This paper deals with the investigation of the behavior of a low speed, dual rotor-single coreless stator, axial flux permanent magnet synchronous machine for small power applications. Firstly, with the use of nonlinear 3D FEM electromagnetic analysis, four models with different magnet topologies are designed, simulated and compared. With criteria such as output power, power factor and torque ripple, the best performing model is selected and a further investigation, regarding the effect of the disk rotor material on the behavior of the machine, is conducted. The simulation results show how the different types of commercially available steel types affect the magnetic field and the performance of the machine.
Over the last decades, the increasing interest in the study of axial flux permanent magnet synchronous machines (AFPMSM) has led to a variety of designs and applications for this type of machines. Their uses as generators in small-scale wind turbines, in electrical vehicles and in robotics are some of their usual applications [
With the current availability of high energy magnets, the stators of AFPM brushless machines can be fabricated without cores. Specifically, a coreless design reduces the mass while increasing the efficiency of the machine [
Contributions regarding AFPMSM with iron cores can be found in the literature dealing mainly with the effect of magnet shape on the quality of the electromagnetic torque and the cogging torque reduction [
The machine used in this study consists of a twin rotor with neodymium-iron-boron NdFeB magnets and the coreless stator winding, embedded in resin, located between the two rotors [
The complexity of the machine’s geometry is such that does not allow accurate solution through analytical equations. The finite element method (FEM) was used instead, where the model body can easily be analyzed in several discrete finite elements for which the Maxwell equations can be applied. For this particular model geometry, the nonlinear 3D FEM analysis was selected and achieved using a solver which can be used to compute electromagnetic fields including the effects of eddy currents in moving systems in three dimensions, of the Cobham Opera software [
The under investigation machine (3-phase generator with two rotors and one inner stator) whose parameters are chosen according to the good and safe operation of the machine [
The σr parameter expresses the ratio between inner to outer radius of the active part of the stator winding. The optimum value is σr = 0.577 [
According to the parameters above, the following four Axial Flux Permanent Magnet (AFPM) machine models were designed in 3D while preserving all properties and dimensions (rotor width, B-H curves, stator coils) except the magnet shape. The material for the two rotors is steel and each one has sixteen permanent magnets (neodymium- iron-boron NdFeB) mounted evenly on the surface.
Number of poles p | 16 |
---|---|
Nominal frequency f | 50 Hz |
Nominal rotational speed | 375 rpm |
Axial rotor width | 5 mm |
Axial magnet width | 10 mm |
Axial air gap | 3 mm |
Radius ratio |
Number of magnets | 32 16 per rotor disc |
---|---|
Number of coils Q | 12 4 coils/phase |
Axial stator width | 13 mm |
Outer radius ro | 122 mm |
Inner radius ri | 59 mm |
Number of turns per coil | 210 turns |
The stator is coreless and it consists of twelve concentrated, non overlapping, trapezoidal coils immersed in a resin type material with air characteristics. There is a variety of non overlapping coil topologies such as trapezoidal, rhomboidal, hexagonal and circular coils. Trapezoidal coils can achieve the best use of the magnetic field, however due to their large non active areas, this results in more copper losses. Rhomboidal coils do not have non active areas and copper losses are minimized, but this characteristic has the disadvantage to exploit less magnetic field than the trapezoidal coils. Hexagonal shape is a combination of the previous two coil types which can have significant difficulties in construction process. Finally, circular coils are not preferable due to their limited active part [
Considering the Finite Element Analysis (FEA) models, proper mesh size must be used at the different parts of the machine regarding the accuracy of the computation results. The most dense mesh design is needed for the air-gap area. The number of the surface elements is ~65000, the volume elements ~275000 and the required time for one time-step iteration is ~5 min with Intel Core i5-3570K CPU @ 3.5 GHz, 16 GB RAM and 64-bit operating system.
As previously stated, the impact of magnet design in the machine performance is under investigation. The categorization of the magnets depends on their shape, hence their label categorization as radial, conventional skew, dual skew and finally triangular skew magnets [
In order for the simulation results to be comparable, all model dimensions and test conditions apart from the magnets shape were kept unaltered. The magnets used in the simulation are NdFeB, grade Ν42.
Radial | Conventional skew | Dual skew | Triangular skew |
---|---|---|---|
1512 mm2 | 1469 mm2 | 1641 mm2 | 1688 mm2 |
All four 3D FEM models were simulated in open loop condition as well as under load of 60 Ω/phase in star (Y) formation. All simulations were performed for the nominal speed of 375 rpm. The nonlinear 3D FEM analysis was selected and achieved using a solver which can be used to compute electromagnetic fields, including the effects of eddy currents, in moving systems in three dimensions.
Due to the shape of the magnets, each model displays a different magnetic field, with different magnitude and space distribution. This can be observed in
Using the same OPERA 3D solver, which takes into account the rotor revolution, several time-varying electromagnetic variables were extracted. The nominal speed of 375 rpm was once again applied in the open-loop condition. It was also performed a reversed revolution simulation of equal rotational speed, because of the asymmetric geometry of the conventional and dual skew magnet models.
The dual skew model produces the maximum voltage, followed by the triangular skew model. As regard to the reversed revolution simulations, the results indicate that
Magnet topology | Open loop Voltage (Vrms) |
---|---|
Radial | 129.45 V |
Conventional skew | 122.77 V |
Conventional skew (reverse) | 121.91 V |
Dual skew | 132.68 V |
Dual skew reverse | 131.52 V |
Triangular skew | 131.80 V |
there is small difference in voltage output values in comparison with the normal rotating models. Specifically, conventional skew and its reversed model have a 0.7% difference and dual skew and its reversed model have a 0.9% difference. Consequently, conventional and dual skew magnet topologies can be used for both directions of rotation without having significant variation in output values.
While preserving the nominal rotational speed at 375 rpm, a three-phase star connected (Y) load of 60 Ω/phase was connected.
As expected, each model produces different voltage output and torque waveforms depending on the magnet topology. In
In
The torque waveforms are presented in
Although most published studies refer to similar AFPM topologies, their main focus is the minimization of cogging torque. Despite the lack of stator cores in this type of generator, meaning no cogging torque and less stator weight, there is still interest in studying how these magnet designs affect the torque waveform [
Magnet topology | Input Power Pin (W) | Output Power Pout (W) | Torque average value Τ(Nm) | Voltage rms value Vph (V) | Current rms value Iph (A) | Power factor (%) |
---|---|---|---|---|---|---|
Radial | 731.8 | 664.4 | 18.6 | 115.3 | 1.92 | 90.8 |
Conventional skew | 650.8 | 592.4 | 16.6 | 108.9 | 1.81 | 91 |
Dual skew | 756.4 | 689.5 | 19.3 | 117.4 | 1.96 | 91.2 |
Triangular skew | 746.1 | 681.8 | 19 | 116.8 | 1.95 | 91.4 |
Conventional skew reverse | 648.5 | 592.4 | 16.5 | 108.9 | 1.81 | 91.3 |
Dual skew reverse | 756.4 | 686.3 | 19.3 | 117.2 | 1.96 | 90.6 |
Torque ripple-induced vibration can be amplified because of other mechanical system parts, creating acoustic noise. The effects of torque ripple are unpleasant in more challenging motion control and machine-tool applications because of speed fluctuations that degrade the performance [
As known, the amplitude of torque ripple increases at low speeds. In addition, the effect of the moment of inertia that tends to absorb shaft speed variations, is less significant at lower rate of speed fluctuations. A smooth air-gap torque is particularly desired at low speed [
To achieve the comparison between torque ripple pulsation of the simulated models, the mean square error equation is used. This allows the calculation of the deviation between the waveform of torque ripple of each model and the reference waveform of torque. As reference waveform of torque a straight line, time-invariant and equal to the mean value of each topology, is used.
As the MSE (mean square error) result tends to zero, the torque ripple error diminishes, resulting to values that approach the mean torque value. In comparison, the further the MSE value is distanced from zero, the greater the error and so the torque waveform ripple from the average value [
where:
The calculated results are shown in
Magnet topology | Torque ripple MSE (%) |
---|---|
Radial | 2.3 |
Conventional skew | 3.7 |
Dual skew | 2.2 |
Triangular skew | 3.9 |
Conventional skew reverse | 3.7 |
Dual skew reverse | 2.8 |
Considering this study is intended for the construction of a small scale application, the main desire is to obtain maximum torque and output power for low speed usages, while maintaining the construction lighter (no extra weight from stator cores) and at a minimum level of complexity.
The under investigation simulation models were compared for the same load and revolution speed. Summarizing the already established results, the models that show the best performance regarding the output power and torque, are Dual and Triangular skew magnet models. On the other hand, comparing the torque oscillations the best models are the Radial and Dual skew magnet models. However, as the simplicity and the cost of production must be taken under consideration too, the model selected for further investigation was the Triangular skew magnet topology, as shown in
The selected model with triangular magnets was further simulated for several rotor disk materials. As the magnetic flux orientation of the used magnets is axial, it is necessary that the rotor material presents ferromagnetic characteristics as to assist and amplify the direction and density of the magnetic flux. Therefore, six different types of steel, commercially available, were selected to be tested.
Steel, is actually a lab sample of extremely soft iron with almost no impurities, created for our solver software by Thyssen, as an all purposed steel [
Stainless steel 304 is the most common stainless steel. It is not very electrically or thermally conductive and is non magnetic. It has a higher corrosion resistance than regular steel and is widely used because of the ease in which it is formed into various shapes. Also it has excellent resistance to a wide range of atmospheric environments and many corrosive media. Stainless steel 304 is used for a variety of household and industrial applications such as screws, machinery parts, car headers etc [
Stainless Steel (SS) 416 is a martensitic free machining grade of stainless that can be hardened by heat treatment to achieve elevated strength and hardness. Due to its low cost and ready machinability, stainless steel 416 is readily used in its highly tempered state. It exhibits better machining characteristics than austenitic grades, however, sacrifices corrosion resistance. High sulfur, free-machining grades like Alloy 416 are unsuitable for marine or any chloride exposure situations. Stainless steel 416 can be supplied for any project big or small [
Silicon steels, are used for electrical transformer cores and cores of other electrical devices for the following reasons: a) low hysteresis loss, b) high permeability, c) high resistance and d) virtually eliminated ageing. However, the primary reason is the low hysteresis loss caused due to the impeding action of silicon atoms in the path of eddy currents [
Electrical steel M19, also called lamination steel, is specialty steel tailored to produce certain magnetic properties, such as a small hysteresis area (small energy dissipation per cycle, or low core loss) and high permeability. The material is usually manufactured in the form of cold-rolled strips less than 2 mm thick. These strips are called laminations when stacked together to form a core. Once assembled, they form the laminated cores of transformers or the stator and rotor parts of electric motors [
Plain carbon-mild steel is a metal alloy and it is a combination of two elements, iron and carbon. Mild steel is the most common form of steel as its price is relatively low while it provides material properties that are acceptable for many applications. Mild steel has a low carbon content (up to 0.3%) and is therefore neither extremely brittle nor ductile. It becomes malleable when heated, and so can be forged. It is also often used where large amounts of steel need to be formed, for example as structural steel [
In
The under investigation models, with different rotor material, were simulated. The calculated axial magnetic flux density in a radial length of 90.5 mm, along the z axis is presented in
The axial width of the model is approximately 50 mm. The magnetic flux must be confined in the limits of the axial width. The ferromagnetic properties of the various steel types, used in the rotor disks, provide a path through which the magnetic flux is maintained within the rotor disks. The variety of relative magnetic permeability (μr) of the materials in the linear region and also the effect of the B-H curves on the output open loop voltage are presented in
All steel types, despite their different physical and magnetic properties and chemical composition, seem to have similar effect on the back EMF, with the only exception of
Rotor material type | Relative magnetic permeability (μr) | Open loop phase voltage (Vrms) |
---|---|---|
Steel (soft iron) | ~4600 | 130.7 V |
Stainless steel 304 | 1 | 91.34 V |
Stainless steel 416 | ~750 | 128.3 V |
Silicon steel | ~3500 | 129.8 V |
Electrical steel M19 | ~3700 | 130.2 V |
Mild steel (1020 plain carbon steel) | ~1000 | 128.5 V |
the stainless steel 304 that presents significantly lower output voltage. The later happens because this type of material demonstrates properties similar to air (μr ≈ 1) [
As shown in
As seen from
The purpose of this paper was to investigate the behavior of a low speed axial flux permanent magnet synchronous generator for small power applications, providing options considering the operational behavior, the desirable construction complexity, the availability of material and the cost. Firstly, the chosen parameters of the AFPM machine were indicated, as well as, the calculated variables from the analytical equations. Using nonlinear 3D FEM electromagnetic analysis, the selected AFPM models preserving all properties and dimensions except the magnet shape were simulated. Performance results under both open loop and load were extracted. The simulation results were compared and a further investigation in torque ripple for each model was performed. The
Resistance/phase | Torque | Vphrms | Iphrms | Pin | Pout | Power factor | |
---|---|---|---|---|---|---|---|
(Ω) | (Nm) | (V) | (A) | (W) | (W) | (%) | |
Steel | 18 | 38.7 | 82.3 | 4.6 | 1519.7 | 1139.2 | 75 |
40 | 24.6 | 106 | 2.65 | 966 | 843.11 | 87.3 | |
60 | 19 | 116.8 | 1.95 | 746.1 | 681.8 | 91.4 | |
216.6 | 5.7 | 126 | 0.58 | 224.2 | 220.1 | 98.2 | |
Mild Steel | 18 | 38.8 | 82.7 | 4.6 | 1523.7 | 1141.85 | 74.9 |
40 | 24.4 | 105.6 | 2.64 | 958.2 | 837.4 | 87.4 | |
60 | 17.9 | 113.3 | 1.89 | 703 | 642.2 | 91.4 | |
216.6 | 5.6 | 125.2 | 0.58 | 219.9 | 217.4 | 98.8 |
triangular skew magnets model was chosen because of its high output power, power factor, low cost and the simplicity of production. A more extensive analysis was performed regarding the rotor disk material on the selected model. Finally, the simulations have shown how the different types of commercially available steel affect the magnetic field and the performance of the machine.
This work was supported by the Laboratory of Electromechanical Energy Conversion of Electrical and Computer Engineering Department in the University of Patras, Greece and its members.
Kappatou, J.C., Zalokostas, G.D. and Spyratos, D.A. (2016) Design Optimization of Axial Flux Permanent Magnet (AFPM) Synchronous Machine Using 3D FEM Analysis. Journal of Electromagnetic Analysis and Applications, 8, 247-260. http://dx.doi.org/10.4236/jemaa.2016.811023