Before I delve into this further,I think it would be helpful to present some general equations pertaining to dc motors/generators.They apply under 'normal' operating conditions,that excludes extreme overload,like applying full battery voltage at startup.
The fundamental voltage equation is:
V= E + I x R, , The impressed voltage equals E + the IR voltage drop due to the current in the winding resistance R .E is the back emf,the voltage induced by the fieldflux F in the winding.In our case F is constant.It is instructive to multiply both sides of this expression with the current drawn,we now get a power/loss equation:
VxI = ExI + (I*2) xR , I*2 stands for IxI or I squared.
VxI present input power to the motor (or the output power to the load if the current was reversed and it acted as a generator).ExI represents the power available for delivering mechanical power,the actual output power would be less due to mechanical losses.In HP it would ideally be ExI/746,so if you had 20A at 20 V assuming a 4 V IR drop from a 24V source ,the output power would be 400 Watts the input power 480 Watts and the efficiency 83% (disregarding mechanical and magnetic circuit losses,hysterisis& eddy current which are relatively small).To return to the eqwuation the last term IxIxR presents the resistive loss in the armature winding.
If the device was acting as a generator,that is, if E exceeds V and I woild become negative we get ExI =VxI -(I*2)xR .
So far so good,I hope all this is clear.Now let's turn to the voltage equation again The induced voltage E is proportional to the field flux,the rotational velocity N,and the number of turns T .F is constant so E :: ( NxT).Under no load conditions the IxR term is small, because the current I is small ,if not we would have a very inefficient motor on our hands.This entails that E is close to V, and for a particular applied voltage NxT has to be constant or N :: 1/T.If you reduce the number of turns by say 10% the no load speed has to increase by the same amount for E to remain approximately constant.Conversely if the rewinding of an armature results in a siginificant change in no load speed,there are only two possible explanations,eithe the turns count has changed (quite likely) or the winding resistance has increased VERY substantially,there is no other possible explanation according to accepted theory,based on over a hundred years of experience in the design of electric motors.In my opinion you are actually changing the effective number of turns in the winding.There is nothing wrong with that if the objective is to redesign the motor for a different voltage, or wanted to change the motorspeed for a particular voltage.In all cases the fundamental relationship applies under steady state conditions,during transients when conditions change very quickly ( very sudden voltage or load changes) inductive effects can get into play,and things quickly get complicated.but the system is inherently stable unless we are dealing with destructive overload.Please think this over.
