GB2352783A - A bicycle with planetary gear train - Google Patents

Abstract

A bicycle with a planetary gear train comprises an input shaft 1 directly coupled to pedals of the bicycle, and at least one epicyclic gear 9, 12, 13 which are substantially enveloped by a sealed housing 7. The gear train is integrated into the bicycle frame by being located at a bottom bracket of the bicycle.

Description

2352783 GEARSYSTEM The present invention relates to a gear system for a

bicycle.

The brief was to design and produce a sealed three-speed gearbox of appropriate gear ratios, to which the crankarms attach, located in the same position as, and integrating, the bottom bracket on a bike. Using a single chain, and single front and rear sprockets of appropriate number of teeth and theme of the project was to produce a design that exhibited.

BMX SLmpligity, mountainbike functiongifty Which means that the gearbox should produce a bicycle transmission system that looks as simple as the single speed BMX system, but with the sophistication and performance of a mountainbike system, all in an internalised design.

The benefits of this kind of design, which has not been seen before, are multiple, but in the main:

The gearbox has:

Inherent strength, through materials selection and in-depth design to withstand the harsh environmental factors i.e. crashes, dust, and dirt.

Inherent reliability and efficiency Slick and quick gear changes.

The ability to change gear whilst stationary (or not pedalling).

All gearing parts internalised and sealed to the environment, eliminating any damage caused by the environment, prolonging the life of the product, and Building the gearbox into, and integrating, the bottom bracket.

2 Building the gearbox as a structural part of the frame.

Producing a lighter, stronger rear wheel so; If the wheel is damaged, the gears will remain undamaged, as they are internal. The wheel is cheaper to make, buy and replace.

The most important aspect of any human powered transport is the drivetrain. On existing BMX bikes, which represent the first derivation from the mountainbike, this has been adapted from conventional parts, and so retains similar functional and aesthetic qualities, which may or may not be best for the rigours of the hard riding. The best example of the BSX bike, at this early stage in their development, is made by Profile, an American BMX company. It is an adaptation of the cruiser type of BMX, with 24" wheels, but with short travel mountainbike suspension forks and three gears operated by a conventional derailleur and twist grip gear shifter.

This is really a combination of BMX and MTB and remains to be a derivation of existing technology, and as such there are problems that can be addressed to further develop the BSX bike:

A long chain is required in order to provide the range in tension needed for the three-speed cog system.

A derailleur on a 24" wheel means that is closer to the ground than in normal use, and thus more susceptible to impa( damage, which is of prime importance. This would disable the bike. The drivetrain must be protected.

If the derailleur undergoes an impact that pushes it towards the wheel (which can happen easily) this can bend a part of the frame.

3 Having a rear cog means that the drive side of the rear wheel is 'dished', which means that the spokes are attached more inboard on the hub than the non-drive side. As such, the wheel has uneven stress distribution.

Gear changes can only take place if the rider is pedalling.

Regular maintenance is required to maintain efficient operation.

In order to overcome the major problems indicated above, the solution proposed is to internalise all gear mechanisms. In this way, maintenance will be minimal, and the threat of any impact damage that would stop the gears from working would be negligible. Internal hub gears exist already, and these are analysed below 3. 1, and are conventionally designed to be built into the rear wheel.

A different way of thinking does exist. The idea of a 'gearbox' bike has been tentatively revealed at bike shows by a couple of companies - the idea being to make the have the gearbox built into the frame itself, making it a structural member, like a motorbike. However, as no alternatives exist, this involves using a hub gear with two chains - one linking the pedal driven chainring to the hub, and one to take the output of the hub to the rear wheel. The main advantages are; A stronger rear wheel - no dishing required, only a single sprocket required at the rear wheel.

A more balanced bike, with a more stable centre of gravity - hub gears are heavy, so locating it centrally on the bike (rather than the wheel) helps to balance the front and rear ends of the bike. Of course, the frame will be heavier than normal, but the rear wheel will be significantly lighter, thus producing a better handling bike.

A stronger frame - the bottom bracket area of a bike is subject to all the pedalling loads: by locating the gearbox here it can be stiffened.

4 A smaller chainring - the gears can be tailored so that less chain is used, saving weight and increasing efficiency, whilst providing better ground clearance.

Constant chain length - no derailleur, no need to have a long chain: also means constant tension and more even wear in the chain.

The hub gears used for these bikes are not entirely designed for the task, being borrowed from city bikes. In addition, the use of two chains counteracts one of the main advantages of the idea of the system - that by internalising the gears, parts can be eliminated. Having one chain would be a cleaner solution, and closer to the BMX roots of the BSX bike.

The present invention seeks to provide an improved gear system for a bicycle.

According to an aspect of the present invention there is provided a gear system for a bicycle coupled directly to the pedal rod linking the pedals of a bicycle.

According to another aspect of the present invention there is provided a gear box system for a bicycle including a plurality of gear cogs and a housing substantially enveloping all the gear cogs.

The gear system preferably uses planetary gears.

An embodiment of the present invention is described below, by way of example only, with reference to the accompanying drawings, in which:

Figure I is a perspective view in partial cross-section of a planetary gear set; Figure 2 is a table of component parts against component number; Figure 3 is a plan view and a side elevational view in cross-section of an embodiment of gearbox assembly; Figure 4 is a plan view and side elevational view in cross-section of a drive assembly of the gearbox of Figure 3; Figure 5 is a plan view and side elevational view of an output shaft assembly of the gearbox of Figure 3; Figure 6 is a plan view and side elevational view in cross-section of an output shaft assembly of the gearbox of Figure 3; Figure 7 is a plan view and side elevational view in cross-section of a retainer ring of the gearbox of Figure 3; Figure 8 is a plan view and side elevational view of slip rings of the gearbox of Figure 3; Figure 9 is a plan view and side elevational view in cross-section of an output shaft of the assembly of Figure 6; Figure 10 is a plan view and side elevational view in cross-section of a housing of the gearbox of Figure 3; Figure 11 is a plan view and side elevational view in cross-section of a driver plate of the gearbox of Figure 3; Figure 12 is a plan view and side elevational view in cross-section of a drive flange of the gearbox of Figure 3; and Figures 13a to 13c are plan views of a sun gear, a planet gear and an internal gear of the gearbox of Figure 3.

The Effect of Crank Len A major part in the delivery of power is the crank arm. As has been outlined already, when combined with the 'effective component', this produces the crank torque.

The instantaneous power P developed about the crank spindle is given by:

P=F.L.W (1) Where Fn = component of the pedal force normal to the crank arm ("effective") LC = length of the crank arm W = angular velocity, from vertical, clockwise.

6 Determination of Gear Ratios This section of research brings together the contributing factors so far explained that contribute to the pedalling of a mountain bike, and will be used to aid in the selection of the most desirable gear ratios to be built into the gearbox. These factors are built into a series of graphs and charts to visually aid selection.

Sheldon Brown Formulae From Sheldon Brown (www. sheldonbrown. com), the following formulae were obtained:

Wheel radius (nun) = RADIUS RATIO (2) Crank length (mm) RADIUS RATIO x No. teeth on front (3) No. teeth on back In this case, the gain ratio gives the number of millimetres the bicycle travels for 1 mm rotation of the cranks.

Sheldon Brown Radius Ratios Sheldon Brown has produced a table of radius ratios for varying tyre sizes, against varying crank sizes.

7 Tyre size Tyre radius 165mm 170nmi 172.5mm 175mm 180mm 26 x 2.125 330 2 1.941 1.913 1.886 1.993 26 x 1.9 324 1.964 1.906 1.878 1.851 1.8 26 x 1.5 312 1.891 1.835 1.809 1.783 1.733 26 x 1.25 311 1.884 1.829 1.803 1.778 1.728 26 x 1.0 305 1.848 1.794 1.768 1.743 1.694 Table 2 - ISO 559 Radius Ratios for common crank sizes (http://Www. sheldonbrown.com/ain.html) This allowed a size of tyre to be chosen as required to suit the calculations.

A chart of the radius and gain ratios for the selected rear block was produced, radius ratio is fixed at 1.88, since wheel radius and crank length are unchanged. Wheel radius is for 26 x 2.125 tyre (i.e. 330 mm see Table 2 above); Table 3 - Gain ratios for selected rear block Instantaneous Power The factors of crank length and pedalling rate are essential to the efficiency of pedalling.

The instantaneous power P developed about the crank spindle is given by:

Gear Rear cog no. t Gain ratio 8 th 11 6.86 7 th 12 6.29 6 th 14 5.39 th 16 4.72 4th 17 4.44 3 rd 21 3.59 2 24 3.15 Ist 28 2.70 8 P=F.LY (4) where F,, component of the pedal force normal to the crank arm LC length of the crank arm W angular velocity, from vertical, clockwise rpm = 9.42 rad/sec Inputting this data combined with that from enzail 8 gives; 2200 = Fn x 0. 175 x 9.42 Fn = 1334.55 N Thus, this is the driving force on the crank arm during pedalling at 90 rpm.

From the above, it can be concluded for the described embodiment that:

Optimum cadence is 90 rpm Choose third gear 175 nun cranks give a pedal path circumference; 2 x pi x 175 1099.56 mm x 1099.56 98960.17 mm revs in min Gives gain ratio of 98960.17 x 3.59 = 355267.00 nim movement of bike on one min = 21316.02 m in one hour = 21.3 km/h This was the theory behind the gear tables to follow, for crank lengths of 170 and 175 nim (being most used) and for chainring sizes of 38 and 40 teeth.

9 Analysis Now, by combining, the above information a full analysis of gear ratios can be made taking into account all contributing factors. This will be limited to level ground.

Crank length 170 min, chainring 38 t rpm unsurprisingly produced the highest speed selection, though sacrificing initial acceleration in first gear. The highest speed produced was 40.03 mph, with first gear spinning out at 15.73 mph. With these shorter cranks, it would be expected that with the smaller pedal arc diameter, the top speed would be higher than with the longer cranks, allowing the rider to 'spin' more - i.e. maintain a higher cadence more easily.

Crank length 175 mm, chainring 3&, led to a lower overall top speed (3889 mph), with first gear also spinning out at a lower speed (15.28 mph). However, more important is the gradient of the graph, which indicates how the changes in cog sizes affect the speed of the bike. The ideal solution would be an upward tilting straight line, meaning that there are no major leaps between gears that would require an extra effort on behalf of the rider to maintain an efficient cadence. This is less pronounced at lower cadences, here being almost straight line at 50 rpm, with a slight leap at seventh gear. This was caused by the change from a 14 tooth to a 12 tooth cog. This is magnified as the cadence increases, being well pronounced on the line for 90 rpm.

With a crank length of 170 mm, and the chainring at 40t, each rpm speed profile followed the same as with the smaller chainring, but a increased speeds, with top speed of 42.14 mph at 90 rpm. At the bottom end, first gear at 90 rpm spins out at 16.56 mph, signifying a higher initial resistance to pedalling. With the longer cranks, the profiles follow the same pattern as before, but the increases between this and chart 3 are slightly more pronounced than between charts 1 and 2. The longer cranks produce a smoother change from sixth to seventh gear, and overall, a slightly smoother profile.

The combination producing the optimum gear characteristics is:

Crank length 170 mm Chainring 40 tooth This was combined with the selected gears, with tooth sizes: 24, 17, 14, and 11. This four-speed choice eliminates the leap from sixth to eighth, which would, as well as being easier to pedal, allow quicker shifting between gears. The choice covers the whole block; thus, allowing smaller gears to ease pedalling from a standstill, with the higher gears to allow high speed riding.

Conclusions

Choosing the 'best' gears was to be used a model for the new gear system based on accurate technical data, using the exact set up currently being used on the type of bike the product is aimed at. These calculations are limited by the fact that they only depict the bike being ridden on flat ground, and can only serve as a indication of the gear performance across a known range.

The gear choice is not carved in stone, and is open to changes as they occur. This provides a logical framework for development.

The maximum rider mass was set at 120 kg This gives a weight of 120 x 9.81 = 1177.20 N, since g = 9.81 m/s' With a crank length of 175 nim, this gives a nominal torque of; 1177.20 x 0. 175 = 206. 01 Nm.

The power of rotating force is denoted by:

P = 2xpixnxT (5) where P = Power (watts), n = No. revolutions of crank per second, T = Torque (Nm) 11 Substituting nominal power figure into equation (4); 2200 = 2xpix9OxT T = 233.43 Nm (6) Substituting in the maximum power figure, when the cranks are horizontal; 5000 = 2xpix9OxT T = 530.50 Nm (7) This represents a worst case pedalling scenario.

Using the formula P = FnLW, further torque calculations can be made. With the crank length at 175 mm, and a cadence of 90 rpm, F, was found to be 1334.55 N. Since the force is perpendicular to the crank arm, this can produce a torque if the length of the crank is taken into account:

T = F x d = 1334.55 x 0. 175 = 233.55 Nm (8) This agrees almost exactly with the chosen nominal torque previously calculated. This was a differing method of calculation, but is very close to the other calculated value, differing by 13 %. Of the two, the latter takes into account a quoted power figure, which lends it a enhanced degree of accuracy, though it is not known for what weight of rider this was for. It was more logical to err on the side of caution and proceed with the larger figure, since failure is completely unacceptable. In addition, it was deemed bad practice use a figure to two decimal places, since the calculations are only theoretical.

Consequently, it was sensible to proceed with a nominal torque figure of 250 Nin (9) as first stated.

12 This figure is relevant only to normal cycling, and not the intensive sprinting of the riding outlined in the brief.

This shows that there is torque applied through simple pedalling, or even sprinting, which is measurable, but the dynamic loading is instantaneously changing and difficult to quantify. It is this type of loading that produces catastrophic failure of components, such as the bottom bracket axle. It is therefore of the greatest importance. What is needed is a dynamic factor of safety built into the components to account for these situations. For 'live loads' (shock variable), the factor of safety can be as great as 16, being the maximum load divided by the safe working load.

With the calculated nominal torque, this would mean a maximum nominal of 4000 Nni (For factor of safety 16).

The dynamic load rating for the bearings used is 370ON and 5930N for the ball and cylindrical bearings respectively. The maximum load (on the bearings) anticipated is 8000N. This load would be produced when a 890N load is applied to the pedal.

This shows that the load at the point where the pedal meets the crank arm (in this case where the bearings are positioned) the load is nearly ten times greater than that applied on the pedal itself Therefore, in order to calculate the maximum torque, the value of 800ON should be used.

The crank torque (T) was calculated as T, = (FHxCrLen x cos 0) - (F, x. CrLen x sin 0) (10) Where FHand Fv are the horizontal and vertical force components, CrLen is the crank arm length (crank spindle to pedal spindle) and o is the crank angle with respect to top-deadcentre (TDC).

This takes into account the varying nature of force application, enabling torque to be calculated at any stage within the pedal cycle. The worst case scenario to be considered would be the bike landing from a jump. In this situation, the rider will have the cranks level, with his preferred foot forward. Referring to equation 9 above, this would mean a o angle of 90' from TDC.

So, putting this into equation 9:

Tc = (FH XCrLen x cos 90) - (Fv x CrLen x sin 90) T, = (FHx CrLen x 0) (Fv x CrLen x 1) Therefore, there is no vertical component, which is logical, since the force of the rider landing the bike will be vertical. Now, let CrLen = 0. 175 m, and Fv = 800ON; T, = (8000 x 0. 175 x 1) = 1400 Nm (11) When compared to the nominal torque established already, this represents a dynamic load factor of:

1400 = 5.6 = 6 Factor of safety (12) 250 Understanding Planetary Gears Amount of speed reduction or increase = Pitch diameter of larger gear Pitch diameter of smaller gear This implies that; Speed ratio Larger gear Smaller gear 14 Planetary gears utilise a high speed sun gear meshing with a number of planets, usually three, which mesh with a ring gear (which has internal teeth). The power is transmitted through two or more load paths, than rather the single load path of a simple gear mesh.

The simplest type contains a sun gear, planet gears, a ring gear, and a planet carrier.

When the carrier rotates about the centre of the system, a point on the planet gear not only rotates about the axis of the planet gear, but also about the centre of the system. This is defined as an epicyclic. drive, and is illustrated in Figure 1.

Advantages The advantages of an epicyclic system over more conventional drives are as follows: Load shared between several meshes.

More compact than parallel shaft drives. Significant weight savings.

Smaller and stiffer components - meaning reduced noise and vibration and increased efficiency.

Input and output shaft axes are concentric - saving space and allowing the driving and driven equipment to be in line.

The coaxial feature is very important to automotive transmissions, since it makes rapid speed changes possible without necessitating taking gears out of mesh.

Rotating components can be controlled using clutches and brakes to achieve speed changes.

The resultant radial forces on input and output shafts of planetary gearboxes are zero.

Since the arrangement cancels out all radial forces, the gearbox is in effect, TRANSMITTING ONLY TORQUE. This simplifies the bearing design.

In terms of torque loading, the size of the gearbox required for a given application is dependent primarily on how large the gear pitch diameters and face widths are. These dimensions are determined on basis of tooth stresses imposed by transmitted tooth loads; Tooth load (lb) = toEque (in lb) pitch radius (in) The torque is calculated from the horsepower transmitted and speed of the rotating component; Input torque (in lb) = Horsppower Input rpm Output torque (in lb) = Horsppower Output rpm The torque cannot be considered alone, as the operating speed of the gears has a significant effect on the design definition, but other contributing factors include; Dynamic loading Tooth spacing error No. load cycles Heat generation (proportional to speed) i. e. lubrication i.e. if low speed operate with integral splash lubrication, heat dissipates through gear casing Bearing design strongly dependent on the shaft speeds. i.e. Low speed units = incorporate artificial bearings i.e. High speed industrial = journal bearings. However, there is no clear demarcation between high and low speeds. An arbitrary definition is; High speed = units with pinion speeds > 3600 rpm 16 pitch line velocities > 5000 fpm Where pitch line velocity (fpm) = measure of peripheral of speed of a gear Pi x (pitch diameter On)) x (rpm) 12 Efficiency Though this is much discussed, accurate values are actually difficult to determine, though it is possible to achieve 99%, though this requires the development of a lubrication system. Power losses are split between; Friction losses at gear and bearing contacts.

Windage losses as the rotating components chum the oil and air.

e.g. In high-speed units, churning losses may be greater than frictional losses. Therefore, the type and amount of lubricant, its introduction and evacuation are critical in terms of efficiency.

Journal bearings require significantly more oil flow than anti-friction bearings and generate higher power losses. A reasonable estimate of efficiency for industrial gearboxes is 1-2% power loss per mesh. Therefore, with a three-stage unit, the efficiency will be in the range of 94-97%. At full speeds and lower loads, efficiency will drop off because of churning losses will remain constant.

Materials The most basic decision in the design process is the selection of the gear material and its heat treatment. The strength of a gear tooth is proportional to its hardness. Within a gearbox, the gears are usually alloy steel, which usually carry the greatest load in terms of power transmission per pound of gear and offer high reliability. The gears are usually either through hardened in the range of k 32-43 (Bhn 300-400), or surface hardened in the 17 range of R,, 55-70. The hardness range between these two, R, 43-55 is seldom used as the steel is too hard.

The strongest and most durable mesh is with two surface-hardened gears using the carburising process, which leads to a minimum gearbox size, with savings in materials, machining and handling. The downside is increased costs, and due to the heat treat distortion, grinding after hardening is necessary to achieve high precision.

Suitable grades of steel are AISI 4620, 4320, 8620, 3310, 93 10, and 23 10.

The cheapest treatment is a through hardened pinion and through hardened gear, but with the downside of increased size and weight, suitable grades being AISI 4140 and 4340.

For housing materials, there is a choice between casting and fabrication. Economics favour fabrication for low production numbers, but they also favour casting for high production numbers since; Less material is used, as the casting can be shaped to closely conform to gear configuration, thus leading to a reduction in the weight of the gearbox. Also, there is more flexibility to achieve noise and vibration attenuation.

The British Standard for spur gear analysis, BS 436 Part 3 contains further specific information concerning the effect of surface treatments on gear tooth strength:

IF77?e effect of residual stress at the tooth root is included in this standard. Surface hardening processes, e.g. carburizing, nitriding and induction hardening, induce beneficial compressive residual stress at the surface balanced by tensile residual stress in the region of the caselcore junction. Grinding the tooth surface after hardening can reduce the compressive stress and may leave a tensile stress at the 18 surface. A compressive stress can be introduced (or re-introduced after grinding) by means of controlled shot peening. " This type of information will continue to be developed alongside the gear ratio modelling, with the end objective of bringing the both together in the single product.

Bottom Bracket Axle Analysis Having obtained two conventional cartridge Shimano, BB-UN51 bottom brackets that had undergone catastrophic failure, it proved to be the perfect opportunity to analyse the type of failure, so that the axle in this product should exceed this performance. One example was the left- hand side, and the other was the right hand side.

Both axles underwent exactly the same failure situation. The bikes were being ridden at a local BMX track in Bournemouth, and being jumped over a set of double jumps 21-foot apart. As could be assumed, in these cases, the jumps were not successful, with the rear wheel hitting the second jump, producing a catastrophic load on the pedals and a failure of the pedal axle. The crank arms and pedals were not damaged.

The axle itself has a square profile, with rounded edges, and is tapered along its length. - An internal screw thread allows the fitting of the crank bolt, which pushes the crank arm onto the taper and secures it in place. To remove the crank arm, a special crank extracting tool is required once the crank bolt has been removed. This screws onto an internal screw thread on the crank arm, and acts against the taper to remove the crank arm. The axle is not hollow, only drilled at each end to a depth that allows full insertion of the crank bolt.

For the first example, the fracture areas themselves are well defined and with a coarse finish, whereas the second example has a smoother lined appearance.

With the first example, the coarse area identifies the section involved in the final failure. Evidence of striations is localised and minimal, which according to above, implies that this 19 axle was subject to only a few cycles of high strain loading, which lead to failure. The failure type is low cycle high strain, during which "the general plasticity quickly roughens the surface, and a crack forms there, propagating first along a slip plane. " The second example, with smoother finish and more clearly defined striations shows a differing type of failure. The striations are evident in a different location to the previous example also; being situated on the material after the internal screw has finished. In fact, this section is of a length that actually extended to the bearing contact surface within the bottom bracket. It is possible to see the bearings within the formerly sealed unit. The evidence points to higher cycle strain, and this is backed up by the fact that the bottom bracket as a whole is markedly more aged than the other example - with rust visible on the casing and axle.

The conventional cartridge bottom bracket has been shown unsuitable for the rigours of the desired type of riding. The square profile axle produces stress raisers leading to catastrophic high strain failure in extreme situations. Clearly the components failed in fatigue. It is exactly these circumstances in which the axle should maintain structural rigidity. For the purposes of this project, and alternative design needs to be found and employed.

For years, performance BMXs have used a robust bottom bracket arrangement, whereby the cranks clamp to a solid splined axle, providing a large contact surface area to spread the load. This is now beginning to spread to mountain bikes. A new downhill full suspension bike uses a BMX bottom bracket set-up for this reason.

Shimano have released a crank/bottom bracket partnership designed specifically for downhill under the same principles. The BB-M950 bottom bracket and FC-M952-DH downhill crankarms are well used on the international race circuit. The oversized hollow axle (22 min diameter) provides greater rigidity with no weight increase and the splined crank arm mount increases rigidity of the crank arm-spindle joint. Also the multi-bearing design. "Ball and needle bearings provide wider support to reduce bottom bracket flex".

Gear Ratio Modelling With the gear ratios chosen in 3.2.5. the gear ratios could be calculated. These were; Gear Tooth combination Ratio I St 40/28 1.43 1 2 nd 40/21 1.90 1 3 Td 40/16 2.50 1 4 th 40/12 3.33 1 Table 4. -Chosen ratios One of these gears was decided to be exterior, as the final drive chainring/sprocket combination. Therefore, only three gears needed to be accommodated internally, thus promoting a lighter weight gearbox, and partially simplifying manufacturing processes. This was decided at 40/12, since this produces the shortest possible length of chain, thus exploiting the advantages of the design.

This set-up would require a direct drive through the axle to engage this gear. All other gear ratios would have to pass through the 40/12 final drive too, and so the ratios must differ in order to account for this; So, for l't gear, through the 40/28 final drive; r x 40 = 40 r = 3 = 0.43 (13) 12 28 7 This was carried out for the other gears, giving; 1" 0.43 2n' 0. 57 3rd 0.75 21 Therefore, this requires a step up, followed by a step down. In terms of a planetary array, this would require a stationary ring gear, with input on the planet carrier (from the cranks), and output on the planets and sun gear (to the chainring).

There exist many layouts that can utilise the multiple degrees in planetary systems.

With the axle driving the cage, a speed change would occur between it and the inner cage if the outer cage. Thus, the chainring could be attached to the inner cage, and be driven at a faster speed than the axle, thus producing a speed ratio. Within a conventional gear based planetary arrangement, this is the same as the driving the planet carrier, with the ring stationary, and output from the sun gear.

In order to calculate the possible gear ratios, this is defined by the formula; Rota. speed of shaft and inner cage (I + D,,/D,) x Rota. speed of cage (14) Where Do = Diameter of outer ball race Di = Diameter of inner ball race If we take the established optimum cadence of 90 rpm, and measurements for D,, and Di from an example SKF bearing:

Rota. speed of shaft and inner cage = (1 + 54/38) x 90 = 217.89 rpm (15) So, for an input of 90 rpm, the output of the shaft = 218 rpm, meaning a speed increase with ratio 1:2.42. The above equation can be simplified if it is considered that by dividing the left side by the rotational speed of the cage, a pure ratio can be obtained; Rotation of inner race per rev. driver = I +Diameter outer race (16) Diameter inner race 22 This is quicker to use and understand.

Now involving the decided ratios combined with 40/12 chainring/sprocket set-up:

For l't = 0.43; 0.43 = (I + DO/Dj) DO/Dj -0.57 (17) 2nd = 0.57; 0.57 = (I + DO/Dj) DO/Dj -0.43 (18) 3rd = 0.75 0. 75 = (1 + DO/Dj) DO/Dj = -0.25 (19) It is not possible to have an outer race smaller than an inner race, so there was a problem with this way of thinking. By internalising all four gears and eliniinating the 40/12 combination, the problem was thought be overcome. Also, as small a combination as possible could be used to shorten the chain as much as possible.

With a 1: 1 combination, say 22t: 22t, the ratios are back as they were first calculated.

Gear Tooth Combination Ratio ist 40/28 1.43: 1 2 nd 40/21 1.90: 1 3 rd 40/16 2.50: 1 4 th 40/12 3.33: 1 Table 5 - - Gear ratios Prototype No. 1, which showed the bearing planetary drive principles examined above, which could be transposed to a gear based system using the same equation. Committing to metal gears at this stage would have been expensive and unnecessary. Instead, the SKF bearing, used for calculation above, was used in the actual prototype. This was press fitted 23 to the casing of a sealed Shimano UN-51 bottom bracket, with a chainring spider bonded directly to the casing. Therefore, the casing became the output axle, with the pedal axle as input. A contact was machined which connected the crank arm to the bearing cage, and exterior race of the bearing was press fitted into a shell that was to be held stationary. This completed the prototype.

This prototype was successful, and showed the method of gear ratio creation. The actual operation was subtle and elegant. To the uninitiated spectator, it was not obvious what was actually going on. This was due to the coaxial arrangement, whereby the crankarms were rotated at one speed, driving the bearing cage, and the smaller inside race was driven at a faster speed dictated by the difference in diameters. Chain length was mininlised, with a 22/14-tooth chainring/sprocket combination, and the SKF bearing used in 3.5 giving the gear ratio of 2.42.

This equates to 1:3.8 speed increasing gear system. This is comparable to a 40/11 combination which is representative of a top gear on the desired type of bike.

This gear could be translated straight into the final product. At this stage, the prototype represents a product of its own. It has the clean uncomplicated appearance of a BMX drivetrain, with the hidden technology required by a mountain bike. The operation is smooth and quite deceiving. When constructed with a single planetary arrangement with adequate bearings, this would produce a system using a much smaller chainring, and shorter chain, one of the main aims of the project. At this moment, it could be conceivably be used with a three-speed rear block and a conventional derailleur. This product is a planetary bottom bracket, add the two more ratios and it becomes the final aim of the gearbox.

A feature that has been overlooked is that of a clutch. However, rotating the cranks on the prototype reminded the designer that this was not a problem. The clutch already exists within the freehub of the rear wheel. Thus when pedalling backwards, the gear drive is disengaged as required. This differentiates the gearbox already from existing hub gears, and has simplified it, so already weight has been saved. This is excellent. On the BSX 24 bike, a rear cog from a cruiser BMX would be specified, as this has a clutch mechanism built-in and only a single cog. Compatibility already exists.

As to whether bearings can be used, this area need not require a great deal of investigation. The thought now is that slip will occur under heavy pedalling. In fact, with chainring part locked on the prototype, it was managed to cause slip to occur by hand. This was a heavy duty bearing, and slip was easy to accomplish. Metal gears are used for applications like this for a good reason, and one that should be adhered to.

Ideas Early design ideas took in a wide range of influences and ideas starting initially with the bearing based idea, combined with the desired axle type described above. The main concept prevalent through these ideas was that of the differing rotating concentric diameters producing differing speeds. This is the important aspect of planetary gear systems.

However, early problems encountered were related to how multiple ratios could be achieved. With two degrees of freedom, these systems are difficult to visualise mentally. Time was spent working out exactly what should be held still and what needed to rotate.

A correct schematic representation of the elements involved had been found which assisted with these problems and tallied with layouts found in reference books. From an early stage, it was appreciated that to obtain a properly functioning product, calculations would have to be made from first principle ideas. This became known when the designer began to wander from established planetary systems.

Conical Drive This was a logical development of the first prototype, and underwent serious evaluation. For example, a feasibility study was made into a range of possible set-ups. The principle was that conical discs separated radially arranged balls. By changing the position of these balls, a difference in diameter was established, so that drive took place in the same way as in the single bearing arrangement. Multiple stages of this would produce a magnified effect and increasing gear ratios.

Efforts were made to match the system to the chosen gear ratios, and to fit it in a relevant space. It was found that it could have been made to work somewhat, but sufficient confidence did not exist to develop this further. No backup research could be found to validate the design, so it was decided that to continue would be a gamble. A product was needed of the type which every aspect of it's design could be justified from established traditional ways of thinking. This was not to say that there was no room for innovation, but this would be within a framework of wellestablished technical criteria.

Planeta1y Ideas The diversion to the conical drive and subsequent dismissal of it produced a new focus in development work. The required elements began to show themselves.

The system had to be speed increasing, which narrowed the layout to one or two established methods.

The gears had to be spur gears, and be strong enough to withstand the torque and dynamic loading.

The ratios should mimic the existing system A gear manufacturer was found in HPC Gears, which enabled loading analysis and spatial requirements to be related directly to available parts.

A stripped down and specific brief for the preferred embodiment was now:

To establish system that:

1. Produced three gears of differing speed increasing ratios that were feasible for use on BSX bike.

2. Utilised spur gears from HPC Gears that were:

26 (a) strong enough to take specified torque's and dynamic loads. (b) of a size that would produce a gearbox of size feasible for a BSX bike.

The Wilson Type Gearbox is very similar to the desired layout of the project gearbox, especially when the example gear ratios were stated, 4/1, 2/1, 1.511, 1/1, (and reverse) -4/1. Ignoring the reverse gear, these ratios are within the realm of the project, although adaptation was required to turn these into speed increasing rather than speed reducing ratios.

By reversing the Wilson gearbox, a feasible design can be reached that is technically feasible. In addition, it defined the ratios needed to produce these gears:

A1=3S, A2=2S2 Where A = no. teeth on annular A3=2S3 S = no. teeth on sun (20) The number of teeth in the planer would be chosen so that S + 2P = A Epicyclic Selective Speed Transmission Though the layout above would have been acceptable, areas needed improving. For example, with two stages the same and one requiring a different ratio set-up, this would lead to one stage having a larger diameter. The ideal solution would be three identical stages, giving a constant diameter throughout, meaning that enclosure would be simpler.

Taking an input rpm of 90 rpm the calculations give ratios 1: 3, 1:1.8 and 1: 1. 42, with a 1: 1 chainring/sprocket combination. This corresponds to 40/13, 40/22, and 40/28 and is a closer grouping. However, the best feature is that all three stages are exactly the same, featuring the same ratios:

A1=2S, 27 A2= 2S? Where A = no. teeth on annular A3=2S3 S = no. teeth on sun (21) Torque Distribution Torque distribution is how the input torque is split between the constituent gear parts. This information allows the individual forces on teeth to be established, and thus, the tooth loading will define the necessary gear material, facewidth, modulus, and hardening processes. This will satisfy 2 (a) above.

For the chosen system, with every one of the three stages the same and a single annular braked at any one time, the torque formulas for each separate gear part are:

input output Reaction Ts TC TA Carrier (C) Sun (S) Annular (A) ZJC +Tc -Tj N I N +71 N+1 Table 6 - Chosen arrangement torque equations Given that A = 2S (23) These equations become:

Ts Tc TA - T +TC -Tj 11 :m-c 3 3 Table 7 - Simplified equations applicable to chosen design If the train is transmitting power and is in equilibrium, then the sum of the torques must be zero - TA+ Ts + Tc = 0 (24) 28 Therefore, this was used as a check for any calculations made to verify their validity. Therefore, this is exactly what happened. Using the formulae above and the input torque of 1400 Nm, the following torque values were calculated:

Tc = +1400 Nrn (applied to carrier) (25) Ts = - 466.67 Nrn (applied to sun) (26) TA = - 933.33 Nrn (needed to restrain annulus) (27) Adding these together does indeed give zero. folio.

In order to select the correct gear size, the individual torques and corresponding tooth bending stresses were required for each part of the system. By calculating the highest possible loading on a tooth during loading, this would allow the strongest gears to be specified.

With Tc calculated as 1400 Nm, it was then assumed that this would be split equally between the planets, be this 3 or 5, with each planet having two meshes at any given time. There were differing avenues for the tooth loading calculation, each valid in their own way.

Force Analysis of Spur Gears AGMA Approa AGMA stands for American Gear Manufacturer's Association.

Failure by bending will occur when the significant tooth stress equals or exceeds either Yield Strength or Endurance Limit.

Surface failure occurs when significant contact stress exceeds surface endurance strength.

BS436: Part 3: 1986 British Standard Spur and Helical Gears 29 Part 3. Method for calculation of contact and root bending stress limitations for metallic involute gears This British Standard lays out a full procedure for tooth bending stresses, in every detail. To quote the introductory "Scope and field of application" section:

"This Pail of BS 436 is a general application standardfor spur and helical external gears of accuracy grades 3 to 10 operating at any pitch line speed... 77ze standard covers methods for determining the actual and permissible contact stresses and bending stresses in a pair of involute gears. Stress levels on the tooth flank and in the tooth root are calculated and compared with basic permissible stress levels derived from simple test specimens... Procedures are included for calculating the peak load capacity andfor taking account of variable duty.

Of course this standard contains all the calculations that would ever be needed to confidently select the strongest possible gear material and heat treatnient, and it was originally intended to work through this whole standard to assist with the gearbox design. However, this idea was dropped, as there were too many unknown factors. There was no point in spending the time working through a huge number of calculations unless the designer was sure about absolutely every part. As it was, the results may not have been dependable. Nevertheless, the standard was cut up and the process laid out on A2 paper (See Folio 2) and would be beneficial for subsequent backup work. Subsequent prototypes to the one emanating from this project are consequently recommended to follow this procedure, but for this design, this was deemed to be too in depth, and may distract from other important areas of study.

A simpler process was required that would produce gear selection strong enough for the prototype, which would not undergo the actual demands in the specification.

Chosen Analysis Process The process used to verify gear strength was taken from the initial stages of the AGMA approach, taking the following formulae in this order; Torque, T = d x W, (28) 2 Thus, with the torque known from the previous calculations, W, can be calculated, and substituted into the following equation to calculate the stress:

Stress W (29) LL4:,. 1, KvFmY where F face width (mm) m module (rnm) 11 t - W, tangential load (N) Importantly, this takes into account "meshing and loading at zero velocity", which equates to dynamic loading. This is seen with the inclusion of velocity factor Kv, which is:

Kv 6.1 (30) 6.1 + V where V = pitch line velocity (m/s) This full process was followed, substituting in different module and face width values directly from the HPC Gears catalogue.

Gear Selection This process took a large amount of time, but justifiably so, given its importance to the project. Throughout, it had been crucial that the gearbox should be designed strong enough 31 to withstand the large dynamic forces encountered in operation. In addition, gears had to be chosen to suit the prototype, which only had to work once, running parallel to the derivation of an optimal solution for production models. However, calculations were made based on the worse case scenario for a theoretical best design, and the nominal scenario (input torque 250 Nm) for the prototype.

In SuMMM - Product Functionalfty

The design solution came to be a selective speed epicycle transmission from above except reversed to form a speed increasing system rather than a speed reducing system. The specification of the product was to have three identical planetary stages fulfilling equation (23), with gears of strength withstand the torques (since a planetary gearbox transmits only torque) in equations (25, 26 and 27).

An example of gear system is described below with reference to the accompanying drawings.

Assembly Assembly was carefully achieved, with alterations made to the nylon slip rings (parts no.AP2003, AP2004, see Figure 8) in order to space out the internals as required. Given the very high quality of manufacture, no problems were encountered in aligning the gears. The pins had to be filed down in order to fit the oilite bushed, but that was the extent of necessary modifications. Assembly is as follows:

The first set of pins are fitted to the flange of the input shaft.

Small nylon slip rings are fitted over each pin- The first series of planet gears (already with oilite bearings press- fitted in the bore) are slid over the pins.

More slip rings are added, being left flush with end of the pin.

The output shaft AP2005 (with sun gears bonded at 15 min intervals) slides easily over the input shaft AP2001.

32 Qty 1 drive assembly AP2020 is added, with pins and planet gears already in place on the planet carrier side, with clearance of the sun gears on the inside diameter. This completes the first stage, and provides half of the second stage.

This is repeated to provide the second stage.

The drive assembly containing drive AP2008, which is not a planet carrier and has a bearing contact with the output shaft AP2005, is put in place.

A large slip ring AP2004 is slid over the output shaft, providing a frictionless contact between this and:

Driveplate AP2009 is the final part, being secure to the output shaft via two setscrews.

A circlip then secures the whole assembly.

From discrete parts to full assembly took 3 hours, with time taken up by having to dress the pins to fit properly, and adjust the slip rings to space out the assembly fully.

Performance Coaxial Running Drive was dependent on the input and output shafts being able to rotate coaxially. With the full assembly built up, rotation and drive was achieved, and relatively smoothly too. This was aided by the addition of grease to the gears, but drive from input to output was visible.

Ratio Anglysis In order for a gear ratio to be selected, a single annulus has to be braked. This was achieved manually. Marking a point on the circumference of the crankarm. end of the input shaft, and lining this up with a similar mark on the drive plate and the braked annulus allowed comparisons to be made between input and output rotation. One rotation of the input shaft was made, and the number of rotations of the drive ring were noted, and the resultant angle between the mark on the drive plate and that on the input shaft. Therefore, 33 by calculating the total rotation of the drive plate in degrees, and dividing by 360 (the total rotation of the input shaft), the gear ratio could be found.

Gear Theoretical Ratio Rotation of Flange Actual Ratio First 1 1.42 5100 1 1.42 Second 1 1.80 6450 1: 1.80 Third 1 3.00 10800 1 3.00 Table 8 Comparison of theoretical and actual gear ratios As can be seen, the theory and the reality match perfectly. - Each gear is as required and smoothly realised in the prototype. The power delivery from input to output is smooth and noise free.

Constant Mesh Theoretically, the gear changes should occur without shifting any gears in or out of mesh i.e. constant mesh. This is true of the prototype. The gears are free to rotate on their individual shafts, so that when gear engagement takes place, the two degrees of freedom in the unbraked stages contributes to output drive. The mesh is constant transmitting load between all gears, whatever the speed selected.

Housing The planetary stages are secured within the housing successfully. No lateral movement can be detected, and the mating surfaces contacting the drive flange AP2009 and input shaft AP2001 run together very smoother with a layer of grease. This effectively seals the gearbox.

Gear Change (ref drawin2 no. AP2006 Housing) Provision was made for gear change with a series of three tapped 5mm holes through the housing and lining up with the individual planetary stage annuli. The theory was that by screwing down a set screw (Item 15, part no. NTM5-1 1) the annulus would be braked and a gear engaged. In practice this did not occur.

With a set screw engaged, the assembly as a whole is braked, and the gear is not engaged. This was true for each annulus in turn.

AP2001 ILaput Sha Specification Design riteria

0 Qty 1 off 0 This is the shaft to which the crankarms would attach. It runs insidF the output shaft but drives it at the same time via the gears.

0 Stainless steel 0 It must:

a BS S130 0 provide strength for consistent power delivery 0 Run smoothly inside the output shaft 0 Input shaft, running 0 Provide faces that seal the gearbox when in the housing.

coaxially with output shaft Provides locating feature for a circlip AP2005 (see drawing no.

AP2010) no bearings present 0 Solid design, with a knurled handgrip on one end, gearbox internals retained by circlip on other end 0 5 hrs manufacture.

This was a crucial design element of the gearbox. A central feature of the design is that the input and output axles are coaxial, that is, one rotates inside the other. Original design ideas intended the two to be separated by sealed bearings but this posed assembly problems, that would also complicate machining processes due to the close tolerances requires. The design of this part was hand-in-hand with the output shaft AP2005, and this was originally intended to be a standard mountain bike bottom bracket axle. However, given the stress analysis above this was the wrong way of thinking. The new design gave latitude for a completely new axle design, and so that idea was thrown out.

By doing away with the bearings and the axle, there was complete freedom to design a simplified system that was more representative of the final product, whilst also easing the task of manufacture. Therefore both axles became the bearing surfaces, and the problems were solved.

The axle was designed with function in mind. It was not expected that it would be possible to ride the gearbox, and so end was equipped with a knurled handgrip, allowing handheld operation of the gears. The axle at the other end was extended, so that a crankarm. could be fitted as required. AP2002 Retainer Specification Design Criteria

9 Qty 1 off Must be of dimensions that secure the housing and the shaft when in place.

0 Aluniinium alloy Must not hinder smooth rotation on the input and output shafts.

0 BS L168 Must be slotted to fit over knurled grip.

0 Attaches to part no.

AP2006 Housing Must be firmly se cured to the housing, the only stationary element in the design 0 Addition of nylon washer smooths rotation 0 3 hrs manufacture The design is built around a large number of simultaneously rotating parts. Consequently, problems arise with securing the product within a housing (AP2005). A part was needed to prevent lateral movement of the housing. Therefore, the design of this part arose, being a slotted end plate, securing to the housing via three countersunk Allen key bolts and 36 maintaining its alignment with the input shaft AP2001, whilst not preventing any necessary rotation.

The first design was a simple plate, with the addition of a slotted nylon washer that spaced out the gap between the face of the housing and the knurled grip, giving a very integrated design.

Optimal Desig This would have to be re-designed in direct relation to the housing, although there is no functional problem with this design.

Provision would have to be made for the ftill sealing of the unit from the elements.

The slot could be smaller, given that the knurled handle would no longer be necessary.

AP2003 / AP2004 Slip Ring Large and Small Specification Design C iteria

0 Slip ring, large and 0 Small ring dimensioned to a bore to accept pin DP4.0-24, and small. space out gaps between planet gears YGO.8-18, and drive AP2008.

0 Nylon 66 0 Large ring dimensioned to same bore as output shaft AP2005, allowing simultaneous rotation of two separate parts, AP2030 0 2 hrs manufacture (small, drive assy and AP2009 drive flange.

qty 18) 0 Given that the precision fining of circlips has been removed, these a I hr manufacture (large, parts should be easily modified to adjust the overall fit of the qtyl) parts.

Although every part in the design is critical to the overall efficiency and successful operation of the final product, these small parts bring the whole thing together. With the elimination of the circlips and the subsequent pins, there was a need to ensure that all parts remained equispaced, and that all gears aligned correctly. It was decided to use nylon washers for the following reasons:

37 Easy to modify by hand as the prototype is being assembled to adjust any required spacing. Friction reducing, so act as bushes to assist rotation.

Therefore, basically the theory was to pack the gearbox with these washers to eliminate any lateral play.

Opjunal Desig With a full production design, it would be expected that the dimensional accuracy of all parts would be of a sufficient standard as to eliminate these parts. In fact, the manufacturing quality of the prototype was of a sufficiently high standard as to make this happen. It was just that pins and circlips would have been too expensive and complicated to include.

AP2005 Oytput Shaft Specification Design Criteria Qty 1 off 0 Must form contact comparable to plain bearings with input shaft Stainless steel AP2001 BS S130 0 Must allow location and fixing (by Permabond 601 Retainer) of sun gears, which have a maximum allowable bore of 20 min Running coaxially around input shaft AP2001 Drive flange AP2009 attaches via two set screws 3 hrs manufacture The design of this part was dictated by the strength qualities of the sun gears. A maximum bore of 20 mm was acceptable, and any greater than this would lead to a noticeable decrease in strength. The designer wished to have the biggest bore possible to increase the diameter 38 of the input shaft AP2001, but had to accept the 20 mm and design everything else around that.

The outside diameter was toleranced to provide a free running fit with the sun gears, allowing bonding with Permabond 601 Retainer, which was successful, the assembly shown in drawing no. AP2010.

The drive flange AP2009 attaches to the end via set screws, so this did not require any further machining to the shaft.

Optimal Desig This part has a lot of opportunity for re-design, and for elimination of parts.

A good design would be to combine the shaft and the sun gears as one piece, i.e. have a machined shaft with the gears being an integral part. This would eliminate the need for a bonding process and should lead to an increase in strength. However, this does have repercussions on the internal diameter of drive AP2007, in order to allow assembly.

AP2006 Housing Specification Design Criteria

0 Qty 1 off 0 Must form contact comparable to plain bearings with input shaft AP2001 at one end, and drive flange AP2009 at other.

0 Aluminium. alloy Must allow location and fudng of retainer AP2002.

0 BS L168 Must enclose all moving parts.

0 Secured by retainer AP2002 0 Running fit with input shaft AP2001 0Running fit with drive flange AP2009 0 3 hrs manufacture 39 A casing was required for the prototype, which would provide a stationary reference amongst all the rotating parts. Following the theme of all other parts, no bearings were included to assist with rotation, but the mating surfaces were toleranced to be bearing surfaces instead. This provides a large surface area of contact to carry any load.

Internally, the first 15mm of the housing are the extent of the fine limit in the bore - i.e. the bearing surface area.

The housing is held securely in place by retainer AP2002.

Optimal Design The housing would undergo a complete re-design, because on the prototype it does not take into account assembly on the bicycle. Some form of locating design would be necessary, allowing easy, one handed attachment to the bike frame. This could be a major selling point for the product.

Also, there is no consideration for a shifter mechanism, which would alter the appearance of the housing markedly.

AP2007, AP2008 Drive Specirication Design Criteria 0 Qty 2 off AP2007 0 AP2007 serve as internal gear connectors which act as the planet carriers for the next stage, thus they are drilled for the pins 0 Qty I off AP2008 DP4.024.

0 Aluminium alloy AP2008, being the last stage, is required to support the gears running off it, and so has a smaller internal diameter that provides a BS L168 a running fit with output shaft AP2005.

0 Press fitted to internal gear IN08-72 0 Pins DP4.0-24 (Qty5) attach 0 4 hrs manuacture (AP2007) 0 2 hrs manufacture (Ap2008) As it was not possible to select an internal gear that provided a face for the planet carrier function, this part had to be produced. Locating on the shoulder of the internal gear, AP2007 does not attach to any other part other than by the pins to the next stage, thus keeping it free running. However, AP2008 had to rotate in close proximity to the output shaft AP2005 in order to provide some support for the whole system. Otherwise, it would have been free to move laterally. It did not also require any holes drilled into it given it's location.

Being pushed up against the large slip ring AP2004 and the drive flange AP2009, combined with the inclusion of the small slip rings AP2003, any lateral movement of any part is eliminated.

41 Optimal Desig This is simple to establish, as combining them directly with the internal gears in one part, which would simplify assembly further, could eliminate these parts. In full production, a gear company could be contracted to produce these custom items, which would also lead to weight savings and dimensional reductions. Any decrease in diameter or width would be advantageous.

AP2009 Drive Flange Specification Design Criteria Direct attachment to output shaft AP2005, therefore this 0 Qty I off part is the output from the planetary system.

0 Alurninium. alloy 0 Must allow attachment of standard 22-tooth chainring via standard 5 mm chainring; bolts.

0 BS L168 Must have clearance from housing to allow fitting of 0 Attached to output shaft standard Sachs Silver chain.

AP2005 by two set screws 0 Exterior diameter runs as bearing surface with housing AP2006 0 Exterior Drilled to allow fitting of Shimano IG K 22 chain ring 0 4 hrs manufacture C V 1.

42 This part takes the place of a conventional crankarm spider, allowing the rotation of the output shaft to become usable by attachment of a conventional chainring. This is the part that takes what is a relatively conventional design of gearbox, and makes it specific for the design brief.

At first, an existing crankarm spider was to be used as in the first prototype, but it proved easier to machine a new design about which all dimensions were known. It proved to be a simple design, a disk, with boltholes drilled on the correct PCD.

Provision was made for assembly, and it was decided to use two setscrews, which are accessible through the diameter of the part. Assembly is straightforward, and a circlip locating on the input shaft secures the part to the main assembly.

The outside diameter runs as a bearing surface with the inside of the housing, creating a smooth running system.

The outside diameter is profiled to provide clearance for a chain.

Optimal Design The design is fully functional and acceptable as it is, however, some areas can be improved to maintain the overall strength of the design.

The set screws could be replaced with a more secure system so as to prevent detachment from the output shaft, possibly incorporating a safety feature that detaches the crankarm under crash loading, before damage occurs to the expensive intemals.

More machining could be done so as to reduce the mass of the part, and give the exterior part of the product more of an individual appearance.

43 Sun Gear (Drawiniz No. YGO.8-36 XG) Specification Design Criteria

0 Qty 3 off 0 Strong enough to take nominal load in equation (9).

0 0.8 MOD Of a facewidth that is lends sufficient strength to the design as per equation (29).

0 Heavy-duty spur gear 0 Of a modulus and diameter that produces a compact design.

0 655M13 (En36) steel 0 Must match other gears as per equation (23).

0 36 tooth 0 Facewidth 10 nun 0 Bored to 20 min 0 Bonded to AP2005 with 601 retainer The first decision made was to go for a 0. 8 MOD system, as all meshing gears have to have the same modulus - which is the pitch diameter divided by the number of teeth. This represents the metric system of gear design. Calculations proved its validity, and as shall be shown, it allowed some space saving to occur - which was always a main consideration. Having established the stage formula (23) gear choice was dictated by functional limitations. It is universally accepted that the minimum no. of teeth to be meshed correctly is 18 tooth. So, with the planets assigned this value, the sun gear tooth number comes out to be 36 teeth.

Due to the coaxial nature of the design, the gears had to be bored out from a standard 6 min to 20min, allowing them to slide over the output shaft AP2005, which was appropriately toleranced. The gears required fixing to this shaft, which posed problems until it was decided to use bonding as the method. Research lead to the selection of Permabond Retainer 601whose specification and applications can be found in Appendix Section 20 but in general;

0 Is for high strength retention of close fitting parts 44 Retains slip fitted parts with gaps up to 0-15 nun and may be used to increase the strength of press-fitted parts Typical applications are the retention of shafts/rotors of electric motors, gears, pulleys, sleeves, bushes, oil seals in housing, pins, keys and dowels.

A successful selection, this proved easy to assemble, with the gears separated at 15mm intervals (see Drawing no. AP2010 Output Shaft Assy). Choosing the heavy-duty type of gear leads to an increase in face width of 4mm from normal, and as this is a major factor in the stress calculation (see equation 29), contributes markedly to the overall strength of the gear. This is the proper choice for high impact situations, though without the hardening processes that would be employed in the final product. This was to save money, and time case hardening would have taken another week in manufacturing and an extra E40 for the batch. With these strong gears, the gearbox.

Optimal Desig Combined with output shaft AP2005 and manufacture as one piece (see AP2005forfiurther details).

Planet Gears (XG08-18) Specification Design Criteria

* Qty 9 off (3 per stage) Strong enough to take nominal load in equation (9).

0.8 MOD Of a facewidth that is lends sufficient strength to the design as per Heavy-duty spur gear equation (29).

655MI3 (En36) steel Of a modulus and diameter that produces a compact design.

18 tooth Must match other gears as per equation (23).

Facewidth 10 mm Bored to 8 mm Fitted with flanged oilite bushes QFM64 & QFM6-6 back to back, running on pins DP4.0 24 This was a valid design solution mechanically, but not economically. These were to be hardened and ground Ck53/Cf53 Steel, 62 HRC to a f7 tolerance. This is more representative of a production item, and not a one-off prototype, and would not have been a very clever purchase.

Within a planetary system, 3 or 5 planet gears are conventionally used, arrayed equally around the central sun axis. However, using 5 planet gears would mean an increased need for accuracy during manufacturing, with more holes to drill, and more gears to mesh. It was decided that incorporating 3 planet gears per stage would be acceptable in terms of strength, but also represented a substantial financial saving.

Optimal Dgsn planet gears per stage, running off roller bearings for increases wear.

Internal Gear (IN08-72) Specification Design Critieria

0 Qty 3 off Strong enough to take nominal load in equation (9).

0.8 MOD 0 Of a facewidth that is lends sufficient strength to the design as per equation (29).

0 Internal Gear 0 Of a modulus and diameter that produces a compact design.

0435MIO (En32) steel 0 Must match other gears as per equation (23).

0 72 teeth Facewidth 10 (modified) 0 Mates with AP2007 Drive 0 Price (ea) E21.65 The internal gear had to be 72t, and 0.8 MOD, in order to mesh with the other gears. This narrowed the choice from the HPC Gears catalogue to one type. By keeping to a low 46 number of teeth and a 0.8 MOD, this meant that the ring gear was of a small outside diameter (75 mm) which satisfied a major consideration. If 1.0 MOD had been used, this diameter would have risen to 100 mm, quickly making the gearbox oversized. However, with this not being the case, it was possible to keep the gearbox smaller than the diameter of the 22t chainring to be used. It had to be widened to 10 nim, from 9mm, in order to mesh with the other gears correctly, which was easily obtainable.

This part was in determined the overall dimensions of the prototype, and it's selection was subject to a number of criteria. A problem arising was that the internal gear from one stage should serve as the planet carrier for the next stage (see Main Assembly AP2000). On it's own, the internal gear could not fulfil this purpose. Therefore, an attaching drive plate (AP2007) had to be designed to mate with the shoulder built in to the part. Therefore, the internal gear could be converted into an internal gear planet carrier Optimal Desig Single internal gear/planet carrier arrangement - reduces overall no. parts, quickens assembly, improves strength.

No. teeth is fine, but with further development, the overall diameter could be reduced further, particularly by maintaining strength through a change in material, and through the addition of heat treatment processes, such as those outlined above.

Overall width of part could be reduced, and material removed - in order to save further space laterally, and to lose weight.

47 Tolerancing Decisions AP2001 ILiput Shaft (Stainless Steel S130) 4mm dia., holes interference fit with pins to ensure that they are retained and not able to move, which would lead to the pin rubbing on, or even jamming the Drive [AP2007/2008].

PCD for the three 4 mm diameter holes held to 0.06mm and concentricity of 0.05mm between the PCD and the 14.98 diameter to ensure that the three planet gears are maintained at the optimum diameter to ensure correct mating of the ring, sun and planet gears without binding.

49mm diameter held to 0.03 mm to ensure clearance fit with the housing [AP2006].

AP2002 Retainer (Aluminium. alle L168) AP2003, AP2004 Slip rings (Nylon 66) No tight tolerancing required owing to the assembly design requirements.

AP2005 Ogtput Shaft (Stainless steel S130) 15mm diameter held to 0.03 nun to ensure a slide fit with input shaft AP2001. 19.95mm diameter held to 0.03mm to ensure a running fit with the sun gears. Concentricity between the 15mm and 19.95mm diameter held to 0. 05 mm to ensure correct mating of ring, sun and planet gears.

AP2006 Housing (Aluminium allgy L168) 50mm diameter tolerancing of +0/+0.046mm is to ensure clearance fit with input shaft [AP20011.

80mm diameter tolerancing of +0/+0.046nim is to ensure clearance fit with drive flange [AP2009], but to minimize cost the tight tolerance was restricted to a minimum length of 15 mm, which relates to the mating bearing diameter maximum length of engagement, 48 Concentricity between the 50mm and 80mrn diameter held to 0.05min to ensure drive flange [AP2009] will rotate freely.

AP2007 / AP2008 Drive (Aluminium alloy L168) PCD for the three 4mm diameter holes held to 0.06mm and concentricity of 0.05min between the PCD and the 70mm diameter to ensure the three planet gears are maintained at the optimum diameter to ensure correct mating of the ring, sun and planet gears without binding.

4nim holes interference fit with the pins to ensure that they are retained and not able to move.

30mm [AP2007] and 20nim [AP2008] dia, given clearance fits to ensure 30mm dia. clears the sun gear and the 20mm dia. clears the output shaft dia.

AP2009 Drive Flange (Aluminium alla L168) 20mm diameter tolerancing of +0/+0.03mm is to ensure clearance with Output Shaft.

80mm diameter tolerancing of -0.06/-0.03 is to ensure clearance with Housing [AP2006].

Concentricity between the 20min and 80min diameters held to 0.05min to ensure Drive Flange rotates freely within the Housing [AP2006].

Materials Almost all of the prototype components are of a specification that would be directly transposed to the full production version. These are as follows:

Aluminium. Alloy Parts (AP2002, 2006-9) BS L168 Bars and extruded sections of aluminium - c=er - magnesium - silicon - manganese alloy (Solution treated and artificially aged) (Not exceeding 200 mm diameter or minor sectional dimension) 49 (Cu 4.4, Mg 0.5, Si 0.7, Mn 0.8) Selection of this material was reserved for parts not in main torque situations, such as the housing and drive plates, where weight could be saved over the usage of steel, Stainless Steel Parts (AP2001, 2005) BS S130 18/9 chromium-nickel corrosion-resisting steel (niobium. stabilized) billets, bars, forgings and parts (540 MPa: limiting ruling section 150 mm) With the axle analysis of Section 3.5. it was apparent that a coaxial steel shaft input/output arrangement was easily the best solution, giving strength to the critical areas. The above specification more than fitted the application. Both this and the aluminiurn alloy above are absolutely perfect for the product, and no more need be said. The fact that they are aircraft grade materials says it all.

Sun and Planet Gears (XG08-36, XG08-18) Heavy-duty spur gears, En36 steel, as per the technical sheets in Appendix Section 18 in order to meet the equations (9) and (11). These are suitable for heat treatment such as carburising, which is the optimal solution and as such, are the correct selection for a production unit. With the material qualities, combined with wide facewidth (10 nun) and modulus (0.8), the high strength could only be compromised by the extent of the bore - the larger the bore, the weaker the gear becomes. Strength can be optimised by increasing the number of planets to five per stage.

The sun gears, with their large bore of 20 nim are compromised in this way, although the choice of Permabond 601 Retainer does go some way to assist the strength of the join with the output shaft.

Internal Gear (IN08-72) En32 steel, the strength aspect of the planetary system is in the mesh between sun and planets, allowing the internal gear to be of a lower and thus cheaper specification. En32 can be case hardened, and its normal tensile strength is 430 MPa.

Sealing is in the form of a layer of grease between the housing AP2006 and the input shaft AP2001 and drive flange AP2009. For the prototype, this is an adequate solution, and the internals rotate smoothly. With the mating surfaces toleranced to produce a running fit, this is possible, and the grease fills the gap.

This would not be suitable for the final design, being inappropriate for the loading applied, causing the case to rub on the contact surface. More appropriate would be a proper sealed bearing arrangement on each end of the housing, sealing the whole gearbox from the harsh environment, and providing a load bearing contact.

The gear ratios in the prototype match the theoretical perfectly. And these mimic gears found on existing mountainbikes perfectly. Actually, the ratios correspond to a traditional system with a 40/28, 40/22, and 40/13 chainring/sprocket combination. This is dependent on the chainring and sprocket numbers being equal. These are the recommended manufacturer's ratios, but they are open to adjustment, simply by changing the size of the chainring or sprocket. Therefore, the user can alter the system with a minimum of fuss, and with no alteration to the internals.

All gears are easily produced, and the constant mesh arrangement leads to consistently smooth running throughout the gear choices. Although the gears can be noted visually by means of attaching a crankarm. to the nonhandle side of the input shaft, it is more impressive to the uninitiated simply to handle the prototype. In this way, the required input torques for each gear can be physically quantified, and the function of the product more readily understood.

51 The prototype was designed with manual operation in mind on one end of the input axle, with the provision of a knurled grip. The other end is extended past the drive flange, and is of a diameter to allow simple attachment of a crankarm (see Drawing no. AP2000). This provides a single sided demonstration design that allows the main principle to be shown i.e. the differing comparative rotation speeds of the crankarm (input) and drive flange (output). This was designed solely for the purpose of demonstration, but to represent the ideal input shaft / crankarm solution, only one part need be changed - the input shaft.

Producing a new splined input shaft as per the recommendations above that would mate with existing cranks (i.e. Shimano XTR) would be the only conversion necessary to make the unit rideable, and this would be exactly how production units would function.

In fact, the crankarm interface could become an extension of the design, making it an integral part that comes with the gearbox. This would be something of a second generation feature, as the first generation would require compatibility with existing components to promote the initial sales that would fund the development of the second generation product.

The purpose of the bottom bracket is to allow the bottom bracket axle to rotate with pedalling relative to the stationary bottom bracket shell, and this is how this question should be judged.

In the prototype, the crank arms rotate relative to the stationary housing on the input shaft fulfilling the design criteria for a bottom bracket. In this case, the bottom bracket axle has become the input shaft, also acting as planet carrier for the primary planetary stage. This is a successful integration.

The three gears have been successfully internalised, and thus the optimal solution of a single, shortened chain, smaller chainring, and sprocket (with pedal back clutch) has been realised in the prototype.

52 This fully satisfies one of the major aims of the project, and has successfully produced a design that has advantages over existing products.

With a larger than standard bracket shell dimension, the frame housing for the gearbox would deal with the dynamic forces at this critical areas better than the traditional mountainbike, with its small diameter bottom bracket. In addition, because the exterior dimension exceeds even the dimension of a BMX bottom bracket (which is universally recognised to be stronger than a mountainbike) it would require a specifically designed frame. This would be built from scratch, and, as such, would optimise the strengths of the size.

The prototype dimensions are fully representative of the final unit size, which is a major achievement. It would have been easy to go down the wrong path leading to an outside diameter in the region of 100 mm, and an increased overall width too. However, the design is perfectly adequate for attachment to a bike as it is. The housing will become the bottom bracket shell, though this may require a change in material if the frame is to be steel. This entails that the gearbox internals could be added and removed as required in a simple manner.

Offsetting the weight savings against the weight of the prototype leads to a weight increase on the bike in the region of 400g, which is acceptable. However, this can be put in context by the fact that no concessions for weight savings were made in the design were made, so it should be able to match the weights so that none is added over conventional systems.

It should be remembered that this mass has become part of the frame, located low down and thus improving stability of the bike at high speed, and producing a lighter rear wheel and thus generally improving handling.

The gearbox can therefore compete with the conventional system in terms of weight and cost as well as performance.

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Claims (8)

1. A gear system for a bicycle coupled directly to the pedal rod linking the pedals of a bicycle.

2. A gear box system for a bicycle including a plurality of gear cogs and a housing substantially enveloping all the gear cogs.

3. A gear system or gear box according to claim 1 or 2, including a plurality of planetary gears.

4. A gear system or gear box according to claim 1, 2 or 3, including one or more epicyclical gears.

5. A gear system or gear box according to claim 4, providing speed increasing ratios.

6. A gear system or gear box according to any preceding claim, including three gear ratios.

7. A gear system substantially as hereinbefore described with reference to and as illustrated in the accompanying drawings.

8. A gear box substantially as hereinbefore described with reference to and as illustrated in the accompanying drawings.