In order to transmit power from the motor to the driving wheels some form of transmission must connect the two, gears being the type most used on Gauge O locomotives. As driving wheels do not normally rotate at more than 750 rpm and motors run at least 2500 rpm this must include a means of speed reduction. Most motors have a shaft runs along the locomotive, i.e. it is at right angles to the axles. The reason for this is size and power. A motor small enough to fit transversely is unlikely to have enough power to be useful. A second function of the gearing is therefore to provide a right-angle turn between the motor shaft and the axle.

Before getting into details, it is worth reviewing the different types of gears available.

The ratio of two spur, bevel or crossed helical gears is given by the ratio of the numbers of teeth. Thus, if the driver gear has 10 teeth and the driven gear 20 teeth, the gear ratio is 20/10 = 2. The speed of the driven shaft is one half the speed of the driver shaft.

For worm gears, the ratio is the number of teeth of the worm wheel divided by the number of starts of the worm. The example in Figure 4 shows a 4-start worm and 48 tooth wheel giving a 48/4 = 12:1 ratio.

The pitch diameter is an “average” of the outer diameter of the tips of the teeth and the inner diameter of the gaps between the teeth, and is the diameter at which the teeth of properly meshing gears contact each other. For proper meshing, therefore, the spacing of the shafts is equal to one half of the sum of the pitch diameters of the two gears.

The diametral pitch (DP) is the tooth spacing, and is equal to the number of teeth divided by the pitch diameter. Module is the inverse: the pitch diameter divided by the number of teeth. DP is usually applied to imperial gears, and module to metric gears. For O gauge locomotives, the DP is typically about 60 and over, or the module is 0.5 or lower.

Despite the development of more efficient arrangements the simplicity and compactness of this type of gearing result in its still being extensively used.

Once the performance requirements of a locomotive have been established the next step in determining the suitability of a motor is to decide on the gear ratio necessary to meet these requirements. The arithmetic required for this is described here, or alternatively Tables 1 and 2 can be used to find the most suitable gear ratio.

The optimum ratio is calculated from the no-load speed of the motor by means of the following formula.

Gear Ratio = (rpm x K x D)/(336 x MPH)

where rpm = no-load motor speed on nominal voltage,

D = prototype wheel diameter in inches (if D is in mm, in the formula above 336 becomes 8534),

MPH = desired maximum train speed.

K is a factor to take account of the fall in speed of the motor when loaded. Its value depends on the slope of the particular motor characteristic but 0.75 is sufficiently accurate for the initial stage of motor selection. It can be corrected later if this is found to be necessary.

Taking a typical mixed traffic locomotive as an example, if the driving wheel diameter is 6ft, the desired train speed 75mph and the no-load speed of the proposed motor 6000 rpm, the optimum gear ratio will be:

(6000 x 0.75 x 72)/(336 x 75) = 12.9 to 1

This will give a theoretical ‘no-load’ speed of 100mph.

It is unlikely that the exact gear ratio will be obtainable and therefore the nearest suitable one will be used.

In Table 1 use the train speed and driving wheel diameter to find the driving axle rpm.

In Table 2 use the driving axle rpm obtained from Table 1 and the motor rpm under no-load conditions, which can be obtained from either the motor data sheets or manufacturer's data, to find the gear ratio. The final figure is an approximation but is suitable for model purposes.

Note: The gear ratios shown in the table have been calculated to take account of the loss of speed in a loaded motor.

Table 1. Driving axle rpm (to nearest 5rpm).

Table 2. Gear ratio to nearest whole number.

Improvements in efficiency of the gears can be justified for different reasons:

• The locomotive can haul a longer train or mount steeper gradients,
• It is less susceptible to voltage drops which may occur on large layouts,
• The same train can be pulled using a smaller and lower current motor, which reduces the current drawn from the controller.

The efficiency of a particular set of gears is greatly influenced by the tooth accuracy and finish, the accuracy of mounting, the material from which the gears are made, the type of thrust bearing and the quality of the lubrication. As a general rule, the efficiency decreases with increasing gear ratio. The figures quoted here are only estimates, but generally are accurate enough for our purposes.

Table 3. Approximate efficiencies of gearsets.

The percentage efficiency of multi-stage gearing is the efficiency of the first stage multiplied by the efficiency of the subsequent stages expressed as decimals. For example, a three stage gearbox having two spur stages 85% efficient) and a helical gear stage (75% efficient) would have an nominal efficiency of 85 x 0.85 x 0.75 = 37%.

For worm gearing, the efficiency of the drive to falls rapidly as the ratio increases, particularly if the lubrication is inadequate. Failure to appreciate this has resulted in many disappointments. Although efficiencies exceeding 50% are obtainable with high quality worm gears mounted in separate enclosed gearboxes with proper lubrication, the efficiency of 'standard model quality' open worm drives becomes very low at ratios above about 20:1 and the use of a two-stage worm and spur drive or crossed helical gearing will give greater haulage capacity at the desired speed. If the best use is to be made of the motor power the fitting of the latter may well be considered justified for all ratios.

The efficiency graph (Figure 5) shows average efficiency curves for a range of worm gear combinations. As a general guide, the efficiency of properly mounted worm gears should fall within a band 5% above or below the average efficiency curve illustrated. If a particular gearing combination efficiency falls below that band it needs to be inspected to discover where the fault lies. It is very important to ensure that slight backlash is present in a worm drive and that the gearbox frame does not distort under load. In extreme cases distortion of the box can cause total lock-up of the drive.


Figure 5. Typical gear efficiencies for model quality worm gearsets.

Commercially produced gearing falls into three broad types. The decision to select a particular type would be influenced by the duty to be performed and the cost.

The least expensive type are those gears made for general use in toys and construction models. They are produced in hard plastics such as nylon or delrin and have a fairly simple tooth form. These gears are suitable for light duties. Where a large gear ratio is required involving the use of a worm there may be no proper wormwheels, and this can lead to inefficient gearing and high tooth wear. They cannot be recommended for use in large locomotives required to haul heavy trains regularly.

More expensive gears are satisfactory for all duties. They are cut to a correct involute tooth form from suitable materials, e.g. steel worm and hard brass wormwheels or steel pinions and hard brass spur gears. For highest quality, worms are of hardened and polished steel, and spur gears and wormwheels of phosphor bronze. They are available in a range of sizes and pitches so that almost any ratio can be made up.

There are many gear suppliers not necessarily related to the model railway trade. A web search for the chosen type of gear, and size if possible, will provide many links.

This article originally appeared in the Gauge O Guild Manual. It was developed for the GOGWiki by Nick Baines.