Measuring Torque with Angle Sensors

This article reviews a technique for measuring torque with angle sensors which was first used in the 1950s. Although it has many advantages, the technique seems to have fallen out of fashion but is now making a comeback thanks to new developments in inductive angle sensors.

Measuring the torque applied to a stationary, metal shaft is usually straightforward. Provided the shaft’s elastic limit is not exceeded, the amount of twist in the shaft is proportional to torque. Measure the degree of twist; look up the shaft material’s Young Modulus; apply a mathematical formula from the Engineer’s Handbook and hey presto – you’ve got a pretty good measurement of torque.

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

Measuring torque with strain gauges
A more accurate way is to measure the twist in the shaft using strain gauges or surface acoustic wave (SAW) devices. 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’s ever had to use strain gauges in anger will tell you – there’s a big difference between strain gauge theory and strain gauge practice. Strain gauges tend to have big temperature coefficients and a nasty habit of coming unstuck in tough conditions. Measuring torque using strain gauges or SAW devices in the lab is often fine but not a realistic proposition for many industrial applications.

Measuring torque with angle sensors
There’s another way. It’s not at all new but it seems to have been forgotten. It was first used in the 1950s to measure torque in engines – most notably in the turbo-prop engines for the Hercules / C-130 cargo aircraft. The technique measures the twist and hence 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. For simplicity, Figure 2 below shows just the demodulated sinusoidal signal.

Figure 2 – 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. Accordingly, the phase shift is directly proportional to applied torque. Using a multi-speed resolver with a high number of cycles (e.g.128) only a small amount of twist is required to produce a significant phase shift. In other words, it’s a highly sensitive technique and suitable for measuring twists of <1 degree or even <0.1 degrees. This means that the shaft need not necessary be long. Indeed the length of shaft needed for this approach can be <25mm. 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 famously robust, reliable and accurate – that’s why they get chosen for all the tough jobs in aerospace, military, oil and gas equipment. Since they are non-contact devices there’s no need for any slip-rings or radio frequency signal transportation.

So, why has this technique fallen out of 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 notoriously expensive. Furthermore, specifying a resolver’s drive and processing electronics can be tricky. Since modern engineers are mostly familiar with digital electronics, they are perhaps reluctant to get to grips with analogue electronics and measuring phase shift of AC signals.

New generation inductive sensors
Nowadays, resolvers are increasingly being replaced by their more modern replacements – inductive encoders or ‘incoders’. Incoders operate using the same inductive principles as a resolver but use printed circuits rather than the bulky and expensive wire wound transformer constructions. This is important in minimising the incoder’s bulk, weight and cost whilst maximising measurement performance. Incoders also 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 offer the same kind of operational advantages – high precision, reliable measurement in harsh environments. What’s more, they are the perfect form factor for angle measurement – 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 eradicates the need for slip rings in the same way as resolvers.

Figure 3 – Measuring torque and absolute angle with inductive encoders

There is no need to specify and source separate electronics because all the incoder’s electronics are already within its stator. Advantageously, 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 and 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 starin gauge technique, there is no danger of damaging the equipment with excessive or shock applied torque and, what’s more, this technique provides two measurements – angle and torque for less than the cost of measuring torque with a strain gauge.

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

Measuring torque with inductive encoder

Fig 4 – Inductive encoders used for torque measurement on a 300mm shaft – stator on left and rotor on right

For more information, contact :

Mark Howard
Zettlex UK Ltd
Newton Court, Town Street, Newton, Cambridge CB22 7PE UK
T: +44 (0) 1223 874 444
F: +44 (0) 1223 874 111


Zettlex has a worldwide network of resellers and distributors. To find your local representative please visit

February 2018


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