Projects:2020s1-2511 Small-Scale Torque Gauge

Introduction

In order to estimate mechanical power delivered by a rotating machine, it is necessary to measure two variables, torque (T) and angular velocity (omega). Angular velocity is typically measured using an encoding wheel. Commercial torque gauges are typically very expensive and operate over a range that is too large for small desktop projects. In this project, we will construct a small torque gauge that is based on a spaceframe (3D-truss) together with commercially available strain gauges.

Project Team

Supervisors

• Dr. Andrew Allison
• Dr. Derek Abbott

Students

• Bohan Liu
• Weixi Tao

Background

This project aims to construct a small-scale torque gauge that is based on a spaceframe (3D-truss) together with commercially available strain gauges. Strain gauge that converts applied force or torque into a change in electrical resistance. Using strain gauges to build a strain gauge load cell to measure the torque. That has a lower cost and can be used in small desktop projects. The initial test of concept would involve the measurement of a three-phase permanent magnet machine over a range of operating conditions. In principle, this apparatus could measure dynamic time-dependent torque, as well as steady-state torque. Besides, the torque gauge could be used to measure a range of different machines for future projects and can be used as a teaching aid demonstration in the experimental class.

Technical Background

Strain Gauge

The strain gauge is the essential component of small-scale torque gauge. It is a device used to measure the strain on an object or stresses generated by

machinery. The general strain gauge consists of insulating flexible backing, which embeds different size metallic foil pattern [1]. A strain gauge takes advantage of the physical property of electrical conductance. Metallic foil would deform as the object deforms, causing the change of strain gauge electrical resistance. When measuring, ensure that the gauge is stretched or compressed within the limits of its elasticity without breaking or permanent deformation. When the gauge is stretched, the metallic foil will become longer and thinner and increase the strain gauge's electrical resistance. On the contrary, when the gauge is compressed, the metallic foil will become shorten and broaden and decrease the electrical resistance of strain gauge [2]. By accurately measuring the change of strain gauge resistance, the magnitude of the induced force on the object can be inferred.

The resistance of a standard strain gauge ranges from 30Ω to 3000Ω. When measuring under the elastic limit of the given gauge material, the resistance of strain gauge may change only one percent. If more force is applied to cause a more significant resistance change, it may cause permanent deformation of the metallic foil and damage the strain gauge. Thus, in order to apply gauge to actual measurement, it is necessary to measure extremely small changes in resistance with high accuracy.

Load Cell

The Wheatstone bridge circuit is using two series-parallel arrangements of resistances connected between a voltage supply terminal and ground producing zero voltage difference between the two parallel branches when balanced. The output voltage can be calculated by formula:

The strain gauge load cell is constructed to find the small changes in resistance more accurately. It uses the Wheatstone bridge principle to measure the output voltage by detecting the sensed force through the deformation of multiple strain gauges. Replacing the resistors in Wheatstone bridge to strain gauges, the magnitude of the force applied on the object will change the magnitude of the resistance, thereby changing the output voltage. Only replace one resistor to strain gauge in Wheatstone bridge is called Quarter-bridge circuit. When using the Quarter-bridge circuit in actual operation, the accuracy of the measurement is greatly affected by temperature and wire resistance. Half-bridge circuit, which replaces two resistors to strain gauges, can reduce the influence of these two factors and make the circuit more responsive to the applied force. Because the wires connected between two strain gauges and circuit have equal length and the effects of wires tend to be cancelled. On the other hand, the effects of temperature change also cancelled since both strain gauges will either increase or decrease resistance by the same proportion in response to changes in temperature [3]. Another way is replacing all resistors in Wheatstone bridge to strain gauges, and it is called full-bridge circuit. It is more sensitive than half-bridge circuit, but the circuit may be more challenging to build in practical.

Instrumentation Amplifier

Since the change of resistance may be very small in the strain gauge load cell, the output voltage may be tiny and not easy to measure.

The circuit needs to add an instrumentation amplifier to amplify the output voltage for more convenient measurement. The instrumentation amplifier is a type of differential amplifier that has been outfitted with input buffer amplifiers. It consists of a buffered differential amplifier stage with two buffer circuits linked together by three resistors. All resistors have equal value except R_gain. The gain of the circuit is

Methodology

Changing two resistors in Wheatstone bridge to strain gauges. When the motor turn on, two strain gauges would be compressed and another two would be stretched. Measure the output voltage can find the value of torque.

OutComes

There is an approximately linear relationship between torque and output voltage values. The torque can be calculated by measuring the output voltage of circuit.

Future Works

1. Improve the circuit to make the measurement more accurate.

2. Adjust the size of the prototype so that the gauge can measure motors of different sizes.

Reference

[1] A. C. Ugural, Mechanics of Materials, McGraw-Hill Book Co, 1991, pp. 130-134.

[2] W.J. Bock, R. Wisniewski, T.R. Wolinski, IEEE Transactions on Instrumentation and Measurement, vol.41, pp. 72-76, 1992.