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One important direct application of SGs is for the measurement of force or weight. These transducer devices, called load cells, measure deformations produced by the force or weight. In general, a beam or yoke assembly is used that has several strain gauges mounted so that the application of a force causes a strain in the assembly that is measured by the gauges. A common application uses one of these devices in support of a hopper or feed of dry or liquid materials. A measure of the weight through a load cell yields a measure of the quantity of material in the hopper. Generally, these devices are calibrated so that the force (weight) is directly related to the resistance change. Forces as high as 5 MN (approximately 106 Ib) can be measured with an appropriate load cell.
EXAMPLE 5.10
Figure 5.20 shows a simple load cell consisting of an aluminum post of 2.500-cm radius with a detector and compensation strain gauges. The strain gauges are used in the bridge of Figure 5.16, with V = 2 volts, R1 = R2 = RG = 120.0 W, and GF = 2.13. Find the variation of bridge offset voltage for a load of 0 to 5000 Ib.
Solution
We can find the strain for a 5000-lb load, then the resulting change in resistance, and, from that, the bridge offset voltage. First, we change the force to newtons.
(5000 lb/0.2248 Ib/N) = 22240 N
The cross-sectional area of the post is
A = pr2 = p(0.025 m)2 = 1.963 X 10-3 m2
From Table 5.1, the modulus of elasticity of aluminum is E = 6.89 X 1010 N/m2.
From Equation (5.7), we find the strain
Dl/l = F/EA
Dl/l = (22240 N)/[(6.89 X lO10N/m2)(1.963 X lO10m)]
Dl/l = 1.644 X 10-4 = 164.4 m/m (or min/in)
FIGURE 5.20 Load cell for Example 5.10.
The relation between resistance and strain is given by Equation (5.13) (GF = (DR/R)/(Dl/l), so the resistance is given by
DR/R = 2.13(1.644 X 10-4)
= 3.502 X 10-4
Because R = 120.0 W, DR = 0.04203 W. To get the bridge offset voltage, we note that the post is under compression and, therefore, the resistance will decrease. With no strain, the bridge is nulled. Under a 5000-lb load, the active gauge has R = 119.958 W. Thus, the offset voltage of the bridge is
As the force varies from 0 to 5000 Ib, the offset voltage varies from 0 to 175 mV.
The form of load cell considered in Figure 5.20 is fine for illustrating principles, but real load cells cannot be made in this simple way. The problem is that forces applied to the top of the load cell may cause it to lean or bend, instead of simply compressing. In such a case, one side surface of the beam may experience compression while the other side undergoes tension. Obviously, this will alter the correct interpretation of the result.
Practical load cells are made with yoke assemblies designed so that mounted strain gauges cannot be exposed to stresses other than those caused by the compressional force applied to the cell.
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Related Links:
Strain and Stress
Strain Gauge Principles
Metal Strain Gauges
Semiconductor Strain Gauges
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