The trapezoidal wave or square wave brushless DC motor (BLDC) is a kind of brushless DC motor which is recognized universally (Guo, 2008; Abreu, 2015).
At the same time, magnetic saturation and eddy current losses are ignored, winding are distributed evenly in the smooth surface of the stator, rotor damping effect are Ignored, the wave of rotor magnetic field is square wave, the wave of anti-voltage is trapezoidal wave. Without considering armature reaction effect of stator windings and the mutual inductance between the armature windings, symmetrical three-phase winding and the rotor reluctance do not change with the position of the rotor.
As for the periodic load shape, a trapezoidal wave was used with the flat stage increasingly long, so the next ramp could be considered closer and closer to a ramp after rest, that is, a transient load within a periodic signal.
In the present paper, the load was chosen to be a trapezoidal wave function of time, for three reasons as follows.
(1) The trapezoidal wave ratio, [theta], (1) is defined as the ratio between the heights of the evolving triangle and the top of the trapeze (flat) (see Figure 1):
To allow for a long flat in the trapezoidal wave, it would not be practical to use a vibrating system; but since the aim is to consider only the elastic and dissipative forces, a universal testing machine was used to apply controlled loads with the required profile.
Six different trapezoidal wave forms, as the examples shown in Figure 5, were applied in the experiments.
In order to illustrate the procedure for the trapezoidal case, first consider the trapezoidal wave Nr 2 from the above sequence ([theta] = 4, [t.sub.r] = 0.5 sec., Figure 8).
The next example is the trapezoidal wave Nr 3 ([theta] = 2, [t.sub.r] = 1.25 sec., Figure 9).