A brushless DC motors speed curve is reduced by the effects of motor inductance. Below is a torque speed curve showing curves that both include and do not include the effects of inductance.
The red curves are the motor performance curves with the effects of inductance included. If your design requires your motor to operate above the speed curve that includes inductance you will be disappointed. The curve that includes inductance has a steeper slope caused by the inductance. Since the equation for N (no inductance effects):
N=(V-IR)/Ke
shows that the slope is due to motor resistance, people have calculated the resistance that fits the actual performance curves and termed this Reff, the effective resistance. However this is misleading on multiple counts. The calculated effective resistance is supply voltage (speed) dependent and the motor I^2R losses will be overestimated.
As a three-phase brushless DC motor rotates, voltage is applied to the leads in a particular pattern, termed a 6 Step Drive. The frequency that the motor is commutated as is termed the commutation frequency. At each commutation, one motor lead that is attached to a supply rail is open-circuited and another lead that was previously open circuited is attached to a supply rail. The lead that was previously attached to a supply rail has current flowing in it and this current continues to produce useful torque. The lead that previously was open circuited has no current flowing in it and voltage must be applied across it to overcome the winding inductive impedance.
When the lead with current flowing is open circuited, the phase voltage flies from the supply rail it was attached to by the drive, to the other supply rail, where it is clamped by the drive diodes. Since the back EMF curve is almost at the same level as when the lead was energized, and the torque constant is proportional to the back emf constant, the torque produced by this freewheeling current is almost the same magnitude as produced prior to switching.
In effect the motor inductance acts as a switch inductance resistor, consuming voltage and reducing peak motor speed on one hand, while producing torque and reducing the measured motor current on the other. Since the freewheeling current is not measured, a torque constant calculated from an actual motor performance curves will overestimate the torque constant.
Actual measurements of brushless DC motor stators has shown that there is very little inductance coupled between motor phases, therefore the inductance switched at each commutation point can be approximated by the motor inductance divided by two. Since the effects of inductance is already a secondary effect, the effects of coupled inductance and of losses in laminations due motor lead commutation can be safely ignored. In other words, we will assume no coupled inductance and that the inductor is lossless.
Many drive related effects reduce the motor speed, such as EMI filter resistance, attachment wire resistance and switching transistor resistance. To predict the actual expected motor performance all must included in your motor model. The effects of motor inductance has a significant effect and also must be included in your motor model. Unfortunately, the speed torque curves supplied by manufacturers are regularly incorrect, predicting results that are unattainable in practise. Care is required in any design where minimum speeds are a critical specification.
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