Evaluation of a strain-gauge based torque measurement system
Abstract
This report evaluates and proposes improvements to the SM1009 Strain Gauge torque
measurement system, essential for applications like aviation. Three experiments were
conducted: the sensitivity analysis of diCerent Wheatstone bridge configurations, the sensitivity
analysis of the full bridge configuration and the amplifier, and the static and dynamic responses
to loading and unloading. Relative errors for the first experiment were 3.62%, 8.25%, and 8.67%
for quarter, half, and full bridge respectively. An unexpected increase in relative error from quarter
to full bridge was shown which may be related to humidity, strain gauge placement, and wiring
issues. The second experiment revealed a relative error of 15.5%, likely due to system complexity.
The third experiment highlighted the impact of noise, with filtered data showing a significantly
reduced standard deviation, and revealed an underdamped dynamic response (damping ratio =
0.005640), requiring improvement. Key improvements include implementing humidity protection,
adding a low-pass filter, and increasing the damping ratio to enhance system accuracy and
reliability.
Constant Symbol Value
Supply Voltage 𝑉! 5𝑉
Gauge Factor 𝐺 2.04 ± 1%
Torque Arm Length 𝐿 [𝑚] 1.5 × 10"# ± 5 × 10"$
Torsion Beam Diameter 𝐷 [𝑚] 1.004 × 10"% ± 3.5 × 10"&
Young’s Modulus 𝐸 [𝑃𝑎] 2.07 × 10## ± 5 × 10'
Poisson’s Ratio 𝜈 0.3 ± 0.05
Nominal Gauge Resistance 𝑅( [Ω] 350 ± 0.5
, 1. Introduction
The aim of this report is to identify improvements and enhance the reliability and accuracy of the
torque measurement system in practical applications. Accurate torque measurements are
crucial for ensuring safety in industries such as aviation. 3 diCerent experiments will be
conducted: the sensitivity analysis of diCerent Wheatstone bridge configurations, the sensitivity
analysis of the full bridge configuration and the amplifier, and the static and dynamic responses
to loading and unloading. These experiments can be used to evaluate the torque measurement
system by uncovering sources of errors, analysing changes in sensitivities between diCerent
configurations, and highlighting areas for system optimization.
2. Background Information
2.1. Mechanical System for Torque Measurement
The SM1009 Strain Gauge can be used to understand the strains and stresses in a bending,
torsion, and tension system [1] and is the mechanical system used in our experiments. In terms
of requirements, the strain gauges need to be reliable. The gauge factor is the measure of the
strain gauge’s sensitivity to strain. Therefore, a higher gauge factor is favourable since the relative
error will be lower for a given strain if the output voltage is higher.
Figure 1 - shows the optimal strain gauge arrangement for sensing maximum torsional stresses [2].
The arrangement of the strain gauges on the shaft, as shown in figure 1, significantly influences
the sensing of the strain gauges. For optimal sensitivity, the strain gauges are placed at 45° from
the longitudinal axis. The strain gauges are paired to measure tension and compression.
Moreover, the placement of the strain gauges is important. Ideally, they are situated where the
strain is predicted to be the most uniform and highest, leading to higher output voltages and lower
relative errors. Which is situated at the centre of the length of the beam.
The Wheatstone bridge circuit, as shown in figure 3, is a fundamental circuit that precisely
measures electrical resistance. The output voltage, 𝑉!"# , across the bridge can be expressed as:
𝑅% 𝑅' (1)
𝑉!"# = 𝑉$ / − 3
𝑅& + 𝑅% 𝑅( + 𝑅'
-1-
Abstract
This report evaluates and proposes improvements to the SM1009 Strain Gauge torque
measurement system, essential for applications like aviation. Three experiments were
conducted: the sensitivity analysis of diCerent Wheatstone bridge configurations, the sensitivity
analysis of the full bridge configuration and the amplifier, and the static and dynamic responses
to loading and unloading. Relative errors for the first experiment were 3.62%, 8.25%, and 8.67%
for quarter, half, and full bridge respectively. An unexpected increase in relative error from quarter
to full bridge was shown which may be related to humidity, strain gauge placement, and wiring
issues. The second experiment revealed a relative error of 15.5%, likely due to system complexity.
The third experiment highlighted the impact of noise, with filtered data showing a significantly
reduced standard deviation, and revealed an underdamped dynamic response (damping ratio =
0.005640), requiring improvement. Key improvements include implementing humidity protection,
adding a low-pass filter, and increasing the damping ratio to enhance system accuracy and
reliability.
Constant Symbol Value
Supply Voltage 𝑉! 5𝑉
Gauge Factor 𝐺 2.04 ± 1%
Torque Arm Length 𝐿 [𝑚] 1.5 × 10"# ± 5 × 10"$
Torsion Beam Diameter 𝐷 [𝑚] 1.004 × 10"% ± 3.5 × 10"&
Young’s Modulus 𝐸 [𝑃𝑎] 2.07 × 10## ± 5 × 10'
Poisson’s Ratio 𝜈 0.3 ± 0.05
Nominal Gauge Resistance 𝑅( [Ω] 350 ± 0.5
, 1. Introduction
The aim of this report is to identify improvements and enhance the reliability and accuracy of the
torque measurement system in practical applications. Accurate torque measurements are
crucial for ensuring safety in industries such as aviation. 3 diCerent experiments will be
conducted: the sensitivity analysis of diCerent Wheatstone bridge configurations, the sensitivity
analysis of the full bridge configuration and the amplifier, and the static and dynamic responses
to loading and unloading. These experiments can be used to evaluate the torque measurement
system by uncovering sources of errors, analysing changes in sensitivities between diCerent
configurations, and highlighting areas for system optimization.
2. Background Information
2.1. Mechanical System for Torque Measurement
The SM1009 Strain Gauge can be used to understand the strains and stresses in a bending,
torsion, and tension system [1] and is the mechanical system used in our experiments. In terms
of requirements, the strain gauges need to be reliable. The gauge factor is the measure of the
strain gauge’s sensitivity to strain. Therefore, a higher gauge factor is favourable since the relative
error will be lower for a given strain if the output voltage is higher.
Figure 1 - shows the optimal strain gauge arrangement for sensing maximum torsional stresses [2].
The arrangement of the strain gauges on the shaft, as shown in figure 1, significantly influences
the sensing of the strain gauges. For optimal sensitivity, the strain gauges are placed at 45° from
the longitudinal axis. The strain gauges are paired to measure tension and compression.
Moreover, the placement of the strain gauges is important. Ideally, they are situated where the
strain is predicted to be the most uniform and highest, leading to higher output voltages and lower
relative errors. Which is situated at the centre of the length of the beam.
The Wheatstone bridge circuit, as shown in figure 3, is a fundamental circuit that precisely
measures electrical resistance. The output voltage, 𝑉!"# , across the bridge can be expressed as:
𝑅% 𝑅' (1)
𝑉!"# = 𝑉$ / − 3
𝑅& + 𝑅% 𝑅( + 𝑅'
-1-
