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Written By: 

Preeti Jain
Body in motion usually experience vibration as well as shock. When a mobile falls on a floor, it is subjected to shock. When a vehicle moves on a bumpy road, it experiences vibrations. Likewise, there are many situations, where an object encounters shock and vibrations. Sometimes, they survive and at times, they get damaged. When delicate items like glass, crockery, etc. are packaged properly, they can withstand severe shock and vibrations. Whether a system will survive or not, how do we know this a priori? While some vibrations are desirable, some may be disturbing or even destructive. Hence, often a need is felt to understand the causes of vibrations and to develop methods to measure and prevent them.
An ability of a system to withstand vibrations and shock depends upon the ‘g’ level the system can withstand. To measure these ‘g’ levels, a sensor – accelerometer is used.
An accelerometer is a sensor that measures the physical acceleration experienced by an object due to inertial forces or due to mechanical excitation. Acceleration is defined as rate of change of velocity with respect to time. It is a measure of how fast speed changes. It is a vector quantity having both magnitude and direction. As a speedometer is a meter to measures speed, an accelerometer is a meter to measure acceleration. An ability of an accelerometer to sense acceleration can be put to use to measure a variety of things like tilt, vibration, rotation, collision, gravity, etc. Accelerometers measure in terms of ‘g’ (‘g’ is acceleration measurement for gravity which is equal to 9.81m/s²). Accelerometers are made using tilt sensors. Read more to know what is a tilt sensor and types of tilt sensor.
The term ‘Accelerometers’ refer to the transducers which comprises of mechanical sensing element and a mechanism which converts the mechanical motion into an electrical output.
Theory behind working of accelerometers can be understood from the mechanical model of accelerometer, using Newtonian mechanics. The sensing element essentially is a proof mass (also known as seismic mass).  The proof mass is attached to spring which in turn is connected to its casing.  In addition, a dashpot is also included in a system to provide desirable damping effect; otherwise system may oscillate at its natural frequency. The dashpot is attached (in parallel or in series) between the mass and the casing. The unit is rigidly mounted on the body whose acceleration is of interest.
Image Showing A Regular Accelerometer and Its Schematic

 Fig. 1: Image Showing A Regular Accelerometer and Its Schematic

When the system is subjected to linear acceleration, a force (= mass * acceleration) acts on the proof-mass. This causes it to deflect; the deflection is sensed by a suitable means and is converted into an equivalent electrical signal.
When force is applied on the body, proof mass moves. Its movement is countered by spring and damper.
Image Showing Working of Accelerometer

Fig. 2: Image Showing Working of Accelerometer

Therefore, if    m = proof mass of the body
x  = relative movement of the proof-mass with respect to the frame
c  = damping coefficient
k  = spring stiffness
Deriving Component Capable of Moving With Respect to Sensors Housing

  Fig. 3: Deriving Component Capable of Moving With Respect to Sensors Housing

Thus, with the knowledge of damping coefficient(c ), spring stiffness (k), and proof mass (m), for a useful acceleration sensor, it is sufficient to provide a component that can move relative to sensors housing and a means to sense the movement.
Displacement and acceleration are related by fundamental scaling law. A higher resonant frequency implies less displacement or low sensitivity.
As movement of the proof mass is sufficient for an accelerometer, accelerometers are designed using various sensing principles.
·         Potentiometric
One of the simplest accelerometer type - it measures motion of the proof mass motion by attaching the spring mass to the wiper arm of a potentiometer. Thus position of the mass and thereby, changing acceleration is translated to changing resistance.
Image Showing Schematic of A Potentiometric Accelerometer


Fig. 4: Image Showing Schematic of A Potentiometric Accelerometer

The natural frequency of these devices is generally less than 30 Hz, limiting their application to low frequency vibration measurements. Dynamic range is also limited. But they can measure down to 0 Hz (DC response).
·         Capacitive accelerometers
Capacitive accelerometers sense a change in electrical capacitance, with respect to acceleration. Single capacitor or differential capacitors can be used; differential ones being more common
Capacitive Accelerometer


Fig. 5: Capacitive Accelerometer

In these accelerometers, a diaphragm acting as a mass moves in the presence of acceleration. The diaphragm is sandwiched between the two fixed plates creating two capacitors; each with an individual fixed plate and each sharing the diaphragm as a movable plate. Movement of the diaphragm causes a capacitance shift by altering the distance between two parallel plates, the diaphragm itself being one of the plates.
The two capacitors form the two arms of the bridge; the output of the bridge varies with the acceleration.
Capacitive sensing is most commonly used in MEMS accelerometers. Like potentiometric accelerometers, capacitive accelerometers have true DC response but limited frequency range and limited dynamic range.
·         Piezoelectric accelerometers
Piezoelectric accelerometers employ piezoelectric effect. When piezoelectric materials are stressed, they are deformed and an electric charge is generated on the piezoelectric materials.
In piezoelectric accelerometers, piezoelectric material is used as an active element. One side of the piezoelectric material is connected to rigid base. Seismic or proof mass is attached to the other side. When force (generated due to acceleration) is applied, piezoelectric material deforms to generate the charge. This charge is proportional to the applied force or in other words, proportional to acceleration (as mass is constant). The charge is converted to voltage using charge amplifiers and associated signal conditioning circuit.
Schematic of A Piezoelectric Accelerometer


Fig. 5: Schematic of A Piezoelectric Accelerometer


Compared to other type of accelerometers, piezoelectric accelerometers offer unique advantages –
Wide dynamic range
Excellent linearity
Wide frequency range
No wear and tear due to absence of moving parts
No external power requirement
However, alternating acceleration only can be measured with piezoelectric accelerometers. These accelerometers are not capable of measuring DC response.
·         Piezo-resistive accelerometers
Piezo-resistive accelerometers use piezo-resistive materials, i.e., strain gauges. On application of the force (due to acceleration), resistance of these strain gages changes. The change in resistance is monitored to measure the acceleration.
Piezo-Resistive Accelerometer Schematic

Fig. 6: Piezo-Resistive Accelerometer Schematic


Piezo-resistive elements are typically used in micro-machined structures. They have true DC response. They can be designed to measure upto ±1000 g.
·         Variable inductance accelerometers
Using the concept very similar to the one used in LVDTs, variable inductance accelerometers can be designed.  In these accelerometers, proof mass is made of ferromagnetic materials.  The proof mass is designed in the form of core which can move in or out of the coil.
Variable Inductance Accelerometer


 Fig. 7: Variable Inductance Accelerometer


When the body is accelerated, the proof mass moves. In other words, portion of the core inside the coil changes and so the coil impedance. Thus, the coil impedance is a function of the applied acceleration.
·         Hall Effect accelerometers
Hall Effect accelerometers measure voltage variations resulting from a change in the magnetic field.
If a magnet is mounted/ integrated on a proof mass, the output of the hall element will vary according to the applied force due to the variation of the magnetic field sensed by the Hall element. Hall voltage is calibrated in terms of acceleration.
Pictorial Representation of A Hall Effect Accelerometer


Fig. 8: Pictorial Representation of A Hall Effect Accelerometer


·         Magnetoresistive accelerometers
Magnetoresistive accelerometers employ magnetoresistive effect. Resistance of magnetic materials changes when exposed to varying magnetic field. These accelerometers are similar to Hall Effect accelerometers; the only difference is the use of magnetoresistive material instead of Hall element. Hence, the change in resistance due to the applied acceleration is measured. 
·         FBG Based accelerometers
A fiber Bragg grating (FBG) is a type of distributed Bragg reflector fabricated in a short section of optical fiber that reflects specific wavelengths of light and transmits all others. When a broad-spectrum light is transmitted through the fiber, and the transmitted beam impinges on the grating, a part of the signal is transmitted through, and another part is reflected off. The reflected signal is centered at Bragg wavelengths. Any change in the grating pitch of the fiber caused by strain or temperature results in a shift of Bragg wavelength.  This is the property used for sensing of movement of mass in the accelerometers.
In FBG sensor based accelerometers, the acceleration is coupled to a mechanical load on the FBG. Due to the strain experienced by the FBGs (as a result of applied acceleration), there is a shift in the reflected Bragg wavelengths. Shift in the wavelengths is then calibrated to the level of acceleration.
·         Heated Gas accelerometers
Heat Gas accelerometers measure internal changes in heat transfer due to acceleration. These accelerometers use gas as a proof mass.
Gas is enclosed in a cavity and a heat source is suspended at the center. Two (or more) thermistors are placed at equal distances from the suspended heat source.
Under rest condition (or zero acceleration), the gas is heated to an equilibrium temperature, the heat gradient is symmetrical, and hence two thermistors are at same temperature.
Heated Gas Accelerometer


 Fig. 9: Heated Gas Accelerometer


Under acceleration, the heat gradient become asymmetrical due to convective heat transfer, the gas shifts to the direction opposite the motion (the gas is the inertial mass) causing a temperature gradient. The temperature gradient is calibrated in terms of acceleration.
·         MEMS-Based Accelerometers
MEMS is an enabling technology which allows miniaturization of existing devices, to offer solutions which cannot be attained by macro-machined products. MEMS allows the complex electromechanical systems to be manufactured using batch fabrication techniques, decreasing the cost and increasing the reliability.  It allows integrated systems, viz., sensors, actuators, circuits, etc. in a single package and offers advantages of reliability, performance, cost, ease of use, etc.  This technology is being utilized widely to manufacture state of the art MEMS-Based Accelerometers.
First MEMS accelerometers used piezoresistors. However, piezoresistors are less sensitive than capacitive detection. Most of the MEMS accelerometer use capacitive sensing principle. Typical MEMS accelerometer is composed of movable proof mass with plates that is attached through a mechanical suspension system to a reference frame. Movable plates (part of the proof mass) and ?xed outer plates form differential capacitor. Due to application of the force, proof mass deflects; the deflection is measured in terms of capacitance change.
MEMS Based Accelerometer

 Fig. 10: MEMS Based Accelerometer


SEM photograph of MEMS 3D accelerometer is shown below
SEM Photograph of MEMS Based Accelerometer

Fig. 11: SEM Photograph of MEMS Based Accelerometer

Often user fails to match the required test specifications with the available accelerometer models. Selection of a sensor requires proper understanding of the specifications. The specifications of an accelerometer include dynamic specifications, electrical specifications and mechanical specifications. Some of the important specifications of an accelerometer are as follows:
Sensitive Axis
Accelerometers are designed to detect inputs in reference to an axis; single-axis accelerometers can detect inputs only along one plane. Triaxial accelerometers can detect inputs in any plane.
Dynamic Range
Dynamic range refers to the maximum amplitude vibration that can be measured by an accelerometer before distortion occurs in the amplifier. It is normally specified in ‘g’s.
Sensitivity refers to the ability of an accelerometer to detect motion. Sometimes referred to as the “scale factor” of the accelerometer, it is the ratio of the sensor’s electrical output to mechanical input. It is typically specified in terms of mV/g and it is valid only at one frequency (usually 100 Hz) and at particular temperature (25° C). This indicates the voltage output per g of acceleration
Frequency Response
The frequency response specification shows the maximum deviation of sensitivity over a frequency range. More appropriately known as amplitude response, it is the sensitivity specified over the transducer’s entire frequency range.
The frequency response is specified over a tolerance band; they are specified in percentage and/or dBs, typical bands being ±10%, ±1 dB or ±3 dB.
Upper frequency limit is typically governed primarily by the mechanical resonance of the sensor. Lower frequency limit appears because of “high pass” filtering used for reduction of the low frequency amplifier noise.
Mounted Resonance Frequency
This is the primary (largest) mechanical resonance of the sensor when mounted on the structure. At this frequency, accelerometer shows maximum sensitivity.
Transverse Sensitivity
Transverse sensitivity is the sensitivity of the accelerometer at 90 degrees to the sensitive axis of the sensor. Also referred to as cross-axis sensitivity, it is expressed as a percentage of the axial sensitivity. Ideally, it should be zero, but can be as much as 5%.
Amplitude linearity
Often referred to as amplitude non-linearity, amplitude linearity is a measure of how linear the output of an accelerometer is over its specified amplitude range.
Amplitude linearity specifies the limits to how far the
accelerometer’s output will differ from the perfect linearity. Again, amplitude linearity is only valid at a (usually undisclosed) single frequency.
It is specified as percentage of reading; sometimes expressed in a piecewise manner also.
Output polarity
Output polarity describes the direction of the accelerometer’s output signal (whether it is positive or negative going), given a particular direction of the input acceleration.
Electronic Noise
This is the electronic noise generated by the amplifier circuit. Noise is specified as either “broadband”, or “spectral”. The broadband measurement is a measurement of the total noise energy over a specified bandwidth. Spectral noise is the noise measured at a specific frequency.
Size and Mass
Size and mass of an accelerometer can change the characteristics of the object being tested. The mass of the accelerometers should be significantly smaller than
the mass of the system on which measurement is to be done.


Though accelerometers based on different sensing principles were discussed in the previous sections, MEMS based accelerometers share the major market today, due to their obvious advantages.
Calibration of an accelerometer is to accurately determine its sensitivity at various frequencies of interest. Methods commonly employed to calibrate the accelerometers are:
1.      Gravity Test
The accelerometers having true DC response can be calibrated using this method.
In this method, an accelerometer is placed with its sensitive axis (+ and -) along the direction of gravity and the outputs are noted. Difference between the two readings corresponds to 2 g difference. From this scale factor can be computed.
Gravity Test for Accelerometer Calibration

Fig. 12 :Gravity Test for Accelerometer Calibration

2.      Back-to-back Accelerometer Calibration
This technique is arguably the most convenient method for accelerometer calibration.
Back-to-back calibration involves coupling the test accelerometer directly to a (NIST) traceable double-ended calibration standard accelerometer and driving the coupled pair with a vibration exciter at various frequencies and acceleration (g) levels. Since the accelerometers are tightly coupled together, both experience exactly the same motion, thus the calibration of the back-to-back standard accelerometer can be precisely “transferred” to the test accelerometer. 
Accelerometers are one of those sensors which find numerous applications in academia as well as in large number of industries. These applications range from airbag sensor in automotive applications to monitoring vibrations on a bridge and in many military and space systems. There are a number of practical applications for accelerometers; accelerometers are used to measure static acceleration (gravity), tilt of an object, dynamic acceleration, shock to an object, velocity, and the vibration of an object. Accelerometers are being used nowadays in mobile phones, laptops, washing machines, etc.