Engineering Instrumentation and Measurement Experiments

Experiment No. 2 Calibration of a Electronic Load Cell and a Bourdon Tube-Type Pressure Gage
1 Objective of experiment
The stated objective of the experiment is to familiarize students with the calibration procedure and
method of least squares
2 Background and Theory
The following descriptions of the equipment and the analytic methods for evaluating the data were
obtained from the web resources noted in the bibliography and are consistent with the presentation
in the course textbook.
In a Bourdon tube gauge, a C shaped, hollow spring tube is closed and sealed at one end. The
opposite end is securely sealed and bonded to the socket. As the gauge pressure increases the tube
will tend to uncoil, while a reduced gauge pressure will cause the tube to coil more tightly. This
motion is transferred through a linkage to a gear train connected to an indicating needle. The needle
is presented in front of a card face inscribed with the pressure indications associated with particular
needle deflections.
Two points of the wheatstone bridge are connected to an exciter voltage (from the battery or AC
adapter) and an output analog voltage feed to a A/D Converter. The output voltage being fed in
the A/D varies in proportion to the load applied to the platform of the scale. This occurs since the
weighing platform of a scale is connected to the end of the load cell via a post. The applied force
is transferred from the platform, through the post and onto the aluminum beam. When the beam
bends the strain gauges bend resulting in their resistance value to change and the voltage changes
in proportion to the load applied to the platform.
Least squares or ordinary least squares (OLS) is a mathematical optimization technique which, when
given a series of measured data, attempts to find a function which closely approximates the data
(best fit). It attempts to minimize the sum of the squares of the ordinate differences (called residuals)
between points generated by the function and corresponding points in the data. Specifically, it is
called least mean squares (LMS) when the number of measured data is 1 and the gradient descent
method is used to minimize the squared residual. LMS is known to minimize the expectation of
the squared residual, with the smallest operations (per iteration). But it requires a large number of
iterations to converge.
An implicit requirement for the least squares method to work is that errors in each measurement be
randomly distributed. The Gauss-Markov theorem proves that least square estimators are unbiased
and that the sample data do not have to comply with, for instance, a normal distribution. It is also
important that the collected data be well chosen, so as to allow visibility into the variables to be
solved for (for giving more weight to particular data, refer to weighted least squares).
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