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.

2.1 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

Analysis of Magnetic Field 2.1 Structure and Drive Modes Analysis of Magnetic Field Stator Magnetic Field of Stator Magnetic Field of Rotor Rotor 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. 3

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.

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

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. © 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 6

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.

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

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

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

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. © 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 11

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. © 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 12

Rotor Magnet embedded 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. 13

Rotor Magnetic loop 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. 14

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

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

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

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

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. © 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 19

Hall sensor 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. 20

Controller 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. 21

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

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

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

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. © 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 25

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

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

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

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

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

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

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. © 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 32

θ = 0° Two 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. 33

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. 34

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. © 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 35

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.

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.

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.

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

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. © 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 40

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. © 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 41

2.2 Mathematical Model Back EMF wave of integral pitch winding 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. 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. © 2012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd. 43

2.2 Mathematical Model 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. 44

Six status with two phase conduction mode Torque ripple 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. 45

2.2 Mathematical Model State equations 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. 46

2.2 Mathematical Model Transfer function 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. 47

2.3 Characteristics Analysis Mechanical characteristic 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. 48

Load torque characteristics 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. 49

Stable running condition Necessary condition: crossing point 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. 50

Regulation characteristic 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. 51

Dynamic characteristics 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. 52

Dynamic characteristics 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. 53

Dynamic characteristics 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. 54

Efficiency o 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. 55