ELECTRIC TRACTION - PART – 10 - COEFFICIENT OF ADHESION & THREE PROBLEMS

COEFFICIENT OF ADHESION

This is the ratio of the tractive effort force just necessary slip the wheels on the track to the adhesive weight.

It reduces with increase in the speed.

It is represented as μ.

μ = tractive effort to slip wheels/adhesive weight

It is usually less than one.

The normal value of μ with dry rails is 0.25 and maximum value is 0.3 when the track has been cleaned well.

If the rails are wet or greasy the value lies between 0.5 to 0.2

IMPORTANCE OF COEFFICIENT OF ADHESION

There is a minimum value of tractive effort at which driving wheels will not slip and the maximum value depends upon the dead weight over the driving axles. [Axle means a shaft on which a wheel rotates]

F is directly proportional to W

F = μ W [if ‘F’ is Newton and ‘W’ in ton]

F = μ 98.1 W in Newton

This means to haul (draw slowly or heavily) a train, there is a certain minimum weight of locomotive. Again, the maximum allowable weight on each driving axle is limited by the strength of track bridges etc., to between 15 and 30 ton.

TRAILING WEIGHT

That part of the weight of the locomotive engine which rests upon the rear pair of driving-wheels.

PROBLEM – 01

A locomotive accelerates a 400 ton train up a gradient of 1m in 100 at 0.8 kmphps. Assuming the coefficient of adhesion to be 0.25, determine the minimum adhesive weight of the locomotive. Assume train resistance 40 N per ton and allow 10 percent for the effect of rational inertia.

PROBLEM – 02

A train weighing 250 ton is accelerated up a one percent gradient with an acceleration of 1 kmphps. Determine the minimum adhesive weight of a locomotive for this purpose if the coefficient of adhesion is 0.2. Assume train resistance as 50 N/t and allowance for rotational inertia 10 percent.

PROBLEM – 03

A goods train weighing 300 ton is to be hauled by a locomotive up a gradient of 1% with an acceleration of 1 kmphps coefficient of adhesion 20% track resistance 45 N/t and effective masses 10% of dead weight. If axle load is not to exceed 20 ton determine the weight of locomotive and number of axles.