Locomotive horsepower

[chefjavier]

http://www.geocities.com/guilford_350/

Fix your link.. You need give an space after the quote in order for the link to establish.

[chefjavier]

Try this link for locomotives power.

http://www.locophotos.com/

Enjoy!

[GP40-2]

Dynamometers do not measure horsepower, they measure torque!

Bingo! We have a winner!

That's because torque is the ONLY force a reciprocating engine (gas or diesel) produces. I'll repeat that for the "experts" on this forum: The diesel engine on a locomotive is designed to produce "X" amount of torque to turn the traction alternator. "Horsepower" ratings are derived from the torque output at a given RPM; it is never the other way around.

Diesels rely more on torque than do gas engines, application for application....or am I wrong?

Both types of engines rely on torque and ONLY torque to produce useful work. Torque is the only force they produce. The difference between a (typical) gas and diesel is their torque curves occur at different RPM's.

[beaulieu]

And they're geared 85:16? So their motors can exceed 9729 lb-ft of torque?

The 85:16 ratio is for the SD70MAC.  The SD70ACe is 83:16.  I don't know what either of their torque limitations is (although the SD70ACe does have a higher limitation than the SD70MAC has) -- to me it's whatever the software thinks that it is.

SD70MAC uses Siemens 3-phase equipment, SD70ACe switched to Mitsubishi for the 3-phase drive.

[Virginian]

Torque is twisting force.  Horsepower is work.  The characteristics of a diesel usually cause it to operate at considerably slower speeds than a gasoline engine.  Hence it must produce more torque at a slower speed to achieve like power.

One horsepower equals 550 foot pounds per second.  From that you should be able to calculate anything.    (But, I'll bet 4000 Budweiser Clydesdales could drag any loco anywhere !  If you could only find the right harness. )

[selector]

Thanks for the illucidation.  I still don't know how the prime mover in a locomotive responds to an increased demand for work.  If the operator notches up, take me through the "system" so that we understand what happens as a result of what.   Does the diesel increase revolutions by nearly two times, or does it merely aspirate more, get more fuel, and how does that affect the torque output, which I now understand is the primary motive force once converted to tractive effort by the motors?  (I had always understood that a diesel gets air metered, while fuel is constant.  Probably outdated knowledge now that we have common rail and other improvements...although I don't know if common rail has any application here....what does?)

[Virginian]

Todays diesel engines are computer controlled as to both air and fuel (injectors) metering, but neither have ever been constant flow.  Ideally you would want to have a nearly constant ratio of fuel to air, but rarely has this ever been accomplished throughout the range.  When the operator asks for more power or speed, the diesel will produce more torque and/or a higher speed, which will be utilized by the generator due to it being also stepped up via the field currents at the same time.  Torque will be effected by how much fuel is burned on every combustion stroke, and power will be determined by how fast the torque is produced (i.e. engine RPM).  The traction control will monitor every wheel and control the electrical power going to each motor to limit slip.

[oltmannd]

Thanks for the illucidation.  I still don't know how the prime mover in a locomotive responds to an increased demand for work.  If the operator notches up, take me through the "system" so that we understand what happens as a result of what.   Does the diesel increase revolutions by nearly two times, or does it merely aspirate more, get more fuel, and how does that affect the torque output, which I now understand is the primary motive force once converted to tractive effort by the motors?  (I had always understood that a diesel gets air metered, while fuel is constant.  Probably outdated knowledge now that we have common rail and other improvements...although I don't know if common rail has any application here....what does?)

A locomotive with battery field excitation (e.g. a GP9) works as follows.

The governor is the "brains", whose job is to balance engine speed, fuel and generator excitation.  The governor is basically a fly-ball governor that will adjust the fuel rack to maintain a set engine speed for each notch.  If the load increases, the engine will start to slow down, the fly-balls move toward center, causing (through linkage) the fuel rack to shorten, giving more fuel to the engine.  So, your GP9 in notch 8 will have the engine turing at 835 RPM regardless if the generator field switch is open or closed and whether the locomotive is moving at 10 mph or 70.

That's half the governor's job.  The second half is that it will try to maintain a given rack (fuel) setting for each notch.  That rack setting is set so that the engine will try to produce roughly, a constant, set HP for each notch.  It does this by balancing the generator excitation against the fuel rack using the governor's load regulator (a hydraulic vane motor powered rheostat).  The load regulator is a big rheostat that's in series with the battery and the generator field.

Lets say your GP9 is coasting along at 30 mph with the generator field switch down (generator unloaded) and the throttle in notch 8.  The engine would be turning at 835 RPM with a "long" fuel rack (not much fuel).  Now, you flick the generator field switch up.  The circuit for the generator excitation field is now closed.   The governor knows that it wants a certain fuel rack for notch 8, and right now the rack is "long", so it moves the load regulator to to reduce the rheostat's resistance.  That increases the load, causing the RPM to sag, so the governor increases the fuel.  Still not at the right rack setting?  The govenor move the load regulator some more, and then again and again until the balance point is reached and the locomotive is making it's 1750 traction HP (more or less...)

Now, if the locomotive encounters a grade and starts to slow down, the traction motors spin more slowly, decreasing the back EMF, which increases the load of the main generator, the engine starts to spin more slowly, the govenor shortens the rack to maintain engine speed, but now we're over the rack balance point, so the governor moves the load regulator to reduce the load until the fuel rack is back at it's set, balance point.

Modern locomotives have somewhat more sophisticated methods of doing this, but the principles are the same.

[selector]

Holy smoke!    I'm going to go back and get another degre...in engineering.  Otherwise, it will take me weeks to digest all this.   

Thank-you very much for letting me take your time that way.  A most informative post, oltmannd.

-Crandell

[Alan Robinson]

And then, of course, we have steam locomotives where we can discuss horsepower in multiple ways. There is drawbar horsepower, cylinder horsepower, boiler horsepower, etc. Which is most useful depends on which question you are asking. The same is true for a diesel-electric or any other locomotive.

Ultimately, horsepower is a measure of the rate at which a machine can do work. It is computed by measuring a force times a distance per unit time. One horsepower is equal to 550 foot-pounds per second. It can be 550 pounds moving through a distance of 1 foot in one second, 1 pound moving through a distance of 550 feet in one second, or any equivalent combination. For a rotating machine it is measured by multiplying revolutions per minute times the torque the machine is producing. It is the same thing if you look at the units. It is always a force times a distance divided by a time.

Drawbar horsepower for any locomotive is the ultimate measure of the work it can do. And surprisingly, when the locomotive is pulling to start the train but the train is not yet moving, the work it is doing is zero. That's right, zero. Remember, even a very large force, the starting tractive effort, multiplied by the distance of zero feet per second means the locomotive is doing no work. (But don't tell that to the locomotive!)

Once the train begins to move, the locomotive is doing work. For a steam engine, the tractive effort is limited by two things. One is the adhesion of the drivers at the rails and the weight on the drivers. The other is the force generated by the steam pressure on the pistons averaged through a single driver rotation. A steam engine can produce its maximum tractive effort when it first starts a train and that tractive effort stays more or less constant when the engine is pulling slowly. During this time the horsepower may be quite low because the speed is low. But the horsepower the locomotive generates increases linearly as the train speed increases. (Not exactly true because once the train starts moving, the tractive effort required to keep it moving at first drops. Rolling friction is less than starting friction.)

The steam engine continues to pull the train faster and faster, so drawbar horsepower continues to increase. Sooner or later, and it could be pretty soon depending on the design of the boiler and size of the cylinders, the boiler can't produce all the steam the cylinders require as the speed increases. The engineer pulls back on the johnson bar to admit steam for a smaller portion of the stroke, thus lessening the load on the boiler to a steaming rate it can sustain. As he does this, tractive effort will decrease and soon the train speed will balance with the horsepower the boiler is capable of producing. However, unlike a diesel-electric's prime mover, it is possible to overload a steam engine by overfiring the boiler. There is a lot of smoke, efficiency is terrible but the boiler can produce much more power than it's rating. This is why a steam locomotive can pull any train it can start.

Older steam locomotive were designed to produce their maximum horsepower at quite a low speed. Some of the early mallets designed for drag service would run out of steam at ten miles per hour or perhaps even less. More modern locomotives were designed for higher speed and would produce their best horsepower at speeds of 50 miles per hour or more. Below that speed they would be horsepower limited. This is why it was such a crying shame to take a high performance simple articulated like the C&O's Allegheny type and use it in drag freight service. That locomotive was designed to really move.

Now lets look at a diesel-electric locomotive. There are several more horsepower ratings we need to worry about. The first is the horsepower of the prime mover, a multiple of the maximum rpm and the maximum torque of the diesel engine itself. For a diesel this is an absolute limit. (Unless you cheat and mess with the fuel rack settings, something not designed to assure long engine life.) Another rating has to do with the capacity of the electrical transmission and here things get a little tricky because of the nature of electric motors.

The horsepower rating of an electric motor is a combination of RPM and torque. Ultimately, the horsepower rating is a function of the motor's ability to keep itself cool. Torque is limited by the magnetic field strength which is determined by the amount of magnetic material and the efficiency of the magnetic path and by the current limitation of the electrical windings. When either of these limits are pushed, the motor gets hot. Speed is limited by how fast the motor can turn before it flys apart or experiences other mechanical damage.

For a traction motor, the tractive effort is limited as it is in a steam locomotive by two factors. The first is the factor of adhesion and the weight on the drivers and the second is the motor torque. But the torque limit isn't a fixed number. There is the torque the motor can produce continuously and then there is a time-rated torque limit, say a five minute limit for example. So, when the locomotive is starting a heavy train, the motor can produce a very great torque for the short time it takes to start the train. (But remember, until the train moves the work done, that is drawbar horsepower, is zero.) Typically, the torque required to start a heavy train may not be within the continuous torque rating of the traction motor. As the train starts and begins to accelerate, the torque requirement drops and at some slow speed, usually between 8 miles per hour and 12 miles per hour (depending on the locomotive design and the gear ratio) the torque must fall to within the continuous tractive effort rating of the locomotive. If for any reason the train won't accelerate, the locomotive must reduce the torque so as to avoid damaging the traction motors and this means that the train may stall. Note that this means that a diesel-electric locomotive can start a train that it can't necessarily pull as it may well fail to be able to accelerate the train above it's minimum continuous tractive effort limit.

Fundamentally, a diesel electric locomotive has a different operational characteristic than does a steam engine. A steam engine has the characteristics of a constant torque machine. Torque is at a maximum value at starting but the engine can maintain that value of torque until the boiler steaming capacity forces a reduction. From that point on, boiler horsepower determines the rating of the locomotive. This is why a 2-8-4 may not be able to start any heavier train than a good 2-8-0 but it can pull that train much faster. Higher boiler capacity.

But a diesel-electric is essentially a constant horsepower machine. By this I mean that when it is operating anywhere above it's continuous tractive effort limiting speed, all it's prime mover horsepower is available at any speed. (Note, however, that tractive effort falls off rapidly as speed increases, ever faster than for many modern steam locomotives.) There is no way to "overfire" a diesel engine, so that's it, brother. An electric locomotive, even though it uses the same type traction motor, has no such prime mover horsepower limit. It can always draw more power from the catenery, and it explains why there are electric locomotives of 25,000 horsepower.

So how is a diesel-electric's horsepower measured? By the horsepower of the prime mover. Above the maximum continuous tractive effort speed, that's all that matters. Below that speed, the horsepower of the locomotive at the drawbar is limited by the torque limit of the traction motors, and not by the diesel engine.

Now, did any of that make sense?

[oltmannd]

Holy smoke!    I'm going to go back and get another degre...in engineering.  Otherwise, it will take me weeks to digest all this.   

Thank-you very much for letting me take your time that way.  A most informative post, oltmannd.

-Crandell

All I can say is "God bless the Woodward Governor Company!"

[beaulieu]

One last point the quoted horsepower figure for a locomotive is a conversion of the electric power output from the main generator (alternator), the Brake Horsepower rating of the diesel engine itself is higher. In otherwords an SD60 is producing a little over 2.8MW at full throttle.

[heikke1]

Yes, it makes a lot of sense.

Just want to add for anybody pondering these questions: Drawbar horsepower = tractive force x train speed. This must be equal to driver (driving wheels) horsepower = driver torque x driver rpm. This in its turn (forgetting some losses) is translated to the prime mover (pm) horsepower = pm torque x pm rpm. It is the locomotive control system's job to set the prime mover horsepower at any moment to what is desired at the drawbar (increase/decrease tractive force to change train speed or to maintain constant speed regardless grade). Both torque and rpm are adjusted in low throttle settings. In higher up the pm rpm is kept constant and only the torque adjusted metering fuel and air.

The above ignores the traction motors for simplicity as mere intermediates. Their torque and rpm follow, for any drawbar condition, the corresponding driver values adjusted by the gear ratio: product of torque and rpm remains unchanged. (I admit that this is a simplification, gear losses should be taken into account.)

Conversions from the drawbar values to rotating axle values become simple, if you use watt, newton meter and revolutions per second instead of horsepower, lb ft and rpm (newton meter = watt second).

[Alan Robinson]

This analysis of drawbar horsepower (tractive effort times train speed equals power of the "prime mover") works for a steam locomotive, but not for a diesel electric because at starting, just before the train moves, thediesel-electric's prime mover may be generating significant horsepower but the drawbar horsepower would be zero. It is only once the diesel electric has accelerated the train to the speed where the traction motors can convert all the horsepower of the prime mover into useful work that the drawbar horsepower equals (neglecting conversion losses) the prime mover horsepower. At very low speed much of the prime mover's horsepower could be wasted as heat generated in the traction motors and the overall efficiency of the locomotive could be quite low.

Normally, an engineer would limit this inefficiency by not notching up the speed of the diesel prime mover until the train had begun to accelerate and the current to the traction motors had begun to drop. Newer locomotives do all this automatically, adjusting the engine speed to obtain maximum fuel efficiency. The early diesel electric locomotives such as the EMD FT were all manual machines. The engineer had a load meter which was essentially an ammeter marked with variously colored zones showing how long the traction motors could be operated at any current rating. It was up to the engineer to make sure nothing got fried.

I once had an operating manual for the EMD F3, which had the same kind of controls as the FT. There were very explicit instructions for the engineer to excercise caution at low speeds and prolonged operation at high tractive effort (high current) levels so as not to damage traction motors. This condition would most likely occur when starting a heavy train on an adverse grade. The locomotive might be able to start the train by working the traction motors in the time-limited zone but if the train could not be accelerated so as to drop the current within safe continuous limits, the horsepower would have to be reduced and the train would probably stall. Thus, a diesel electric could start a train it could not necessarily pull.

There was an especially interesting section describing doubleheading procedures to be used with steam locomotives. If it was found that operation at full throttle would not allow for the traction motor current to be kept within safe continuous operating limits, the prime mover power level should be decreased (notched down) in order to transfer more of the work to the steam helper, as the steam engine probably developed its best horsepower at a lower speed than the diesel did. Of course it wasn't possible to overload the steam locomotive, but you could sure give the fireman a hernia if he didn't have a stoker!

Direct current traction motors could be wired in different configurations "on the fly" to control the matching between train speed and current draw. This configuration change required some skill on the part of the engineer to achieve maximum efficiency. More modern locomotives pretty much automated this process and eventually it was all put under microprocessor control. All this not only lessened the work load for the engineer but also reduced fuel consumption.

The advent of alternating current drives offers two other important advantages. An alternating current induction type motor's speed is determined pretty tightly by the frequency of the driving current. This locks all the axles together at the same speed, thus greatly reducing wheel slippage and improving the ability of the locomotive to achieve maximum tractive effort under difficult rail conditions. Because the motors are simpler and more rugged in construction they also reduce maintenance costs even further. They also allow regenerative braking to be performed at lower speeds than direct current traction motors which further saves maintenance costs.

[JayPotter]

An alternating current induction type motor's speed is determined pretty tightly by the frequency of the driving current. This locks all the axles together at the same speed, thus greatly reducing wheel slippage and improving the ability of the locomotive to achieve maximum tractive effort under difficult rail conditions.

I don't understand (1) how AC-traction "locks all the axles together at the same speed" and (2) how this would maximize tractive effort under difficult rail conditions unless each axle were subject to the exact same rail conditions.

 

 

[Alan Robinson]

How AC induction motors "lock all the axles together" is a little difficult to understand at first, but not after a bit of explanation.

We're all familiar with the characteristics of a permanent magnet DC motor, which behaves a lot like an ordinary direct current traction motor. With no load the motor turns very fast with the no-load top speed limited to the point where the back emf (the voltage the motor is generating whenever it is turning, a voltage that opposes the voltage that is making the motor turn) nearly balances the forward emf applied by the power source. The only difference is the relatively small amount of current, and therefore power, required to overcome bearing and windage losses. If we load the motor, it will slow down quite a bit in order to "pull the load", which it does because the reduction in speed means there is less back emf available to counteract the applied voltage and the current draw goes up. It is this increased current multiplied by the applied voltage that is the power to pull the increased load. The more load is applied, the slower the motor turns and the more current it draws until the motor finally stalls. That represents the maximum torque the motor can generate. But it won't generate this high torque for too long or it will burn up due to too much current through the windings. Remember, at stall the current is not limited by the back emf because there is none. It is limited only by the ohmic resistance in the windings.

This means that the load characteristic of a DC motor is not very "stiff." It takes a relatively large change in speed to make a relatively small change in current draw and thus power and torque. On a diesel-electric with DC transmission, each axle has its own motor. If one axle begins to slip due to uneven weight distribution or a slippery spot on the rail, it will speed up quickly with the small reduction in load due to the slipping. Once it really starts to slip its ability to pull its share of the load drops off because sliding friction is much lower than starting friction. Advanced diesel electric dc drives have wheel slip detectors on each axle that will momentarily interrupt or reduce the current to that axle's traction motor whenever wheel slip is detected. This can allow the locomotive to pull a heavier load because even the beginning of a wheel slip is detected and stopped before it can get out of control. This system works pretty well and is almost universal on all modern motive power.

An AC induction motor operates somewhat differently. A three phase motor, like the AC traction motors on modern diesel electric drives, has three, or multiples of three, stationary (non-rotating) windings called stators, each one wired to a different phase. These windings create a rotating magnetic field with the speed of rotation determined by the frequency of the applied current. For a frequency of 60 hz, the rotational speed of the magnetic field of a three pole motor is 3,600 RPM. If we put a permanent magnet inside this rotating field it would turn at 3,600 RPM, dragged around by the turning magnetic field. Some kinds of AC motors are built essentially exactly like this and they are called synchronous motors because the rotation of the rotor is "synchronized" exactly to the rotation of the magnetic field. Some locomotives use this kind of motor and all the axles must turn at the same speed.

An ordinary induction motor works in a similar manner but there are important differences. The rotor of an induction motor consists of a series of "shorted" coil windings arranged around a stack of magnetic plates. This looks a lot like a "squirrel cage", one of those exercise gizmos for hamsters, thus the name squirrel cage motor. When this rotor is inserted in the rotating magnetic field, the rotating field causes induced current (like between the primary winding of a transformer and its secondary winding) in these shorted coils. Because they are shorted, the induced current is very large and this induced current creates a powerful magnetic field in the stack of magnetic plates. The squirrel cage becomes an electromagnet and it begins to turn just as the permanent magnet did in the synchronous motor. This induced magnetic field gets dragged around in a circular motion by the rotating magnetic field. As the rotor begins to spin up and its rotational speed approaches the rotational speed of the rotating magnetic field, the strength of the induced field begins to drop. This is because with less relative motion betweeen the rotating magnetic field and the moving rotor, there is less current induced in the rotor and the rotor electromagnet becomes weaker. The difference between the speed of the rotating magnetic field and the speed of the rotor is called "slip" and is different, and unrelated, to wheel slip on the rail. It is this slip that allows an induction motor to generate torque.

If the rotor accelerates to a speed matching the rotating magnetic field, the induced current drops to zero. Thus, the rotational speed of an induction motor rotor "locks" very nearly to the frequency of the rotating magnetic field, the only difference in speed between the rotor and the rotating magnetic field being the slip required to generate the necessary torque to pull the load. The full load slip of an induction motor is small, amounting to only a few percent (typically 2 to 5%) of the synchronous speed. The motor goes from no load at synchronous speed to full load at a speed only 2 to 5% lower. Compare this to the speed difference for the DC motor between no torque and full torque.

Even a small increase in load, which slows the rotor just a bit, causes a rapid and large increase in induced current in the rotor and a correspondingly rapid and large increase in torque to pull the load. This is what we mean when we say that an induction motor drive is very "stiff." If the load on an axle is reduced to zero (really wet or oily rail), the axle speed doesn't run away but instead accelerates only up to the zero slip speed. If the load on the axle increases, the slip increases and the torque on that axle increases very quickly with only a very small decrease in speed.

An AC transmission uses squirrel cage induction traction motors. But instead of being supplied with a constant frequency current as we would find in our homes, these motors are supplied with a variable frequency (and variable voltage) three phase power generated electronically inside the locomotive by means of high power variable frequency solid state inverters. These inverters take the output of the generator (or alternator) driven by the diesel electric engine and create three phase alternating current the traction motors need. When the locomotive is first starting the train, the frequency is very low so the synchronous speed is low. As the locomotive accelerates the load the frequency (and voltage) of the current supplied to the traction motors increases linearly. Double the frequency and you double the speed. All the motors always turn together at the same speed, the speed determined by the frequency. If one of the axles is on a patch of wet or oily rail, it will slip a little but only enough that the speed of the axle increases until the torque lowers to the slipping torque and no lower. As soon as the axle moves to clean rail and the slipping stops, the torque automatically increases as the axle speed drops to match the others. It is as though all the motors were locked together with a chain drive that uses slightly stretchy chain. There can be a small amount of difference between the speed of one motor and another but only as much as the stretch in the chain will allow. The "electrical chain" is pretty stiff to the point that all the wheel diameters in a locomotive must be matched in order to avoid overloading the motor with the biggest diameter wheel. In practice, any difference of diameter greater than 1/2 inch or so between the largest and smallest wheel (using 40" to 42" diameter wheels) is enough to cause real problems. A 1/2" diameter difference will cause a difference of perhaps 20% between the power applied to the two axles. You can see that it doesn't take very much slip to cause the power to be automatically reapportioned among all the axles to minimize slip and maximize tractive effort. And it's all automatic and comes along free for the ride with AC transmission. This is why it is becomming more and more popular as the cost of solid state inverters comes down and their reliability and power output goes up.

[JayPotter]

How AC induction motors "lock all the axles together" is a little difficult to understand at first, but not after a bit of explanation.

All the motors always turn together at the same speed, the speed determined by the frequency. If one of the axles is on a patch of wet or oily rail, it will slip a little but only enough that the speed of the axle increases until the torque lowers to the slipping torque and no lower. As soon as the axle moves to clean rail and the slipping stops, the torque automatically increases as the axle speed drops to match the others. It is as though all the motors were locked together with a chain drive that uses slightly stretchy chain. There can be a small amount of difference between the speed of one motor and another but only as much as the stretch in the chain will allow. The "electrical chain" is pretty stiff to the point that all the wheel diameters in a locomotive must be matched in order to avoid overloading the motor with the biggest diameter wheel.

So, basically, all of the axles turn at the same speed until it's necessary for the speed of a slipping axle to change in order to correct the slip by reducing the torque.  I understand that concept. 

And I understand the wheel-diameter issue in relation to EMD units.  However I don't understand why wheel diameters would have to be matched exactly on GE units since they have a separate inverter for each axle.

[Alan Robinson]

Jay, you have a good point. GE's latest AC transmissions utilize individual inverters for each axle for exactly the reason you state. Each axle's inverter operates at the proper frequency to match that axle's drive wheel diameter. This eliminates drive wheel diameter variation as a problem. Even though each inverter may operate at a slightly different frequency, the effect is the same as I described formerly.

GE's latest control scheme for the inverters incorporates smart wheel slip control with each inverter changing its frequency on a real time basis under microprocessor control to minimize wheel slip. This gives the best possible adhesion factor under all track conditions and is reflected in the very high tractive effort these locomotives are capable of delivering.

EMD's AC drive technology uses a single inverter per truck, so each inverter powers two or three axles, but both inverters operate at the same frequency. This system reflects the simpler design I described earlier, the inverter doesn't have to change frequency when an axle suffers wheel slip. The frequency stays the same, the slipping axle merely speeds up a bit which lessens the slip between the rotating magnetic field and the motor rotor which automatically reduces the torque and limits the wheel slip. It doesn't eliminate the slip, merely limits it to a very small value where tractive effort doesn't suffer much. The missing load due to the slipping axle is shifted to the other axles, with their stator/rotor slip increasing just enough to increase their torque to take up the load shed by the slipping axle. When the slippery axle regains its footing the whole system equalizes out again automatically with no need to change the frequency.

In GE's advanced scheme, the control system can detect if an axle begins to slip. The ultimate in control allows a slipping axle to reduce power while operating at the same frequency (this is done by modifying the voltage sent to that traction motor) and this means that all the axles really do turn at the same speed. The point to remember is that AC transmission make such precise control much easier to implement that it is with DC traction motors. The added complication of the individual inverters per axle pays off in much better adhesion factors and higher tractive efforts. In addition, AC traction motors are much simpler in construction and are much more reliable than their DC counterparts. There are no brushes or commutators, only the stator windings and the monolithic rotor and two bearing sets.

DC transmissions will probably continue to be used for some time in some switchers and lower powered locomotives because they are cheaper to build. But with the rapidly lowering costs of AC transmission, this technology will probably become universal for all new power in the fairly near future.

[heikke1]

This analysis of drawbar horsepower (tractive effort times train speed equals power of the "prime mover") works for a steam locomotive, but not for a diesel electric because at starting, just before the train moves, thediesel-electric's prime mover may be generating significant horsepower but the drawbar horsepower would be zero. It is only once the diesel electric has accelerated the train to the speed where the traction motors can convert all the horsepower of the prime mover into useful work that the drawbar horsepower equals (neglecting conversion losses) the prime mover horsepower. At very low speed much of the prime mover's horsepower could be wasted as heat generated in the traction motors and the overall efficiency of the locomotive could be quite low.

You are right that in starting from a standstill the prime mover power is at first not shown as traction motor power output but consumed as heat loss. I felt that for the sake of clarity I can lump that together in what I expressed "(forgetting some losses)". My argument is that the moments when the prime mover power goes mostly to heating traction motors (+ some other losses) represent a small fraction of a locomotive's working hours. Once the locomotive starts gaining speed and higher voltage has to be applied to counter the increasing back emf of the traction motors, more power is drawn from the prime mover. This increase, however, goes to useful work and the losses' share of the total diminishes. DC series motor represents a very low ohmic resistance at a standstill. Therefore only a low voltage is needed to drive through it  enough current to produce the torque and thus the tractive force allowed by the adhesion. So only a fraction of the prime mover's full horsepower can be applied at first (and consumed as heat). How significant the loss power is (absolute and relative to the useful power) during the cycle of starting and accelerating a train? It would be interesting to see a graph showing the loss and useful powers vs. speed for a typical DC locomotive on a typical train from a standstill until the traction motors are switched in parallel and up to the speed that the adhesion allows the full application of the prime mover power. 

[oltmannd]

How AC induction motors "lock all the axles together" is a little difficult to understand at first, but not after a bit of explanation.

We're all familiar with the characteristics of a permanent magnet DC motor, which behaves a lot like an ordinary direct current traction motor. With no load the motor turns very fast with the no-load top speed limited to the point where the back emf (the voltage the motor is generating whenever it is turning, a voltage that opposes the voltage that is making the motor turn) nearly balances the forward emf applied by the power source. The only difference is the relatively small amount of current, and therefore power, required to overcome bearing and windage losses. If we load the motor, it will slow down quite a bit in order to "pull the load", which it does because the reduction in speed means there is less back emf available to counteract the applied voltage and the current draw goes up. It is this increased current multiplied by the applied voltage that is the power to pull the increased load. The more load is applied, the slower the motor turns and the more current it draws until the motor finally stalls. That represents the maximum torque the motor can generate. But it won't generate this high torque for too long or it will burn up due to too much current through the windings. Remember, at stall the current is not limited by the back emf because there is none. It is limited only by the ohmic resistance in the windings.

This means that the load characteristic of a DC motor is not very "stiff." It takes a relatively large change in speed to make a relatively small change in current draw and thus power and torque. On a diesel-electric with DC transmission, each axle has its own motor. If one axle begins to slip due to uneven weight distribution or a slippery spot on the rail, it will speed up quickly with the small reduction in load due to the slipping. Once it really starts to slip its ability to pull its share of the load drops off because sliding friction is much lower than starting friction. Advanced diesel electric dc drives have wheel slip detectors on each axle that will momentarily interrupt or reduce the current to that axle's traction motor whenever wheel slip is detected. This can allow the locomotive to pull a heavier load because even the beginning of a wheel slip is detected and stopped before it can get out of control. This system works pretty well and is almost universal on all modern motive power.

An AC induction motor operates somewhat differently. A three phase motor, like the AC traction motors on modern diesel electric drives, has three, or multiples of three, stationary (non-rotating) windings called stators, each one wired to a different phase. These windings create a rotating magnetic field with the speed of rotation determined by the frequency of the applied current. For a frequency of 60 hz, the rotational speed of the magnetic field of a three pole motor is 3,600 RPM. If we put a permanent magnet inside this rotating field it would turn at 3,600 RPM, dragged around by the turning magnetic field. Some kinds of AC motors are built essentially exactly like this and they are called synchronous motors because the rotation of the rotor is "synchronized" exactly to the rotation of the magnetic field. Some locomotives use this kind of motor and all the axles must turn at the same speed.

An ordinary induction motor works in a similar manner but there are important differences. The rotor of an induction motor consists of a series of "shorted" coil windings arranged around a stack of magnetic plates. This looks a lot like a "squirrel cage", one of those exercise gizmos for hamsters, thus the name squirrel cage motor. When this rotor is inserted in the rotating magnetic field, the rotating field causes induced current (like between the primary winding of a transformer and its secondary winding) in these shorted coils. Because they are shorted, the induced current is very large and this induced current creates a powerful magnetic field in the stack of magnetic plates. The squirrel cage becomes an electromagnet and it begins to turn just as the permanent magnet did in the synchronous motor. This induced magnetic field gets dragged around in a circular motion by the rotating magnetic field. As the rotor begins to spin up and its rotational speed approaches the rotational speed of the rotating magnetic field, the strength of the induced field begins to drop. This is because with less relative motion betweeen the rotating magnetic field and the moving rotor, there is less current induced in the rotor and the rotor electromagnet becomes weaker. The difference between the speed of the rotating magnetic field and the speed of the rotor is called "slip" and is different, and unrelated, to wheel slip on the rail. It is this slip that allows an induction motor to generate torque.

If the rotor accelerates to a speed matching the rotating magnetic field, the induced current drops to zero. Thus, the rotational speed of an induction motor rotor "locks" very nearly to the frequency of the rotating magnetic field, the only difference in speed between the rotor and the rotating magnetic field being the slip required to generate the necessary torque to pull the load. The full load slip of an induction motor is small, amounting to only a few percent (typically 2 to 5%) of the synchronous speed. The motor goes from no load at synchronous speed to full load at a speed only 2 to 5% lower. Compare this to the speed difference for the DC motor between no torque and full torque.

Even a small increase in load, which slows the rotor just a bit, causes a rapid and large increase in induced current in the rotor and a correspondingly rapid and large increase in torque to pull the load. This is what we mean when we say that an induction motor drive is very "stiff." If the load on an axle is reduced to zero (really wet or oily rail), the axle speed doesn't run away but instead accelerates only up to the zero slip speed. If the load on the axle increases, the slip increases and the torque on that axle increases very quickly with only a very small decrease in speed.

An AC transmission uses squirrel cage induction traction motors. But instead of being supplied with a constant frequency current as we would find in our homes, these motors are supplied with a variable frequency (and variable voltage) three phase power generated electronically inside the locomotive by means of high power variable frequency solid state inverters. These inverters take the output of the generator (or alternator) driven by the diesel electric engine and create three phase alternating current the traction motors need. When the locomotive is first starting the train, the frequency is very low so the synchronous speed is low. As the locomotive accelerates the load the frequency (and voltage) of the current supplied to the traction motors increases linearly. Double the frequency and you double the speed. All the motors always turn together at the same speed, the speed determined by the frequency. If one of the axles is on a patch of wet or oily rail, it will slip a little but only enough that the speed of the axle increases until the torque lowers to the slipping torque and no lower. As soon as the axle moves to clean rail and the slipping stops, the torque automatically increases as the axle speed drops to match the others. It is as though all the motors were locked together with a chain drive that uses slightly stretchy chai

-Don (Random stuff, mostly about trains - what else? http://blerfblog.blogspot.com/) 

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