Team Accelerometer

Team Accelerometer - STUDY OF AN ACCELEROMETER Michael...

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STUDY OF AN ACCELEROMETER
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Michael Singerman Endri Hoxha Drew Rosecrans Michael Singerman Drew Rosecrans Endri Hoxha Q1 We have modelized an accelerometer based off of the Analog Devices ADXL150. Accelerometers are used to measure acceleration. In this report, we will look at the step response of this accelerometer under normal conditions and in extreme conditions of very high acceleration, such as a car crash. To begin, we will find a physical model of the accelerometer, and then combine it with an electrical sensor's model. To derive the equation for the accelerometer, we begin with the simple relation F=ma. We are concerned with the relation of the position between the accelerometer casing and the mass within. x m represents the mass position, while x c represents the position of the case. F represents the force on the mass. The symbol k represents the stiffness of the spring, and f the coefficient of viscous friction on the damper. The above equation is simply a force balance. Below, we will simplify the differential equation.
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Michael Singerman Endri Hoxha Drew Rosecrans The final differential equation of the system is: Once we perform a Laplace transform on this differential equation, we arrive at the following: This is the transfer function of the accelerometer, which links the position of the mass to the case acceleration. It follows the general form of a second order transfer function, The block diagram for the sensor is below.
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Michael Singerman Endri Hoxha Drew Rosecrans We model the sensor with two transfer functions. The first is for the filter that the combined signal goes through, and the second a low pass filter. A diagram of the circuit is shown below. There is a sine wave generator which is fed through two capacitances, based on the position of the accelerometer. The sine is negated through one and left alone through the other. These signals are compared and recombined through the rest of the circuit. The position of the accelerometer directly governs the relation between C1 and C2. The transfer function of section (A) is as follows: Where G and τ 1 are calculated from the circuit.
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Michael Singerman Endri Hoxha Drew Rosecrans Finally, the combined signal is sent through a first order low pass filter with unity gain, whose transfer function is: We have chosen tau2 for the purposes of modelization to truncate frequencies above 2500π radians based on the frequency of the sin wave used to generate the comparison signal in the sensor and the usual oscillations of the accelerometer. The electrical part of the sensor was modelized using transfer function blocks instead of full
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This note was uploaded on 09/18/2011 for the course EC 101 taught by Professor Staff during the Spring '09 term at INSA Toulouse.

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Team Accelerometer - STUDY OF AN ACCELEROMETER Michael...

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