I have three DC shunt-wound motors in series. Each motor has a coupling to a transmission. I am trying to work out (mathematically, as opposed to intuitively), what happens if the coupling was to drop in one motor (motor 2) resulting in no load on that motor.

Intuitively I know that that motor will speed up and eventually the centrifugal force will result in destruction of that motor if the supply isn't shut off in time.

The supply voltage is 600 V so there is 200 V across each DC motor.

  1. When the coupling drops and there is no load, does the current result in excessive torque and increase the DC motor's RPM?
  2. As the motor's RPM increases, does the back EMF increase, resulting in a reduction in the current in the motor armature?
  3. What is happening to the voltage across the motor? Increasing or decreasing? Is it P=VI, so current decreases due to back EMF, so the voltage across that motor increases? Where does the back EMF come into play mathematically?

enter image description here

  • \$\begingroup\$ Shunt motors? So you have 3 armature / field parallel combinations connected in series? \$\endgroup\$
    – user80875
    Mar 9, 2019 at 22:53
  • \$\begingroup\$ You have revealed in a comment that these motor are connected to a drive control module and that the motor shafts are coupled together mechanically. You have ignored my question about whether these are really shunt motors. Energizing the armature and field with the same variable voltage complicated things considerably. I am voting to close the question as unclear. \$\endgroup\$
    – user80875
    Mar 10, 2019 at 0:45
  • \$\begingroup\$ The purpose of my question is to understand from a mathematical point of view what happens to the voltage and current across each motor armature if the coupling was to drop on one motor. I would like to know the effect on the RPM for each motor \$\endgroup\$
    – N Jey
    Mar 10, 2019 at 5:53
  • \$\begingroup\$ yes they are DC Shunt wound motors, I will attach a image to my question \$\endgroup\$
    – N Jey
    Mar 10, 2019 at 6:12
  • 1
    \$\begingroup\$ The added image does not show shunt motors, it shows separately excited motors. You have not mentioned the power level. I suspect that the power level is high enough that each motor should have a separate field control. All of the information scattered in comments should be in the question. \$\endgroup\$
    – user80875
    Mar 10, 2019 at 13:33

1 Answer 1


There are two major effects here you might be neglecting:

  1. Shunt motors self-regulate (when driven by constant voltage). If the load drops, speed increases => back EMF increases => current lowers => torque lowers => speed no longer increases.
  2. Current through each motor in the string is the same, so one affects the other.

Effect (2) means effect (1) is compromised a little - motor 2 will start to consume more and more of the string's voltage before it reaches self-regulation.

Thus, intuitively what will happen is motor 2 will start to speed up due to loss of load. Back EMF will increase which will reduce current available to the whole string. Reduction in string current will reduce back EMF in motors 1 and 2 slightly, increasing voltage available. String will find new stable point where voltage is shared and current is same for each motor.

So when each motor was loaded it might look like this:

V1 = 200V
V2 = 200V
V3 = 200V
I = 10A

Then when motor 2 loses its load, the distribution of voltages shifts to something like this:

V1 = 100V
V2 = 400V
V3 = 100V
I = 5A

So motors 1 and 3 have halved in torque and therefore halved in speed (same load), while motor 2 has doubled in speed with half the torque (load dropped by a quarter). Motor 2 is essentially robbing the string of its power by over-spinning.

  • \$\begingroup\$ So the best way for the Drive Control Module to determine there is no load is to measure the voltage through feedback across each individual motor and to trip the circuit if that differential voltage between the motors varies by some delta voltage? In this specific example the RPM of each motor is not monitored because they are all connected to separate transmission that actually drive a common ring gear. Control system determines RPM by the supply voltage and assumes the same RPM for all the motors (because of common load). \$\endgroup\$
    – N Jey
    Mar 10, 2019 at 0:09
  • \$\begingroup\$ Ah, that's tricky. Maths is one thing, real world circumstances are another. Your proposal sounds reasonable, but you'd need a system view to properly evaluate. \$\endgroup\$ Mar 10, 2019 at 0:33
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    \$\begingroup\$ A halving in torque does not imply a halving in speed. Depending upon the load it may stall. Similarly if the voltage increases the speed of a shunt motor may remain the same depending upon whether the field is in saturation. \$\endgroup\$ Mar 10, 2019 at 2:22
  • \$\begingroup\$ All good points Kevin. Lots of non-ideal effects in the real world. I was going to update my answer but the image added to the original question has also thrown a spanner in the works - looks like the armature and field windings are wired separately, which probably renders my thoughts process invalid. \$\endgroup\$ Mar 10, 2019 at 8:05
  • \$\begingroup\$ Apologies Heath, I have amended the picture I noticed an error. They are on separate circuits. \$\endgroup\$
    – N Jey
    Mar 10, 2019 at 10:39

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