PLANETARY GEARS – INTRODUCTION
A shift gearbox enables the rider to move at different speeds while pedalling constantly. According to the rules of physics you gain more torque with speed – reducing ratios and you lose torque with speed – increasing ratios. Thus we can ride up a hill conveniently without breaking into sweat – but we need more time and if we are in a hurry we can gear up – but then we don’t have that much torque for accelerating or riding up a hill. What is commonly known as gear, consists of three gear components, because it has an input shaft, an output shaft and – not forgetting – a housing as the third gear element – which is of course not rotating. It is similar with a hub as a whole, but the gear shafts are arranged a little bit unusual – more figuratively: the sprocket represents the input shaft, the hub shell represents the output shaft and the third component is the hub axle, which is fixed non-rotating in the bike frame.
Planetary gears were not invented by space research, but it got its name from the arrangement of the gear components like a planetary system: several planet wheels (named also ‘planets’) placed in a cage called the planet carrier ( also named ‘arm’) revolve around a central sun gear (‘sun’). The planets mesh with the sun gear and a ring gear. These three gear components form a simple planetary gear train with three gear shafts. A planetary gear train can be operated in two configurations, you can find both of them in the geared hubs section. In a dual shaft gear one of the gear shafts is fixed thus presenting the housing / support. One of the two remaining gear shafts can be defined as the input shaft, the other shaft then works as the output shaft. This configuration is installed in most of the geared hubs. In a triple shaft gear all shafts are revolving which gives you the choice to drive two shafts and get one output shaft (summation gear) or to drive one shaft and receive two shafts as output (power divider). Some geared hubs also contain this gear configuration (summation gear) in which the ‘housing’ is formed by the axle as the fourth gear component being fixed.
SIMPLE PLANETARY GEAR TRAINS (DUAL SHAFT GEAR)
In a simple planetary gear train configured as dual shaft gear one of the gear shafts is fixed thus presenting the housing / support. The gear ratio depends on the gear component which is the fixed part. The sun always meshes with the planets which transfer the torque collectively to the ring gear. A planetary gear allows to transfer much more torque compared with a standard spur gearing of the same size, since several gears always mesh with each other. Most planetary gear trains in geared hubs contain three or four planets. The stationary gear ratio is is the ratio between the numbers of teeth of the ring gear to the teeth of the sun gear.
Stationary planet carrier
In this configuration the sun and ring gear are the rotation components whereas the planet carrier forms the stationary part. This is a so called stationary gear – principally a normal spur gearing with all components just rotating around their own axis but non-revolving. Sun and ring gear have different rotation directions. This configuration is not applied in hubs due to the different rotation directions, but you will sometimes find it in some industrial planetary gears or in automatic transmissions in cars or buses in which the reverse gear is implemented in that way.
Stationary ring gear
In this configuration sun and planet carrier are the rotation components whereas the ring gear forms the stationary part. It is a so called epicyclic gear, since the planet carrier is rotating and the planets revolve around the sun. This configurations allows even higher ratios than the stationary gear (i12+1) and can be found in most of the industrial planetary gears. It is very rarely applied in hubs, since you will need finely graded ratios in bikes – but you will find it in a cordless screwdriver. The Rohloff Speedhub contains a planetary gear train with fixable ring gear.
Stationary sun
In this configuration planet carrier and ring gear are the rotation components whereas the sun gear forms the stationary part – it can be fixed with the shaft. This is an epicyclic gear as well, but only small transmission gear ratios are achievable – that’s why this configuration is ideal for geared hubs. Driving the planet carrier leads to a speed increasing ratio with the factor 1+ (1/i12), always being between >1 and <2 – depending on the stationary gear ratio i12. Driving the ring gear (reverse power flow) leads to a speed decreasing ratio with the reciprocal factor, always being between <1 and >0,5. Remember for this configuration: the bigger the ring gear compared to the sun (leading to a bigger ratio i12), the closer is the ratio of this gear train. A second thing to remember for this configuration affects the rotation speed of planet carrier and ring gear: the ring gear always rotates faster than the planet carrier.
Direct gear
It is also possible to join two gear components together thus achieving a direct gear where the ratio is skipped leading to i=1:1. Coupling e.g. sun and planet carrier – the sun must remain revolvable – leads the ring gear to rotate with the same speed as the planet carrier. Some antique hubs (e.g. Fichtel & Sachs Doppeltorpedo) have applied a direct gear in that way.
Deactivated gear
In some hubs it may also be the case that the planet carrier is driven and the sun is pivoted – actually two unfixed components exist. The ring gear (as output member) will revolve slightly due to inner friction at first, but it is not able to transfer any torque. You could prevent the ring from turning and the sun gear would start to rotate then. In this way the output component of a gear train is deactivated and another gear train can get operative (applied e.g. in Shimano Nexus Inter 7).
STEPPED PLANETARY GEAR TRAINS
A simple planetary gear train provides three speeds when operated as an epicyclic gear with stationary sun: a hill gear, a direct gear and a fast gear. If you want to achieve closer gear ratios, then – according to the first thing to remember – the ring gear must be enlarged, but this would increase the hub considerably in diameter. Alternatively you could combine a second planetary gear train trying to achieve the desired overall gear ratio, but this would increase the intricacy of the hub. A stepped planetary gear train allows to achieve closer or wider ratios within one gear train.
Non shiftable stepped planetary gear trains
A small sun gear meshes with the bigger wheel of a staged gear wheel (stepped planet) and the smaller wheel of the stepped planet meshes with the ring gear (in normal size). This can be compared with two cascaded reduction stages leading to an increasing of the stationary gear ratio i12. Stepped planetary gear train with one sun only are applied in some antique hubs (e.g. Sturmey-Archer Model ‘AM’), as well as in contemporary hubs (e.g. Shimano Nexus Inter 8).
Shiftable stepped planetary gear trains
A shiftable stepped planetary gear train also contains stepped planets as described above, but every wheel of a stepped planet meshes with a corresponding sun gear, which can be selectively fixed or rotatable on the axle unit. All stepped planets are situated in a common carrier and there is only one ring gear, which could be at any position – but is mostly placed around the medium-sized sun /planet. Fixing one sun at one time result in different stationary gear ratios – the other suns must remain pivotable and fulfil a compensation movement only. With dual staged planet you receive an additional hill gear and – operating the gear also reverse – an additional fast gear, resulting in five speeds all in all. Stepped planetary gear trains are pretty common in geared hubs, e.g. the SRAM ‘Spectro S7’ model contains only one shiftable stepped planetary gear train which allows seven speeds thus gaining a good price-performing ratio due to the relatively simple gear structure. The more stages a stepped planet has, the longer it gets – and the planet cage as well – which leads to awkward balance of forces. That’s why a triple stepped planetary gear train is the highest of what you will find within hubs.
DIFFERENTIAL PLANETARY GEAR TRAINS
As already mentioned, it is also possible to operate a planetary gear train as a triple shaft gear. Some hubs contain a differential planetary gear train as summation gear, i.e. two gear components are driven and the output member revolves with the superposition of both initial speeds. This allows to get additional individual gear rations – similar to the stepped planetary gear train. In hubs with a differential planetary gear train always the planet carrier or the ring gear is the output member, never the sun. The speed of the ring gear as output member is the superposition of the single ring gear speeds which would perform when only the sun was driven (fixed ring gear) or only the planetary carrier was driven (fixed sun). The speed of the planet carrier as output member is the superposition of the single planet carrier speeds which would perform when only the sun was driven (fixed ring gear) or only the ring gear was driven (fixed sun). So let’s run through both these possibilities when planetary carrier or ring gear are driven with constant speed and the sun with more and more speed.
Ring gear as output member
Sun does not rotate: This presents an epicyclic gear with small ratio, the ring gear rotating faster than the planet carrier (small speed increasing ratio). Sun rotates slower than the planet carrier: a driven sun causes the ring gear rotating ‘relatively’ against the sun – like in the stationary gear, i.e. the ring gear will rotate slower (even smaller speed increasing ratio). Sun rotates at same speed with planet carrier: Both components can be viewed as linked together achieving a direct gear (1:1 ratio). Sun rotates faster than planet carrier: The ring gear reverse rotates faster more and more referred to the planet carrier (stationary gear) thus leading to a progressively reducing ring gear speed (speed reducing ratio). Sun rotating i12 – times faster than the planet carrier: The ring gear rotates backward – caused by the sun rotation – as fast as it rotates forward – caused by the planet carrier. The resulting ring gear speed gets zero (output standing still). Sun rotates faster than before: The ring gear rotates backward faster than it driven forward. The resulting ring gear speed gets negative (output rotating backward).
Planet carrier as output member
Sun does not rotate: This presents an epicyclic gear with small ratio, the planet carrier rotating slower than the ring gear (close speed reducing ratio). Sun rotates slower than the ring gear: A driven sun causes the planet carrier rotating in sun direction – like in the epicyclic gear with large gear ratio, i.e. the planet carrier will rotate faster (even closer speed reducing ratio). Sun rotates at the same speed with ring gear: Both components can be viewed as linked together achieving a direct gear (1:1 ratio). Sun rotates faster than ring gear: The planet carrier will rotate faster more and more – by the sun rotation – and both driving speeds will add up. The resulting planet carrier speed will get more and more faster compared to the ring gear (now speed increasing ratio).
Features of the differential planetary gear trains
As you can see, the gear ratio in these configurations depends on the factor i12 AND on revolution speed of the driven elements. Both configurations allow speed increasing and speed reducing ratios without having to revert the power transmission (like in the dual shaft gear). With the ring gear as output member it would even be possible to cause the output member standing still or driving reverse. The possibility to design the gear ratios freely make this operation mode very interesting for hubs, but it makes hubs with a differential planetary gear train also more complex: since you have at least to drive one input member with variable speed you will need one addition planetary gear train. Among the hubs containing a differential planetary gear train is the SRAM I-motion 9 as a contemporary hub and also some antiques hubs like the Sachs Elan or some Sturmey-Archer 3 or 4-speed hubs.