceleration. These devices can also be adapted easily to a useful format for measuring rotational acceleration or for measuring vibrational acceleration at low frequencies (below twenty hertz). For measuring the acceleration of rapidly vibrating objects, piezoelectric transducers have proven to be particularly effective, provided that certain precautions are observed. A piezoelectric transducer cannot be used to measure constant acceleration (a vibrational frequency of zero). This limitation results from the fact that at zero frequency, no mechanical energy is being input into the crystal, and so electrical energy (output) cannot be continuously removed.

When measuring vibrational acceleration, there is a limiting highest frequency beyond which the accelerometer output will be inaccurate. The accelerometer, like all other mass-spring systems with little damping resistance, has a resonant frequency, which is a frequency at which the vibration amplitude is extremely large. When any electromechanical transducer is driven at its resonance frequency, its sensitivity is at a maximum. Thus, as the resonance frequency is approached, the transducer response increases, making the output inaccurate by being too high. For a piezoelectric accelerometer, the small mass and the stiff spring (the crystal) yield a high resonant frequency, usually between 20 and 150 kilohertz. Below 20 percent of the resonant frequency, the response of the accelerometer is relatively "flat"; that is, the sensitivity does not change appreciably and the test yields accurate measurements. Thus, a piezoelectric accelerometer may be used with complete assurance that results accurate to within 4 percent are being obtained over a frequency range from 2 to 20 percent of the transducer's resonant frequency. Frequencies above this range may be used if an appropriate correction factor is applied to the output in order to compensate for the increased sensitivity.

Another type of accelerometer is the peak-value accelerometer, which measures either the time at which an object attains a specified acceleration level or the maximum acceleration in a process that is rapidly completed (such as an impact). Peak-value accelerometers are usually employed over a frequency range from ten hertz to twenty kilohertz.

The range of the input acceleration levels over which the accelerometer sensitivity remains approximately constant is defined as the range of amplitude linearity. Although amplitude linearity is theoretically linear even at zero acceleration, a practical lower limit is imposed on this range by the noise level of the matching electronics. This limit may be as low as one-millionth of a g when measuring accelerations with very small amplitudes, such as the vibration of circuit-board components under actual-use conditions. The upper limit of the linear range is imposed by either the nonlinear response of the piezoelectric element or the fragility of the transducer when subjected to extremely high accelerations, such as thousands of g's.

Since the sensitivity of a piezoelectric accelerometer increases with acceleration, the upper limit of amplitude linearity is usually taken to be the acceleration at which the sensitivity increases by 1 percent. This acceleration may be as high as one hundred thousand g's for some models used in shock testing. For the accurate measurement of the intense shock pulses produced during explosive blasting, the accelerometer must have a very wide frequency range and an excellent transient response. These requirements are met by designing an accelerometer with an extremely high resonance frequency, on the order of 250,000 hertz, so that shock pulses as short as 2.0 x 10^-5 seconds may be recorded. A wide and relatively flat frequency range of response is mandated in order to reproduce electrically the very sharp edges of typical transient pulse peaks. Many accelerometers are also given an environmental rating that establishes the maximum allowable vibration and shock input. As a safety precaution, this rating is set substantially lower than the actual damage limits of the transducer.

Applications

Accelerometers have been successfully used for many diverse applications, which can be subdivided into several general areas: geology, navigational and inertial guidance systems, industrial vibration and impact measurement, basic scientific research on musical instruments, and smartphone and tablet technology.

Accelerometers are used in geology for surveying by inertial positioning, locating mineral concentrations, and measuring seismological disturbances. Either three single-axis accelerometers or one three-axis accelerometer is mounted on a gyroscopically stabilized platform so that it will be isolated from vibrational vehicular motion. By knowing the starting position and by measuring the acceleration of a survey vehicle along the three axes, researchers can compute the velocity and the displacement along each axis. A vertical accelerometer is employed to detect concentrations of underground minerals by measuring local increases in the acceleration of gravity that are attributable to concentrations of mass.

In seismology, extremely accurate seismographs called accelerographs are used to measure the tremors that are produced by earthquakes. In order to properly record the ground motion during an earthquake, accelerographs typically feature three accelerometer sensors to detect motion along each of the three axes. The vertical sensor records the vertical motion of the ground as the primary wave, a longitudinal compression wave known as the P-wave, passes the observatory. The horizontal sensors record the more slowly moving horizontal shear wave, called the S-wave, which usually follows the P-wave. The time between the arrivals of the P-wave and the S-wave determines the distance to the earthquake's epicenter, or point of origin. The farther away the earthquake is, the longer the time lag between the arrival of the P-wave and that of the slower-moving S-wave. The distance from the seismograph to the epicenter can be easily calculated by measuring this time lag. In addition to determining the epicenter of an earthquake, accelerograph data yield the period of vibration of the waves, the duration of the shock, and the magnitude of the earthquake.

Inertial guidance systems employ accelerometers as sensors for navigation controls. Gyroscopes are used to maintain perpendicular reference directions for three accelerometers. Once the orientation is set, each accelerometer output represents the net axial components of gravitation and acceleration. A computer can subtract the known effects of gravity to provide a corrected signal. This signal keeps the vehicle on course by taking into account changes in direction and velocity. The airborne computer of an inertial system has at its disposal all necessary information about the vehicle's flight path. By comparing the intended flight path with directions and velocities computed from the accelerometer data, the computer can correct deviations by energizing the appropriate flight controls.

There are many industrial applications for the measurement of vibrational acceleration. Potentially destructive vibrations of a ship's hull can be measured and corrected before a potential problem becomes an actuality. The automobile industry uses accelerometers that are clamped onto the dashboard of a car in order to study vertical vibration, acceleration during pickup, braking power, side loads on tires, and deceleration under crash conditions. Perhaps the most important use of accelerometers by the automobile industry has been their incorporation into the triggering device for air bags. When a car decelerates at a rate greater than ten g (the equivalent of decelerating from thirty miles per hour to a full stop in less than one-tenth of a second), the accelerometer closes a switch that detonates a capsule of sodium azide. The explosive decomposition of this chemical compound rapidly produces about 0.05 cubic meter of nitrogen gas, which fills the air bag in the steering column in four-hundredths of a second. The air bag fills the space between the driver and the steering column to a one-third-meter thickness, which decreases by a controlled leak to several centimeters during the deceleration. Although the driver's upper torso experiences a force greater than 0.5 metric ton during the deceleration, the air bag will decelerate him or her to rest without serious injury.

Impact, or shock motion, is a transient disturbance that involves a significant change in position during a relatively short time interval. The need to measure shock motion accurately has become an important issue in the flight and missile fields, where size and weight do not allow for large safety factors. The accurate testing of expected shock phenomena is necessary to ensure the fail-safe operation of a system in a variety of circumstances and hostile environments. Shocks typically encountered in aerodynamic systems vary from less than one g to many thousands of g's, with durations from millionths of a second up to one second. The transducer that is best suited to measure shocks over this wide dynamic range is the piezoelectric accelerometer. The response of an aerodynamic system to an impressed shock motion is evaluated in terms of its damage potential, which is approximately proportional to the magnitude of the accelerometer output.

In the scientific analysis of musical instruments, accelerometers have proven to be invaluable for mapping the complex vibration patterns that occur on an instrument's oscillating surface. For example, when a violin body is driven at certain frequencies, complex vibrational patterns with many nodal lines (regions of no vibration) are known to form over the top and back plates. If an accelerometer is moved across the surfaces until its output response is zero, it can be used to determine the exact location of the nodal lines. Thus, an accurate "map" of the vibrating surfaces of a violin, known as a modal map, may be constructed. Determining these modal vibration patterns is the first step toward the scientific design of better and more responsive musical instruments. Accelerometers have been similarly employed for the modal mapping of French horn bells under actual playing conditions, revealing that the vibration pattern of the bell while the horn is being played varies considerably depending on the type of metal used and its thickness.

Accelerometers are commonly used in consumer electronics such as smartphones and tablets. Such devices contain a built-in accelerometer that can determine which way the device is being held and adjust the display accordingly, from portrait to landscape orientation or vice versa. Various applications, or apps, designed for these devices also make use of the built-in accelerometer. Accelerometers allows fitness apps to measure speed and steps taken, sleep-monitoring apps to detect when a person moves in his or her sleep, and certain games to incorporate tilt-based player controls, among others. In addition, many personal electronic devices use accelerometers to detect if the device has been dropped, at which point certain safety measures can be taken before it hits the ground, such as unloading the read-write heads of the hard disk drive in order to prevent loss of data or damage to the disk.

Context

The first known earthquake detector was constructed in China in the year 132 CE by Chang Heng. This device could be considered a primitive type of peak accelerometer because it registered earthquake tremors above a certain minimum value. It consisted of a bowl with eight bronze dragons positioned around the rim. Each dragon held a marble in its mouth. When an earthquake shook the device, the acceleration along certain directions would cause a marble to fall into the mouth of a frog waiting below. By noting the axes along which the marbles had dropped, one could determine the approximate direction of the tremor.

In the Western world, it was Galileo Galilei (1564–1642), a pioneer in the study of experimental science, who first conceived of the idea of acceleration and the importance of measuring it. Since he did not have time-recording devices that were accurate enough to measure the acceleration of an object in free fall, he measured the acceleration of balls rolling down an inclined plane. During the nineteenth century, the first mechanical seismographs were constructed to measure earthquake tremors, but accurate accelerometers were not possible until the advent of the electromechanical age in the twentieth century. Although the first electromechanical accelerometers were devised for more precise seismographic measurements, their smaller size and greater accuracy soon ensured a plethora of other uses.

Accelerometers have found modern applications in virtually all fields of science and technology, and new uses and requirements have resulted in smaller, more durable, and more accurate devices. For example, a group of acousticians studying the violin needed a small, sensitive, nonmassive accelerometer with a dynamic range wide enough to be used over the entire audio spectrum. Since no device that met their criteria existed, they contracted with an accelerometer-manufacturing company to design, engineer, and produce it. The success of this venture indicates the myriad uses of accelerometers, as well as the pervasive interaction between science and technology.

Principal terms

ACCELERATION: the change in velocity of an object divided by the time over which the change occurred, commonly expressed in units of meters per second per second, or meters per second squared

ACCELERATION OF GRAVITY: the average acceleration of an object in free fall, ignoring air resistance; expressed in g's, where 1 g equals 9.8 meters per second per second

FREQUENCY: the number of vibrations occurring during a time interval; expressed in hertz or kilohertz, where one hertz equals one oscillation per second and one kilohertz equals one thousand hertz

PIEZOELECTRIC MATERIAL: a crystalline material that generates an electric charge when subjected to mechanical stress or deformation

TRANSDUCER: any device that transforms energy from one form to another, such as mechanical motion into an electrical signal

Bibliography

André, Paulo Sérgio de Brito, and Humberto Varum, eds. Accelerometers: Principles, Structure and Applications. Hauppauge: Nova Sci., 2013. Print.

Asimov, Isaac. Understanding Physics. Vol. 1. New York: Walker, 1966. Print. This excellent volume includes detailed discussions of acceleration, force, vibration, and resonance. For readers who wish to acquire the fundamental background that is necessary to understand the mechanical aspects of accelerometers.

Asimov, Issac. Understanding Physics. Vol. 2. New York: Walker, 1966. Print. This companion volume to the above entry provides detailed discussions of the basic electrical and magnetic phenomena behind the transduction aspects of accelerometers.

D'Alessandro, Antonino, and Giuseppe D'Anna. "Suitability of Low-Cost Three-Axis MEMS Accelerometers in Strong-Motion Seismology: Tests on the LIS331DLH (iPhone) Accelerometer." Bulletin of the Seismological Society of America 103.5 (2013): 2906–13. Print.

Frank, Randy. Understanding Smart Sensors. 3rd ed. Norwood: Artech, 2013. Print.

Herceg, Edward E. Handbook of Measurement and Control. Pennsauken: Schaevitz, 1972. Print. This handbook is an authoritative treatise on the history, theory, and application of many types of sophisticated transducers, including the accelerometer.

Hunt, Frederick. Electroacoustics: The Analysis of Transduction, and Its Historical Background. New York: Amer. Inst. of Physics, 1982. Print. This monograph contains a long and detailed introduction that places electroacoustic transduction in its historical setting, a section on electromechanical coupling, and a section on applications.

Robin, Laurent. "Consumer Electronics Turn to MEMS for Gesture Control, Precision Location." EE Times. UBM Tech, 28 July 2011. Web. 17 Jan. 2014.

Strong, W. J., and G. R. Plitnik. Music, Speech, and Audio. Provo: Soundprint, 1991. Print. This nontechnical treatment of sound and electroacoustic transduction includes discussions of modal-mapping techniques for the study of musical instruments.