With constant torque, the output power will be directly proportional to speed. Therefore you would expect the input power to be proportional to speed. Since the input voltage is constant, you might expect the current to be less with reduced power, but actually the current is relatively constant and the power factor is lower. That is essentially due to the need for the magnetizing flux to remain constant.
There are a lot of variables in motor designs. Two induction motors can have the same voltage, frequency, speed and torque specifications but have significantly different rated current and power factor. There are a number of performance goals in addition to the basic requirement to design a motor with a specific speed and torque rating. Typical goals would include high efficiency, high power factor, low locked-rotor current and high safety margins for operating temperature.
For for economic reasons, manufacturers try to use the same laminations for several motor configurations. To allow interchangeability of motor brands, a limited number of standard motor diameters have been established.
The above factors lead to a lot of anomalies in the detailed performance parameters of motors.
