Does the back EMF limit the voltage the motor can accept and hence it's speed?
Hmm. I think you're a little confused. Back-emf limits the motor speed because it dictates how much voltage you need to achieve a given speed.
Would an ideal motor have a very high Kt and very low Kemf?
No. (The symbol \$K_e\$ is usually used for the back-emf constant, by the way.)
If you use SI units (Nm/A for \$K_T\$, V/(rad/s) for \$K_e\$), then \$K_T = K_e\$ for DC motors and permanent-magnet synchronous motors (aka "brushless DC"), and depending on the type of motor and how you define \$K_T\$ and \$K_e\$, the ratio of the two should be a fixed proportionality constant.
Proof of why this is true for DC motors:
At constant operating point (constant speed, voltage, current, torque):
- \$V_T = K_e \omega_m + IR\$
- \$T_m = K_T I\$
(\$V_T\$ = terminal voltage, \$\omega_m\$ = motor angular velocity, \$I\$ = motor current, \$R\$ = motor resistance, \$T_m\$ = torque, including frictional losses)
Electrical power in = \$V_T I = K_e \omega_m I + I^2 R\$
mechanical power out = \$T_m \omega_m = K_T I \omega_m \$
Losses = \$I^2 R\$
Conservation of energy means electrical power in = mechanical power out + losses
This is true if and only if \$K_e = K_T\$.
What happens if the back emf voltage reaches the input voltage, does the motor stop running?
No -- what happens is that the ability of the motor to produce torque decreases with speed. Back-emf voltage "uses up" voltage from the electrical power source; the remaining voltage available to the motor is what's left for IR drop in the motor and the inductance drop \$L \frac{dI}{dt}\$, and since torque is proportional to current I, the available torque decreases. The system reaches equilibrium at some point where the electromagnetic torque matches the motor's mechanical load. If you increase the mechanical load, current will increase to match that torque as speed slows down, making more IR drop voltage available.
Is a bigger Kt always better?
No. Rule of thumb with DC motor selection (also true for brushless DC motors to a large extent) -- pick a motor with a \$K_T\$ and back-emf constant such that the supply voltage you have available is well-matched with the back-emf at your maximum speed. You usually want back-emf voltage to be 80-95% of the supply voltage, but the exact number depends on the load torque and the IR drop in the motor at that operating point.
If you pick a \$K_T = K_e\$ too high, you'll run out of voltage and won't be able to achieve the speed you need. If you pick a \$K_T = K_e\$ too low, the current needed to achieve the torque you need will be higher than necessary.
Century old motors were well built! And probably conservatively designed because electricity was new; they didn't know which corners you could safely cut.
In those days, everything mechanical was designed for easy maintenance; nuts, bolts, taper pins; simple tools to take the whole lot apart, adjust to take up wear, reassemble and use for another 10000 miles. Run out of parts? Turn another one to fit!
I had a 1910-era lathe still capable of turning within about 0.002" (traded it for a 1928 model!) and my 1840s watch is keeping very good time.
In an era of relatively cheap labour and expensive materials, this made sense. Who knows, we may end up back there some day!
Meantime it's worth studying how things from another era are made; partly to keep the skills alive and partly because good engineering is good engineering, from any era.
Just to clarify because this seems to have hit a nerve : I'm not simply equating long life with good engineering. What makes these motors good engineering is the skill with which they met their design goals using materials and techniques available at the time.
And long life was almost certainly one of them; reliability (not measured as MTTF but the ratio between MTTF and MTTR) i.e. easy repair, and efficiency. Swapping motors for a fix is not the issue; replacing brushes, re-lining bearings or (major job!) rewinding the motor was what happened - and what the motors were designed for. It's NOW we kinda-sorta-fix things by replacing motors.
We haven't improved THAT much on 92% efficiency in a motor in the last hundred years, but we do it with a lot less copper and iron. We can equally well admire a modern brushless motor with sealed bearings and no maintenance for ten years; they can both teach us something.
Best Answer
This touches on basically two things: AC current and electrical machines. Let's start with the first.
The war of the currents was very, very long ago. In a time where there was only theoretical understanding of switching power supplies, but no means to actually implement this kind of device. In order to distribute power over long distances, you want to reduce the current as much as possible because current is what causes losses. So you want to have very high voltages, in the 400kV-4MV range. However, as you distribute out towards smaller and smaller units, the required physical size of such conductors as well as safety issues require the use of lower voltages. In homes, you want to use safe low voltages, i.e. <600V. For medium scale distribution, something in between is preferred, nowadays standardized to 10-40kV. So for grid-scale distribution, you require at least two big conversion steps.
By far the easiest and most reliable way to do this is with transformers. They are solid-state, very well understood, absolute lowest complexity. Of course, transformers only work well with AC current of some kind, and in order to minimize overall transformer size but avoid the worst parts of skin and proximity effects, we chose about 50-60Hz as the AC frequency. This is why things are the way they are now.
However, this does not mean that AC is 'better' than DC. At the time, using AC was the better choice. Nowadays, DC is. At least for grid purposes.
AC is a much less efficient way of transporting large amounts of power. It is required for transformers, but otherwise it is horrible. It is very easy to do a first-order calculation to see how bad this is.
Take a distribution system that has a 1000V conductor insulation rating, i.e. I can safely transport energy at 1000V. Let's say I want to transport 1000W of power over here. This means that I can either do 1000V, 1A or 707VAC, 1.4A. It is immediately clear that DC resistance losses in this transmission line will be \$I^2=(\sqrt{2})^2=2\$ times as high for AC compared to DC. Or alternatively, a transmission line with equal current rating will be able to carry \$\sqrt{2}\$ times the power when operated with DC instead of AC.
However, there are more distribution advantages to DC. The most prominent is skin effect, although the proximity effect is something you might also want to look up. Skin effect causes changing current to bunch up near the surface ('skin') of a conductor. This means that the current density is not uniform over the conductor cross-section, and this causes the effective resistance of the wire to increase as frequency goes up. Especially when dealing with very high currents like in transmission lines, this can cause tens or hundreds of percents of effective resistance increase. A mitigation is to use hollow wires, wound plate or Litz wire, but these are fairly expensive methods.
Now, with DC transmission being very clearly the best solution of power transmission, why don't we do that everywhere? The reason is simply of cost and complexity. Even though we have very efficient and reliable DC-to-DC grid converters nowadays, they are inherently much more complex and still measurably less reliable than old fashioned transformers. Until very recently (post-2000!) the increased cost of maintenance and increase in downtime weren't worth the 40+% reduction in effective grid losses.
So that is why ideally, you want to use DC everywhere where otherwise AC would be used. Now onto the machine discussion.
This also boils down to an efficiency/performance vs. cost discussion. Very analogously to the transmission line argument, DC motors have performance that is very favourable for use in transportation equipment. AC motors generally sport piss-poor stall torque, whereas torque at stall is maximum for DC motors. Also, power density is much better with DC motors, reducing physical size, weight, etc. All very nice things for transportation. Also, it is very easy to do regenerative braking on DC motors, whereas AC motors require some more work in order to regenerate into a battery.
The downside is obvious: they need brushes, and those require maintenance. AC induction motors are basically safe life, so they don't ever need maintenance. Even though they are technically inferior in most ways, lately they have been increasingly employed in public transportation. The biggest downsides of yore - very pronounced cogging despite using skewed squirrel cages, lack of torque, complexity of frequency drives (yes, most public transportation runs from DC transmission lines, so you need to do conversion to AC with a machine drive of sorts) have basically been sorted out. Also, AC induction motors scale better with higher power - a 1MW induction motor is actually smaller than a DC brushed variant. And apparently - I don't have the exact stats but this is what I have been told - the slightly lower efficiency and drive concerns are easily offset by lower maintenance.