Gear Design

Gear nomenclature diagram
Gear nomenclature

A well-designed gear drive is the result of getting correct a number of features, including choice of type and form, sizing, material and heat treatment.

As the latter two features are covered in the Metallurgy and Hardening pages respectively, this article will concentrate on the more geometrically related points.

Note: As the majority of motorcycle gears are of the spur (straight cut) sort, this brief article will avoid complicating the subject with other types, such as helical, bevel, worm, etc.

The Purpose of Gearing

Gearing is used to achieve a change in the speed, torque, and direction of a power source as well as simply to transmit rotary motion from one shaft to another.

In some cases the potential for slip is acceptable, or even advantageous, so belt and other direct friction drives could fit the bill.

However, in the context of internal combustion engines, the need for positive, synchronised drives, giving fixed, consistent transmission ratios is vital and can only be achieved through the use of toothed components - gears or sprockets.

Although these two positive drive approaches have their own advantages/disadvantages for engine timing and final drive transmission, it is in the intermediate gearbox that gears have always been ubiquitous, due to their ability to allow the selection of an increasingly large number of gear ratios from within a relatively compact unit.

Gear Tooth Geometry

Gear tooth contact pic
Involute gear contact diagram showing
movement of contact point (blue line)
along each mating tooth surface

Although other shapes of gear tooth flanks have been tried (and, in the case of cycloidal, still are used), the involute curve has become the standardised form in engineering which all automotive manufactures conform to.

Involute curve contruction diagram
Involute curve construction

Its main advantage is that the contact between two mating teeth occurs in a fixed plane, irrespective of the relative sizes of the gears. (see animation alongside)

Involute gearing is also quieter, more tolerant in errors of centre distance and easier to accurately manufacture.

The Involute tooth form can best be described as being generated by the end of a taut line as it is unwound from the circumference of a circle.

The circle from which the line is unwound is known as the Base Circle.

Gear Tooth Proportions

Before the adoption of the metric Module system, gear tooth sizes were standardised by their Diametral Pitch (DP), which was a nominal figure, not an actual measurement, that was equal to the number of teeth divided by the pitch diameter (in inches).

Most motorcycle gearbox pinions would have been in 10 to 16 DP range, with other less loaded components, such as timing gears, being around 20 or 24 DP.

Gear tooth profiles diagram
Gear tooth profiles

Gear Tooth Modifications

With spur gears (straight cut teeth), the total number of teeth in any pair on parallel shafts is always the same, this being numerically equal to twice the centre-distance multiplied by the diametral pitch of the gear teeth.

AMC gearbox housing drg
AMC gearbox housing drawing

The AMC designed gearbox (also used on later Nortons) had its main and layshafts mounted at 2.100" centre distance and used gears of 10 DP tooth size, resulting in each of the four gear pairs adding up to 42-teeth, the combinations originally being 13-29t, 14-28t, 18-24t and 20-22t

However, in later years, some of the gearbox ratios that resulted from these 'standard' gear pairs were deemed not ideal for the ever-larger capacity machines and otherwise unattainable ratios were obtained by a process known as Tooth Correction, whereby gear pairs with sum totals of 41-teeth, such as 18-23t, 19-22t and 20-21t, were made to mesh at the same shaft centre distance.

Taking the 18/23t pair as an example; what tooth correction involves is cutting 18-teeth on a pinion blank that is really sized for 19-teeth, and then meshing it with a standard 23-tooth gear. By this means a ratio can be obtained that falls between that of the nearest standard pairs of 18/24t and 19/23t.

When even finer tuning of gear ratios is required (as in racing), the same tooth correction technique can be applied to both of the mating gears, with the result that the sum total of teeth in a gear pair from the example above drops to only 40.

Comparison of positive shifted tooth profile diagram
Standard and positively corrected tooth profiles

Although, this little trick is a useful means of obtaining 'in-between' gear ratios that would not otherwise be possible, the main reason for performing tooth correction is to prevent the undercutting of pinions with small numbers of teeth (less than 13t for 20° pressure angle gears).

By shifting the cutter further away from the pinion centre (giving POSITIVE correction), a different part of the involute curve is used, resulting in a tooth form that is both wider at its base and narrower at its tip, caused by the increased addendum and decreased dedendum distances.

In order to compensate for this change of pinion form, it is necessary for the mating gear to have an equal amount of NEGATIVE correction applied, giving it correspondingly decreased addendum and increased dedendum distances.

In cases where an especially extreme amount of tooth correction was being proposed, it was the normal practice in the AMC design office for a draughtsman to plot the resulting tooth shape, scaled up by 20-times or more, by carefully rotating a tracing of a standard rack about the drawing of the gear in question, and at the decided separation, in order to check that the profile was satisfactory.

Comparison of Standard and Stub tooth profiles diagram
Standard and Stub tooth profiles

Another form of modification that gives stronger teeth for the same outside diameter is known as 'stub' teeth, which are designated by a two-figure symbol, such as 10/12.

The first number denotes that the teeth are spaced at 10 DP, but the second number says that they are only as deep as those of 12 DP. However, although the resulting teeth are stronger than those of standard form, the length of contact between mating gears is shortened, offsetting this advantage to a degree as well as raising the noise level.

Gear separation forces are also increased, tending to bend shafts, whilst the smallest number of teeth that can be actually cut is 18.

From a production point of view, another drawback of stub gears is the need to stock a separate range of special cutters/hobs, as the standard types cannot produce the required forms.

Gear Drawing Specifications

So far, apart from the number of teeth and the diametral pitch, the only other piece of information that has been mentioned is the Pitch Circle, which is actually only a nominal diameter that lies approximately mid-depth of the teeth.

Sample Gear Cutting Data table
Sample Gear Cutting Data table

When it comes to drawing up a specification for the manufacture of a gear, it is necessary to include other more practical measurements, as shown in the following sample gear cutting table:

The Pressure Angle (see nomenclature diagram above) was standardised at AMC to just two values: 20° and 14½°, to suit the stocked range of gear cutters (although 25° versions were also manufactured).

The Checking Pins referred to were accurately sized cylindrical pins that would be nested in the spaces of opposing teeth (or, in the case of a gear with a odd number of teeth, as near directly opposite) which would stand slightly proud of the top of the teeth, in order that measurement over them could be taken with a micrometer.

Once again, the pin diameters were standardised, with a set for each Diametral Pitch, and the checking measurement would be obtained from a comprehensive set of tables in the Machinery's Handbook.