If the steel cylinder is contracted it gets shorter, but also thicker. When it is pulled lengthwise, it also gets a bit thinner. How thick or thin it gets depends on the basic mass of the steel. It's obvious that if the steel body is very bulky, higher forces are needed to contract it to a given dimension than if it were very thin. This fact is helpful when building force transducers for different purposes: smaller transducers are used for lower nominal forces, larger transducers for higher nominal forces
. Here, the nominal force denotes the intended maximum load
of the sensor.
But let's return to the strain gauge. A force transducer generally contains four SGs, connected in a "ring" in a Wheatstone bridge circuit
, which we are not going to explain in any more detail here (learn more about it in the reference book 'An Introduction to Stress Analysis and Transducer Design using Strain Gauges
'). What's important is that the SGs are firmly attached to the steel of the transducer, and therefore undergo the same deformations it does. When the steel is deformed, the resistance of the strain gauge
changes, as mentioned above. So, the output signal from the bridge circuit provides information on how great this deformation
is. From this, we can calculate the force acting on the SG. This is how the force
From a mathematical point of view, it is interesting to see that the force transducer functions solely on the principle of linear relationships
. Hence, the force is proportional to the mechanical stress (σ=small sigma), σ is proportional to the strain. The relative change in resistance is proportional dependent on the strain. Finally, the output signal of the Wheatstone bridge is linearly proportional to the relative change in resistance of the SG.