Cantilever and Strain Gauge

Please refer to the attached pdf file for complete question with mentioned figures and tables.

1. The cantilever and strain gauge act as the transducer in a force-measuring instrumentation system as shown in FIGURE 2. An applied force FT (the true force) is the input to the system and the output is FM (the measured force). Ideally FM should equal FT.

(a) If a weight of 50 N is applied to the end of the cantilever, calculate the strain produced half way along its length, using the data given in the table below.

(b) If the strain gauge is positioned half way along the cantilever calculate the strained resistance of the gauge for a downward force of 50 N.

(c) The strain gauge is placed in a bridge circuit as shown in FIGURE 3, opposite. Calculate the output voltage of the bridge for an applied force of ±50 N to the end of the cantilever.

(d) The output of the system simply consists of a ±1 V, centre-zero, voltmeter whose scale has been recalibrated to read ± 100 N. Calculate the required voltage gain of the amplifier.

(e) A serious problem with strain gauges is that they are temperature sensitive. The gauge metal used in the gauge in FIGURE 1(b) has a temperature coefficient of α = 0.00015 °C-1, and the gauge resistance of 120 Ω is quoted at 20°C. Calculate the percentage error in the reading caused by a temperature rise to 30°C and when the gauge is subject to a 100 N load. Assume all other components in the system remain at the ambient temperature of 20°C.

(f) FIGURE 4(a) shows four strain gauges fixed to a cantilever. The gauges have been carefully chosen for matched characteristics. For the downward force shown, the two gauges on the upper surface of the beam are stretched and therefore subject to a positive strain +e and will undergo a change of resistance ΔR = +eGR0. The two gauges on the lower surface are compressed and subject to a strain -e and will undergo a change of resistance ΔR = -eGR0. The four gauges form the arms of a bridge circuit as shown in FIGURE 4(b). Show how this arrangement can:
(i) give an enhanced output signal
(ii) largely compensate for the deleterious effects of temperature variations.