Starting tractive effort

As a starting tractive effort is for locomotives and traction vehicles the highest possible tensile force called at the start of driving from a standstill. Since the starting tractive effort significantly influences the ability of a traction vehicle to start a train , it is therefore of particular interest for the driving dynamics . The starting tractive effort is to be measured in such a way that it can overcome the (initial) driving resistance forces of a train and thus accelerate it.

For the nominal starting tractive effort, it is often not the maximum power of the drive unit that is decisive, but the weight on the drive wheels ( friction weight ) and the coefficient of adhesion between wheel and rail or roadway. The starting tractive effort is limited by the adhesion limit. The starting tractive force that can actually be achieved under the respective local conditions can be considerably below the ideal characteristic value, since the decisive coefficient of adhesion is not a constant.

Frictional limit

The starting tractive effort can be read from the tractive effort-speed diagram. Here it is 350 kN. The transition speed here is around 20 m / s or 72 km / h.

In order to generate tensile forces, a tangential force must act on the contact surface between wheel and rail. A normal force perpendicular to it is a prerequisite for such a tangential force . This normal force results from the frictional weight and the acceleration due to gravity . The relationship between the tangential force and the normal force is called the adhesion coefficient.

{\ displaystyle F_ {T} \ leqq \ mu _ {H} \ cdot m_ {R} \ cdot g}

The adhesion limit describes the point at which the tractive force developed on the wheel becomes greater than the transferable force and the wheel begins to skid . So as long as the tractive force in locomotives does not exceed the frictional connection limit specified by the maximum permissible axle load and the adhesion coefficient, a tractive force can be transmitted.

Modern high-performance locomotives have engine torques that can fully utilize the adhesion limit. If the torque increases at the frictional connection limit, the wheels spin and the power cannot be brought to the rails. In this case, the torque must be reduced to such an extent that the sliding friction changes back to static friction and the maximum possible force can be transmitted again. With electronic control of static friction can be approached without reserve to the limit by the the limit micro-slip is controlled.

Up to the so-called transition speed , locomotives can be driven at the traction limit. From this point on, the traction limit no longer limits the tractive effort of a locomotive, but its performance . The transition speed for diesel locomotives is in the range of 10 to 15 km / h and for electric locomotives between 50 and 80 km / h.

Frictional weight

The portion of the weight of the locomotive that is supported by the driven axles is called the friction weight . The part of the weight that is supported by the running axles only has a minor influence on the effective traction of the traction vehicle.

In modern locomotives, all axles are usually driven, which is why the service weight corresponds to the friction weight . In the case of locomotives with additional running axles, on the other hand, only part of the service weight is effective as a friction weight.

Adhesion coefficient

In the first approximation, the coefficient of adhesion corresponds to the coefficient of static friction , which is why this is often used in the literature. However, the value of the coefficient of adhesion is usually higher than that of the coefficient of static friction. Under laboratory conditions, adhesion coefficients from wheel to rail of up to 0.8 can be achieved. In practice, however, the adhesion coefficient is subject to numerous influences, which is why such high values do not occur:

Material pairing and their properties: material, strength of wheel and rail
Condition of the contact surface: shape of wheel and rail, surface condition
Condition of the contact surface: weather conditions (dryness, moisture, snow, ice), leaves
Driving speed
Sliding speed: In arcs, the wheel sets cover a longer distance outside than inside. Since the two wheels are firmly connected by the wheelset shaft, the prevailing differential speed is compensated for by sliding movements.

The extent to which the theoretically existing coefficient of adhesion is used depends largely on the properties of the traction vehicle. Influencing factors can be the gear set relief , drive arrangement , drive control, in particular the wheel slip control and graduation of the tractive force. Therefore, adhesion coefficients between 0.3 and 0.36 are usually achieved.

Since the coefficient of adhesion between wheel and rail depends on the surface condition of the rails and the coefficient of adhesion can be greatly reduced, especially in rain or through leaves, it is common for traction vehicles to improve the adhesion with sand. This can be spread in front of the wheels by means of a sand spreader when starting to prevent skidding in bad weather conditions.

example

A four-axle locomotive (e.g. DB class 152 ) with an axle load of 21.7 t and a friction weight of 86.7 t achieves a starting tractive effort of 300 kN with a friction coefficient of 0.35. By increasing the friction weight, the starting tractive effort can be increased with the same coefficient of adhesion. This was done , for example, with DSB EG 3100. With a mass of 132 t, this achieves a starting tractive effort of 400 kN. This high tractive effort is required for the freight trains weighing up to 2000 tons on the 15.6 per mille gradients in the Great Belt Tunnel between Denmark and Sweden.

literature

Dietrich Wende: Driving dynamics of rail traffic . 1st edition. Vieweg + Teubner Verlag, Dresden 2003, ISBN 978-3-519-00419-6 .
Helmut Lehmann: Driving dynamics of the train journey . 3. Edition. Shaker Verlag, Aachen 2012, ISBN 978-3-8440-1259-0 .
Žarko Filipović: Electric Railways . 5th edition. Springer Vieweg, Wettingen 2013, ISBN 978-3-642-45226-0 .

Individual evidence

↑ ^a ^b compare DB IVE Vorlesung_Bremstechnik_2007 section "Fundamentals of friction coefficient wheel / rail µH = f (v, place, time)"
↑ Wende, Dietrich: Fahrdynamik des Eisenbahnverkehr . 1st edition. Teubner, Stuttgart 2003, ISBN 3-519-00419-4 .
^ Bendel, Helmut .: The electric locomotive: structure, function, new technology . 2., arr. and additional edition Transpress, Berlin 1994, ISBN 3-344-70844-9 .
↑ ^a ^b Filipović, Žarko: Electric railways . 5th edition 2015. Springer Berlin Heidelberg, Berlin, Heidelberg 2015, ISBN 978-3-642-45227-7 .

[DB_IVE-1] re DB IVE Vorlesung_Bremstechnik_2007 section "Fundamentals of friction coefficient wheel / rail µH = f (v, place, time)"

[2] Wende, Dietrich: Fahrdynamik des Eisenbahnverkehr . 1st edition. Teubner, Stuttgart 2003, ISBN 3-519-00419-4 .

[3] Bendel, Helmut .: The electric locomotive: structure, function, new technology . 2., arr. and additional edition Transpress, Berlin 1994, ISBN 3-344-70844-9 .

[:0-4] Filipović, Žarko: Electric railways . 5th edition 2015. Springer Berlin Heidelberg, Berlin, Heidelberg 2015, ISBN 978-3-642-45227-7 .