Rotor Resistance

Investigating the torque-speed curve it is apparent that the rotor circuit resistance has significant impact on speed at which maximum torque occurs. The plots below illustrate two cases, with low rotor resistance on the left and high rotor resistance on the right.

It can be seen from the plots that a high rotor resistance will provide a high starting torque, leading to rapid acceleration of the mechanical system. This is desirable since during starting the stator current is significantly above the rated current. Short acceleration times reduce the stress on the power system caused by high currents.

While high starting torques are desirable, high rotor resistance results in a relatively high slip during normal running operation. As torque is porportional to rotor joule losses divided by slip, high resistance causes increased losses and reduced efficiency during normal operation.

The above points cause a problem. For most applications it is desirable to have:

However, designs with high starting torque will have low efficiency at rated speed and designs with high efficiency will have low starting torque. In order to resolve these confilicting requirements, two steps must be considered:

  1. Careful consideration of the application requirements
  2. Designs of motors with variable rotor resistance.

Application Requirements

Many motor applications will not need both high start torque and high rated efficiency. Alternately, the requirement for either high start torque or efficiency may be so significant that it over-rides other requirements. Consider two examples:

Fan Load

Fans and rotary pumps typically have a torque requirement that varies as either the square or cube of mechanical speed. When driving a fan, the motor must provide rated torque at rated speed, but at lower speeds the torque demand is significantly lower. A fan application will therefore not usually require significant starting torque, efficiency during steady operation at rated speed is the over-riding concern.

Variable-torque high-inertia loads

This type of load typically includes mechanical punches and reciprocating rod pumps used in oil production ("nodding donkeys"). In the case of a reciprocating pump, the mechanical laod varies with time, some of the time the motor is working against gravity to lift oil out of the ground, at other times, it is working with gravity as the rod falls. The speed range of this system is significant, requiring very high torques at low speeds. When the motor is at high speed (as the rod falls) the torque (and efficiency) requirement is minimal. In this case high torque at low speed is the over-riding requirement.

Varirable Rotor Resistance

Although it is common to think of low frequency conductors as having a constant resistance, the resistance of all ac conductors is a function frequency. Induced currents in conductors act to oppose the originating magnetic field. As a result, the depth of penetration of the magnetic field into the conductor will vary with frequency. (The magnitude of the induced voltage is a function of rate of change of flux, and therfore a function of frequency)

Skin Depth

The skin depth of a conductor is defined as the depth at which the magnitude of a magnetic field has fallen to 1/e of the magnitude of the surface. We can approximate this as the depth at which currents are actually flowing in the conductor. Skin depth is given by

where

Since the frequency of the stator magnetic field seen by the rotor conductors is a function of slip, the actively conducting region of the rotor bars will be a function of slip. Hence, the effective roto resistance will be a function of slip. The table below plots skin depth for aluminum (σ ≈ 2.9×107) in a machine with a 60Hz supply.

SlipSlip Frequency (hz)δ (mm)
0.0251.576.3
0.053.054.0
0.0835.042.8
0.16710.029.6
0.33320.020.6
0.5030.017.1
0.66740.014.8
0.83350.013.2
1.060.012.0

The table above indicates a number of important points:

  1. No matter how deep a rotor bar, only the top 12mm conducts at standstill
  2. Medium-large machines with bars deeper than 12mm will have varying rotor resistance
  3. Smaller machines with bars less than 12mm deep will have effectively constant rotor resistance

As an example, a machine with a rectangular bar 72 mm deep will have a resistance 6 times smaller at low slips than it will at starting.