Why do trains (Locomotives) does not have differential ?

Differential gear, in automotive mechanics, gear arrangement that permits power from the engine to be transmitted to a pair of driving wheels, dividing the force equally between them but permitting them to follow paths of different lengths, as when turning a corner or traversing an uneven road. On a straight road the wheels rotate at the same speed; when turning a corner the outside wheel has farther to go and will turn faster than the inner wheel if unrestrained.

Take a look at these wheels:

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If you throw these two pictures at someone and ask them which part of the wheel keeps the train on the tracks, they would probably tell you that the flange is what keeps the wheels on tracks. That's only a half-told story at best. Flanges are only a fail-safe mechanism.

Main Mechanism

Here is the main mechanism and it is brilliant.

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Suppose the track turns left. The train’s right wheels now have to travel more than the left wheels because at the turn the outer rail track on the right is longer.

What do we infer? The right wheel has to cover a longer distance for the outer rail compared to the left wheel, so the right wheel has to turn faster than the left wheel. If the right wheel doesn't turn faster, it will create undesirable forces leading to derailing the train.

But there is a problem here. What is the problem? Go back to the first image, do we see a differential there? NO!

Differentials

Differentials are essential in maintaining stability while turning. The differential distributes output in a smart way to make the turning as smooth as possible.

This video explains the function of a differential.

Link credits : Martin Thoma

Watch the below video if you wish to know more about the constructional aspects of the differential.

Rail Wheel Differential Design

Because trains don't make sharp turns like automobiles, adding a differential would be a potential waste of resources. Instead, the rail wheels themselves are design to act like a differential when negotiating turns.

The train wheels are conical in shape, the whole wheel-set shifts a bit to the right if the track curves left and visa versa.

Given the previous example of turning left, the point of contact for the right wheel is at a larger diameter of the cone compared to the left wheel. Therefore, if the right wheel now makes one circle it travels further than the left wheels and the train moves along the curve smoothly.

Enjoy this amazing animation on the same (ignore the zoom sign and click on the image if the animation doesn't play on its own):

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​Kudos to whoever made this! :)

Please note the varying black lines in the above .png, they represent varying point of contacts.

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The flange kicks into action if this mechanism does not function well enough to turn the train safely. The flange is never in contact with the tracks and any contact would lead to undesirable wear and tear.

Listen to Dr. Richard Feynman. He will kill you with his explanation. He must have been one hell of a teacher!

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