Measuring the rotation angle of large diameter shafts
04 January 2011
Traditional rotary encoders can be readily fitted to shaft diameters of less than 50mm, but what happens if your design needs a much larger diameter through shaft or bore? Mark Howard describes the traditional approach and a new, robust, more accurate approach using inductive sensors
There are many devices for measuring shaft angle. Potentiometers are simple and low cost, but are not suitable for harsh environments or continuous rotation. Resolvers are reliable even in tough conditions but their high cost, weight and bulk mean that they are restricted to ‘high spec’ applications. Optical encoders are not as robust as resolvers but are widely available, keenly priced and are often the automatic choice for engineers. There are many types, the most popular having a small (typically less than 13mm diameter) input shaft with incremental pulse or absolute digital output. Through shaft versions are available but the bore is usually limited to less than 50mm. Above this, encoder prices increase dramatically and availability dwindles.
So how do you measure the angle of a large diameter through-shaft of, say, 76mm or more? Traditionally, a smaller ‘secondary’ shaft is used and its motion geared to the larger ‘primary’ shaft. In other words, the angle of the primary is measured indirectly from the angle of the secondary. For many years, this has been the approach in gun turrets, rotary tables, radar antennas, security cameras, large motors, medical scanners and telescopes. Large bores are often needed for slip rings, cables, hydraulic pipes or fibre optics.
The motion of the secondary shaft is usually geared from the primary shaft but it could also be driven from a toothed belt or chain. Since the secondary shaft is usually small, there is a wide choice of rotary encoders and mechanical mounting is easy. If absolute (rather than incremental) angle of the primary shaft is required, then additional reduction gearing or a multi-turn encoder can be used.
‘Indirect’ approach: the problems
The angle of the primary shaft is calculated from the angle of the secondary – assuming that the rotation of the secondary varies proportionately with the primary. Not unreasonable? As ever, the devil is in the detail and, in practice, there are problems with this assumption. As a general rule, if the required measurement accuracy is less than one degree, indirect measurement is probably not going to work reliably – or at least not for long. There are two parts to the problem – accuracy and reliability.
Referring to the list at the foot of this article: each effect listed, on its own, is probably not a major influence on accuracy; however, their accumulation (or ‘stack-up’) is. Experience shows that factors 1, 2, 3, 5 and 10 are more significant than most engineers expect. A common misconception in 1 is that an encoder with 1,000 counts per revolution is accurate to 1/1000th part of a revolution, but resolution is not the same as accuracy. Moreover, accuracy calculations should account for thermal coefficients (2) and thermal expansion/contraction (3) at the temperature extremes.
Factor 4 is not normally an issue in geared systems thanks to the use of anti-backlash gears, but truly anti-backlash belts or chains have yet to be invented. Factor 9 is notable, as this is often overlooked. A typical design approach is that if the primary gear has 100 teeth and the secondary gear ten, then – because the gears are coupled and cannot ‘slip’ – when the primary makes one full rotation, the secondary gear will have rotated ten times.
That much is true. However, when the primary gear rotates 0.37125 times, the secondary will not have rotated exactly 3.7125 times. This is because there is a tolerance on gear teeth position around the gear’s pitch circle. This will cause a periodic non-linearity. In other words, inaccuracy. Depending on how good the gears are, the secondary will have rotated 3.7125 +/- 0.1000 times.
Reliability will be limited by the number of moving parts, the diligence of the maintenance crew and the system’s susceptibility to fouling.
As a general rule, if the position of an object is to be measured accurately then the measurement should be made at, or close to, the object. Measuring shaft angle directly simplifies the system and reduces the tolerance stack up, improving accuracy and reliability. So why doesn’t everyone use direct measurement? The reason is that, until recently, large bore rotary encoders were disproportionately expensive, delicate and difficult to fit.
Ring style optical encoders have been around for years but are expensive, bulky, need careful installation and are prone to failure when fouled. Similarly, large bore resolvers have been around for many years but their price, complex electrical supply/signal processing and bulk make them unsuitable for most mainstream applications.
New generation inductive devices enable a simple, effective and accurate way to measure the angle of large diameter shafts. These devices work on similar principles to contactless resolvers and are just as reliable in harsh conditions. Rather than wire spools or windings they use printed, laminar windings. This enables the construction of a low profile, annular encoder that is particularly suitable for large diameter shafts. The electrical interface is simple – dc voltage in, absolute digital data out, while the mechanical arrangement of these devices is simple and avoids gearing. The result: a simple, compact, lightweight, low inertia, accurate and reliable solution.
Mark Howard is with Zettlex
Factors affecting accuracy in an indirect system coupled by gears (not exhaustive):
1 Encoder measurement accuracy.
2 Encoder thermal coefficients – i.e. drift in encoder’s output due to temperature.
3 Differential thermal expansion in gears, shafts, bearings, mounts, etc.
4 Gear backlash.
5 Gear Wear.
6 Concentricity of gears on shafts.
7 Gear train/tooth strain versus torque.
8 Shaft concentricity.
9 Variation of gear position with shock or vibration.
10 Tolerance on gear tooth position around the pitch circles.
11 Tolerance on primary and secondary shaft centre distance.
12 Variation in shaft centre distance - due to load or bearing clearances.
13 Variations in lubrication – due to amount, type and thermal effects.
14 Mechanical friction – especially stiction at low speeds/torque.
15 Effect of foreign matter on gear teeth surfaces.
16 Twist due to torque in shafts.
17 Shaft bending due to side loading.
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