   This Technical Design Article (TDA) presents a basic analysis of a three-phase multi-pole Permanent Magnet Brushless (PMB) DC motor in order to understand the testing parameters for 3Ø Power Modules used to drive the field coils for commutation. There are four additional pages to this TDA, Three theoretical analysis pages, variable setup Analysis 1, commutation Analysis 2, triplet waveform injection Analysis 3 and one Test Summary page showing theoretical analysis to empirical conclusions.  It is assumed that the reader is familiar with Faraday's Law and its application for generating an EMF.  From Faraday's Law we prove that the PMB DC Motor is also a generator that will produce a voltage output based on the RPM of the motor. This voltage Vk is a constant based on 1000 RPM.  This implies that as we apply a current to the coils to commutate the motor the resulting force is either increased or decreased depending on the actual RPM of the motor and the phase relationship of the applied voltage to  Vk. For further reference, a review of AC poly-phase induction motors will help understanding the equation set. We will also be presenting this analysis in a different perspective to address the PWM concepts of applied voltage to the motor. Most theoretical analysis of a motor uses a common assumption that the commutation is continuous.  Although our initial analysis will make this assumption, we are going to include Pulse Width Modulation (PWM) along with many other techniques and principles that are very different compared to the standard analysis of constant commutation type motors, hence, the commutation of a PMB motor is totally electronically controlled.  The 3Ø H-Bridge drive electronics along with the empirical data that will be compared to the theoretical analysis as proof of concept. A detailed explanation of the test system used for the data collection is in the Bridge Test System TDA. The Bridge Test System TDA only addresses the field coils without commutation. Data using a PMB motor under various loads and speeds will be added at a later date as time permits. The following TDA's will also address controlling the motor in a servo application requiring positive position feedback and the addition of position encoders to the motor. Your comments are welcome and I may be reached at Sal (JT) for technical discussions # BASIC MODEL - 3Ø PERMANENT MAGNET  BRUSHLESS MOTOR We will start by looking at the motor as a mechanical device that will supply some type of mechanical force to a load connected to the shaft of the motor. We will then look at the electrical characteristics that produce this mechanical force. The motor is an angular or rotational device,.that is, it rotates 360° to complete one revolution. The actual design of the motor will determine the number of 360° electrical revolutions that's executed to obtain one mechanical 360° revolution.  This is determined by the number of poles the motor has. Hence, if the motor has two poles then it will take one electrical to one mechanical revolution. Then the more poles the more electrical revolutions will be required to produce one mechanical revolution. Another interesting phenomenon is the commutation is totally controlled electrically and the motors speed is directly proportional to the DC voltage applied. Therefore the speed may be varied by varying the duty cycle or amplitude of the applied voltage to the motor field coils. One of the main advantages of the PMB motor is that commutation is controlled electrically therefore reversing the motor is electrically a given by reversing the electrical sequence.

The following diagrams shows some various types of PMB DC motors, the relationship of the number of poles to the stator poles, some of the limitations and advantages. The diagram below shows a two-pole motor and its associated coils. From following the current paths for commutation [AB, BC, CA} we see that we require one electrical period of 360° or 2 Radians.  A PMB motor would generally have the same number of poles to match the coils to stator magnets. Each energizing of the coils would cause the motor to turn 60° to obtain one revolution per electrical period. It is very easy to manufacture two pole motors. Most hobby or very low cost systems would use these types of motors.  Two pole motors have high speed and torque fluctuations. The largest of these markets are miniature fans for laptops and other electronic devices that require airflow and not too concerned with torque ripple.    Top

# TWO POLE PERMANENT MAGNETCORE AND POLE ALIGNMENT  The diagram below shows a four-pole motor and its associated coils. Following the same current paths as the two pole motor for commutation [AB, BC, CA} we see that we require two electrical periods of 360° or 4 Radians. This type of motor is also easy to manufacture however the cost is higher than a simple two pole motor mainly because of raw materials and machine assembly time.  Each energizing of the coils would cause the motor to turn 30° therefore obtaining one mechanical revolution per two electrical periods. The increase in the number of poles produces lower torque ripple than the two pole motor. These types of motors are used in many variable speed devices such as power tools or other areas that require a relatively good torque and wide speed range. Some application areas include hazardous gaseous environments because there is no arcing since it is a brush less system.

# FOUR POLE PERMANENT MAGNETCORE AND POLE ALIGNMENT  The diagram below shows a six-pole motor and its associated coils. Again following the same current paths of the previous two and four pole motors for commutation [AB, BC, CA} we see that we require three electrical periods of 360° or 6 Radians, hence, each energizing of the coils would cause the motor to turn 20° therefore in order to obtain one mechanical revolution we require three electrical periods. The increase in the number of poles produces a much lower torque ripple than the two or four pole motors and makes this motor a better choice for the more critical applications. This type of motor is also relatively easy to manufacture with today's technology and the cost is a very competitive with brush type motors in its category.  These types of motors are used in critical applications like X,Y tables and numerical control applications where wide RPM speed variations and smooth torque are required. They have very good torque and smooth speed control than its predecessors, the two and four pole motors. Another application area is the automotive area for power windows and electric power steering and electric pumps.

# SIX POLE PERMANENT MAGNETCORE AND POLE ALIGNMENT As we have shown the number of poles determine the number of electrical periods required for a single mechanical revolution. Representing this as an equation we get: Electrical Revolutions of 360°=. , Hence: A six pole motor would require three electrical periods to complete one mechanical revolution. This means that in order to achieve 600 RPM,or 10 RPS we would have to commutate the motor at 30 Hertz electrically. In the next section we will look at the theoretical analysis of the PMB motors torque and speed. Other concerns will also be covered when using PMB motors. If all you require is a shaft turning with no position information then a straight driver will suffice. However, most servo applications require some position feedback of the shafts angular position. This will require some type of encoder system to be attached to the rotor. We will also discuss some of the encoder systems used on these motors. For this part of the discussion and analysis we will be looking at just simple commutation.