A Study of Cogging Torque Reduction Methods in …

1 146 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS , August 2012A Study of Cogging Torque Reduction Methodsin brushless DC MotorTeeradej Srisiriwanna1andMongkol Konghirun2,Non-membersABSTRACTThe Cogging Torque is undesirable effect in thebrushless dc (BLDC) motor, causing vibration andaudible noises. It arises from the rotor permanentmagnet interacting with the steel teeth on the sta-tor. This paper studies the various Reduction meth-ods of Cogging Torque when designing a BLDC mo-tor. These Methods can be categorized according tothree parts of motor structure, , air gap length,rotor and stator parts. The finite element methodmagnetic (FEMM) is primarily used to analyze thecogging Torque among these different Reduction meth-ods. In this paper, a 4-pole, 24-slot BLDC motor isfocused with variations of air gap length, rotor, andstator parts in order to Study its Cogging Torque re-ductions.

2 Finally, the FEMM simulation results arepresented to validate these Reduction : brushless DC Motor, Finite-ElementMethod Magnetic, Cogging Torque1. INTRODUCTIOND uring the past few years, the brushless dc(BLDC) motor has been becoming popular in indus-trial applications such as air conditioners and blowersas the high efficiency is concerned. It also offers com-pact size, comparing with the same rating of induc-tion motor. As its overall cost continued to decrease,it has the great opportunity to become a dominantforce in the market of abovementioned industrial ap-plications [1]. Unfortunately, one of main disadvan-tages of BLDC motor is the Cogging Torque , causingthe undesirable effects to the motor, , vibrationand audible noises. The Cogging Torque arises fromthe rotor permanent magnet interacting with the steelteeth on the stator. It exists even there is no statorcurrent flowing into the stator windings.

3 Basically, itis caused by an uneven air-gap permeance resultingin the magnets constantly seeking a position of min-imum reluctance. In a well-designed BLDC motor,the Cogging Torque should be minimized [2]. Thereis a number of Reduction Methods of Cogging torqueswhile designing a BLDC motor such as increase of airManuscript received on July 15, 2012 ; revised on October18, ;2 The authors are with Department of Electrical Engineer-ing, Faculty of Engineering,King Mongkut s University of Tech-nology Thonburi Tungkru, Bangkok, 10140, Thailand., and length, larger number of slots/pole, thicker toothtips to prevent saturation, minimizing slot opening,magnetic slot-wedge usage, magnet skewing, magnetpole shaping, addition of dummy slots, and lowermagnet flux density[1]-[4].The objective of this paper is to present the com-parison of five Methods for Cogging Torque reductionby means of analysis of finite element method.

4 Theair-gap length adjustment, slot opening, number ofslots/pole, magnet flux-density and dummy statorslots are adjusted in order to see the effects of coggingtorque Cogging Torque Reduction METH-ODSIn [1], the Cogging Torque equation has been de-rived asTcog= 12 2gdRd (1)Where gis the air-gap flux, R is the air gap re-luctance and is the rotor position. In this section,the Cogging Torque reductions in each part of motorstructure can be separately explained as Air-gap length [2]The distance between rotor and stator refers toair-gap length. The air-gap length may be varied ac-cording to the size of motor. In [2], the suggestedair-gap length range for very small motor, mediumsize motor, and large motor are , , , respectively. The coggingtorque can be simply reduced by means of increasingair-gap length, resulting in lowering the dR/d in (1),thereby reducing the Cogging Torque . However, whenincreasing air-gap length, its reluctance is a result, the gis finally lowered.

5 In turn, thecogging Torque is lowered as well. To keep the samepermeance coefficient at operating point in the de-magnetization curve, the magnet width is required tobe increased to keep the Rotor structure [1]In this part, there are three Methods related tothe permanent magnet that can reduce the coggingtorque as follows: Magnet pole shaping. The rate of change in airgap flux density at magnet edges has effect on cog-ging Torque . Generally, this method can reduce theA Study of Cogging Torque Reduction Methods in brushless DC Motor147cogging Torque by designing either magnet width ormagnet length decreased. In this method, the desiredtorque decreases because less magnet flux is availableto the stator winding. Skewing. This method is basically making thedR/d zero over of each magnet face. In theory,the Cogging Torque can be completely eliminated. Inreality, it may not perfectly reach zero, but be sig-nificantly reduced.

6 Skewing can be implemented oneither the magnets or the slots. Both have disad-vantages. Skewing the magnets increases the magnetcost. Skewing the slots increases the copper lossesdue to increased slot length, resulting in the longerwire. Lowering magnet flux density. Referring to (1),the Cogging Torque can be simply reduced by decreas-ing the air-gap flux. Thus, the lowering the magnetflux density by changing the magnet grades, directlyreduces the air-gap Stator Structure [2]In this part, there are four Methods related to thestator structure that can reduce the Cogging torqueas follows: Proper thickness of stator tooth tips. If thesestator tooth tips are too thin, then they are likelysubject to magnetic saturation, increasing the cog-ging Torque . The thickness of tooth tips should bethe same width of slot opening. Slot opening. The width of slot opening affectto the Cogging Torque . Reducing the width of slotopening to reduce permeance variation between teethof stator, the Cogging Torque will decrease as well.

7 Increasing the number of slots/pole. When thenumber of slots/pole is close to 1, the number of slotbecomes more important. Increasing the number ofslots affects the decreasing Cogging Torque . Addition of dummy slots. It makes the bifurcateteeth in the tooth overhang to modulate the perme-ance variation to reduce the Cogging Torque . It hassimilar effect as the double number of slots. In thiscase, the Cogging Torque frequency would be double. Adding magnetic slot wedges. The stator slotopenings are closed by wedges made soft magneticcomposite materials. The effect of this Cogging torquereduction method is similar to that of the minimizingslot opening between the FINITE ELEMENT ANALYSIS [5]The fundamental physical equations that describethe electromagnetic fields are given by Maxwell sequations as .B= 0(2) E= dBdt(3) H=J(4)Equations (2)-(4) are presented in terms of vectorfield variables E, B and H, but these equations areusually solved by using vector potential magnetic vector field B can be written in termof the vector potential as:B= A(5)Also, the relationship between H and B is ex-pressed as follow:H= (6)Vector potential equation for magnetic field is ob-tained by substituting equations (5) and (6) in equa-tion (4), yields (r.)

8 A) =J(7)To numerically solve equation (7), the finite ele-ment method is used. In this paper, the open sourcesoftware FEMM version is employed. This soft-ware is able to solve two-dimensional partial differen-tial :Modeling4pole/24slots BLDC motor FEMM modelling though LUA scriptThe FEMM also supports LUA scripting LUA scripted library can be used to draw the148 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS , August :FEMM mesh of BLDC of the BLDC motor in FEMM through theprocess of drawing as shown in All motor pa-rameters can also be specified in the LUA modelling, meshing of finite elements willsolve problem differential equation in modelling ofBLDC motor. The meshing yields approximately30,000 nodes and 50,000 elements. To improve theaccuracy of Cogging Torque calculations, the meshingaround the arcs and corners has to be higher resolu-tion as shown in is a well know fact that by increasing the mesh-ing resolution, a higher accuracy in estimation canbe reached but only to a certain extent.

9 Where bythe increase of meshing nodes of 20,000 to 140,000produces an increase in accuracy of [6] Simulation stepsIn the simulation, the model can be drawn inFEMM software or imported as an AutoCAD material and mechanical properties are specifiedby setting the LUA script. The domain is meshedand the boundary conditions are determined by software uses a triangular element to mesh thedomain and linear functions to approximate the solu-tion. There are approximately 35,000 nodes for entireBLDC motor model. After setting the meshing, thecogging Torque for the initial rotor position is calcu-lated by using the weighted stress tensor method. Aflowchart of FEMM simulation is provided in meshing process and Cogging Torque calcula-tion are performed before the rotor position is in-creased by a certain degree. These processes are re-peated and results are recorded at each :Simulation steps on Cogging Torque position until the final rotor position is this paper, the FEMM simulation is finished at45 degree.

10 The flux distribution of a 4-pole, 24-slotBLDC motors is shown in SIMULATION RESULTSIn this paper, a4-pole, 24-slot BLDC motor is usedas reference design. Its specifications and materialsare given in Tables 1 and 2, section discusses the simulation results ofthree main Methods for reducing the Cogging torqueof this reference design of BLDC motor. Firstly, thesimulation results of reduced Cogging Torque by meansof the air-gap length from mm to mm is shownin As expected, the increase of air-gap lengthresults in the Reduction of Cogging Torque . The cog-ging Torque is reduced due to lowering the dR/d andthe g. In this Fig., the Cogging Torque waveform isrepeated every 15 mechanical degree per slot. Sec-ondly, the Reduction of Cogging Torque in terms of ro-tor structure by lowering magnet flux density is stud-ied. Three magnet grades are selected as shown inTable 3. Clearly, the Cogging Torque is reduced whenusing the magnet with lower flux density (or lowergrade) as seen in The peaks of Cogging torqueA Study of Cogging Torque Reduction Methods in brushless DC :Flux distribution of 4-pole, 24-slot 1:Specifications of reference BLDC ValuesUnitRated Power1kWRated Voltage220 VNumber of Poles4-Rated Speed1500rpmNumber of Stator Slots24-Outer Diameter of Stator125mmInner Diameter of Stator65mmMinimum Air Diameter of rotor48mmLength of Rotor40mmThickness of Magnet8mmSlots opening2mmWidth of teeth6mmTable 2:Materials of Reference BLDC SteelRotorM-19 SteelMagnetCeramic 8for NdFeB40 MGOe, SmCo27 MGOe, and Ceramic8are , , and , , the Reduction of Cogging Torque in terms ofstator structure by lowering slot opening, increasingslot/pole, and use of dummy slots are evaluated.