CHAPTER 3 QUADRUPLEX WINDING REDUNDANCY BRUSHLESS DC MOTOR

Transcription

1 26 CHAPTER 3 QUADRUPLEX WINDING REDUNDANCY BRUSHLESS DC MOTOR 3.1 INTRODUCTION This chapter presents the desin of new quadruplex windin redundancy peranent anet brushless dc otor. The desin is carried out based on the requireent specification and interface drawin of the otor for electroechanical actuator application in aerospace echanis. The new quadruplex windin technique for reliability requireent is introduced. List of ajor coponents for the stator assebly and rotor assebly is provided. The otor volue is apportioned fro the iven overall diensional constraint. Assuin the value of airap flux density, the nuber of conductors for back-emf and torque requireent is calculated. 3.2 DESIGN CONSIDERATION Before desinin the otor for required specification, the fundaental desin issues are considered. The size of the otor to produce the desired torque for radial flux otors stated as 2 T KD L (3.1) Where, T is torque in N K is a otor constant D is the airap diaeter, L is the stack lenth,

2 27 Torque is linearly proportional to lenth Torque is proportional to diaeter squared The ability to produce force increases linearly with diaeter ( D) and force produces torque which is proportional to radius (D/2) Motor Diaeter Mechanical power output is directly proportional to torque whereas the torque is proportional to square of the diaeter as iven in 3.1. A otor havin larer diaeter enerates ore echanical power which states the otor diaeter should be axiized. There are constraints that liit the diaeter of the otor. The iportant constraint in this application is space liitation and interface with the echanis. The ass and inertia of the otor also plays a ajor role in operation of the otor in space echanis requirin axiu torque to inertia ratio. The torque to inertia ratio of a otor decreases as the square of the diaeter. The diaeter of the otor should be selected based on the above constraints. iven by Alternate equation for the developent of torque in a otor is T PB IL( D / 2) (3.2) where P = No. of poles, B = Airap flux density. In order to increase the power output for a fixed diaeter otor the electrical loadin and anetic loadin shall be increased Active Motor Lenth The torque developed by the otor is directly proportional to the active lenth of the otor. But by increasin the lenth, the ass and volue

3 28 of the otor et increased. Also the resistance of the windin depends on the core lenth and hence the resistive loss increases as loner copper wire is required for ore active lenth. Therefore, increasin the otor active lenth does not iprove the efficiency of the otor Apere-Turn Apere turn is the product of nuber of turns and the windin current. The windin inductance increases square of the nuber of turns. Hih inductance affects the otor electrical tie constant. The windin resistance is proportional to resistive loss. Increase in nuber of turns increases the resistive loss. But increase in nuber of turns reduces the windin 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 ass of the stator core which affect the power density and increase in slot current increases the arature reaction field. This increases the core loss in the anets and decreases the airap flux density due to stator core saturation Airap Flux Density In peranent anet brushless dc otor the anetic loadin is axiized to et the required torque output and this requires hih enery peranent anet aterial. The airap flux density will increase by increasin the pereance coefficient of the anetic circuit. Hih pereance coefficient iplies larer anet lenth and shorter effective airap lenth. Decreasin the effective airap lenth increases the coin torque. And hence for a hih anetic loadin the volue of the anet aterial and its

4 29 enery product should be hih and ferroanetic aterial is required to concentrate the flux. The saturation in the stator core teeth also liits the iproveent in the airap flux density Nuber of Poles The selection of pole nubers depends on the airap diaeter. Increasin the nuber of poles in a fixed area decreases the anet width to accoodate the additional anets. With this the anet leakae flux increases which reduces the flux density in the airap. Increasin the nuber of poles increases the rotational frequency of the otor. The core loss depends on the rotational frequency of the otor. The hystersis 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 otor which decreases the efficiency. The advantae of ore poles is that the overhan lenth will be reduced and which reduces the end windin resistance and inductance. The back iron thickness ets reduced by increasin the nuber of poles. In a hih perforance brushless dc otor the desin oal is to iprove the tradeoff between the electrical loadin and anetic loadin by findin a ethod to increase one in anner that does not diinish the other. 3.3 MAGNETIC CIRCUIT DETAILS Brushless peranent anet otor operation relies on the conversion of enery fro electrical to anetic to echanical and anetic enery which depends on spatial distribution of flux in the otor plays a central role in the production of torque. A siple eoetry of the anetic field can be found analytically to deterine the anetic field distribution in

5 30 the otor. The direction of anetic field is assued for the preliinary desin of the otor (Duane C. Hanselan 1994). The stator and rotor structure of brushless dc otor is shown in Fiure 3.1 and 3.2. The anetic circuit odel of one flux loop shown in Fiure 3.3 coposed of one half of the two anets and associated stator and rotor back iron. The anetic field due to windin current is not considered. By considerin Rr and R s to be neliible with respect to anetic circuit can be siplified as shown in Fiure 3.4. R and R l, the Fiure 3.1 Bldc otor stator-rotor structure Fiure 3.2 Peranent anet and anetic aterial structure

6 31 R r R s Fiure 3.3 Manetic circuit odel of the structure = Rotor back iron reluctance = Stator back iron reluctance 2 R = Reluctance of the one half of airap with copensation for slottin r /2 = Flux source of one half of the anet 2 R = Reluctance of one half of the anet /2 = Airap flux flowin throuh one half of the airap cross section area R l = Reluctance odelin the flux leakae fro anet to anet Fiure 3.4 Siplified anetic circuit

7 32 The airap pereance describes the net pereance seen by the anet flux that enters the stator. This flux eanates fro cross sectional area is iven by 1+ A = L (3.3) p 2 the airap pereance. P is P = o p 1+ 2 e (3.4) = Effective airap lenth, e l = + k (3.5) e c r p = Manet pole pitch =Manet fraction k = Carter coefficient c l = Manet radial thickness = Physical airap lenth The airap flux with the above equations 1 = 1+ k k / r c l PC r (3.6) PC = Pereance coefficient k = Manet leakae factor l

8 33 The flux concentration factor, C = A A (3.7) C The airap flux density, B = 1+ k k / PC r c l B r = Reenance flux B r (3.8) 3.4 DESIGN APPROACH The desin approach starts with basic otor eoetrical constraints. The volue for stator assebly and rotor assebly is apportioned fro the iven overall diensional specification of the otor. The otor stack lenth and airap diaeter are fixed based on the desiner experience. Once the otor volue is fixed, the anetic loadin for the torque production is calculated. The anetic circuit details deterinin the nuber of poles and slots are worked out. The pereance coefficient and anet operatin point is found for the anetic circuit. The size, shape and enery product of the anet are deterined to axiize the anetic loadin. Once the anetic loadin is calculated to carry axiu flux in the iven anetic circuit, the electrical loadin is worked out. The current required to enerate the required otor output torque is then deterined. Given the desired back-emf at rated speed, the nuber of conductors for eneratin the back-emf is calculated. The phase inductance and windin resistance are coputed fro the windin inforation. The proposed work describes the desin and developent of brushless dc otor havin four independent windin in its arature assebly as per the specification requireent of otor for electroechanical actuator application. The desin of arature stator assebly, peranent anet rotor assebly and Hall sensor assebly are worked out. Arature desin is a quadruplex three phase star connected windin separately housed in four

9 34 quadrants of the arature stator providin physical and electrical isolation of each quadrant windin for reliability and redundancy. The peranent anet rotor assebly is desined conforin to the quadruplex arature in which each quadrant of the arature and the anet rotor perfors independently as a separate brushless dc otor. The Hall sensor assebly is a triplex redundancy separate assebly housed in the stator core to sense the rotor position for six step coutation loic. 3.5 SPECIFICATION REQUIREMENT OF THE MOTOR Table 3.1 Requireent specification of the otor 1 Type PM BLDC torque otor-fraeless 2 Windin Quadruplex redundancy three phase windin 3 Position sensor Latch type Hall effect device (Triplex redundancy) 4 Coutation schee Six step trapezoidal coutation 5 Stall torque (a) 8 N per quadrant at 12.4 A (Noinal) (b) 32 N total at 49.6 A 6 No-load speed 1000 supply voltae of 75V DC 7 Insulation resistance >100M at 250V DC 8 Torque constant 0.66 ± 7% N/A 9 Back-EMF constant 0.66± 7% V/(rad/s) 10 Windin resistance 2.4 ± 10%, (line-line) 11 Windin inductance 10.2 ± 30 H, (line-line) 12 Rotor inertia 8.8 e-4 ± 10% K² 13 Coin torque < 2 % of Peak torque 14 Ripple Torque < 15 % of Peak torque 15 Load cycle As per the sketch 16 Diension As per the interface drawin 17 Operational 80 C teperature 18 Drive electronics Four independent power drives for the four sets of windins. PWM type. Switchin frequency 10 khz.

10 Interface Drawin Fiure 3.5 Interface drawin of the otor

11 SPECIFICATION DERIVED Table 3.2 Desin oal Motor Supply Voltae Three phase windin in each quadrant Current per quadrant Current for four quadrants Load cycle Hall sensors for six sequence coutation Overall diensions Stator outer diaeter, (ax) Rotor inner diaeter, (in) Fraeless bldc otor 75 V, DC Star connection 12.4 A 12.4 * 4 = 49.6 A As per sketch Triplex redundancy As per interface drawin Rotor inertia 8.8e-4 K ² Overall stator lenth (ax) Overall rotor lenth (ax) Arature stack lenth Windin overhan inner diaeter Operational teperature Maxiu torque per quadrant Total torque: (8N * 4 quadrant) No-load speed@ 75 V, DC C 8 N (Noinal) 32 N (Noinal) 1000 rp Line to line Windin resistance 2.4 ohs ± 10 % Line to line Windin inductance 10.2H ± 30 % Three sets of Hall sensor sinal output for redundancy. Independent four quadrant windin desin for windin isolation and redundancy.

12 LIST OF MAJOR ELEMENTS (1) Peranent anet rotor assebly Rotor back iron rin Peranent anets Pottin copound (2) Arature stator assebly Electrical laination sheet Slot insulation Copper wire Lead wires Solder wire, lead Flux Heat shrinkable sleeves Epoxy bondin resin Pottin copound Hall effect sensors and PCB (3) Tools and fixtures Laination stackin fixture Coil windin fixture Stack holdin fixture durin windin Overhan forin fixture Arature pottin fixture Rotor anet assebly fixture Stator-rotor assebly fixture Testin fixture

13 MAGNETIC CIRCUIT PHYSICAL DIMENSIONS Based on the desin input and output requireents and the iven overall diensions two-third of the annular volue is apportioned for stator assebly and one-third to the anet rotor assebly since hih coercive anets is used for the rotor desin. This apportionent eets the windin overhan inner diaeter needed and the inner diaeter of the stator stack is taken as 77 for anetic circuit calculations. The followin input diensions are worked out fro the iven volue constraints. The anetic circuit details are calculated with the followin diensions. Stator outer diaeter Stator inner diaeter Stack lenth Physical airap lenth Rotor outer diaeter Rotor inner diaeter The torque otor diaeter and lenth is specified and fixed. The torque output of the otor which is the product of electrical loadin and anetic loadin is found by calculatin the work done per revolution (W r ). W r = (Total anetic loadin) * (Total electrical loadin) Electrical loadin = IZ Manetic loadin = P Where I = Windin current in Apere Z =No. of conductors P = No. of poles

14 39 W r =(P ) (IZ) (3.9) T= D LBq (3.10) where B = Airap flux density in Tesla q = Apere conductors T = Torque in N Torque developed by the otor is iven by T = 2 2 D LBq (3.11) The anetic loadin is provided by hih enery rare earth peranent anets in the rotor assebly. The radial thickness of the anet is apportioned fro the rotor return rin. The undesired coin torque in the otor is also depends on anet width. The anet width is selected such that it reduces the coin torque. The volue of the anet is worked out and the anet pereance coefficient is calculated. The anet operatin point is found fro the hih enery anet deanetization curve. Assuin the airap flux density over the pole arc and with the values of D and L, the needed Apere conductors to develop the required torque is found out usin the above relation. Once the total anetic loadin and total electrical loadin are worked out, the nuber of poles and slots are selected. The ai of the proposed work is to select slot-pole cobination based on the followin constraints. 1. Nuber of slots for quadruplex windin redundancy 2. Nuber of poles conforin to the stator quadruplex redundancy 3. To keep the coin torque iniu. 4. To reduce the core losses

15 QUADRUPLEX WINDING REDUNDANCY TECHNIQUE This thesis focus on the desin of brushless dc otor with quadruplex redundant three phase star connected windin in the arature stator for reliability requireent of electroechanical actuator. The present application requireent needs four independent otors operation in sinle anetic core for functional redundancy of the actuator syste. A new windin ethod is adopted in stator assebly to isolate four quadrant windins electrically and physically fro each other for quadruplex windin redundancy. Fiure 3.6 Quadruplex windin arature stator The torque otor requireent of quadruplex windin isolation puts constraint in selectin the nuber of poles in steps of two. Twelve poles are suitable for the apportioned airap diaeter but the quadruplex windin isolation is not possible with three poles per quadrant. Hence eiht poles or sixteen poles are the possible options for this confiuration. In this work the eiht poles and twenty four slots confiuration is selected initially and the analytical calculations are carried out to find the anetic loadin and electrical loadin. Flux density in the airap is ensured in the finite eleent

16 41 analysis. The anetic circuit details are validated with the analysis result. Based on the desin siulation the fabrication of the otor is carried out. For the eiht poles twenty four slots confiuration, each quadrant has six slots for three phase windin and the slots per pole per phase is one for eiht poles rotor. Three coils are used to wound for three phase windin of a quadrant. The 23 SWG copper wire is selected for the assued current density around 10 A/² for the iven duty cycle. The slot space factor is around 0.4 for the calculated nuber of turns in the slot for the required torque. While windin the arature coils only two-third of the desined turns were able to put into the slots due to overhan lenth liitation constraint for echanical interface with the echanis. Also the line to line resistance value eets the requireent specification with this two-third calculated turns. To overcoe the overhan proble two otor confiurations, 48 slots stator and 60 slots stator with coon 16 poles rotor, are desined. To reduce the nuber of conductors the anetic loadin is increased by increasin the anet volue and chanin enery product of the anets fro 25 MGOe to 28 MGOe. The anetic circuit is iterated to the increased anetic loadin. The analytical desin is validated with finite eleent analysis software and anetic circuit details are plotted for coparison. Based on the siulation results the above two proto type otors (Interal slot and Fractional slot) are developed. Both the otor are experientally tested and the results are tabulated for coparison of all the four quadrants perforance output COGGING TORQUE The ajor disadvantae of brushless dc otor is production of undesired coin torque and ripple torque. Coin torque is due to interaction between the rotor peranent anets and the tooth of the stator. It is enerated by the interaction of airap flux and stator reluctance variation in the airap. The rotor tends to alin to the stator teeth even without windin

17 42 excitation. This coin torque superiposed on the desired output torque causes vibration and acoustic noise in the otor while runnin. Techniques to reduce coin torque play a proinent role in otor desin. Coin torque is iven by T co dr d (3.13) Where is the airap flux and R is the airap reluctance. akin dr d In this desin stator slots are skewed to reduce coin torque by near zero value over anular rotation of the torque. Skewin can be done either for anet or to the slots. Skewin the anet increases the anet cost. Skewin the slots increases the ohic loss because the increased slot lenth requires lon wire. Both interal slot pitch and fractional slot pitch confiurations are considered for the stator assebly desin. The stator slots are skewed for one slot pitch for interal slot confiuration and half slot pitch for fractional slot confiuration. The coin torque reduction technique in rotor assebly is also adopted. The pole pitch is selected such that the pole slot cobination reduces the coin torque. The deerit of skewin the stator slots is, it reduces the developed torque by skew factor as the effective Apere-turn under the pole pitch is reduced. Liitin the anet width to reduce the coin torque lowers the anetic loadin. The anitude of the coin torque for the torque otor confiuration with and without skewin is evaluated usin finite eleent analysis tool. However it is possible to eet the coin torque specification by introducin one slot pitch skew for the interal slot and half slot pitch for fractional slots.

18 LOAD CYCLE Tie in sec Fiure 3.7 Load cycle of the otor The load cycle per quadrant of the otor for ball screw actuator echanis is iven in Fiure 3.7. The peak load current is 12.4 Apere and no-load current is 1.5 Apere per quadrant. Load cycle : 1225 seconds Peak load duration : 25 seconds No-load duration : 1200 seconds For the iven periodic and interittent duty cycle, the equivalent RMS current producin the sae loss is calculated for the selection of copper conductor diaeter for the arature windin. I = 3.3 A (Continuous RMS current) The ae of the copper wire is selected based on the current density and resistance per phase requireent. Norally class C insulation with current density in the rane of 10 A/² to 15 A/² is suested for space rade application. For the current density around 11 A/² for continuous

19 44 operation, 23 SWG copper wire with bare conductor diaeter of 0.61 and cross sectional area of ² is selected. Total ean lenth of the copper wire is calculated to find the line to line windin resistance. The nuber of conductors per coil is calculated fro back-emf constant and speed of rotation. The slot space factor is ensured for windin the coils in the slot cofortably and within the overhan liitation for interfacin the arature with the echanis PERMANENT MAGNET MAGNETIC CIRCUIT The different types of peranent anet aterial available are Alnico, Ferrite, Saariu Cobalt (SCo) and Neodyiu Iron Boron (NdFeB). At roo teperature NdFeB has the hihest enery product of all coercially available anets. The hih reanence and coercivity perit arked reductions in otor size for the sae output copared with otors usin Ferrite (ceraic) anets. For the anetic circuit consistin of peranent anet, hih pereable ferroanetic aterial and airap, the operatin point of the anet is calculated with the followin equations. related by By Guass s law the flux density in the anet and airap are B A B A (3.14) B A H 0 A l (3.15) B H B H A A l (3.16) B H 2W V (3.17)

20 45 where B = Manet flux density A = Manet area B = Airap flux density A = Airap area = Airap lenth l = Manet thickness H = Field density of the anet W = Manetic enery stored in the airap V = Volue of the anet 3.13 BACK-EMF AND NUMBER OF CONDUCTORS taken. Fro the iven requireent specification, the followin values are Torque constant, Back-EMF constant, No-load speed Supply voltae K t = N/A K b = V/(rad/sec) = 1000 rp = 75 V The back-emf, E is found fro the back-emf constant, E = K b x (rad/sec) = 67.5 V Nuber of conductors required to enerate the back-emf is worked out fro the basic relation, E Surface velocity, v = BLv Dn s /s No. of conductors for eneratin the torque for six step coutation is found fro the followin relation.

21 46 E Z = (3.18) BL Dn s where n s is revolution per second The calculated nuber of turns is distributed in the stator volue dependin upon the pole-slot cobination SUMMARY The requireent specification of the electrical otor for the electroechanical actuator in the space echanis is iven. The perforance and eoetrical input data are derived fro the specification for the desin of the advanced otor. The echanical and electrical interface drawin for the otor in the actuator echanis is provided. The approach for the desin of the otor is explained briefly. The insiht of new quadruplex windin redundancy technique is investiated. The continuous RMS current for selection of copper wire is worked out for the iven operation load cycle. The ain diensions are worked out fro the iven volue constraint. The ajor considerations for the desin of the otor are also listed. The effect of coin torque on the perforance of the otor and the ethod to liit the coin torque is also studied.