Using Angle Sensors for Torque Measurement

Table of Contents

Measuring Torque with Strain Gauges
Measuring Torque with Angle Sensors
New Generation Inductive Sensors


This article evaluates a technique for torque measurement - which was first used in the 1950s - with angle sensors. Although it has numerous advantages, the technique had become unpopular but is now making a comeback thanks to new developments in inductive angle sensors.

Torque measurement

Torque measurement using inductive angle sensors – first used in aerospace engines for Hercules and C-130 aircraft.

Measuring the torque applied to a stationary, metal shaft is usually uncomplicated. If the shaft’s elastic limit is not exceeded, the amount of twist in the shaft is proportional to torque. To get a pretty good measurement of torque, users have to measure the degree of twist; look up the shaft material’s Young Modulus; and apply a mathematical formula from the Engineer’s Handbook.

However, measuring torque in a continuously rotating shaft is trickier. There are multiple ways to do it but the most common method is to infer torque from the amount of power required to rotate the shaft. This typically means measuring the current supplied to the motor driving the motion. It is easy, elegant but imprecise because current consumption depends on other factors such as voltage supply, speed, temperature, bearing condition, etc.

Measuring Torque with Strain Gauges

Measuring the twist in the shaft using strain gauges or surface acoustic wave (SAW) devices is a more precise way. This is accurate but has the complication of requiring either a slip ring or some wireless method of signal transfer between the strain gauges on the shaft and the outside world. As any engineer who has ever had to use strain gauges in anger will tell - there is a huge difference between strain gauge theory and strain gauge practice. Strain gauges are inclined to have big temperature coefficients and have an annoying habit of coming unstuck in difficult conditions. Measuring torque using strain gauges or SAW devices in the lab is usually fine but not a practical proposition for many industrial applications.

Measuring Torque with Angle Sensors

Nevertheless, there is another way. It is not a new one rather a forgotten way of measuring torque. It was first used in the 1950s to measure torque in engines, especially in the turbo-prop engines for the Hercules/C-130 cargo aircraft. The technique measures the twist and therefore torque in a shaft by measuring the phase shift between two ‘multi-speed’ resolvers mounted an aligned on the shaft. (‘Multi-speed’ refers to the resolver’s output: a 2-speed resolver has a cyclical output which is absolute over 180 degrees; a 36-speed resolver has a cyclical output which is absolute over 10 degrees etc.)

As the shaft rotates, each resolver produces two signals, one of which varies as a sinusoid and one which varies as a cosinusoid. Figure 1 shows just the demodulated sinusoidal signal for simplicity.

Measuring torque and absolute angle

Figure 1. Torque measurement using multi-speed resolvers.

When zero torque is applied, the signals from the two resolvers show zero phase shift. As torque is applied, the phase of one output appears to shift relative to the other. Correspondingly, the phase shift is directly proportional to applied torque. Using a multi-speed resolver with a high number of cycles (for example, 128) only a small amount of twist is required to produce a significant phase shift. Put differently, it is a highly sensitive technique and suitable for measuring twists of <1 degree or even <0.1 degrees. This means that the shaft need not necessarily be long. Indeed the length of shaft required for this approach can be <25 mm. This can be achieved using a deliberately flexible shaft or by arranging the resolvers concentrically – one inside the other – and connecting the inner and outer parts of the shaft using a (very) stiff torsion spring.

Unlike strain gauges, resolvers are known to be robust, reliable and precise, which is why they get selected for all the demanding jobs in aerospace, oil, military and gas equipment. Since they are non-contact devices, there is no need for slip-rings or radio frequency signal transportation.

Then, why is this technique not in fashion? Perhaps one reason is that resolvers have also fallen out of fashion. Pancake or slab resolvers (flat with a big hole in the middle) are the ideal shape for measuring torque but they are infamously expensive. Moreover, specifying a resolver’s drive and processing electronics can be problematic. Since modern engineers are mostly accustomed to digital electronics, they are perhaps unwilling to familiarize themselves with analog electronics and measuring phase shift of AC signals.

New Generation Inductive Sensors

Currently, resolvers are increasingly being replaced by their more recent replacements: inductive encoders or ‘incoders’. Incoders operate using the same inductive principles as a resolver but use printed circuits rather than the massive and expensive wire wound transformer constructions. This is significant in minimizing the incoder’s weight, bulk, and cost while maximizing measurement performance. In addition, incoders offer the simple and easy-to-use electrical interface: DC power in and serial data out.

Since incoders are based on the same fundamental physics as a resolver, they provide the same kind of operational advantages such as high precision, reliable measurement in harsh environments. Furthermore, they are the perfect form factor for angle measurement, which is flat with a big hole in the middle. This allows the shaft to pass through the middle of the incoder’s stator with the rotor attaching directly to the rotating shaft. This eliminates the need for slip rings in the same way as resolvers.

Measuring torque and absolute angle

Figure 2. Measuring torque and absolute angle with inductive encoders.

There is no requirement to specify and source separate electronics because all of the incoder’s electronics are already within its stator. Beneficially, incoders are available with up to 4 million counts per revolution and so only a tiny angular twist is enough to give high resolution torque measurement.

The thermal coefficient of an incoder is small compared to what can be achieved with the very best strain gauge arrangements. Any dynamic distortion effects from shafts with high angular speed can be eradicated by using the same clock signal to trigger readings in both encoders.

Unlike the strain gauge technique, there is no danger of damaging the equipment with excessive or shock applied torque and, further, this technique provides two measurements: angle and torque for less than the cost of measuring torque with a strain gauge.

It’s an early technique that has gone out of fashion, probably because resolvers have gone out of fashion. The modern inductive encoder is renewing the use of inductive physics for angle measurement and with it, reviving this useful, robust and effective method for torque and angle sensing.

Inductive encoders

Figure 3. Inductive encoders used for torque measurement on a 300 mm shaft – stator on left and rotor on right.


This information has been sourced, reviewed and adapted from materials provided by Zettlex.

For more information on this source, please visit Zettlex.

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