- Question 1 17 Marks Consider Using A Pair Of Strain Gauges Attached On A Beam To Measure Tensile Stress That The Beam 1 (186.5 KiB) Viewed 15 times
(c) and (d).
Thank you very much in advance.
Question 1 (17 marks) Consider using a pair of strain gauges attached on a beam to measure tensile stress that the beam is subject to, as shown in Fig. 1 (a). The measurement system is a bridge circuit consisting of two strain gauges and two fixed resistors as shown in Fig. 1 (b). The supply voltage is V₂, gauge factor for both gauges is G, the bridge is balanced (R1 = R2, Rg1 = Rg2) when there is no force applied. Rg1 R1 Pot (duny) Rg₂ B R2 Fig. Q1 (a) Fig. Q1 (b) (a) When a small tensile force is applied to the beam, derive the output voltage V, in terms of the given parameters and the strain e. [5 marks] (b) Suppose the measured output voltage V₁ = 65µV, given that V₂ = 5V, G = 2.3, Young's modulus of the beam is 250 x 10° Newton/m². Determine the corresponding strain and stress. [4 marks] (c) If R1 and R2 are not perfectly matched, assume R1 = 1.05R2, derive the offset error voltage caused and express it in %FSD (Full Scale Deflection). Is this offset voltage systematic error or random error? If it is systematic error, how to completely eliminate it? [4 marks] (d) If use an analogue-to-digital converter (ADC) to digitalise the measured voltage for further processing, to ensure a resolution of 0.002V, how many digits should be used at least to represent the output signal? [4 marks]