Accelerometer
An accelerometer is a device that measures the proper acceleration of an object. Proper acceleration is the acceleration of the object relative to an observer who is in free fall. Proper acceleration is different from coordinate acceleration, which is acceleration with respect to a given coordinate system, which may or may not be accelerating. For example, an accelerometer at rest on the surface of the Earth will measure an acceleration due to Earth's gravity straight upwards of about g ≈ 9.81 m/s2. By contrast, an accelerometer that is in free fall will measure zero acceleration.
Highly sensitive accelerometers are used in inertial navigation systems for aircraft and missiles. In unmanned aerial vehicles, accelerometers help to stabilize flight. Micromachined micro-electromechanical systems accelerometers are used in handheld electronic devices such as smartphones, cameras and video-game controllers to detect movement and orientation of these devices. Vibration in industrial machinery is monitored by accelerometers. Seismometers are sensitive accelerometers for monitoring ground movement such as earthquakes.
When two or more accelerometers are coordinated with one another, they can measure differences in proper acceleration, particularly gravity, over their separation in space—that is, the gradient of the gravitational field. Gravity gradiometry is useful because absolute gravity is a weak effect and depends on the local density of the Earth, which is quite variable.
A single-axis accelerometer measures acceleration along a specified axis. A multi-axis accelerometer detects both the magnitude and the direction of the proper acceleration, as a vector quantity, and is usually implemented as several single-axis accelerometers oriented along different axes.
Physical principles
An accelerometer measures proper acceleration, which is the acceleration it experiences relative to freefall and is the acceleration felt by people and objects. Put another way, at any point in spacetime the equivalence principle guarantees the existence of a local inertial frame, and an accelerometer measures the acceleration relative to that frame. Such accelerations are popularly denoted g-force; i.e., in comparison to standard gravity.An accelerometer at rest relative to the Earth's surface will indicate approximately 1 g upwards because the Earth's surface exerts a normal force upwards relative to the local inertial frame. To obtain the acceleration due to motion with respect to the Earth, this "gravity offset" must be subtracted and corrections made for effects caused by the Earth's rotation relative to the inertial frame.
The reason for the appearance of a gravitational offset is Einstein's equivalence principle, which states that the effects of gravity on an object are indistinguishable from acceleration. When held fixed in a gravitational field by, for example, applying a ground reaction force or an equivalent upward thrust, the reference frame for an accelerometer accelerates upwards with respect to a free-falling reference frame. The effects of this acceleration are indistinguishable from any other acceleration experienced by the instrument so that an accelerometer cannot detect the difference between sitting in a rocket on the launch pad, and being in the same rocket in deep space while it uses its engines to accelerate at 1 g. For similar reasons, an accelerometer will read zero during any type of free fall. This includes use in a coasting spaceship in deep space far from any mass, a spaceship orbiting the Earth, an airplane in a parabolic "zero-g" arc, or any free-fall in a vacuum. Another example is free-fall at a sufficiently high altitude that atmospheric effects can be neglected.
However, this does not include a fall in which air resistance produces drag forces that reduce the acceleration until constant terminal velocity is reached. At terminal velocity, the accelerometer will indicate 1 g acceleration upwards. For the same reason a skydiver, upon reaching terminal velocity, does not feel as though he or she were in "free-fall", but rather experiences a feeling similar to being supported on a "bed" of uprushing air.
Acceleration is quantified in the SI unit metres per second per second, in the cgs unit gal, or popularly in terms of standard gravity.
For the practical purpose of finding the acceleration of objects with respect to the Earth, such as for use in an inertial navigation system, a knowledge of local gravity is required. This can be obtained either by calibrating the device at rest, or from a known model of gravity at the approximate current position.
Structure
A basic mechanical accelerometer is a damped proof mass on a spring. When the accelerometer experiences an acceleration, Newton's third law causes the spring's compression to adjust to exert an equivalent force on the mass to counteract the acceleration. Since the spring's force scales linearly with the length change and because the spring constant and mass are known constants, a measurement of the spring's compression is also a measurement of acceleration. The system is damped to prevent oscillations of the mass and spring interfering with measurements. However, the damping causes accelerometers to have a frequency response.Many animals have sensory organs to detect acceleration, especially gravity. In these, the proof mass is usually one or more crystals of calcium carbonate otoliths or statoconia, acting against a bed of hairs connected to neurons. The hairs form the springs, with the neurons as sensors. The damping is usually by a fluid. Many vertebrates, including humans, have these structures in their inner ears. Most invertebrates have similar organs, but not as part of their hearing organs. These are called statocysts.
Mechanical accelerometers are often designed so that an electronic circuit senses a small amount of motion, then pushes on the proof mass with some type of linear motor to keep the proof mass from moving far. The motor might be an electromagnet or in very small accelerometers, electrostatic. Since the circuit's electronic behavior can be carefully designed, and the proof mass does not move far, these designs can be very stable, very linear with a controlled frequency response.
In mechanical accelerometers, measurement is often electrical, piezoelectric, piezoresistive or capacitive. Piezoelectric accelerometers use piezoceramic sensors or single crystals. They are unmatched in high frequency measurements, low packaged weight, and resistance to high temperatures. Piezoresistive accelerometers resist shock better. Capacitive accelerometers typically use a silicon micro-machined sensing element. They measure low frequencies well.
Modern mechanical accelerometers are often small micro-electro-mechanical systems, and are often very simple MEMS devices, consisting of little more than a cantilever beam with a proof mass. Damping results from the residual gas sealed in the device. As long as the Q-factor is not too low, damping does not result in a lower sensitivity.
Under the influence of external accelerations, the proof mass deflects from its neutral position. This deflection is measured in an analog or digital manner. Most commonly, the capacitance between a set of fixed beams and a set of beams attached to the proof mass is measured. This method is simple, reliable, and inexpensive. Integrating piezoresistors in the springs to detect spring deformation, and thus deflection, is a good alternative, although a few more process steps are needed during the fabrication sequence. For very high sensitivities quantum tunnelling is also used; this requires a dedicated process making it very expensive. Optical measurement has been demonstrated in laboratory devices.
Another MEMS-based accelerometer is a thermal accelerometer. It contains a small heater in a very small dome. This heats the air or other fluid inside the dome. The thermal bubble acts as the proof mass. An accompanying temperature sensor in the dome measures the temperature in one location of the dome. This measures the location of the heated bubble within the dome. When the dome is accelerated, the colder, higher density fluid pushes the heated bubble. The measured temperature changes. The temperature measurement is interpreted as acceleration. The fluid provides the damping. Gravity acting on the fluid provides the spring. Since the proof mass is very lightweight gas, and not held by a beam or lever, thermal accelerometers can survive high shocks. Another variation uses a wire to both heat the gas and detect the change in temperature. The change of temperature changes the resistance of the wire. A two dimensional accelerometer can be economically constructed with one dome, one bubble and two measurement devices.
Most micromechanical accelerometers operate in-plane, that is, they are designed to be sensitive only to a direction in the plane of the die. By integrating two devices perpendicularly on a single die a two-axis accelerometer can be made. By adding another out-of-plane device, three axes can be measured. Such a combination may have much lower misalignment error than three discrete models combined after packaging.
Micromechanical accelerometers are available in a wide variety of measuring ranges, reaching up to thousands of gs. The designer must compromise between sensitivity and the maximum acceleration that can be measured.
Applications
Engineering
Accelerometers can be used to measure vehicle acceleration.Accelerometers can be used to measure vibration on cars, machines, buildings, process control systems and safety installations. They can also be used to measure seismic activity, inclination, machine vibration, dynamic distance and speed with or without the influence of gravity. Applications for accelerometers that measure gravity, wherein an accelerometer is specifically configured for use in gravimetry, are called gravimeters.