CHAPTER 3 DESIGN OF THE LIMITED ANGLE BRUSHLESS TORQUE MOTOR

33 CHAPTER 3 DESIGN OF THE LIMITED ANGLE BRUSHLESS TORQUE MOTOR 3.1 INTRODUCTION This chapter presents the design of frameless Limited Angle Brushless Torque motor. The armature is wound with toroidal winding to meet the requirement of cogging free and to have a smooth distribution of flux throughout the airgap. Unlike the conventional brushless dc motors which are typically wound for two or more phases and operated with position sensors commutation logic, the LABLT has single phase winding which does not require any position sensor and commutation logic for limited angle rotation. The design is carried out based on the specifications and interface requirement with the scanning system for the servo actuator in the aerospace mechanism. The motor volume is apportioned from the given overall dimensional constraints. The magnetic loading and electrical loading are calculated to meet the torque requirement. The number of poles in the motor is selected to meet the required constant torque region. The empirical design data such as resistance, inductance, torque constant, back-emf constant and weight of the motor are presented. 3.2 SPECIFICATION REQUIREMENT OF MOTOR The requirement specifications are derived based on the volume available and interface constraints of servo actuator in scan mirror

34 mechanism. The requirement specifications of motor and drive are given in Table 3.1 and Table 3.2 respectively. The interface drawing of the limited angle rotary actuator for scan mirror mechanism is shown in Figure 3.1. Table 3.1 Requirement specification of limited angle brushless torque motor 1. Motor Type Frameless Brushless DC configuration 2. Peak torque 2.5 Nm 3. Peak power 50 watts(max) 4. Continuous torque 1.0 Nm 5. Continuous power 30 watts 6. Speed of operation 2.62 rad/sec (max) 7. Constant torque region ± 20º (80% of peak torque) 8. Electrical time constant 4.0 ms ± 30 % 9. Back emf constant, K b 1.25 V/(rad/sec) ± 7 % 10. Torque constant, K t 1.25 Nm/A ± 7 % 11. Rotor inertia <4.0 *10-4 kg m 2 12. Resistance 13. Inductance 30 mh ± 30 % 14. Operating voltage 28 V 15. Operational temperature -20 to 100 C 16. Outer Diameter 175 mm (max) 17. Inner diameter 85 mm 18. Length 54 mm (max) 19 Weight 5.0 Kg (max) Table 3.2 LABLT drive requirements 1 Excursion Angle ± 20º 2 Position accuracy 0.75 3 Input voltage ±12V, ±5V 4 Rate selection 1 deg/sec, 2 deg/sec, 3 deg/sec 5 PC interface RS232 6 Position sensor 10 bit encoder (Absolute type)

Figure 3.1 Interface drawing of the motor 35

36 3.3 DESIGN CONSIDERATION 3.3.1 General Torque Equation Before designing the motor for required specification, the fundamental design issues are considered. The size of the motor to produce the desired torque for radial flux motors stated (Hanselman 1994) as 2 T KD L (3.1) where, is torque in Newton meter K is motor constant D is airgap diameter in meter L s is stack length in meter From the Equation (3.1) the torque is linearly proportional to stack length and square of the airgap diameter, moreover the ability to produce force increases linearly with diameter (Kenjo & Nagamori 1985). Also, the force equation is given by Force, F = B g I L (3.2) and Torque, T = F R (3.3) where B g = Air gap flux density in Tesla I = Winding current in Ampere L a = Active length of conductor in meter F = Force in Newton R = Radius in meter T = Torque in Newton meter

37 The LABLT works on the basic principle current carrying conductor placed in the magneti. The force multiplied by radius results in torque output of the motor. This force/torque is proportional to the direction and the magnitude of the current and the air gap flux density. Since the permanent magnet flux density is fixed, the direction and magnitude of the force/torque depends on the direction and magnitude of the input current. 3.3.2 Motor Diameter Mechanical power output is directly proportional to torque whereas the torque is proportional to square of the diameter as given in Equation (3.1). A motor having larger diameter generates more mechanical power which states that the motor diameter should be maximized. There are constraints that limit the diameter of the motor. The important constraint in this application is size limitation and interface with the mechanism to be driven. In addition to the constraint stated the mass and inertia of the motor also play a major role in the operation of the motor in space mechanism requiring maximum torque to inertia ratio (Praveen et al 2011). The torque to inertia ratio of a motor decreases with the square of the diameter. The diameter of the motor should be selected based on the above constraints. The torque developed in the motor is given by (Miller 1989) T PBgIL(D / 2) (3.4) where P = Number of poles, B g = Airgap flux density. In order to increase the power output for a fixed diameter of motor the electrical loading and magnetic loading shall be increased.

38 3.3.3 Active Motor Length The torque developed by the motor is directly proportional to the active length of the motor. But by increasing the length, the mass and volume of the motor get increased. As the resistance of the winding depends on the core length and hence the resistive loss increases as longer copper wire is required for more active length (Ragot et al 2010). Therefore, increasing the motor active length increases the loss thereby decreasing the efficiency of the motor. To summarize by increasing the active length the torque developed by the motor is increased by sacrificing efficiency. 3.3.4 Ampere-Turn Ampere turn is the product of number of turns and the winding current. The winding inductance increases square of the number of turns. High inductance affects the motor electrical time constant. The winding resistance is proportional to resistive loss. Increase in number of turns increases the resistive loss. But increase in number of turns reduces the winding current for the required torque and hence copper loss is reduced as it is proportional to square of the current. If the conductor size is constant, the cross sectional area increases as turns increases. The increase in slot area increases the mass of the stator core which affects the power density and increase in slot current increases the armature reaction field (Mitcham et al 2004). This increases the core loss in the magnets and decreases the airgap flux density due to stator core saturation. 3.3.5 Airgap Flux Density In permanent magnet brushless dc motor the magnetic loading is maximized to get the required torque output and this requires high energy permanent magnet material. The airgap flux density is increased by improving

39 the permeance coefficient of the magnetic circuit. High permeance coefficient implies larger magnet length and shorter effective airgap length. Decreasing the effective airgap length increases the cogging torque. Hence, for a high magnetic loading, the volume of the magnet material and its energy product should be high and a ferromagnetic material is required to concentrate the flux. The saturation in the stator core teeth also limits the improvement in the airgap flux density. The attempt to increase the airgap flux density is also limited by the saturation in the stator core teeth. 3.3.6 Number of Poles The selection of pole numbers depends on the airgap diameter and increasing the number of poles in a fixed area decreases the magnet width to accommodate the additional magnets. With this, the magnet leakage flux increases which reduces the flux density in the airgap. By increasing the number of poles the rotational frequency of the motor is increased (Kenjo & Nagamori 1985). The core loss depends on the rotational frequency of the motor. The hysteresis loss is directly proportional to frequency and eddy current loss is directly proportional to square of the frequency. The increase in rotational frequency increases the core loss in the motor which decreases the efficiency. The advantage of more poles is that the overhang length is reduced and thereby the end winding resistance and inductance are reduced. The back iron thickness gets reduced by increasing the number of poles. In a high performance brushless dc motor the design goal is to improve the tradeoff between the electrical loading and magnetic loading by finding a method to balance the two in a manner that does not diminish the other (Hanselman 1994).

40 3.4 LABLT CHARACTERISTICS The output torque of the LABLT motor is directly proportional to the armature current and hence the torque versus armature current plot is a straight line with a slope equal to the torque sensitivity. The output torque also depends on the magnet rotor position. The toroidal wound LABLT provides constant torque for a limited angle and beyond this torque gradually reduces to zero on further rotation as shown in the Figure 3.2. The constant torque region depends on the segment angle of the armature winding and the magnet pole. ( ) 2 (3.5) where 2 = Constant torque region = Armature winding angle = Magnet pole arc Constant Torque region Torque Torque (Nm) in Nm -45-0 +45 Rotor position in Mechanical degree ( ) Figure 3.2 Ideal torque characteristics

41 3.5 LABLT CONFIGURATION The proposed motor configuration has single phase toroidal armature winding around the stacked lamination core, having four segments spread over 85 mech. for the four pole rotor designed for the given electrical specification. Figure 3.3 Configuration of LABLT motor All the four winding segments are connected two in series and parallel to form a single phase winding for cumulative torque production. The permanent magnet rotor assembly is configured for four poles and PM are fixed on the four slots milled in the magnetic stainless steel ring. Approximately two third of the given annular volume is apportioned for the armature stator assembly and one- third for the permanent magnet rotor assembly.

42 From the given overall dimensions and configuration, the radial dimensions are apportioned for the design and analysis. Rotor ring inner diameter = 85 mm (given requirement) Rotor ring radial thickness = 9.0 mm Magnet thickness = 9.0 mm Magnet rotor outer diameter = 114 mm Physical radial airgap = 0.5 mm Armature coil thickness = 4.0 mm Magnetic airgap length = 4.5 mm Armature core thickness = 7.0 mm Armature coil Inner diameter = 115 mm Armature core inner diameter = 123 mm Armature core outer diameter = 137 mm Armature outer diameter = 145 mm Armature housing outer diameter = 175 mm (given requirement) Armature core length = 44 mm (given requirement) dimensions. The design details are worked out using the above apportioned 3.6 DESIGN OF ELECTRICAL AND MAGNETIC LOADING Based on the specification and performance requirements within the given overall dimensions, approximately two-third of the annular volume is apportioned for stator and one-third to the magnet rotor since high coercive magnets are used for the rotor design. When the armature windings are

43 excited, the conductors under the pole-arc will provide the torque for the rotor to rotate in CW or CCW direction depending of the direction of the current. In a four pole torquer, the total torque developed is four times of the one quadrant. The direction of the current under each pole arc should be such that the torque developed by each quadrant is additive. All the four quadrant armature windings are wound and connected to meet the terminal resistance, inductance and peak torque requirements. 3.7 PERMANENT MAGNET OPERATING POINT Magnet radial length in the direction of orientation = 9.0mm Effective magnetic airgap length = 4.5mm Permeance Coefficient Approximate = 2 Magnet operating flux density from the demagnetisation curve shown in Figure 3.4 is greater than 0.7 Tesla, therefore accounting for leakage, the average flux density of 0.6T is used for further design calculations. Figure 3.4 Demagnetisation curve of 28MGOe - Sm 2 Co 17

44 3.8 ARMATURE WINDING DESIGN For the required constant torque region of ±20º mechanical a four pole configuration is selected for the design. The magnetic circuit detail are worked out taking the average airgap flux density of 0.6T across the magnetic airgap of 4.5 mm since the high coercive samarium cobalt magnets are used. The number of armature conductors is worked out in order to meet the requirements of peak torque with 2 ampere current (given, K T =1.25Nm/A and Peak Torque = 2Nm) and terminal resistance below 8. Radial coil thickness = 4.0 mm (apportioned) Assuming 25 SWG copper wire (d=0.579mm), the number of conductors are calculated for the required torque, with two quadrant in series and parallel. Therefore, the actual current in the conductor is one ampere. For one ampere current, the current density for 25 SWG is 3.8 A/mm², which is well within the continuous operation rating. 3.8.1 Number of Conductors Per Segment Armature coil top layer diameter = 122 mm Armature coil bottom layer diameter = 116 mm Therefore the radial coil thickness = (122 116) / 2 = 3 mm No. of layers for 3 mm coil thickness = 3/0.579 = 5 layers (approximately) Segment angle Average diameter = 85º (mechanical) = (122+116)/2=119 mm Average Arc length of segment Top Layer 119 85 88.27 mm 360

45 For conductor diameter of 0.579 mm, approximately 140 conductors for one layer and hence for five layers the total number of turns for one segment is worked out to be 140 5 = 700 conductors. 3.8.2 Resistance of the Coil per Segment For the apportioned armature coil and core radial thickness, the mean length of the turn is calculated for estimating the terminal resistance. 11 mm 50mm Figure 3.5 Mean turn length With reference to the Figure 3.5, Mean length of the turn = 50+11+50+11 = 122 mm For 700 conductors per segment, the total length of the wire per segment is 85.4 m. The standard resistance of 25 SWG copper wires for 1000 m The resistance for 85.4 m, is 87.45 85.4 7.468 1000 For the given specification of windings are interconnected in such a way that the total terminal resistance is around 7.5 he interconnection diagram is shown in Figure 3.6.

46 Figure 3.6 Winding interconnection Hence the total resistance of the winding after interconnection is (R1 R 2) (R 3 R 4) given by R t 7.468 R R R R 1 2 3 4 Since R 1 = R 2 = R 3 = R 4 supply current I = 2A (given, K T =1.25Nm/A and Peak Torque = 2.5Nm) 3.9 CONSTANT TORQUE REGION Constant Torque (Nm) 100 % 80 % Torque (Nm) -45-21.5-17 0 +17 +21.5 +45 Mechanical degree ( ) Figure 3.7 Constant torque region

47 Constant torque region ( ) 2 (85 51) 2 = ±17º mechanical. torque is From the Figure 3.7 constant torque region at 80% of 2.5 Nm peak = ±21.5º (80% peak torque) 3.10 MAGNET ROTOR DESIGN The magnet pole arc is selected based on the required peak torque of 2.5Nm and a nominal torque of 2Nm in the constant region is ± 20º mech. To obtain the peak torque and the airgap flux density 0.6T is chosen for calculation with the selected configuration of the motor using high coercive Samarium Cobalt magnets for the design. Magnet pole arc, = 51º Radial thickness, l m = 9 mm Axial length of the magnet, = 44 mm Length of airgap, g= 0.5 mm Magnetic airgap length, l n = 4.5 mm p = 90 Residual flux density, B r = 1.1Tesla

48 Hence, Magnet fraction, m p 51 0.566 90 Flux concentration factor, 2 1 m C 0.722 m Permeance coefficient, l g C m PC 2.77 Airgap area, Ag 2232.415 10 m 6 2 C Airgap flux density, Bg r 1 (1/ PC) 0.583 T Airgap flux, 6 g BgAg 0.583 2232.415 10 1.301mwb 3.11 TORQUE CONSTANT, K t The ratio of peak torque to the peak armature current is torque constant. This value is constant and independent rotor position or speed within the constant torque region. T 2.5 K t A 2 1.25 Nm / A 3.12 MOTOR INDUCTANCE The calculated inductance for individual segment is given below: Number of conductors / segment, n = 700 Relative permeability of silicon steel, r = 435 Area of cross section, A = 44 7 10-6 m 2

49 Length of the magnetic path, l = 3.14 130 10-3 m L 2 n o ra l L 2 700 4 10 7 435 44 7 10 6 3.14 130 10 3 = 230 mh per segment Therefore the effective inductance for the four segments connected in series parallel will be lower than the individual segment value. The four coils are connected in such a manner to get cumulative torque for the segments under North and South poles. The measured value for all four segments at the input terminal is 36.5mH, which is meeting the requirement specification. 3.13 PEAK POWER For the given surface velocity of 0.149rad/sec and 700 conductors/ segment the voltage generated in one segment is 1.652V. Hence total back EMF, E = 1.652 2 = 3.304 V Input power P = EI + I 2 R = 3.304 (2) + 2 2 (7.5) = 36.48 W Hence the peak power is 36.5 W which is well within the requirement specification.

50 3.14 MOMENT OF INERTIA OF THE ROTOR Moment of inertia plays a significant role in designing a motor. It decides the motor torque as the motor weight depends directly on the inertia component. Area of the magnet = 351.20 10-6 m 2 Volume of the magnet = 351.20 10-6 (44 10-3 ) = 15.44 10-6 m 3 Mass/magnet = Density volume = 8400 kg/m 3 15.44X10-6 = 0.1297 kg. Moment of Inertia of Magnets = 0.5 4M (r 2 1 -r 2 2 ) = 2.6 10-4 kg m 2 Similarly, Weight of the iron ring = 0.8493 kg Moment of inertia of the ring = 8.0843 10-5 kg m 2 Total moment of inertia = 3.408 10-4 kg m 2 3.15 WEIGHT OF THE TORQUE MOTOR The approximate weight of the armature stator is obtained as Stator weight = Copper + Armature core +Stator housing = 0.788 kg + 1.016 kg + 1.27 kg =3.074 kg (approx) without potting The approximate weight of the magnetic rotor is obtained by calculating the volume of the plain rotor and steel density.

51 Rotor weight = Rotor Ring+ Magnet = 1.101kg +0.519 kg = 1.62 kg (approx) Total weight of motor = Stator + Rotor = 4.694 kg (approx) Including the weight of potting compound and harness weight, the total weight of the LABLT motor will be less than 5 kg (max). 3.16 SUMMARY From the requirement specifications the performance and geometrical input data are calculated for the design of LABLT motor. The magnetic loading and electrical loading are worked out to meet the required peak torque in the constant torque region. The designed values of various LABLT motor parameters are summarised in table 3.3. Table 3.3 Summary of designed values of LABLT motor S. No Parameter of motor Value 1. Flux density at airgap 0.6 T 2. Conductor diameter 0.579mm 3. Number of conductors/ segment 700 4. Resistance 7.468 ohm 5. Constant torque region ± 21.5 6. Magnet pole arc 51 7. Radial thickness 9mm 8. Axial length of magnet 44mm 9. Pole pitch 90 10. Torque constant 1.25Nm/A 11. Peak power 36.48W 12. Total moment of inertia 3.408 10-4 kg m 2 13. Total weight of motor 4.694 kg