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Accuracy, resolution, repeatability and all that stuff

Author : Dr. Darran Kreit is Technical Manager of Zettlex UK

06 April 2016

The terminology and fairly esoteric technical concepts applied to instrumentation are confusing. Nevertheless, they are crucial to selecting the right measuring instruments for your application.

A new generation inductive IncOder

Get the selection wrong and you could end up paying way over the odds for over specified transducers; get it wrong and your product may lack critical performance.

This article focuses on position transducers and explains some of the terminology; key considerations of specifying appropriate instrumentation for your application and some common pitfalls.

Most engineers get confused about the differences between precision and accuracy. We can explain the difference using the analogy of an arrow fired at a target. Accuracy describes the closeness of an arrow to the bullseye.  

If many arrows were shot, precision equates to the size of the arrow cluster. If all arrows are grouped together, the cluster is considered precise. A perfectly linear measuring device is also perfectly accurate.

Specifying requirements

Just specify high accurate and high precise measuring instruments every time and you’ll be ok. Unfortunately, there are some big snags with such an approach. Firstly, high accuracy, high precision instrumentation is always expensive. Secondly, high accuracy, high precision instrumentation may require careful installation and this may not be possible because of vibration and thermal expansion. Thirdly, some types of high accuracy, high precision instrumentation are delicate and will suffer failure with changes in environmental conditions.

The optimal strategy is to specify what is required. In a displacement transducer in an industrial flow meter for example – linearity will not be a key requirement because it is likely that the fluid’s flow characteristics will be non-linear. More likely, repeatability and stability over varying environmental conditions are the key requirements.

In a CNC machine tool, for example, it is likely that accuracy and precision will be a key requirement. Accordingly a displacement measuring instrument with high accuracy (linearity), resolution and high repeatability even in dirty, wet environments over long periods without maintenance are key requirements.

A good tip is always to read the small print of any measuring instrument’s specification – especially about how the claimed accuracy and precision varies with environmental effects, age or installation tolerances. Another good tip is to find out exactly how an instrument’s linearity varies. If the variation in linearity is monotonic or slowly varying, the non-linearity could be easily calibrated out using a few reference points. For example, for a gap measuring device this could be done with some slip gauges. Such a process is unlikely to be practical but it might be practical to compare the readings in a look up table against a higher performance reference device such as a laser interferometer.

An accurate shot (left) and precision shooting (right)

A common pitfall - optical encoders

Optical encoders work by shining a light source onto or through an optical element – usually a glass disk. The light is either blocked or passes through the disk’s gratings and a signal is generated. The glass disks are amazing – with tiny features that allow manufacturers to claim high precision. What is often not explicit is what happens if these tiny features are obscured by dust, dirt or grease. In reality, even small amounts of foreign matter can cause mis-reads.  What’s more, there is seldom any warning of failure – the device simply stops working altogether. What is less well known is the issue of accuracy in optical encoders and optical encoder kits in particular.

Consider an optical device using a 1” nominal disk with a resolution of 18bits (256k points). Typically the claimed accuracy for such a device might be +/-10 arc-seconds. However, what should be in big bold print is that the stated accuracy assumes that the disk rotates perfectly relative to the read head and that temperature is constant. If we consider a more realistic example, the disk is mounted slightly eccentrically by 0.001” (0.025mm).

A perfectly mounted optical disk requires such fine engineering that cost becomes prohibitive. In reality, there is a measurement error because the optical disk is not where the read head thinks it is. If we consider a mounting error of say 0.001” then the measurement error is equivalent to the angle subtended by 0.001” at the optical track radius. To make the maths easy let’s assume that the tracks are at a radius of 0.5”. This equates to an error of 2milliradians or 412 arc-seconds. In other words, the device with a specification accuracy of 10 arc-seconds is more than 40 times less accurate than its data sheet.

If you get an optical disk to be positioned accurately to within 0.001” of an inch you are doing really well. Realistically, you’re more likely to be in the range 2-10 thousandths of an inch so the actual accuracy will be 80-400 times worse than you might have originally calculated.

An alternative approach

The measurement principle of a resolver or a new generation inductive device, such as an IncOder is completely different. Measurement is based on the mutual inductance between the rotor (the disk) and the stator (reader). Rather than calculating position from readings taken at a point, measurements are generated over the full face of both the stator and rotor. Consequently, discrepancies caused by non-concentricity in one part of the device are negated by opposing effects at the opposite part of the device. The headline figures of resolution and accuracy are often not as impressive as those for optical encoders. However, what’s key is that this measurement performance is maintained across a range of non-ideal conditions.  

The quoted measurement performance of the new generation IncOders is not quoted based on perfect alignment of rotor and stator but realistically achievable tolerances are accounted for in any quoted resolutions, repeatability’s and accuracies. Further, stated performance for inductive devices is not subject to variation due to foreign matter, humidity, life-time, bearing wear or vibration.

Zettlex’s IncOder range of inductive angle encoders has become a trusted position sensor for harsh environments. The range includes mini IncOders at 37mm diameter with up to 17bit resolution, midi IncOders at 58mm diameter with up to 19bit resolution and maxi IncOders from 75mm up to 300mm diameter with up to 22bit resolution. 


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