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2.3 Appendix
2.3.1 The Handling of Angles in the Motor Control
In the brushless DC motor control, the input voltage into a motor is varied according to the shaft angle of a
motor.
It should be noted that the mechanical shaft angle of a motor (mechanical angle), the output angle of a
resolver (resolver angle) and the angle which determines the voltage applying to a motor (electrical angle)
are not always equal depending on number of poles. The definitions of terms in this document are as follows.
• Mechanical angle The mechanical shaft angle of a motor
• Resolver angle The angle output from an R/D converter
• Electrical angle The angle which determines the voltage applying to a motor
• The number of resolver poles The ratio of mechanical angle to resolver angle (mechanical angle :
resolver angle=1 : the number of resolver poles)
• The number of motor pole pairs The ratio of mechanical angle to electrical angle (mechanical angle :
electrical angle=1 : the number of motor pole pairs)
Example : When the number of resolver poles is 2, the number of motor pole pairs is 4.
When the mechanical shaft rotates once, the resolver angle rotates twice and the voltage to the motor
rotates 4 times. In this case, the controller device doubles the resolver angle (number of motor pole
pairs/number of resolver poles) and calculates the applied voltage to the motor. The number of poles
needs to be considered for the angular offset.
The reason for increasing the number of motor pole pairs in the brushless DC motor is because it enables to
increase the torque(rotation power of the motor). Since the number of poles of the VR resolver is more than
2, the mechanical angle, the electrical angle and the resolver angle are usually not equal. On the other hand,
when the number of resolver poles and the number of motor pole pairs are same, the electrical angle and the
resolver angle become equal.
Figure 2.8 shows an example of the angular relation when the number of resolver poles =2, the number of
motor pole pairs=4.
Figure 2.8 Pole and the Angle of the relationship
When the number of resolver poles is large, the absolute value of the mechanical angle can not be
determined.(The mechanical angle X degree and X + 180degree can not be distinguished.)
For the motor control, the relative angle can be used for the rotation control as long as the number of motor
pole pairs >= the number of resolver poles. For the VR resolver, the number of poles is always more than 2
because of its mechanism.