Question 1 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 V, gauge factor for both gauges is G, the bridge is balanced (R1 = R2, Rg1 = Rg2) when there is no force applied. Rg1 R1 Rg1 (dummy) Vs V R$2 (active) A B Rg2 R2 T 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.

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Question 1
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 V, gauge factor
for both gauges is G, the bridge is balanced (R1 = R2, Rg1 = Rg2) when there is no force applied.
T
Rg1
R1
Pg1 (dummy)
Rg2
(active)
A
B
Rg2
R2
T
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.
(b) Suppose the measured output voltage V₁ = 65μV, given that V = 5V, G = 2.3, Young's
modulus of the beam is 250 × 10° Newton/m². Determine the corresponding strain and stress.
(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?
(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?
Transcribed Image Text:Question 1 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 V, gauge factor for both gauges is G, the bridge is balanced (R1 = R2, Rg1 = Rg2) when there is no force applied. T Rg1 R1 Pg1 (dummy) Rg2 (active) A B Rg2 R2 T 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. (b) Suppose the measured output voltage V₁ = 65μV, given that V = 5V, G = 2.3, Young's modulus of the beam is 250 × 10° Newton/m². Determine the corresponding strain and stress. (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? (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?
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