Torque Measurement Using Inductive Angle Sensors

Table of Contents

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


This article reviews a method for measuring torque with angle sensors which was initially used in the 1950s. Although it has a number of advantages, the method seemed to have become outdated until now when it is making a comeback owing to new developments in inductive angle sensors.

Hercules and C-130 aircraft

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 typically direct. Given that the shaft’s elastic limit is not surpassed, the amount of twist in the shaft is proportional to torque. Measure the degree of twist; find the shaft material’s Young Modulus; apply a mathematical formula from the Engineer’s Handbook and in the end one can have a pretty good measurement of torque.

Measuring torque in a constantly rotating shaft is difficult. There are many ways to perform it but the most common technique is to infer torque from the amount of power needed to rotate the shaft. This typically means measuring the current supplied to the motor driving the motion. It is simple, elegant but inaccurate because current consumption depends on other factors such as speed, bearing condition, voltage supply, temperature etc.

Measuring Torque with Strain Gauges

A more accurate way is to measure the twist in the shaft using surface acoustic wave (SAW) devices or strain gauges. This is accurate but has the complication of requiring either a slip ring or some wireless technique of signal transfer between the strain gauges on the shaft and the outside environment. As any engineer who has ever had to use strain gauges in anger will state – there is a huge difference between theory and practice of strain gauge. Strain gauges tend to have big temperature coefficients and a horrid habit of getting unstuck in challenging conditions. Measuring torque using strain gauges or SAW devices in the lab is frequently fine but not a accurate proposition for many industrial applications.

Measuring Torque with Angle Sensors

There is another way. It is not at all new but it looks like it has been forgotten. It was initially used in the 1950s to measure torque in engines – particularly in the turbo-prop engines for the Hercules / C-130 cargo aircraft. The method 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 two-speed resolver has a cyclical output which is absolute more than 180 degrees; a 36-speed resolver has a cyclical output which is absolute more than 10 degrees etc.)

As the shaft rotates, each resolver creates two signals, one of which differs as a sinusoid and one which differs as a cosinusoid. For simplicity, Figure 2 below illustrates just the demodulated sinusoidal signal.

multi-speed resolvers.

Figure 2. Torque measurement using multi-speed resolvers.

When zero torque is applied, the signals from the two resolvers exhibit zero phase shift. As torque is applied, the phase of one output seems to shift relative to the other. Consequently, 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 necessary to produce a substantial phase shift. In other words, it is an extremely sensitive method and suitable for measuring twists of <1 degree or even <0.1 degrees. This means that the shaft need not essentially be long. Indeed the length of shaft necessary for this method can be <25 mm. This can be accomplished using an intentionally flexible shaft or by organizing the resolvers concentrically – one inside the other – and linking the outer and inner parts of the shaft using a (very) stiff torsion spring.

In contrast to strain gauges, resolvers are notably reliable, robust and accurate – that is why they get selected for all the tough jobs in military, aerospace, oil and gas equipment. Since they are non-contact devices there is no need for any slip-rings or radio frequency signal transportation.

So, why had this method become outdated? Perhaps one reason is that resolvers have also become outdated. Slab or pancake resolvers (flat with a big hole in the middle) are the perfect shape for measuring torque but they are extremely expensive. Moreover, stating a resolver’s drive and processing electronics can be problematic. Since contemporary engineers are mostly familiar with digital electronics, they are perhaps unwilling to get to grips with analog electronics and measuring phase shift of AC signals.

New Generation Inductive Sensors

These days, resolvers are progressively being substituted by their more modern replacements – inductive encoders or ‘incoders’. Incoders function using the same inductive principles as a resolver but use printed circuits instead of the bulky and expensive wire wound transformer constructions. This is vital in minimizing the incoder’s bulk, cost and weight and at the same time maximizing measurement performance.

Incoders also offer the easy to use simple electrical interface:- DC power in and serial data out. Since incoders are based on the same central physics as a resolver they offer the same kind of operational benefits – high precision, reliable measurement in challenging environments. Moreover, they are the ideal form factor for angle measurement – flat with a big hole in the middle. This enables the shaft to pass through the middle of the incoder’s stator with the rotor attaching directly to the rotating shaft. This removes the need for slip rings in the same way as resolvers.

Measuring torque and absolute angle

Figure 3. Measuring torque and absolute angle with inductive encoders.

There is no necessity to identify and source separate electronics because all the incoder’s electronics are already within its stator. Favorably, incoders are available with up to 4 million counts per revolution and therefore only a miniature angular twist is sufficient to provide high resolution torque measurement.

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

In contrast to the strain gauge method, there is no danger of damaging the equipment with unnecessary or shock applied torque and, moreover, this method provides two measurements – torque and angle for less than the cost of measuring torque with a strain gauge.

It is an old method that had become outdated, possibly because resolvers had become outdated. The latest inductive encoder is renewing the use of inductive physics for angle measurement and with it, restoring this useful, robust and effective technique for torque and angle sensing.

Inductive encoders

Figure 4. 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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