What happens when we increase load on a motor?
The relatively simple types of motors that operate without an electronic control unit are electromagnetically self regulated. The DC motors tend to operate at a speed determined by the applied voltage. AC motors operated at a speed that is determine by the applied frequency but requires the voltage that is appropriate for the frequency. When the load is increased, the speed drops or tends to drop. That causes an electromagnetic imbalance that results in increase current. The increased current causes the motor to develop more torque. The balance is restored when the torque supplied by the motor matches the torque required to maintain the speed of the load.
Every motor has a speed vs. torque capability curve. Every load has a speed vs. torque demand curve. The motor will operate at the intersection of the two curves. The various types of motors have differently shaped torque vs. speed capability curves, but their general nature is for the curve to slope downward from high torque at zero speed to zero torque high speed, with torque on the vertical axis and speed on the horizontal axis.
Electronically controlled motors are much the same, but the controllers adjust and limit the operation along an infinite number number of essentially vertical torque vs. speed curves that can be produced for a range of operating speeds. The controller limits the maximum torque by limiting the current.
That is the general concept for all electromagnetic motors. The detailed theory of operation differs among the many types of motors and control schemes, but the overall concept is generally the same for all of them.
See curves below for squirrel cage induction motor (SCIM), wound rotor induction motor (WRIM), series DC, shunt DC, permanent magnet DC (PMDC) synchronous and electronic speed controlled motors. Note that the some curves cross the maximum safe current line indicating that the current must be limited during starting.