# Using Angle Sensors for Torque Measurement

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

This article evaluates a technique for torque measurement - which was first used in the 1950s - with angle sensors. Although this technique has several advantages, it had become unpopular. Now the technique is having a resurgence thanks to new developments in inductive angle sensors.

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 the torque. To get a relatively good measurement of torque, users just 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 this 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 and elegant, but also imprecise because the 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 method. This is accurate but has the complication of requiring either a slip ring or another 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 will tell you - there is a huge difference between strain gauge theory and strain gauge practice. Strain gauges are inclined to have big temperature coefficients and also 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 is often impractical for many industrial applications.

## Measuring Torque with Angle Sensors

Nevertheless, there is another method. This is not a new way, but 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.

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 does not necessarily need to 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 still popular? Perhaps one reason is that resolvers are no longer popular. Pancake or slab resolvers (flat with a big hole in the middle) are the ideal shape for measuring torque but they are extremely 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 the phase shift of AC signals.

## New Generation Inductive Sensors

Currently, resolvers are being increasingly 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 a massive and expensive wire wound in 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.

Incoders are based on the same fundamental physics as a resolver, meaning they provide the same kind of operational advantages including high precision, and reliable measurement in harsh environments. Furthermore, they are the perfect form factor for angle measurement, i.e. 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.

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

With incoders 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 at up to 4 million counts per revolution and so only a tiny angular twist is enough to give a 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 a high angular speed can be eradicated 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 of torque and angle sensing.

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.