To calibrate the Velocimeter, relate the voltage signal from the velocimeter to the velocity of the tip during free vibration.
The tip displacement during free response can be described as:
(1) .
(For more information on the free response solution see: Free Vib Eqn Solution. and the Mathcad Document.)
The velocity is found by differentiating Equation 1 with respect to time and is represented by:
(2) .
At a given point in time, relate the tip velocity (derivative of the displacement with respect to time) to the voltage indicated by the Velocimeter. This is easily accomplished if you find the relationship when cos(*t) or sin(*t) equals zero.
Notice that whenever the displacement is zero, the cos(*t)term in the displacement equation must be zero. When the displacement is zero, the velocity equation reduces to:
(3) .
From the displacement versus time data, we can measure A, t, and . From these measurements we can determine the magnitude of the velocity at a given point in time. For the same time, we know the voltage indicated by the Velocimeter. By plotting the velocity versus the voltage and determining the slope of the plot, we will have a calibration factor between voltage and velocity.
Use the LVDT and/or Strain Gauges to measure the tip displacement of the apparatus. Simultaneously, measure the voltage indicated by the Velocimeter. You must make these measurements at the same time because you will be comparing the tip velocity (displacement) to the indicated voltage.
