1. Mathematical Model and Characteristics Analysis of the BLDC motor
Chapter 2
Mathematical Model and Characteristics Analysis of the BLDC motor
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd.

2. 2.1 Structure and Drive Modes
2.2 Mathematical Model
2.3 Characteristics Analysis
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 2

3. Analysis of Magnetic Field
2.1 Structure and Drive Modes
Analysis of Magnetic Field
Stator
Magnetic Field of Stator
Magnetic Field of Rotor
Rotor
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© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 3

4. 2.1 Structure and Drive Modes
Operation principle
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd.

5. 2.1 Structure and Drive Modes
θ = 240°
θ = 0°
θ = 120°
Operation principle
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 5

6. Comparison of BLDC motor and DC motor
Similarities: No-load gap magnetic field Back EMF
Differences: Structure
Principle
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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7. Similarities and differences between BLDCM and PMSM
trapezoidal wave/square wave BLDCM
sinusoidal wave PMSM
Similarities: PM rotor, usually position sensor mounted, synchronization with electrical commutation.
Differences: No-load gap magnetic field, current, voltage, torque density, position sensor precision.
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd.

8. Stator position sensor Signal processing circuit
Structure of BLDC motor
Stator
Motor structure
Rotor
Stator position sensor
Position sensor
Rotor position sensor
Power switch circuit
Controller
Signal processing circuit
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 8

9. Structure of BLDC motor
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 9

10. Structure of BLDC motor
Armature core
B-H curve of permanent magnet
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 10

11. Armature winding Winding types Integral pitch winding Y-connected
Distributedwinding
△-connected
Short pitch winding
Phase number（2-phase, 3-phase, 4-phase, 5-phase）
Pole-pair number (1-pole pair, 2-pole pairs, 3-pole pairs)
Speed
Torque ripple
Cost
Pole-pair ↑ ↓ ↑
Phase ↑ →
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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12. Structure types of PM rotor
Surface mounted
Structure types of PM rotor
Magnet embedded
Magnetic loop
Surface mounted
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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13. Rotor
Magnet embedded
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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14. Rotor
Magnetic loop
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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15. 2.1 Structure and Drive Modes
Position sensor
electromagnetic type
photoelectric type
magnetic type
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 15

16. Principle of electromagnetic type position sensor
Photoelectric type
Magnetic type
Advantages: Large output signal, reliable performance, long operation life, low operation environment requirements.
Disadvantages: Big volume, poor Anti-interference ability.
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 16

17. Principle of photoelectric type position sensor
Electromagnetic type
Photoelectric type
Magnetic type
Advantages: Reliable performance.
Disadvantages: Big volume, large cost, poor dependability.
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 17

18. Principle of magnetic type position sensor
Electromagnetic type
Photoelectric type
Magnetic type
Principle of hall element
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 18

19. Principle of magnetic type position sensor
Electromagnetic type
Photoelectric type
Magnetic type
Small volume, digital signal output, easy to use and low cost.
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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20. Hall sensor
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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21. Controller
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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22. Signal processing unit with logic circuit
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 22

23. Signal processing unit with ASIC
MC33035
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 23

24. Signal processing unit with MCU
MSP430F149（ 16bit，8M ）
Executive instruction
Storage instruction
A/D transformation
Communication with host and other peripheral equipment
Real-time program debugging
External interrupt
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 24

25. Signal processing unit with DSP
DSP ( Digital Signal Processor）
TMS320F28335
Higher precision（32bit）
Faster speed（150MIPS）
Enhanced features
Higher cost
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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26. Drive modes of BLDC motor
Half-bridge type
Full-bridge type
Power switch circuits
C-Dump type
H-bridge type
4-switches type
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 26

27. Half-bridge type switch circuit
Advantages: Few power switches, low cost, simple control.
Disadvantages: Large commutation torque ripple, low winding availability.
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 27

28. Full-bridge type switch circuit
Advantages: Small commutation torque ripple, winding availability Disadvantages: Many power switches, high cost, complex control.
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 28

29. C-Dump type switch circuit
Advantages: Few power switches, low cost, complex control;
Disadvantages: Large commutation torque ripple, low winding availability.
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 29

30. H-bridge type switch circuit
Advantages: Small commutation torque ripple, high winding availability.
Disadvantages: More power switches, high cost, complex control.
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 30

31. Four-switch mode Few power switches, low cost, complex control.
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 31

32. Questions and problems
1. Take the Y-connected three-phase BLDC motor with full-bridge control mode for example, give out the steps for determine the logic of commutation.
2. Analyze the corresponding commutation condition and draw out the magnetic-motive force in each condition, then determine the initial position of θ. Draw out the voltage diagram of each phase and the control logic of power switches and hall elements respectively.
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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33. θ = 0° Two phase conduction mode
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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34. Signal of power switches
Terminal voltage
Hall signal
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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35. logical relation for forward rotating
V1=HA&（！HB）
V2=HA&（！HC）
V3=HB&（！HC）
V4=HB&（！HA）
V5=HC&（！HA）
V6=HC&（！HB）
logical relation for backward rotating
V1=HB&（！HA）
V2=HC&（！HA）
V3=HC&（！HB）
V4=HA&（！HB）
V5=HA&（！HC）
V6=HB&（！HC）
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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36. θ = 0° Three phase conduction mode
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd.

37. Signal of power switches
Terminal voltage
Hall signal
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd.

38. Logical relation for conduction V1=HA V2=!HC V3=HB V4=!HA V5=HC V6=!HB
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd.

39. Position detection by sensor
θ = 0-; HAHBHC=001.
θ = 0+; HAHBHC=101.
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
© 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 39

40. 2.2 Mathematical Model
Fundamental physical quantities and their relationship
Torque equation
Potential equation
Voltage => Current => Torque => Speed => EMF
Voltage balance equation
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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41. 2.2 Mathematical Model No-load magnetic field
Axial potential direction, tangential moving direction, radial magnetic direction
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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42. 2.2 Mathematical Model Back EMF wave of integral pitch winding
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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43. 2.2 Mathematical Model Back EMF wave of integral pitch winding
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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44. 2.2 Mathematical Model
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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45. Six status with two phase conduction mode
Torque ripple
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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46. 2.2 Mathematical Model State equations
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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47. 2.2 Mathematical Model Transfer function
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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48. 2.3 Characteristics Analysis
Mechanical characteristic
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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49. Load torque characteristics
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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50. Stable running condition
Necessary condition: crossing point
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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51. Regulation characteristic
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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52. Dynamic characteristics
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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53. Dynamic characteristics
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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54. Dynamic characteristics
Permanent Magnet Brushless DC Motor Drives and Controls, First Edition. Chang-liang Xia.
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55. Efficiency o
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