Question

maximum voltage needed by dc motor

Answer 1

maximum voltage needed is 15 volt which normal battery has. see the pic below.this is enough for a general dc motor to work 
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Answer 2

(back ) emf  =    phi * Z * N  / 60     * ( P / A)    = k w

phi = magnetic flux through a conductor
Z = number of armature conductors (turns)
N = rotations of the motor per minute. =  60 w/(2 pi)
w = angular speed of the motor
P = number of poles
A = number of parallel paths in the armature.
             = 2 for simplex wave winding of the motor/generator
            = P  for simplex lap-wound motor /generator

maximum voltage is given by the above equation.

If operating current I and internal resistance R or armature resistance is given, then
   back emf = voltage across motor = input voltage V - I R