OPTIMIZATION OF SMALL AC
SERIES COMMUTATOR MOTORS*)
BY
R. H. DIJKEN
I Thesis, Technological University Eindhoven, October 1971.
Promotors: Prof. Dr Ir H. C. J. de Jong and Prof. Dr Ir J. G. Niesten.
Philips Res. Repts Suppl. 1971, No. 6.
CONTENTS
INTRODUCTION
1
1. THE SMALL SERIES MOTOR
4
1.1.
1.2.
1.3.
1.4.
1.5.
1.6.
1.7.
1.8.
1.9.
Characteristic features of small series motors
The choice of the type of stator
Some important parameters
Formulas for the resistance of the rotor
Formulas for the resistance of the stator
A simplified description of the motor
Imperfections of the simplified description
Optimization
Conclusions
2. SATURATION IN
2.1. The normalized
2.2. The normalized
2.3. Solution of the
2.4. Conclusions
SMALL SERIES MOTORS
magnetization curve
electrical differential equation
normalized electrical differential equation . . .
3. IRON LOSS IN SMALL COMMUTATOR MACHINES . . . .
3.1. The iron loss in the stator
3.2. A method of measuring the iron loss in the rotor
3.3. The types of steel sheet considered
3.4. Measuring methods and results
3.4.1. Magnetic measurements
3.4.2. Iron-loss torques with DC excitation
3.4.3. Thickness and resistivity of the various types of steel sheet
3.4.4. Iron-loss torques with AC excitation
3.4.5. Non-insulated steel sheet
3.4.6. A solid steel stator
3.4.7. Brass as shaft material
3.4.8. A hollow steel shaft
3.4.9. A 12-mm steel shaft
3.5. Conclusions
4. THE CARTER FACTOR OF SEMI-ENCLOSED ROTOR SLOTS
OPPOSITE SMOOTH-FACED STATOR POLES
4.1. Simulation of the air-gap field by means of a resistance network .
4.2. Determination of the carter factor with the aid of a two-dimensional resistance network
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4.3. Measuring m e t h o d a n d results
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4.4. Graphical determination of t h e carter factor of semi-enclosed
slots
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4.5. Conclusions
66
5. THE ACTIVE INDUCTANCE OF A ROTOR COIL OF SMALL
COMMUTATOR MACHINES WITH RESPECT TO COMMUTATION
5.1. T h e relation between brush wear a n d t h e spark voltage between
brush a n d segment
5.2. The current in the commutating coil
5.3. T h e m e t h o d of measurement
5.4. Description of the rotors and stators measured
5.5. Measuring results
5.6. Evaluation of the results of the measurements
5.6.1. T h e active inductance
5.6.2. The spark decay time with respect to the length of the
sparks
5.7. Conclusions
6/
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79
104
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105
105
6. TEMPERATURE DISTRIBUTION AND HEAT TRANSPORT
IN SMALL COMMUTATOR MACHINES
106
6.1. Losses in small c o m m u t a t o r machines
106
6.2. A thermal network
107
6.3. Conclusions
113
7. DESCRIPTION, DIMENSIONING AND OPTIMIZATION . . .
7.1. T h e concepts of description, design, dimensioning a n d optimization
7.2. A m e t h o d of optimizing electric machines
7.3. Examples of descriptive formulas
7.4. Examples of dimensioning formulas
7.5. Examples of optimization formulas
7.6. Rotor and stator resistances as parameters in dimensioning and
optimization formulas
7.7. U s e of air-gap induction, current density a n d specific load as
parameters in the development of similarity relations
7.8. Current density and specific load as parameters in dimensioning
and optimization formulas
7.9. Magnetic induction in the iron and air-gap induction as parameters in dimensioning and optimization formulas
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7.10. Analysis of the rotor-dimensioning formula
7.10.1. The optimum value of the relative rotor length
7.10.2. The optimum value of the relative flux-conducting rotor
width
7.11. The optimum value of the relative flux-conducting rotor width at
constant current density
7.12. Conclusions
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126
8. THE OPTIMIZATION METHOD
8.1. Formulas for the volume, weight and cost of the steel sheet required
8.2. Formulas for the volume, weight and cost of the winding wire of
rotor and stator
8.3. The motor to be optimized and the starting points for the optimization calculation
8.4. Survey of parameters used
8.5. The computer programme
8.6. Specimen calculation
8.7. Results of the specimen calculation
8.8. Evaluation of the results
8.9. Comparison with the results of measurement
8.10 Conclusions
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162
List of symbols
163
References
176