# Gear Trains Basics

A gear train is a power transmission system made up of two or more gears. The gear to which the force is first applied is called the driver and the final gear on the train to which the force is transmitted is called the driven gear. Any gears between the driver and the driven gears are called the idlers. Conventionally, the smaller gear is the Pinion and the larger one is the Gear. In most applications, the pinion is the driver, this reduces speed but increases torque. This is also a function of ATO popular geared motors.

Types of gear trains

1. Simple gear train 2. Compound gear train 3. Planetary gear train

Simple Gear Train – Simple gear trains have only one gear per shaft. The simple gear train is used where there is a large distance to be covered between the input shaft and the output shaft.

Compound Gear Train – In a compound gear train at least one of the shafts in the train must hold two gears. Compound gear trains are used when large changes in speed or power output are needed and there is only a small space between the input and output shafts.

Planetary Gear Train – A planetary transmission system (or Epicyclic system as it is also known), consists normally of a centrally pivoted sun gear, a ring gear and several planet gears which rotate between these. This assembly concept explains the term planetary transmission, as the planet gears rotate around the sun gear as in the astronomical sense the planets rotate around our sun. Planetary gearing or epicyclic gearing provides an efficient means to transfer high torques utilizing a compact design.

We have known that “If two gears are in mesh, then the product of speed (revolutions) and teeth must be conserved”. Let’s check this simple rule with a help of an example. If you turn a gear with 6 teeth 3 times and is meshed with a second gear having 18 teeth, then the driving gear with 18 teeth (6 x 3) will move through the meshed area. This means that the 18 teeth from the second gear also move through the meshed area. If the second gear has 18 teeth, then it only has to rotate once because 18 x 1=18. Also, the second gear will be turning slower than the first because it is larger, and larger gears turn slower than smaller gears because they have more teeth.

Gear Ratio for Simple Gear Train

Consider a simple gear train shown below. Notice that the arrows show how the gears are turning. When the driver is turning clockwise the driven gear is anti-clockwise. Further assume driver gear #1 has 20 teeth and rotates at 100 rpm. Find the speed of driven gear #2 having 60 teeth.

• N1 = 100 rpm
• Z1 = 30 teeth
• N2 =?
• Z2 = 60 teeth

Solving the equation above for N2, we have:

N2 = (Z1/Z2) * N1 = (30/60) * 100 = 50 rpm

Let’s add a third gear to the train. Assume gear 2 drives gear 3 and gear 3 has Z3 = 20 teeth. Here the driver is gear #1 and the final driven element is gear #3. Gear #2 in between is called the idler gear. Find the speed of driven gear #3? Well, since gears 2 and 3 are in mesh, our conservation law says that:

N2 * Z2 = N3 * Z3

We could do the arithmetic (N3 = (Z2/Z3) * N2 = (60/20) * 50 = 150 rpm) to find N3. Or, we could note that, since both N1*Z1 and N3*Z3 are equal to N2*Z2, they must be equal to each other.

• N1 * Z1 = N3 * Z3
• So,
• N3 = (Z1/Z3) * N1 = (30/20) * 100 = 150 rpm.

What does this prove?

“An idler gear between a driver and driven gear has NO effect on the overall gear ratio, regardless of how many teeth it has”.

(Note that Z2 never entered into our computation in the last equation.)

Suppose now that we add a fourth gear with Z4 = 40 teeth to our developing gear train. Its speed must be N4 = (Z3/Z4) * N3 = (20/40) * 150 = 75 rpm. Again, by using the conservation principle, we have:

N4 = (Z1/Z4) * N1 = (30/40) * 100 = 75 rpm.

We can continue like this indefinitely, but the two fundamental learning objectives here are:

• The number of teeth on the intermediate gears does not affect the overall velocity ratio, which is governed purely by the number of teeth on the first and last gear.
• If the train contains an odd number of gears, the output gear will rotate in the same direction as the input gear, but if the train contains an even number of gears, the output gear will rotate opposite that of the input gear. If it is desired that the two gears and shafts rotate in the same direction, a third idler gear must be inserted between the driving gear and the driven gear. The idler revolves in a direction opposite that of the driving gear.

Major Caveat

Note that everything said to this point assumes a simple gear train where each of the gears in the gear train is on its own, separate shaft. Sometimes gears are ‘ganged’ by keying or otherwise welding them together and both gears turn as a unit on the same shaft. This arrangement is known as compound gear train and it complicates the computation of the gear ratio, to some extent.

Compound Gear Train

The figure below shows a set of compound gears with the two gears, 2 and 3, mounted on the middle shaft b. Both of these gears will turn at the same speed because they are fastened together, i.e. Nb = N2 = N3

When gear 1 and gear 2 are in mesh:

1. N1 * Z1 = N2 * Z2
2. It’s still true that:
3. N1 * Z1 = Nb * Z2
4. Nb = (Z1/Z2) * N1

If gears 3 and 4 are in mesh:

1. Nb * Z3 = N4 * Z4
2. Therefore,
3. N4 = (Z3/Z4) * Nb = (Z3/Z4)*(Z1/Z2) * N1

So the end-to-end gear ratio is (Z1*Z3)/ (Z2*Z4) and it does depend on the intermediate gears; unlike the previous case when each gear could turn on its own separate axis. Note that the resultant gear ratio is just the product of the two separate gear ratios: (Z1/Z2)*(Z3/Z4).