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# Measuring torque with angle sensors

12 December 2017

### Dr Darran Kreit discusses a technique for measuring torque with angle sensors which was first used in the 1950s. Although it offers many advantages, the technique had fallen out of fashion but is now making a comeback due to new developments in inductive angle sensors.

##### Figure 1.

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 you should have a good measurement of torque.

Measuring torque in a continuously rotating shaft is more difficult. There are several ways to do it but the most common solution 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 and temperature.

Torque measurement with strain gauges?A more accurate solution is to measure the twist in the shaft using strain gauges or surface acoustic wave (SAW) devices. While this is accurate, it does have 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. It is important to understand that there is 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 OK, but is not a realistic proposition for many industrial applications.

There is another solution – which many have forgotten and which was first used in the 1950s to measure torque in engines. The technique measures the twist, and therefore the torque, in a shaft by measuring the phase shift between two ‘multi-speed’ resolvers mounted an aligned on the shaft. 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).

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 only a small amount of twist is required to produce a significant phase shift. This makes it a highly sensitive technique that is suitable for measuring twists of <1° or even <0.1°. It is not necessary for the shaft to be long – 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 stiff torsion spring.

Unlike strain gauges, resolvers are robust, reliable and accurate. They are non-contact devices so there is no need for slip-rings or radio frequency signal transportation. One reason that this technique fell out of fashion is probably because resolvers also fell 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 costly expensive. Furthermore, specifying a resolver’s drive and processing electronics can be tricky. Since today’s engineers are mostly familiar with digital electronics, they are also, perhaps, reluctant to get to grips with analogue electronics and measuring phase shift of AC signals.

?The new generation?Today resolvers are increasingly being replaced by more modern solutions – inductive encoders or ‘incoders’. Incoders operate using the same inductive principles as a resolver but use printed circuits rather than wire wound transformer constructions. This is important to minimise the incoder’s bulk, weight and cost while maximising its measurement performance. Incoders also offer the simple and easy to use electrical interface – DC power in and serial data out.

##### Figure 2.

Because incoders are based on the same fundamental physics as a resolver they offer the same kind of operational advantages, including high precision and 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 eliminates the need for slip rings in the same way as resolvers. (Figure 2 demonstrates torque and absolute angle measurement with inductive encoders.)

Because all of the incoder’s electronics are already within its stator there is no need to specify and source separate electronics. Incoders are also available with up to four million counts per revolution, so just a tiny angular twist is enough to give high resolution torque measurement.

The thermal coefficient of an incoder is small when compared to what can be achieved with strain gauge arrangements and any dynamic distortion effects from shafts with high angular speed can be eliminated 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. This technique also provides two measurements – angle and torque – for less than the cost of measuring torque with a strain gauge.

Measuring torque with angle sensors may be an old technique but, the addition of the modern inductive encoder is now rejuvenating the use of inductive physics for angle measurement and with it, rejuvenating this useful, robust and effective method for torque and angle sensing.

Dr Darran Kreit is technical manager at Zettlex UK.