It is a tradeoff, hence actual wound-rotor motors expose the rotor windings so that a resistance can be added during start, and tapered off or just removed when at speed. The resistance added is actually not tremendous, usually from 1 to 5 times the DC resistance of the rotor.
The initial problem, is that at at start, a typical induction motor can draw up to 1000% rated current. For large (> 200 HP motors) this can severely stress the supply. Pullout torque (torque required to either start the rotor, or drop it out from near synchronous speed) is directly related to slip. Increasing resistance in the rotor, effectively increases the slip, which increases the torque.
As more resistance is added to the rotor, the peak torque curve is moved closer and closer to zero speed. That is the sweet spot for starting a wound rotor motor; lowest inrush current, highest slip, highest torque. Adding more resistance will reduce the available torque, as the slip begins again to decrease.
You can run Wound Rotor motors in a variable speed mode, if you can control the resistance, but that is generally very inefficient.
Consider that basically, an induction motor at standstill is a transformer, with an essentially shorted secondary. When power is applied to the stator, a voltage is induced into the rotor, which, being shorted develops the current which creates the magnetic field to pull the rotor along with the stator's rotating field.
Okay, since the induction motor is a transformer when starting (at zero speed), there are reactances to deal with. The reactance actually causes the induced voltage (and current, and generated magnetic field) to be out of phase with the stator field, generally lagging by about 90 degrees, so the magnetic interaction between the rotor and stator is fairly weak.
If pure resistance is added to the rotor circuit, the phase lag starts to grow smaller. (Note that different constructions of the rotor bars, with different resistances are used to permanently affect the torque curves of many motors). Add enough resistance, and the phase lag reduces to the point of what the motors design slip is, which corresponds to its maximum design torque.
The problem with leaving the resistance in circuit (aside from power dissipation) is that as the motor speeds up, and approaches its synchronous speed - slip, now you have advanced the rotor/stator magnetic phase, resulting in reduced torque at the shaft.
Hoisting applications such as this typically have a spring loaded brake that is released when the motor is energized. If the Control system responds to a motor overload condition the spring actuated mechanical brake brings the motor and pulley to a stop.
I've also installed Variable Frequency Drives (VFDs) on 3 phase hoisting applications. This requires ordering a constant torque drive and installing a braking resistor. When the Motor is called to come to a stop - the inertia of the hoisted load turns the motor until the brake is released. The coasting of the motor due to the inertia of the load results in generating voltage back into the drive. Installing a braking resistor gives the drive the ability to dump the generated power onto the resistor, which is dissipated as Heat. In my applications the combination of a mechanical brake and the braking action of the VFD has resulted in a quicker stop than the mechanical brake alone.
As far as mechanical damage - the motor brake and drive train should be designed to withstand a couple of times the dynamic forces that can occur within the system.
Mechanical Brakes will wear and need to be adjusted and replaced due to normal wear and tear.
As far as Electrical damage - again the Motor should properly fit the application. From an electrical damage standpoint - in dealing with a single or 3 phase motor - heat is what will damage the motor. Most VFDs and VFD rated motors have an integral heat sensor called a ptc. The VFD can be configured to sense the temperature of the motor and shut down the system if it gets to hot. In this condition you would be relying on the mechanical brake to bring the system to a safe stop.
Best Answer
The basic principle is simple - torque is proportional to armature current * magnetic flux. In a permanent magnet or shunt wound motor you can assume that flux is constant, so torque is just proportional to current.
However this does not take into account internal friction, windage, and magnetic losses. When the motor is running free these losses cause it to draw a no-load current (Io). Subtracting Io from total current draw leaves you with the portion that produces output torque.
Power = rotational speed x torque. As more load is applied the motor draws more current, which increases torque. However as current flows through the windings their resistance causes the effective voltage to drop, so speed decreases. Below 50% rpm the power output will also decrease, reaching zero at stall.
In a series wound motor the situation is different, because flux is not constant. With no load a series wound motor will speed up until friction and windage losses match the internal torque supplied by Io. This rpm could be very high, perhaps even high enough to destroy the motor. When a load is applied the resulting torque is proportional to current squared, because both armature and field currents contribute to magnetic force.