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BRIDGE TESTPMB MOTORSWEBSITE INFO
ANALYSIS 1ANALYSIS 2ANALYSIS 3TEST SUMMARY

There are many companies that make Permanent Magnet Brush less Motors and all have there own variety of variables they use to for the analyse of the motor. I reviewed many of these sites and took the variables that made the most sense and came up with the set in Table 1.0.

For simplicity an in order to help present the analytical sections of this TDA we are going to present the following naming convention along with a set of symbols that define specific parameters of the PMB DC motor. We will reference these parameters throughout the analysis. The analysis that we will present will be in two states, Steady State or Static performance and Commutating or Dynamic performance. Our main objective is to use the data collected for proof of concept in order to develop a reliable test criteria for the Hybrid Power Modules Test System as defined in the Bridge Test System TDA. Characterising a motor However, would require the addition of a dynamometer along with a few other parameters.  As stated previously we will cover this in another TDA.

Symbol

Description

Units

Terminal Resistance

Ohms or (impedance Z)

Inductance of he phase coils ABC

Henry

Torque Constant

Ounce-Inches / Amp

Torque Output of Motor

Ounce-Inches / Amp

Motor Current

Amps

Most Efficient Motor Current

Amps @ RPM

Motor Efficiency

Percent % {0 to 100}

No Load Motor Current

Amps @ RPM

Input Motor Power

Watts

Motor Mechanical Output Power

Watts

Motor Voltage Generator Constant

Volts / 1000RPM

Generator Constant in radian format

Volts / Radians / Sec

Voltage at Motor terminals

Volts

Revolutions Per Minute

RPM

Battery Supply Voltage

Volts

Line A to Line B Generator Voltage

Volts

Line B to Line C Generator Voltage

Volts

Line C to Line A Generator Voltage

Volts

Applied Voltage to terminals A-B

volts

Applied Voltage to terminals B-C

volts

Applied Voltage to terminals C-A

volts

Number of steps of the motor for 2

integer

rotational position index 0,1..n

integer

The following shows relationship between DELTA (Line to Line) and WYE (Line to Neutral) vectors. In the WYE configuration the coil and line currents are equal and the line voltage is  times the coil voltage. In the Delta configuration the coil voltages are equal and the line currents are  times the line current. The equation sets derived here are for the purpose of characterizing system block functions. The actual losses within the motor are not covered here except where they have direct connections to the equation set. The manufacturing efficiency and design parameters of the motor are usually supplied by the manufacture. We will discuss motor efficiency and characterizing in a later article.   Top

Line to Line and Line to Neutral
Delta to Wye Vectors

img2.jpg

Phase ab was selected as the 0 reference which we will explain later in the analysis. The voltage equations for both line to line and line to neutral as follows.
The Line to Neutral voltage is 
The Line to Line voltage is

3 SYSTEM PHASOR REPRESENTATION

3- wire Line to Line "DELTA"

4 Wire Line to Neutral "WYE"

4 WIRE  "WYE"  SYSTEM CIRCUIT
img5.jpg

3 WIRE  "DELTA" SYSTEM CIRCUIT

img2.jpg

The applications of Faraday's Law states that an EMF will be generated due to the magnetic field (Flux) and the field windings passing in proximity to each other. This EMF is the Motor Voltage Generator Constant and for a typical 6 pole motor is in the range of 1 to 6 volts / 1000 RPM, where the average is around 2.5 volts/1000 RPM. The motor manufacturer will give this constant in the motor specifications. The contributing factors of this constant are the magnetic field strength, the coil size and the number poles. Since this is in a rotating environment, then in order to use this in our analysis we have to transform this to an angular or polar domain, hence; Volts /Radians/Seconds relating to electrical revolutions. Converting this to seconds is a preference and does not matter in the final analysis as long as the labels are in domain order. First rule of analysis if the labels do not make sense neither will the results.

    Hence:   

Keeping the terms in the proper domains, the conversion to electrical rotation radians/seconds (Rotational Position per Second) is also required. From the previous page,the Electrical revolutions with relation to the mechanical revolutions is defined as . Therefore the Electrical Radian/Seconds to mechanical rotation is defined as:

  Hence:      This now satisfies the domain changes and labeling.

The 3 Motor Generator equations that define the EMF generated Line to Line  ,   ,    and Line to Neutral  ,      using phase ab as the 0 reference are as follows. Plotting these equations gives us a better perspective of the voltage levels of the two systems.  For those who want to research this further, these equations are derived from applications of poly-phase systems and phasor geometry.

Voltage equation set for 3 wire DELTA system, Line to Line

               

Voltage equation set for 4 wire WYE system, Line to Neutral

   

   

Generator Voltage developed at 100 RPM
6 pole permanent magnet brushless motor
img5.jpg

Page 2 covers the creation of the applied voltage equation set to commutate the motor.
Page 3 covers the application  analysis of the Bridge Test System data comparisons.

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