Introduction to Diesel Train Physics
Aim - this section describes the general key physics of diesel Locomotives operation.
Index
Diesel Electric - Tractive Effort
Diesel Mechanic Transmission - Power and Tractive Force
Introduction
The Diesel locomotive as the name implies is driven by a diesel engine. The diesel engine, or prime mover, produces the power to drive the locomotive forward and pull the train. The power produced by the prime mover is transmitted to the driving wheels, by a number of different transmission systems including mechanical transmission, electric traction motors, or hydraulic drive systems. The diesel typically is cheaper to operate then a steam locomotive, and some of the other advantages include the fact that they can be operated in multiple units with a single driver, they can be started or sindexped almost instantaneously compared to a steam locomotive which requires time to build up steam.
To understand the performance of a diesel locomotive the following three subjects will be considered:
- Diesel Transmission Systems
- Power
- Tractive Effort
- Adhesion
Once the above three elements are considered in conjunction with the train resistances, we can model the overall performance of the train.
Transmission Systems
Unlike an electric motor or a steam engine, a diesel engine is not well suited to driving the locomotive wheels directly. As a result power from the prime mover is transferred to the wheels by an intermediate transmission system. The four types of transmission system widely employed are:
- Electric - the diesel engine drives a generator, which provides power for electric motors that drive the wheels.
- Mechanical - a series of gears is used to match the diesel engine speed to the speed of rotation of the wheels.
- Hydraulic - one or more torque converters is used either alone or in parallel with a mechanical gearbox to transfer power from the engine to the wheels.
- Hydro-mechanical - (or partial hydraulic) combines a hydraulic transmission using one or more torque converter stages at lower speeds with a mechanical transmission using one or more gears, friction clutches or fluid couplings at higher speeds.
- Output at Engine Shaft (Prime Mover) - This is the power that is provided by the diesel prime mover, and in the case of the Deltic locomotive it was 3,300hp. Typically, in some instances, this is the "rated power" of the locomotive. In other instances, power required by the auxiliary devices, such as the fan, batteries, etc is subtracted from the prime mover output power to give a "power available for traction" value, with this value being quoted as the "rated power" of the locomotive. In both cases this power is supplied to the generator, etc, and thus the power supplied to the rail will be less then this value.
- Generator Input - This the power that is supplied to the generator in order to produce the energy required to drive the traction motors. It will be noted that there has already been a small reduction in power to support the operation of auxiliary equipment, such as auxiliary generator, radiator fan, etc.
- Generator Output & (Traction) Motor Input - This is the power that is available to drive the traction motors, and again a small amount of power has been lost due to generator.
- Rail HP - This is the power that is available to drive the locomotive forward and measured at the wheels of the locomotive. Again, power losses have occured due to work in the traction motors and gearing transmissions.
- Drawbar HP - This is the power that is available to drive the locomotive forward, and power losses have occured due to losses in the traction motors and gearing transmissions. The main loss in power in this instance is due to the resistance to movement that the locomotive presents.
- Constant Torque Zone - In this zone torque produced by the motor is constant, and hence the motor produces a constant tractive force. The power of the motor is increasing to its maximum value.
- Constant Power Zone - In this zone, which generally commences when the locomotive reaches the point known as "speed of maximum continuous force", power remains constant in this zone, and tractive force decreases with the speed of the locomotive.
- High Speed Zone - Once we move past the maximum speed of the motor, we see the both of the power, and the tractive force decreasing.
- Maximum Tractive Force - is the maximum force that can be applied to the wheels without causing damage to the locomotive, or exceeding its adhesion limits. This force is shown by the blue curve in the graph below. For our demonstration model, 50,000lbf.
- Continuous Tractive Force - indicates the point at which the maximum continuous or constant force that can be produced on the wheels to drive the locomotive forward. Typically Force = Power / Speed. Thus as the speed increases the force will decrease, as shown by the red curve in the graph below. For our demonstration model, 30,000lbf @ 19.5 mph.
- Maximum Speed - is the maximum design speed that the locomotive can operate at, and is shown by the green line on the graph below. In our demonstration model, it is 90 mph. The tractive force does not go to zero at this point, instead it falls at a dramatic rate as the traction motors may not be capable of providing significant output power beyond this speed.
- Adhesion - Sometimes, a value of adhesion is also provided as a reference. This would indicate the adhesion value of the locomotive at this point of reference.
- Constant Tractive Effort - the AC can maintain a constant tractive effort by monitoring torque levels at their maximum, and preventing wheel slip.
- Variable Frequency Drive - creates a rotating magnetic field which always spins faster then the rotor speed of the traction motor, and thus ensures minimal wheel slip.
- Variable Adhesion - the AC locomotive is able to use weight transfer compensation, thus when a lightly loaded axle is detected force on this axle will be reduced and transferred to a more heavily loaded axle.
Each of the transmission systems has different characteristics.
Tractive Force curves for different types of transmission
Power curves for different types of transmission
There are advantages and disadvantages to each type of transmission.
Electric transmission is able to provide a high starting tractive effort and is able to provide a reasonably constant power output over a wide range of speed. The diesel engine is able to run at full speed and power for most of the speed range of the locomotive. The generator and traction motors required may be relatively large and heavy compared to other transmission systems, increasing the mass and axle load of the locomotive or railcar.
Mechanical transmission is the most efficient with the lowest transmission losses of all the systems. However starting tractive effort is low compared to other forms of transmission and the maximum power output of the diesel engine is only available when travelling at the maximum speed for each gear.
Hydraulic transmission provides a high starting tractive effort, but overall is the least efficient of the transmission systems. However, due to the smaller size and mass of the transmission, diesel hydraulic locomotives are often able to provide a similar power at the drawbar to diesel electric locomotives.
Hydro-mechanical transmission allow the high tractive force available with a hydraulic transmission at low speeds to be combined with greater efficiency of a mechanical transmission at higher speeds.
Some historical attempts to use a diesel engine to drive the wheels directly, without any intermediate transmission are described (in German) on these web pages:
https://www.wikiwand.com/de/Diesel-Klose-Sulzer-Thermolokomotivehttps://www.drehscheibe-online.de/foren/read.php?017,7113509,page=all
There was also an Italian direct drive diesel locomotive built by Ansaldo and powered by a Junkers diesel engine.
Diesel Electric - Power
The amount of force (or effort) available at the rail to drive the locomotive forward will be determined by the diesel engine (prime mover) and the transmission system which converts the mechanical enegry of the prime mover to an energy force at the rails. In the case of a diesel electric DC locomotive, the prime mover drives a DC electric generator, which in turn supplies electricity to the DC traction motors which then drive the locomotive wheels. Each of these power conversions suffer from some form of loss, which means that the full power of the prime mover, is not available to the rails for the diesel's tractive effort.
The following diagram from the BR Deltic Locomotive test report shows the power outputs at the end of each conversion stage. By studying the diagram we can note the following:
Often the amount of power produced at each stage is converted to a fraction of the main output power, and this demonstrates the efficiency of the power conversion process. Ideally this should be 1 (or 100%) in an "ideal" world, however this is never the case, and will always be a lower value then the input power value.
The diagram below shows the power produced by the traction motors of the locomotive, and the tractive force, superimposed onto the same diagram. From the diagram it can be seen that there are broadly three zones of operation for the motors as follows:
Because of this power characteristic, diesel locomotives are often called "Constant Power" machines.
Diesel Electric - Tractive Effort
In specifying a diesel locomotive it is quite common to define a design tractive effort curve against the locomotive speed. The diagram below shows an example of one.
The following points are worth noting from the diagram:
Relationship between Power and Tractive Force
The Rail HP can be converted to tractive effort (force) by one of the following formulas, which can be rearranged to convert between Tractive Force and Power or vicer versa.
Metric: TF (N) = Rail Power (W) / speed (metres per sec)
Given that most diesel locomotives have specification information for the tractive forces, we can use the above formula to calculate the maximum rail hp at the design speed of maximum continuous force point, which is then assumed to be constant. Once determined we can then convert backwards again to find the tractive force at any speed.
In more recent years diesel locomotive using AC traction motors have become more popular, as they can produce higher tractive effort (force) then DC locomotives, because of the following possible modifications (see Republic Locomotives site for a more detailed explanation):
Adhesion
The adhesion between the wheels and the rail will determine the amount of force that can be applied to moving the train, and hence the amount of load that the locomotive can haul. A more detail description of adhesion can be found on the adhesion page, and whilst this page principally deals with adhesion on a steam locomotive, a diesel locomotive has similar issues with adhesion. The main difference between steam and diesel traction is that the tractive force of a diesel is constant for the full wheel rotation, whereas due to the operating rods attached to a steam locomotives wheel the force is not even around the full roatation of the wheel.
As with the steam locomotive the diesel will suffer wheel slip if the rotational force exceeds the adhesive force.
Older generation diesel locomotives, similar to steam locomotives, tended to have adhesion values mainly dictated by the weight on the driving wheels of the locomotive. Typically these adhesion values may have been around 33%. Modern locomotive tend to have very sophisticated wheel slip control technologies which "reduces" the slipperiness of the locomotive and produces an apparent increase in adhesion. Typically these values may be around 45%.
Load Hauling Performance
Once the parameters are determined for the ENG file, load hauling performance tests should be undertaken to confirm that the locomotive performance is within acceptable bounds for the locomotive being modelled.
Often in test reports the Traction Draw Bar Tractive Effort (Traction DBTE) is used to describe the pulling power of the locomotive. This is calculated by considering the impact of the locomotive resistance, trailing load resistance, and gross weight ratio, on the tractive effort calculated above. A detailed explantaion of how to calculate this value can be found on pg 48 of the test report in the Useful References section below. This is the amount of force that is available to overcome the resistance offered by the trailing load behind the locomotive. The graph below shows the Traction DBTE for a diesel locomotive, as well as the trailing load resistance for a 300 ton train on various different gradients.
So for example, with a load of 300 ton the Traction DBTE will vary with speed as shown by the green curve. If the train is climbing a 1 in 80 gradient the trailing load resistance is shown by the red curve. The point where the two curves cross designates the "balancing speed", ie the maximum speed that the locomotive can travel when climbing a 1 in 80 grade with a 300 ton load.
Diesel Mechanic Transmission - Power and Tractive Force
In a mechanical transmission power is transferred from the engine to the wheels by mechanical gearing. Each gear produces a more or less constant tractive force for any given rail speed provided that the diesel engine is operating close to the range of maximum torque. Increasing the number of gears allows the tractive force to be better matched to the ideal tractive force curve at different speeds.
Since diesel engine torque varies with engine speed, then there is a similar variation shown in the actual tractive force produced by each gear step.
The torque curve for a diesel engine might look something like this:
Torque and Power curves for BUT Leyland Engine. [Diesel Railway Traction, 1956]
The tractive force curves for a locomotive with mechanical transmission show a similar shape to the torque curve:
Tractive Force curves for Hunslet 500hp locomotive. [Diesel Railway Traction, 1953]
One or more clutch mechanisms are required to connect the engine output to the different gears and the final drive. The operation of the clutch(es) for rail vehicles is normally automatic, although most locomotives and multiple units with purely mechanical gear systems have manual gear selection by the driver. (This is therefore a semi-automatic gearbox.) In order to allow maximum tractive force to be transmitted on starting, the main clutch must be able to slip on starting from rest. This permits the engine output shaft to rotate at a greater speed than required by the input to the gears. As the train accelerates the slippage is reduced until the engine speed matches the speed required by the gears, at which point the engine is able to drive the gears directly. Two types of slipping clutch are commonly used, the friction clutch and the fluid coupling. In most systems the first gear is engaged as soon as the gear lever is moved to the Gear 1 position.
In order to change to a higher gear the engine speed must be reduced to match the input speed of the gear in order to avoid slippage. In the case of automatic gearboxes and some manual gearboxes the engine speed is reduced automatically by a braking mechanism when the gears are changed. Other manual gearboxes, including the Wilson epicyclic gearbox require the driver to close the throttle in order to reduce the engine rpm before the next highest gear is engaged. With most mechanical transmissions the process of changing gear may take 5 or 6 seconds in total, with the tractive effort dropping to zero for approximately 1 second. Some gearboxes such as the SSS Powerflow have been designed to provide uninterrupted tractive force.
In each gear, the speed and power of the engine increases as rail speed increases. The maximum power output of the engine is only achieved at the maximum speed for each gear.
[Source: The Science of Railways - Lee Towers]
If the speed of the diesel engine becomes too low, for example because a train with a manual gearbox is climbing a gradient and the driver has not changed to a lower gear at the appropriate time, then power output will fall and the diesel engine will begin to labour and may eventually stall.
Mechanical transmissions generally include a 'freewheel' which allows the engine to idle whilst the train is coasting at speed, for example when descending a gradient.