Figure 1. Bending Beam Deflection
People have known for centuries that heavy objects deflect spring supports more than light ones do. Take, for example, a fly fisherman as he casts his line and catches a fish. The fishing pole is a flexible tapered beam, supported at one end by the fisherman’s grip and deflected at the far end by the force of the line leading to the fish. If the fish is fighting vigorously, the pole is pulled down quite a bit. If the fish stops fighting, the pole’s deflection is less. As the man pulls the fish out of the water, a heavy fish deflects the pole more than a light one does
This knowledge of the deflection effect in the example of the springy rod is not confined to the human race. As we watch movies of monkeys in the trees, we realize that they too have some understanding of this principle.
The phenomenon that is demonstrated in Figure 1 relates to the deflection of a bending beam under load. We could also determine the relationship between the deflection of a coil spring and the force that causes it. For example, when the fisherman hangs his catch on a fish scale, a heavy fish pulls the scale’s hook down farther than a light one does. Inside that fish scale is nothing more complicated than a coil spring, a pointer to mark the position of the end of the spring, and a ruler-like scale to indicate the deflection and thus the weight of the fish.
We can demonstrate a more exact quantitative relationship by running an experiment. We can calibrate a coil spring of our own choice by clamping the top end of it to a cross bar, connecting a pointer at the lower end of the spring, and mounting a ruler to indicate the deflection as we place weights in a pan hanging from the lower end of the spring.
On our particular scale, we note that the resolution of the ruler is 1⁄20th of an inch, because the marks are 1⁄10th of an inch apart. This is because we can distinguish between two readings of about half the distance between the marks.
With no weight in the pan, take a reading of the pointer on the ruler. Next, apply a one-pound weight and note that this particular spring is deflected one mark on the ruler from the original reading. Add another weight, and the deflection is one mark more. As we add more weights, we record all the readings. The table is a record of the weight versus deflection data that we recorded.
Figure 2. Deflection versus applied weight.
If we plot these data on a graph, as shown in Figure 2, we find that we can connect all of the points with a single straight line. An algebra or geometry teacher would tell us that the equation of this line is:
The idea that the transfer function of the spring scale is exactly a straight line occurs to us only because the measurements did not have enough resolution. Our straight line graph is only a rough approximation of the spring’s true characteristics.
We have now demonstrated the two basic components of a load cell: a springy element (usually called a flexure), which supports the load to be measured, and a deflection-measuring element, which indicates the deflection of the flexure resulting from the application of loads.