Accelerometer

Accelerometers

An accelerometer is a device for measuring acceleration and gravity induced reaction forces. Single- and multi-axis models are available to detect magnitude and direction of the acceleration as a vector quantity. Accelerometers can be used to sense inclination, vibration, and shock. They are increasingly present in portable electronic devices. An accelerometer measures the acceleration and gravity it experiences. Both are typically expressed in SI units meters/second2 (m·s-2) or popularly in terms of g-force. The effects of gravity and acceleration are indistinguishable, following Einstein's equivalence principle. As a consequence, the output of an accelerometer has an offset due to local gravity. This means that, perhaps counter intuitively, an accelerometer at rest on the earth's surface will actually indicate 1 g along the vertical axis. To obtain the acceleration due to motion alone, this offset must be subtracted. Along all horizontal directions, the device yields acceleration directly. Conversely, the device's output will zero during free fall, where the acceleration exactly follows gravity. This includes use in an earth orbiting spaceship, but not a (non-free) fall with air resistance, where drag forces reduce the acceleration until terminal velocity is reached, at which point the device would once again indicate the 1 g vertical offset. For the practical purpose of finding the acceleration of objects with respect to the earth, such as for use in an inertial navigation system, the correction due to gravity along the vertical axis is usually made automatically, e.g. by calibrating the device at rest.

Modern accelerometers are often small micro electro-mechanical systems (MEMS), and are indeed the simplest MEMS devices possible, consisting of little more than a cantilever beam with a proof mass (also known as seismic mass) and some type of deflection sensing circuitry. Under the influence of gravity or acceleration the proof mass deflects from its neutral position. The deflection is measured in an analog or digital manner. Another type of MEMS-based accelerometer contains a small heater at the bottom of a very small dome, which heats the air inside the dome to cause it to rise. A thermocouple on the dome determines where the heated air reaches the dome and the deflection off the center is a measure of the acceleration applied to the sensor. Single-axis, dual-axis, and triple-axis models exist to measure acceleration as a vector quantity or just one or more of its components. MEMS accelerometers are available in a wide variety of measuring ranges, reaching up to thousands of g's. 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. One of the most common uses for MEMS accelerometers is in airbag deployment systems for modern automobiles. In this case the accelerometers are used to detect the rapid negative acceleration of the vehicle to determine when a collision has occurred and the severity of the collision. The widespread use of accelerometers in the automotive industry has pushed their cost down dramatically.

PRINCIPLE OF OPERATION OF AN ACCELEROMETER In the following work the term ‘accelerometer’ is used to designate the entire transducer, normally comprising a mechanical sensing element and conversion of the signal from the mechanical to the electrical domain. Derivation of the Motion Equation The measurement of acceleration always relies on classical Newton’s mechanics. Normally the acceleration to which a body is subjected is of interest; the accelerometer being rigidly attached to that body. The transducers which are the subject of this research programme make use of a sensing element consisting of a proof mass (also referred to as seismic mass) which is suspended by a spring; acceleration causes a force to act on the mass which is consequently deflected by a distance ‘x’ as shown in fig. 2.1. Some form of damping is required; otherwise the system would oscillate at its natural frequency ‘Tn’ for any input signal.

To derive the motion equation of the system, D’Alembert’s principle is applied, where all real forces acting on the proof mass are equal to the inertia force on the proof mass. From the stationary observer’s point of view, the sum of all forces in the y direction is: