Hunting oscillation Totally Explained

Everything about Hunting Oscillation totally explained

The classical Hunting oscillation is a swaying motion of a railway vehicle caused by the coning action on which the directional stability of an adhesion railway depends.
   Below a certain critical speed, the motion is damped out, above this speed the motion can be violent, damaging track and wheels, and potentially causing derailment.
   It was discovered towards the end of the 19th Century, when speeds became high enough to encounter it. Remedial measures, particularly in the design of suspension systems have been introduced since the 1960s, permitting speeds exceeding 180mph (290km/h).
   It arises from the interaction of adhesion forces and inertial forces. At low speed adhesion dominates, but as the speed increases the adhesion forces and inertial forces become comparable in magnitude, and the oscillation begins at the critical speed.

Classical Wheelset Hunting

Kinematic Analysis

Deeper understanding of the phenomenon inevitably requires a mathematical analysis of the vehicle dynamics, which may not be accessible to all readers.
A kinematic description deals with the geometry of motion, without reference to the forces causing it, so the analysis begins with a description of the geometry of a wheel set running on a straight track. Since Newton's Second Law relates forces to accelerations of bodies, the forces acting may then be derived from the kinematics by calculating the accelerations of the components. The train stays on the track by virtue of the conical shape of the wheel treads. If a wheelset is displaced to one side by an amount y, the radius of the tread in contact with the rail on one side is reduced, whilst on the other side it's increased. The angular velocity is the same for both wheels (they are coupled via a rigid axle), so the larger diameter tread speeds up, whilst the smaller slows down. The wheel set steers around a centre of curvature defined by the intersection of the generator of a cone passing through the points of contact with the wheels on the rails and the axis of the wheel set. Applying similar triangles, we've for the turn radius:
ť :

frac

where a is now a shape factor determined by the wheel wear. This result is derived in reference 2 from an analysis of the system dynamics using standard control engineering methods.

Concluding Comments

The motion of a wheel set is much more complicated than this analysis would indicate. There are additional restraining forces applied by the vehicle suspension, and at high speed, the wheel set will generate additional gyroscopic torques, which will modify the estimate of the critical speed. A real railway vehicle has many more degrees of freedom, and consequently may have more than one critical speed, and it's by no means certain that the lowest is dictated by the wheelset motion.
   However, the analysis is instructive because it shows why hunting occurs. As the speed increases the inertial forces become comparable with the adhesion forces. That is why the critical speed depends on the ratio of the axle load (which determines the adhesion force) to the wheelset mass (which determines the inertial forces).
   Alternatively, below a certain speed, the energy which is extracted from the forward motion is insufficient to replace the energy lost by lowering the axles, and the motion damps out, above this speed, the energy extracted is greater than the loss in potential energy, and the amplitude builds up.
   The potential energy at maximum axle yaw may be increased by including an elastic constraint on the yaw motion of the axle, so that there's a contribution arising from spring tension. Arranging wheels in bogies to increase the constraint on the yaw motion of wheelsets, and applying elastic constraints to the bogie also raises the critical speed. Introducing elastic forces into the equation permits suspension designs which are limited only by the onset of gross slippage, rather than classical hunting. The penalty to be paid for the virtual elimination of hunting is a straight track, with an attendant right of way problem, and incompatibility with legacy infrastructure.
   Hunting is a dynamic problem which can be solved, in principle at least, by active feedback control, which may be adapted to the quality of track. However, the introduction of active control raises reliability and safety issues.
   Shortly after the onset of hunting, gross slippage occurs and the wheel flanges impact on the rails, potentially causing damage to both.

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