LOAD CELLS:
An Introduction to the Design and Use of Strain Gage Load Cells

Part 1

The “Elastic Force Transducer”

People have known for centuries that heavy objects deflect a spring support more than light ones. 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 down 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.

This knowledge about the deflection of a springy rod is not confined to the human race. As we watch movies of monkeys in the trees, we realize that they have some understanding of this principle also.

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 which 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. 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.

Weight	Mark
0	0.5
1	1.5
2	2.5
3	3.5
4	4.5

On our particular scale, we note that the resolution of the ruler is 1/20 of an inch, because the marks are 1/10 of an inch apart. This is because we can tell the difference 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 which we recorded.

Figure 2. Deflection versus applied weight

If we plot these data on a graph, we find that we can connect all the points with a single straight line. An algebra or geometry teacher would tell us that the equation of this line is:

Where:

= Deflection of the spring
= Initial deflection of the spring
= Weight on pan
= Stiffness constant of the spring

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.

Adding Sophistication

We can improve the resolution of the measurements by replacing the ruler with a micrometer having a fine-thread screw, so that we can resolve one-thousandths or even one ten-thousandths of an inch. Now, as we re-run the experiment, we can easily see, by simple visual inspection of the data, that it will not exactly fit on a straight line.

Weight	Mark
0	0.500
1	1.509
2	2.516
3	3.511
4	4.495

When we look closely at the deviation of the data from our hoped-for straight line, we can see that the differences are so small that they are less than the thickness of the graph line. Such a graph would not be useful, since it would not portray any useful information except a gross representation of the zero intercept and slope of the spring’s characteristics. Therefore, in order to present the data in a meaningful form, it is necessary to modify our classical idea about the graphing of data. We will need to magnify the scaling of the graph in such a way that the deviations from a straight line are easier to see.

Rather than graphing “Weight” versus “Deflection,” we can plot “Weight” versus “Deviation from a Straight Line.” Then, it becomes necessary to choose which straight line to use as a reference. One common choice is the “End Points Straight Line,” which is the line passing through the point at zero load and the point at maximum load.

As you can see in Figure 3, the horizontal axis represents the straight line we have chosen to use as a reference. But, notice, we have given up the scaling information about the spring. We can’t calculate the “pounds per inch” constant of the spring from the graphed information. Therefore, for the graph to be most useful, we should print the scaling constant somewhere on the graph.

Also, if we choose “Deviation” for the vertical axis, it is not too useful, since we can’t relate the numbers to the performance of the spring without dividing all the numbers by the full scale output range of the test. We can help the user of the graph by performing that division ahead of time, converting the units on the vertical axis to “Percent of Full Scale.” In our example, we would divide all the deviation numbers by 4.495 (that is: 4.995 – 0.500), the range of the test outputs from no load to full load.

By using “Percent of Full Scale,” we can easily compare the performance of many springs in a way which lets us select the ones which have the characteristics we want. Later on, we will see that springs have many more parameters than just the simple spring constant which was presented earlier in the deflection equation for springs.

Figure 3. Deviation from straight line versus applied weight.

You will notice that our new graph in Figure 3 gives us a much clearer picture of the true characteristics of the spring over the range of interest.

Part 2 - A Rudimentary Load Cell: The Proving Ring NEXT >

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LOAD CELLS:An Introduction to the Design and Use of Strain Gage Load Cells

Part 1

The “Elastic Force Transducer”

Adding Sophistication

LOAD CELLS:
An Introduction to the Design and Use of Strain Gage Load Cells