Mechanics of Train Movement & Coefficient of Adhesion

Mechanics of Train Movement :

The process of moving a vehicle by means of the driving force is known as traction. The motion of the vehicle can be obtained by transferring the tractive effort from the edge of the pinion in the motor armature to the driving wheel through the gear wheel. The driving mechanism of the vehicle is shown in the below figure.

Mechanics of Train Movement

Assume that the torque of the motor is T, then the tractive effort at pinion is given by,
T = force × distance = F1 × (d1/2)
F1 = 2T/d1
The tractive effort transferred to the driving wheel is given by,
Mechanics of Train Movement
In the above equation,
  • F2 = Tractive effort at driving wheel,
  • F1 = Tractive effort at pinion,
  • T = Torque developed by motor,
  • D = Diameter of driving wheel,
  • d = Diameter of the gear wheel,
  • d1 = Diameter of pinion,
  • η = Transmission efficiency,
  • γ = Gear ratio = d/d1.

When the train is in motion, then the frictional force between the wheel and track depends upon adhesive weight and adhesive coefficient and is given by,

F = μ × W

  • μ = Coefficient of adhesion between track and driving wheel,
  • W = Adhesive weight.

Coefficient of Adhesion :

The coefficient of adhesion is defined as the ratio of tractive effort to slip the wheels and adhesive weight.

Coefficient of Adhesion = Tractive Effort to Slip the Wheels/Adhesive Weight

The coefficient of adhesion decreases with an increase in speed. The below table shows the variations in the coefficient of adhesion with speed on dry rails.


Speed in kmph015304560
Coefficient of Adhesion0.250.180.140.120.10

With clean dry rails, the coefficient of adhesion is 0.25. The coefficient of adhesion for wet or greasy rails is 0.08. The coefficient of adhesion of electric traction is higher than steam traction. So, an electric train can accelerate quickly.


In order to obtain rapid acceleration and high tractive effort, the coefficient of adhesion should be maintained high. Whenever the tractive effort goes higher than (μ × W) then slipping will occur. In order to avoid this kind of situation, the tractive effort should be maintained equal to or less than (μ × W).


Factors Affecting Coefficient of Adhesion :

The factors affecting the coefficient of adhesion are listed below.
  • The coefficient of adhesion on a wet rail is lower than that on a dry rail.
  • The presence of oil reduces adhesion.
  • Sanding of rail surfaces improves adhesion.
  • Adhesion in the stationary condition of the wheel on rail is maximum and decreases as the wheel rolls.

Methods To Improve Coefficient Of Adhesion :

In order to improve the coefficient of adhesion, the following methods can be adopted,
  • Application of tractive effort in a gradual manner improves adhesion.
  • Cleaning rail surfaces with sodium metasilicate.
  • Sanding of rails.
  • Stepless control of traction force through the use of thyristors.
  • Mechanisms to detect wheel slip during early stages and to trigger corrective action.
  • The greater the moment of inertia of revolving parts, the greater will be the coefficient of adhesion.

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