CHAPTER 3 BRUSHLESS DC MOTOR

53 CHAPTER 3 BRUSHLESS DC MOTOR 3.1 INTRODUCTION The application of motors has spread to all kinds of fields. In order to adopt different applications, various types of motors such as DC motors, induction motors, synchronous motors, switched reluctance motors from milliwatts to several megawatts emerge. The synchronous motor has the advantages of high torque, precision and accuracy but it has poor speed regulation which limits its application. An induction motor has the advantages of simple structure and low price but results in low power factor. A switched reluctance motor without winding or permanent magnet in the rotor has a simple structure and low price. It has high torque over a wide range of speed, but noise and torque ripple limit its applications. DC motors are widely used in electric traction, rolling mill, hoisting equipment and in automation and control. In conventional DC motors, the mechanical commutation is implemented using brushes which result in mechanical friction, noise, electric spark and radio interference. These drawbacks can be overcome by brushless DC motors (BLDC). Since permanent magnets are placed in the rotor, they are also known as permanent magnet brushless DC (PMBLDC) motors. The BLDC motor is developed on the basis of brushed DC motors. In NEMA standard MG7-1987, a BLDC motor is defined as a type of self- synchronous rotary motor controlled by electronic commutation, where the rotor is a

54 permanent magnet with rotor position sensor, and the related commutation circuit could be either independent or integrated to the motor. In 1955, Harrison and Rye developed a thyristor-based commutation circuit for a BLDC motor. 3.2 CONSTRUCTION AND PRINCIPLE OF BLDC MOTOR BLDC motor is an inverted DC motor where the armature winding is placed on the stator, and the permanent magnet is on the rotor. In order to control the speed and direction of rotation, a rotor position sensor, a control circuit and power controller are included in the BLDC motor system. Figure 3.1 shows the block diagram of BLDC motor system. Input Supply Power Converter BLDC Motor Control Circuit Rotor Position Sensor Figure 3.1 Block diagram of BLDC drive The stator structure of the BLDC motor is similar to that of the synchronous or induction motor. Single or multi phase symmetrical windings are embedded in the stator. Generally, star-connected windings are preferred in which three phase windings are symmetrically connected without a neutral point. The common winding types used in BLDC motors are concentrated full pitch windings, distributed full pitch windings and distributed short pitch windings. In the concentrated full pitch winding, the wires of same the phase are placed in the same slot which leads to better trapezoidal back EMF. In the

55 distributed winding, the coils are dispersed evenly over the surface of the stator which leads to better cooling of the winding. In short pitched winding, the windings are shortened at the end of the winding which helps to save the copper material and weaken the torque harmonics. The rotor of the BLDC motor is constituted by the permanent magnets with certain pole pairs. These magnets can be placed in many ways on the rotor. The different types of radial field rotors are shown in Figure 3.2. The surface mounted PM rotors and surface inset PM rotors are used in the high power density machine. In the surface mounted machine, the magnets are mounted on the outer periphery of the rotor lamination which provides the highest air gap flux density as it directly faces the air gap without any interruption such as part of the rotor lamination. The drawbacks of this structure are lower structural integrity and mechanical robustness due to the snugly fitment of PM in the rotor laminations. Hence they are not preferred for the high speed applications. In the surface inset machines, the PM is placed in the grooves of the outer periphery of the rotor laminations and this provides uniform cylindrical rotor surface. This structure is mechanically robust compared to the surface mounted machines. In the interior PM machines, the rotors are placed in the middle of the rotor lamination. This structure is mechanically robust and hence suited for high speed applications. The manufacture of this structure is more complex than the surface mount and inset magnet motors. The position sensors in the BLDC motor are meant to detect the rotor position and transform it into corresponding electrical signal. These electrical signals provide the correct commutation information for the logic circuit. Due to the correct commutation of the winding, the BLDC motor

56 rotates continuously. Various kinds of position sensors such as electromagnetic, photoelectric and magnetic sensors are available. The hall sensor which is a type of magnetic sensor is widely used in BLDC motors because of its compact size, low price and convenient operation. Figure 3.3 shows the diagram of a typical hall sensor. (a) (b) (c) (d) Figure 3.2 Different types of radial field rotor (a) Surface PM (b) Surface inset PM (c) Interior PM (d) Interior PM with circumferential orientation

57 Figure 3.3 Hall sensor The working principle of BLDC motor is as that of the brushed DC motor. In the brushed DC motor, the feedback is implemented using a mechanical commutator and brushes whereas in a BLDC motor, it is achieved using multiple feedback sensors. 3.3 MATHEMATICAL MODELING OF BLDC MOTOR The BLDC motor model using differential equations and state space equations is presented here. The stator has the star-connected concentrated full pitch winding and the rotor has a nonsalient pole structure. The hall sensors are placed symmetrically at 120 electrical degree interval. The following assumptions are made. 1. Eddy current losses, hysteresis losses, armature reaction, cogging effect and core saturation are neglected. 2. The distribution of the magnetic field in the air gap is thought as a trapezoidal wave with the flat top width of 120 electrical degree. 3. The conductors are distributed continuously and evenly on the surface of the armature. 4. The solid state switches in the power circuit possess ideal characteristics.

58 The matrix form of phase voltage is expressed as [ ] [ ] [ ] [ ] [ ] [ ](3.1) where is stator resistance per phase is self inductance per phase and is the mutual inductance and and are phase currents and are instantaneous induced electromotive force (EMF) and all are assumed to be trapezoidal. The instantaneous EMF can be represented as ( ) (3.2) ( ) (3.3) ( ) (3.4) where ( ) ( ) and ( ) are the back EMF function of phase and with the maximum magnitude of. ( ) ( ) ( ) ( ) ( ) ( ) ( ) [( ) ( ) ] (3.5) is the peak value of flux linkage from the rotor magnets.

59 + i L R v e - Figure 3.4 Equivalent circuit of BLDC motor The equivalent circuit of the BLDC motor is shown in Figure 3.4. The mathematical model based on phase voltages are not applicable to the system with delta connected stator winding. The matrix form of line voltages of delta-connected system is expressed as [ ] [ ] [ ] [ ] [ ] [ ] ( ) The electromagnetic power transferred to the rotor (3.7) Ignoring the mechanical loss and stray loss, the electromagnetic power is totally converted into kinetic energy (3.8) Hence the electromagnetic torque [ ( ) ( ) ( ) ] (3.9)

60 In the electromechanical system, the motion equation can be expressed as (3.10) where is the load torque in is the moment of inertia in is the friction coefficient The state space model of BLDC motor is obtained by algebraic transformation of differential equations of the motor. Three phase currents, angular velocity and position of the rotor are selected as state variables. (3.11) where [ ] ( ) ( ) ( ) ( ) ( ) ( ) [ ] [ ] [ ]

61 3.4 MECHANICAL CHARACTERISTICS OF BLDC MOTOR Mechanical characteristics denote the relationship between the speed and electromagnetic torque with constant supply voltage. The control scheme of any electrical motor mainly depends on the mechanical characteristics of the motor. In each phase of the BLDC motor, the back EMF is in the trapezoidal shape and the phase current is in the rectangular shape. The conduction period of the phase current is aligned with the flat top of the back EMF to generate the maximum torque and is shown in Figure 3.5. The speed of the motor is controlled by the supply voltage. When the load torque increases, the speed drops, and the drop in speed is directly proportional to the phase resistance and the load torque. eas ebs Ep 210 30 150 330 Ep -Ep ecs -Ep ias ibs ip -ip ip -ip ics -ip eas ias ebs ibs ecs ics Po 0 q r Figure 3.5 Back EMF, current and power of PMBLDC motor

62 BLDC motors are ideally suited for the constant torque applications, as the field is fixed and the torque is proportional to the armature current. The operation beyond the base speed is the constant power region as shown in Figure 3.6. At the base speed, the sum of the back EMF of two conducting phases approaches the amplitude of the supply voltage, and the power controller loses its ability to control the phase currents. Hence, PWM or chopping is no longer possible. The current controller is said to be in saturation state and the maximum current is injected to the motor for higher value of torque. As the speed increases further, the torque and currents fall off abruptly. Constant power region is generally maintained up to 2-3 times of the base speed. T0 T Intermittent Operating region Trated Continuous Operating region Constant Torque Region Constant Power Region 0 wb w Figure 3.6 Speed Torque characteristics of PMBLDC motor 3.5 CONVENTIONAL CONVERTER TOPOLOGY The speed control of the BLDC motor is achieved with the power electronic converter modules. The BLDC motor can be operated in full wave mode, in other words with six step inverter or in half wave mode. In the full

63 wave mode, each phase is operated for 240 electrical degrees whereas, in half wave mode, each phase is operated for 120 electrical degrees. Number of converter topologies emerges for half wave mode. T1 Dr1 Cf Vs a D1 A phase DC supply Cf B phase C phase Dr2 Vs b T2 D2 D3 T3 Figure 3.7 Split phase converter 3.5.1 Half Wave Mode The popular converter topologies for the half wave mode are split phase converter, C-dump converter, variable DC link converter and variable voltage converter with buck-boost at the front end. In the half wave mode, the windings carry positive current alone. In the split phase converter topology, the BLDC motor requires one switch per phase winding. The power switches T1, T 2 and T 3 are connected to the three phase windings of the BLDC motor and unidirectional current flows through the winding. The schematic diagram of the converter is shown in Figure 3.7. The unidirectional current handling capability of this converter results in underutilization of the motor. Four quadrant operations are possible in this converter with proper switching of power devices.

64 The C-dump converter was proposed by Walter & Stephen (2007) and is shown in Figure 3.8. In the C-dump converter, more than one switch per phase but less than two switches are resorted, in the other words switches for phases. In this circuit, the energy stored in the capacitor during turn off intervals of the phase switches is fed back to the supply during turn on intervals. The drawback of this circuit is production of larger commutation ripples. A B Vd Cd D2 D3 C D1 Tr C0 T1 T2 T3 Figure 3.8 C-Dump converter Variable DC link converter has the advantage of variable DC voltage input to the machine windings. The converter has two stages: the first stage is a step down chopper which gives the variable DC voltage to the machine, and the second stage is machine side converter for handling the energy between DC link and the machine. The chopper switch is properly synchronized with the switches in the machine side converter. Four quadrant operations are possible with this converter. Instead of step down chopper, buck-boost converter can be connected at the front end of the converter. In this type, the DC link voltage can be varied from zero to twice the DC source voltage. In low speed operation, the front end buck-boost converter acts as a buck converter whereas in high speed operation, it acts as a boost converter to increase the voltage given to the motor. The circuit diagram of the converter is shown in Figure 3.9.

65 Tc Dc D1 D2 D3 i1 T1 T2 T3 Vdc Cd L C V Phase A Phase B Phase C Vas Vbs Vcs ic ias ibs ics Figure 3.9 Variable DC link converter 3.5.2 Six Step Inverter Topology Full Wave Mode The schematic diagram of six step inverter is shown in Figure 3.10. The power switches T 1,T 2,T 3,T 4,T 5 and T 6 are used to synchronize the three phase currents according to the signals generated by hall sensors with the back EMF of each phase. If the BLDC motor has 180 magnetic arc rotor, two phase conduction mode is preferred, and if the motor has 120 magnetic arc rotor, three phase conduction mode is preferred. Two phase conduction mode is preferred, as the BLDC motor used here has 180 magnetic arc rotor. T1 T3 T5 T4 T6 T2 Figure 3.10 Six step inverter In the two phase mode, two of the motor windings are energized at a time and upper bridge switch carries the positive current and lower bridge

66 switch carries the negative currents. The conduction interval of each phase is determined by the hall sensor output. The sum of the torque generated by the two windings constitutes the total torque. 3.6 SIMULATION RESULTS The machine parameters of BLDC motor used in this work is given in Table 3.1. Figure 3.11 shows the simulated output of six step inverter-fed BLDC motor. The input voltage of 310V DC is given to the inverter. Initially, the motor is operated at the no load and the speed of the motor reaches the rated speed of 4600 RPM at 0.03sec. At 0.1 sec, a load of 2.2Nm is applied and the speed of the motor reduces from its rated speed of 4600RPM to 4000 RPM. The reason for the reduction in speed is the absence of the speed regulator. Positive torque is produced since the EMF and stator currents are synchronized with each other. The ripple present in the torque characteristics is due to the absence of the current controller. Table 3.1 BLDC motor parameters Motor rating 1.1HP Voltage (line-line) 250 V Rated Current 4.52 A Peak Current 13.5A Rated Torque Peak torque 2.2Nm 6.6Nm Pole Pairs 2 Speed Inertia 4600 RPM 1.8 kgcm2 Stator Phase Resistance 3.07 Stator Phase Inductance 6.57mH

Back EMF in V Stator Current in A Torque Nm Speed in RPM 67 5000 4000 3000 2000 1000 20 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time in secs (a) 15 10 5 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Time in Secs (b) 150 100 Back EMF Stator Current * 5 50 0-50 -100-150 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 Time in Secs (c) Figure 3.11 Simulated output of six step inverter fed BLDC motor for (a)speed(b)torque (c)back EMF and Stator current

68 3.7 APPLICATIONS In recent years, the BLDC motor has achieved a sparkling expansion in the automotive, aerospace and household equipment industries due to its higher efficiency, longer lifetime, low noise and good speed-torque characteristics. In addition to the hardcore of automotive drives, the BLDC motors are used in air conditioners, wiper blades, electric doors and power seats. Air driven and hydraulic type transmission devices are being replaced by motor driven equipment in the aerospace industry. Special structure and position sensorless BLDC motors are widely used in the aerospace industry. In gyroscope and robotic arms, high speed centrifugal pumps and in high speed cameras with a few thousand revolutions per minute, the BLDC motor is used. Generally in the electric appliances and compressors, induction motors are used. But due to the low efficiency and poor power factor, the induction motors are replaced by the BLDC motors. They are used in the household appliances like vacuum cleaner, agitator, hair drier, cameras and electric fans. BLDC motors are also used as spindle motor drive in VCD, DVD and CD players. 3.8 CONCLUSION In this chapter, the construction and principle of operation of BLDC motor are presented. The BLDC motor is modeled using differential equation and state space equations. Full wave mode of operation and different topologies of half wave mode are also presented. Inverter-fed BLDC motor is simulated in MATLAB and the results are analyzed in this chapter.