MEASUREMENT OF LINEAR DISPLACEMENT USING LVDT

MEASUREMENT OF VIBRATION USING PIEZOELECTRIC TRANSDUCERObjectives To understand the principle/operation of piezoelectric sensor for vibration measurement.

To determine the calibration curve for the input output data To calculate accuracy and non-linearityApparatus/Equipments required Piezoelectric sensor kit with Motor assembly Digital Multi Meter Power supplyDescription of Piezoelectric SensorA piezoelectric sensor is a device that uses the piezoelectric effect, to measure changes in pressure, acceleration, strain or force by converting them to an electrical charge. A piezoelectric transducer has very high DC output impedance and can be modeled as a proportional voltage source and filter network. The voltage V at the source is directly proportional to the applied force, pressure, or strain. The output signal is then related to this mechanical force as if it had passed through the equivalent circuit.A detailed model includes the effects of the sensor's mechanical construction and other non-idealities. The inductance Lm is due to the seismic mass and inertia of the sensor itself. Ce is inversely proportional to the mechanical elasticity of the sensor. C0represents the static capacitance of the transducer, resulting from an inertial mass of infinite size. Ri is the insulation leakage resistance of the transducer element. If the sensor is connected to a load resistance, this also acts in parallel with the insulation resistance, both increasing the high-pass cutoff frequency.

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Fig.1 Circuit diagram of a typical Piezoelectric SensorOperating principle: Piezoelectric effect

Depending on how a piezoelectric material is cut, three main modes of operation can be distinguished: transverse, longitudinal, and shear.

Transverse effect

A force is applied along a neutral axis (y) and the charges are generated along the (x) direction, perpendicular to the line of force. The amount of charge (Cx) depends on the geometrical dimensions of the respective piezoelectric element. When dimensions a, b, c apply,

Cx= dxy Fy b/a where a is the dimension in line with the neutral axis, b is in line with the charge generating axis and d is the corresponding piezoelectric coefficient.Longitudinal effect

The amount of charge produced is strictly proportional to the applied force and is independent of size and shape of the piezoelectric element. Using several elements that are mechanically in series and electrically in parallel is the only way to increase the charge output. The resulting charge is

Cx=dxxFx n Where dxx is the piezoelectric coefficient for a charge in x-direction released by forces applied along x-direction (in pC/N). Fx is the applied Force in x-direction and n corresponds to the number of stacked elements. Force applied and the element dimension.Signal Conditioning Circuit

Fig.1 Block diagram for Signal Conditioning CircuitPiezoelectric sensors require some precautions when connecting to sensitive electronic components. First and foremost, the voltage levels created by hard shock can be very high, even around 100-V spikes.

More than likely, an op amp will be used to interface these sensors to an A/D converter, either discrete or on a microcontroller. One tip is to choose a high-input-impedance op amp to minimize current. Signal conditioning in a single stage can prepare the input from the shock sensor directly into an A/D converter.

Experimental Procedure

The voltage output from many measurement systems suffers from two primary shortcomings:

1. The output voltage can be noisy.

2. The sensitivity of the output voltage can be lower than desired

To overcome the above problems, an electrical circuit is designed for conditioning the output voltage from the sensor before displaying the signal. The circuit will use performs two primary functions, each of which is intended to compensate for one of the above shortcomings.

The circuit will:

1. Low-pass filter the output signal from the sensor. This will reduce the high-frequency noise in the sensors output voltage.

2. Amplify the output signal from the sensor.

This will increase the sensitivity of the overall measurement.

Fig.2 Experimental setup for vibration measurement using piezoelectric sensor1. Calibrate the sensor to the measurement system 2. Adjust the speed knob of the motor 3. Take readings for vibration by increasing value of speed5. Plot the graph for velocity and acceleration 7. Determine the best fit straight line using least squares method.8. Calculate the Sensitivity / Accuracy / LinearityOBSERVATION TABLE

S.NoInput (v)Output

Velocity (mm/s)Acceleration(mm/s2)

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2.

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4.

5.

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7.

8.

9.

10.

11.

12

13

14

15

16

Signature of staff/facultyFormula

Accuracy (%) = True value observed value / True value Non linearity ( %) = Best fit value - observed value / Best fit value ResultsAn experiment is carried out to determine the calibration curve of piezoelectric vibration sensor and static characteristics such as Sensitivity, Accuracy and Nonlinearity. The calculated values are given below:

1. Equation of calibration curve for the input output data 2. Sensitivity of the piezoelectric vibration sensor:

3. Maximum non linearity : %

4. Maximum Error: %

Frequency response of a piezoelectric sensor; output voltage vs. applied force

Gain Amplifier

Low pass Filter

Precision Rectifier

Display

Sensor