Wednesday, February 7, 2007

Train Dynamics

Dynamics of Locomotives or Train.

How does a train negotiate a curve? It doesn’t have differential!
What are the advantages of dividing it into compartments?
How can an engine which weighs much less than the combined weight all compartments/ bogies pull it?


These questions were posed to us by our Prof Sibi Chacko - I remeber him explaining the first answer... Second and third - i was absent...

Two days back i got a reply saying it is almost the same thing what he said...

"So MY Explanation"...

The answer to the first question lies in the geometry of the tracks and the wheels –

The wheels of the train are as shown below in figure 1 –


Now when going in a straight line – both the wheels touch at the same level.

When it is about to negotiate a curve – the level of point of contact of one of the rail is kept a bit higher than the other. This will result in a tilting of the train and the wheels will act like they are part of a cone – which rolls in a way that there is zero velocity at the apex and max velocity at the base – in effect rotate about the apex.

This will provide differential velocities for the two wheels. The outer wheel takes a bigger turn traveling more and inner wheels take a smaller radius curve and travels less.

This tilting also adds to the stability of the train. This can understood by taking the moment due to Centrifugal force and the Weight about the points where wheel touches the ground.

It is shown in figure 2.


It is a bit exaggerated one. The joining point of the two blue lines will be the centre of the curve that is being negotiated.

Question 2.

Simple answer – For ease of taking curve and to reduce the starting and accelerating torque that is required.

How it will reduce the starting/accelerating torque? – Answer is answer to Q3.

Question 3.

From topic on Traction you can understand that the maximum force available at the wheels is Static Friction force.
Also the maximum force without application of torque required to break away a body to rolling is equal to the rolling friction – from topic Breaking away into motion.

So it is obvious.
Even if the total weight of the compartments is pretty high, engine can still pull the train.

But then why compartmentalization??
It will reduce the maximum starting torque required. Also it will reduce the force required to accelerate the train.

How?
Compartments are connected not by a rigid connection – but by a flexible or spring connection.
At the time of starting the engine will have to pull only the first compartment – After it starts moving it pulls the other. So again the acceleration is only for a single compartment, the second.

Like wise is the movement of train.

To increase the available traction at the wheels, at times slight amount of sand is applied between track and wheels, by putting sand on track.

1 comment:

Anonymous said...

Hmm nice info. The no-differential thing was told by Sibi sir, also he had told about DC motors are being used even in Diesel engines. But I didnt know about the spring-compartment thing. That is so obvious and simple!