Measuring torque with angle sensors

A technique for measuring torque with angle sensors first used in the 1950s is making a comeback due to new developments in inductive angle sensors.

By Dr. Darran Kreit, Zettlex UK February 1, 2018

Measuring torque in a continuously rotating shaft is difficult and there are several ways to do it. 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 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 fine, but it’s not realistic for many industrial applications.

There is another solution, which was first used in the 1950s to measure torque in engines, that many have forgotten. The technique measures the twist, and therefore the torque, in a shaft by measuring the phase shift between two ‘multi-speed’ resolvers mounted and 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 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. The phase shift is directly proportional to applied torque. Using a multi-speed resolver with a high number of cycles requires a small amount of twist to produce a significant phase shift.

This makes it a very sensitive technique 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.

Resolvers are robust, reliable, and accurate and they are non-contact devices. There is no need for slip-rings or radio frequency signal transportation. One reason this technique fell out of fashion is 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 and expensive. Specifying a resolver’s drive and processing electronics can also be tricky. Since today’s engineers are mostly familiar with digital electronics, they are also, perhaps, reluctant to get to grips with analog electronics and measuring the phase shift of ac signals.

The new generation of sensors and resolvers

Today resolvers increasingly are being replaced by more modern solutions—inductive encoders or "incoders." Incoders operate using the same inductive principles a resolvers, but they use printed circuits rather than wire-wound transformer constructions. This is important to help minimize the incoder’s bulk, weight, and cost while maximizing its measurement performance. Incoders also offer a simple and easy to use electrical interface—dc power in and serial data out. 

Because incoders are based on the same fundamental physics as a resolver, they offer the same kind of operational advantages. They are also 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 also are available with up to four million counts per revolution so 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 strain gauge arrangements. Any dynamic distortion effects from shafts with high angular speed can be eliminated using the same clock signal to trigger readings in both encoders.

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 helping rejuvenate the use of inductive physics for angle measurement and this effective method for torque and angle sensing.

Dr. Darran Kreit is technical manager at Zettlex UK. This article originally appeared Dec. 12, 2017, on the Control Engineering Europe website. Edited by Chris Vavra, production editor, Control Engineering, CFE Media,

MORE INNOVATIONS keywords: Angle sensors, measurement 

  • The most common solution to measure torque is to infer torque from the amount of power required to rotate the shaft.
  • A technique used in the 1950s measures the twist, and therefore the torque, in a shaft by measuring the phase shift between two ‘multi-speed’ resolvers mounted and aligned on the shaft.
  • Modern resolvers use angle measurement, which is also ideal for measuring torque because it has the form factor.

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