My question is driven by the plot below. We see that acceptable operating range of a motor is between 50-100% of the rated load. Below 40% or so the efficiency of the motor drops off dramatically.
What is the cause of this phenomenon?
First, efficiency of an electric motor is just output power divided by input power. Input power is your electrical input power, which is V*I. Output power is your mechanical output power, which is speed*torque.
Given that, we can see that efficiency for every motor is going to be 0% at no load (i.e., maximum speed at 0 torque). Efficiency will then increase as torque increases until it reaches a maximum and then it will start to drop off until stall torque is reached. At this point, the efficiency is 0% again because the speed will be zero.
The other way to ask your question is why is efficiency low at low loads? Friction is the main cause of inefficiency at low loads. Losses due to friction are essentially constant with respect to load so at low loads, the majority of your input power may be used to overcome friction. As the load increases, friction plays a smaller and smaller roll in the overall efficiency. Granted, other inefficiencies begin to occur at larger loads ($I^2R$ losses, copper losses, stray load losses, etc.) but in a well-designed motor the efficiency will peak in the 80-100% load range.