Problems with the ‘Indirect’ Approach
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 <1 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.
Inaccuracy comes from the number of factors in the (indirect) system’s tolerance stack up. For a system coupled by gears, these factors include (but are not limited to):
- Encoder measurement accuracy.
- Encoder thermal coefficients – i.e. drift in encoder’s output due to temperature.
- Differential thermal expansion in gears, shafts, bearings, mounts, etc.
- Gear backlash.
- Gear Wear.
- Concentricity of gears on shafts.
- Gear train/tooth strain versus torque.
- Shaft concentricity.
- Variation of gear position with shock or vibration.
- Tolerance on gear tooth position around the pitch circles.
- Tolerance on primary and secondary shaft centre distance.
- Variation in shaft centre distance – due to load or bearing clearances.
- Variations in lubrication – due to amount, type and thermal effects.
- Mechanical friction – especially stiction at low speeds/torque.
- Effect of foreign matter on gear teeth surfaces.
- Twist due to torque in shafts.
- Shaft bending due to side loading.
Each of these effects alone is probably not a major influence on accuracy. The problem arises because all these effects stack together. Experience shows that factors #1, 2, 3, 5 and 10 are larger than most engineers expect.
A common misconception in #1 is that an encoder with 1,000 counts per revolution is accurate to 1/1000th of a rev. If you read the small print in the encoder specification, it soon becomes clear that resolution is not the same as accuracy. Also, any 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 because most engineers know about antibacklash gears and will use them if required. Unfortunately, truly anti-backlash belts or chains are 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 has 10 teeth, then – because the gears are coupled (i.e. cannot jump a tooth) – when the primary rotates once the secondary gear rotates 10 times. This part is true, but 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.
As regards reliability, most engineers know that the reliability of any mechanical system is proportional to the number of parts in it – especially moving parts.
Gear, pulley or chain systems are susceptible to foreign matter – especially in a large reduction gear train. This can often be overlooked by engineers who expect their equipment will always be operated within the specified envelope and all servicing will be done by diligent, skilled personnel who always replace baffles and seals.
Experience shows this is wishful thinking. Foreign matter often arises from unexpected, sometimes bizarre, conditions. Examples of foreign matter to consider are dust, sand, mud, rain, snow, ice, hail, condensation, insects, rodents, rodent waste, mould, fungus, rogue mechanical tools, rogue mechanical fasteners, swarf (from original production), particles (from wear), coffee (from accidental spillage), cola, pollen, air-borne seeds, vegetation, water residue, smoke/cordite residue, insect faeces/secretions, snails, worms, brake/clutch dust, hair, textile fibres. Far-fetched? In my experience, unexpected foreign matter is to be expected. Recently, a CCTV had a major product recall after their housings became the ideal place for wasps to build their nests. Dead bees, bits of honeycomb, larvae, honey, pollen and bee waste will defeat a gear and optical encoder system.