BRUSHLESS DC MICRO-MOTOR WITH SURFACE MOUNTED …

Rev. Roum. Sci. Techn. – Électrotechn. et Énerg., 59, 3, p. 237–247, Bucarest, 2014

BRUSHLESS DC MICRO-MOTOR WITH SURFACE MOUNTED PERMANENT MAGNETS

NICOLAE-MIRCEA MODREANU1, MIHAIL-IULIAN ANDREI1,

MIHAELA MOREGA2, TIBERIU TUDORACHE221

Key words: Micro-motor, Brushless DC motor, Surface mounted permanent magnets, Finite element method.

Permanent magnets brushless DC micro-motors are increasingly used in accurate motion control applications and high precision positioning systems. Main problems concerning their manufacture refer to design accuracy and adequate fabrication technology. The study presented in the paper is based on both numerical analysis and experimental assessment of operating characteristics of such a micro-motor with surface mounted permanent magnets, specially conceived for an application in aerospace technologies. An experimental prototype was manufactured based on inventive design, originally tested and refined by simplified 2D numerical simulation. More realistic 3D models are further developed aiming at the optimization of the motor, according to application specific criteria (high torque, precision in speed control, heating control etc.). The paper presents a 3D reduced model with inclined slots, used in finding an adequate design for the minimization of the cogging torque.

1. INTRODUCTION

The electric motors commonly called brushless DC motors have the principal constructive components and operating characteristics of the three-phase synchronous motors, with the field winding replaced by a salient pole armature with permanent magnets. For the construction presented here, all ends of the phase windings are accessible, making possible either delta or star external connection of the windings, as much as other functional connections, according to application characteristics. It is possible to feed the three-phase winding from a DC power source, through an inverter; sensible command of the inverter might produce precise speed tuning and motion control. Brushless DC motors are usually integrated in motion control and positioning systems, associated with electronic circuits and components, which require the access to a DC power source [1, 2].

1 ICPE, 313 Splaiul Unirii, 030138 Bucharest, Romania, E-mail: [email protected], [email protected]

2 “Politehnica” University of Bucharest, 313 Splaiul Independentei, 060042, Bucharest, Romania, [email protected], [email protected]

Aurel Câmpeanu et al. 2

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These motors are usually incorporated in low power and variable speed systems. Compared with classic DC motors, the operation reliability is higher, the fabrication is simpler and the concept is more compact. Brushless DC motors do not need the mechanical commutation system, which commonly causes reliability and maintenance problems, as much as unwanted sparks. High-speed operation, up to ten thousands cycles per minute, becomes in this manner more feasible [3, 4]. When motors in the same power range are compared, the brushless DCs operate with higher efficiency, but they are more expensive than classic DC motors. A critical aspect of brushless DC motors lies in their excessive heating especially when operated at high speeds [5]. The developed heat is due mainly to the iron and copper losses located in the stator. The interior ventilation being limited, an inadequate design of the machine from thermal point of view could entail an irreversible demagnetization of the permanent magnets.

Motor concept based on numerical simulation opens a reasonable way for comparison between different designs; for the same required working conditions the most economical and efficient one is chosen; specialized literature reveals various optimization criteria, i.e. winding design improvement [6], or thermal problems consideration [7]. Different constructive options could have various consequences; their assessment is also feasible by numerical analysis [6–8].

The paper is focused on the presentation and performance analysis of a very small power brushless DC motor model, with surface mounted permanent magnets. The design of the motor was assisted by computer simulation, using commercial software (FEMM [9] and Comsol Multiphysics [10]); 2D simplified numerical models were then used for the virtual testing and evaluation of several conceptual versions, finally converging to the outcome of the first physical model. Starting from the finite element 2D Comsol model, a 3D more realistic model was further developed for the evaluation of operating performances; it also enables the designers to decide on the most adequate constructive adjustments in conjunction with specific mounting, operation services and environmental working conditions.

2. PHYSICAL MODEL DESCRIPTION

Figure 1 shows the initial version of the motor, built by Icpe [11]. This high precision and high speed micro-motor (≈ 6 000 rpm) is conceived to be used in aerospace communication systems where it should provide the torque for orbital correction of small dimensions satellites. Its particular construction, with the magnets mounted on the external armature has advantages for this specific application. When compared with common motors of the same power, one could observe its important torque and the significant provided moment of inertia J; it is also characterized by high efficiency and an economical power-to-weight ratio.

3 Dynamical processes in salient pole synchronous machine 239

Fig. 1 – Four poles DC micro-motor with permanent magnets mounted on the exterior armature (the rotor) and three-phase winding with its iron core (the stator) mounted on a fixing plate.

The rotor is built with two pairs of permanent magnets; they are symetrically positioned and stuck inside a case, made of magnetic soft iron. The rotating shaft is included in the same assembly; it is supported by a precision bearing fixed on the shaft by a security ring. Neodymium based permanent magnets (NdFeB) were choosen due to their superior magnetic properties: remnant flux density – (1.1 – 1.3) T, coercive field strength – (800 – 1050) kA/m, maximum energy density – (240 – 290) kJ/m3. NdFeB permanent magnets have a relatively poor thermal stability; the temperature coefficients are – 0.11%/oC for magnetic flux density and – 0.55%/oC for magnetic field strength.

Stator assembly is mounted on a fixing plate together with the exterior element of the bearing, so that the concentric positioning of the assemblies is provided. The magnetic core of the stator is built of laminated electric steel HF20, 0.2 mm, because operation at high speed generates important eddy current losses. The three-phase four-pole winding, distributed in nine slots and two layers is made of insulated copper wires.

Several experimental tests were prepared for the prototype of the micro-motor introduced before. The settings were carefully choosen, following feasibility criteria and reliability of the outcomes. This experimental setup is used for the experimental validation of the numerical models, as a practical tool for further optimization of the micro-motor and for testing new characteristics produced by variation of constructive elements.

3. NUMERICAL MODELS

2D numerical models. One simplified bidimensional numerical model of the motor was firstly developed for finding some of its characteristics and for testing and evaluating the influence of constructive parameters change. The electric machine with radial magnetic flux and negligeable side effects is commonly considered with parallell symmetry; a cross-sectional plane could thus be used as computational 2D domain. The precision is typically better for longer magnetic cores, but the 2D model usually gives reasonable results for short magnetic cores


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too, and many computational models have proven this assumption. Even if the length of the presented motor is considerable smaller than its diameter, we assumed this simplified representation as the first step of numerical simulation.

The 2D model was described and implemented independently in two software versions, both based on the finite element computational method. FEMM [9] has the advantage of being handy, very accesible and it already became a common tool complementary to classic design [11]; it is however limited only to 2D models and to stationary magnetic field problems. Comsol Multiphysics [10] was tested here by the design team and it was adopted for further development of the simulation, i.e. the study of rotor movement, various operating conditions analysis, creation of a 3D numerical model, the analysis of the thermal behaviour.

A 2D geometry was created and refined based on operation performance criteria presented further in the paper; it represents a cross-section in the middle of the core-length (Fig. 2a). The magnetic field sources are the permanent magnets and the three-phase current-fed stator winding. Equation (1) is the mathematical expression of the magnetic field problem, in terms of the magnetic vector potential, as shown in [11] and [12],

( ) ( )1/μ –∇ × ∇ × =rΑ JΒ . (1)

In the computational domain, both the current density and the magnetic vector potential have only one non-zero component, on z direction (perpendicular to the computational plane):

J = Jze z and A = Aze z , (2)

where J z is considered the equivalent current density, associated to the entire cross-sectional area of the slot. The remnant magnetic flux density Br is non-zero only in the permanent magnets regions and μ is the magnetic permeability, of constant known value in the magnets and equal to the value for free space in the other subdomaines. Non-linear magnetic characteristics were considered for the iron core of the rotor and for the laminated rotor core. The permanent magnets have parallel magnetization. For the magnetic field analysis, the active power losses are neglected.

A magnetic insulation type boundary limits the computational domain on the surface of the external armature, which is considered a magnetic absorbant material (Dirichlet condition),

Az = 0. (3)

For the numerical analysis, a triangular finite element mesh with quadratic Lagrange elements was generated (Fig. 2b); the mesh density was refined to some extent, according to an accuracy test performed before the magnetic field true analysis.


a. main geometry in the cross-sectional computational plane

b. finite element mesh with quadratic Lagrange elements

Fig. 2 – Computational domain for the 2D simplified model (pictures with Comsol software [10]).

3D numerical model. More realistic simulation was necessary for the optimization of the design and one simplified 3D representation of the micro-motor was built. It is important considering non-symmetric constructive elements, like inclined slots, for the minimization of the cogging torque. The thermal analysis is another significant issue requiring a 3D model; the assesment of the current design solution and identification of possible excessive heating spots related to the mounting system or to specific operation conditions are important design and validation stages of the concept [7, 11].

The 3D numerical model considering inclination of the slots is further presented in its Comsol Multiphysics implementation [10]; the geometry is built by extrusion of the 2D cross-section shown in Fig. 2a, while the stator is also constrained to rotation limited by controlled angles. The model is exclusively used for no-load operating conditions and does not need to include the frontal components of the windings and the mechanical system (frontal closure elements of the case and mounting plate). It is only a partial 3D representation of the micro-motor, built for the cogging torque evaluation; it considers the rotation in magnetostatic operating conditions and it is solved using the magnetic vector potential formulation (1). No symmetry could be identified for the reduction of the model. Adequate boundary conditions ensure the magnetic insulation of the motor; regarding the magnetic vector potential A, the proper boundary condition ( n× A = 0) is set on the surface of an air volume which surrounds the 3D simplified geometry. Figure 3a shows the geometry for 10 degrees inclination and Figure 3b displays a convenient discretization mesh of the same structure, resulted from the trade between accuracy and available computational resources. Depending on the inclination angle, the discretization mesh generates a number of degrees of freedom in the range 3.3 ... 3.9 milions. The iterative method of conjugate gradient


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with SOR preconditioning is applied to solve the large system of equations, using 8 GB RAM.

a. 3D domain with inclined stator slots b. discretization mesh

Fig. 3 – 3D model in Comsol Multiphysics.

4. COMPUTATIONAL AND EXPERIMENTAL RESULTS

Computation of the magnetic field distribution. The stationary magnetic field is analysed, for comparison, with both FEMM and Comsol software packages. Magnetic field distribution is determined for no-load operation and respectively for different connections and feeding conditions of the three stator phase windings.

a. un-loaded motor (randomly choosen position of the rotor vs. the stator)

b. two phases are connected in series and fed by the rated current; the third phase is un-loaded

Fig. 4 – Magnetic field spectra (field lines and flux density colored maps) (in Comsol [10]).

Figure 4a shows the magnetic field lines and the colored map (greyscale) of the magnetic flux density for the un-loaded motor, while Fig. 4b reveals the magnetic flux density distribution with two phase windings connected in series and fed by the rated current; the analysis is performed with Comsol Multiphysics. By


postprocessing, one could determine some derived results: magnetic flux on the polar surface, electromotive force, averaged electromagnetic torque, cogging torque.

Evaluation of the induced electromotive force. One of the validation tests used to assess the precision of the simplified 2D numerical model refers to the evaluation of the electromotive force determined for the machine operating as generator under no-load condition, at 1000 rpm rotational speed. Table 1 shows the peak values of the electromotive force Epeak induced in one phase winding and the derived constant [ ] V/1000 rpmEk resulted from simulations with FEMM and Comsol Multiphysics, compared with the experimental results.

Table 1 Electromotive force

Epeak [V] kE V

1000 rpm

⎡

⎣ ⎢

⎤

⎦ ⎥

FEMM - 0.571 Comsol Multiphysics 0.334 0.583

Measurement 0.302 0.536

The oscillograms in Fig. 5 show the measured induced electromotive forces for one phase (a) and for the three phases of the stator winding (b). The peak values determined on the graphs are comparable with the computed ones.

a. one phase b. three-phase symmetrical system

Fig. 5 – Oscillogrames of the induced emfs measured at 1000 rpm speed.

Electromagnetic torque computation. Electromagnetic torque assessments used the Maxwell’s Stress Tensor, integrated on a cylindrical surface through the middle of the air-gap, where the discretization mesh was properly refined. Figure 6 shows the cogging torque, an operating quantity significant for the no-load operation conditions; it is computed over 15 geometrical degrees (30 electrical degrees), for comparison, by the 2D FEMM and Comsol simplified models and by the 3D


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Comsol model introduced earlier. One could observe the perfectly comparable outputs (same order of magnitude, same variation trend) and the small values, insignificant for operation at rated power. True values of the torque, for on-load operation conditions were computed by the two 2D models; Fig. 7a reveals the torque-angle characteristic determined when one single phase winding is fed and Fig. 7b shows the same type of characteristic when two phase windings are connected in series and fed at the rated current.

Fig. 6 – Cogging torque computed with FEMM vs. Comsol software, and 2D vs. 3D model.

The results obtained with FEMM and Comsol software packages are practically identical. One could also notice that cogging torque maximum local values are two orders of magnitude lower than the maximum local values of the averaged on-load torque (Fig. 7). The peak-value of the electromagnetic torque computed for one phase-winding is 0.5897 mNm, while the cogging torque values are under 8·10-3 mNm, which means under 1% of the averaged torque of the motor in normal operation conditions (three-phase winding simmetrically fed at rated current).

Comsol Multiphysics 3D finite element model was further used for an optimization study, considering the technological inclination of the stators’ slots; the cogging torque distribution was computed for a movement of the rotor over 30 geometrical degrees; inclinations of 5, 10, 15 and 20 degrees were considered and compared with no-inclination (0 degrees case). Fig. 8 shows all the computed cogging torque distributions and allows the assessment of the best inclination. As one could observe, the inclinations with 5 and 20 degrees are not suitable because the cogging torque presents higher local peaks than the no-inclination construction; the inclinations with 10 and 15 degrees produce the best results, i.e. the true reduction of the cogging torque peak values. This computational analysis suggests the best configuration of the construction, suitable for the prototype of the micro-motor. The 3D model could further contribute to the magnetic problem analysis, for the evaluation of on-load performance.


a. one single phase-winding fed with rated current

b. two phase-windings connected in series and fed with rated current

Fig. 7 – Torque-angle characteristics computed with FEMM vs. Comsol Multiphysics software packages.

Fig. 8 – Cogging torque computed by the 3D model, for different inclination angles of the stators’

slots (0, 5, 10, 15, 20 degrees)


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5. COMMENTS AND CONCLUSIONS

The work presented here includes a review of the concept, design and assessment experience aimed at fabricating a brushless DC permanent magnets micro-motor for aerospace applications. The construction is similar to a sinchronous motor with magnets mounted on a rotating exterior armature. With performance levels imposed on the torque, rotation speed, movement control, efficiency, fiability etc., related to the specific usage, the micro-motor prototype is designed and produced by Icpe, based on an original concept assisted by numerical simulation and experimental testing. The paper shows some stages of the project. Prototype fabrication and experimental tests validated two types of numerical models, both based on the finite element method: a 2D model (the cross-sectional plane) and a 3D model containing the magnetic core, the permanent magnets and the active part of the winding. For the computation of the magnetic field solution and derived quantities (cogging torque, on-load electromagnetic torque, induced electromotive force) both types of numerical models proved their utility as prospective tools for the optimization of the design and for operation characteristics pre-determination. The relative errors between the computed quantities with two different software packages (FEMM and Comsol Multiphysics for 2D problems) are under 2% for the torque-angle characteristic, while the errors fall under 10% when experimental and computational results are compared. The cogging torque values are situated in the same range and show the same distribution trend when computed with the 2D models against the 3D Comsol model. Prediction of various operation characteristics and optimization of the design could be performed using the 3D model; its proficiency is demonstrated for the computation of the cogging torque when different inclinations of the slots are considered.

ACKNOWLEDGEMENTS

The prototype of the micro-motor was fabricated within a research project from the STAR programme by the Center for Special Electrical Machines at Icpe. Extensive computational work was developed at the Laboratory of Numerical Methods, at the “Politehnica” University of Bucharest. The authors kindly appreciate the logistic support.

Received on March 28, 2014

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BRUSHLESS DC MICRO-MOTOR WITH SURFACE MOUNTED …