Switched Reluctance Machine (SRM)

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1 Switched Reluctance Machine (SRM) 3D FEA Analysis using MagNet Jerry Foshage - RCT Systems 1 Wind and Water Power Technologies Office eere.energy.gov

2 Acknowledgment & Disclaimer Acknowledgment This material is based upon work supported by the Department t of Energy, Office of Energy Efficiency & Renewable Energy, under Award Number DE-EE Disclaimer This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. 2 Wind and Water Power Technologies Office eere.energy.gov

3 Background This effort studied novel concepts for an Axial Gap Reluctance Machine to capture energy from marine hydrokinetic sources and compared their attributes to a Radial Gap Reluctance Machine which was designed under a prior Department of Energy program for the same application. Detailed electromagnetic and mechanical analyses were performed to determine the validity of an Axial Gap Switched Reluctance Machine concept and to provide a direct comparison with the existing conventional Radial Flux Switched Reluctance Machine designed during the Advanced Wave Energy Conversion Project. While 2D FEA is sufficient for the radial machine analysis, this alternate axial gap topology requires 3D FEA. Infolytica s Magnet FEA tool enabled timely analysis of the 3D structures and were key to the on time completion of the project. 3 Wind and Water Power Technologies Office eere.energy.gov

4 Baseline Machine Comparison The axial gap machine topology changes the orientation of the flux that is switched flowing axially rather than radially and the poles themselves are long radially, as opposed to the radial flux machine that has pole pieces that are long axially. 4 Wind and Water Power Technologies Office eere.energy.gov

5 Rotary SRM Requirements Parameter Machine Requirements System Requirements Rated Force (Linear, kn) 100 Rated Speed (Linear, m/s) 1 Stroke (m) 5 SRM Requirements Linkage Interface Requirements System Power Air Gap Shear Force (Circumference, kn) Diameter at Airgap (m) Pole Number 24 Diameter Overall (m) 1.2 Length per Phase (of 3) (m) 0.4 Length Overall (m) 2 Weight (lb) Air Gap/Drum Diameter Ratio 3.2 Torque (knm) Max Angular Speed Linear) (rad/sec) Electrical Frequency Linear) (Hz) Max PTO Point Power (kw) 100 Rated Average Power (Wave Input, kw) 60 Continuous Rotation Test Mode (kw) Wind and Water Power Technologies Office eere.energy.gov

6 Radial Gap Machine Design Overview Three phases are isolated magnetically and electrically Variable Reluctance (VR) machines have a large negative stiffness due to ferromagnetic attraction Structural & bearing stiffness must be 5-10X for stability Geometry Slice for FEA Parameter Model Unit Pole (N) 28 deg Pole Span deg ID m OD m Mean Gap Dia m Air Gap m Tooth Width m V/(T+V) Length m Thickness sbi m Thickness rbi m Depth ss m Depth rs m 6 Wind and Water Power Technologies Office eere.energy.gov

7 Radial Gap Machine 2D Analysis 7 Wind and Water Power Technologies Office eere.energy.gov

8 Axial Gap Machine Geometry Parameter Model Unit Pole (N) 56 deg Pole Span deg ID m OD m Mean Gap Dia m Air Gap m Tooth Width 2.89 deg V/(T+V) Length 0.9 m Thickness sbi m Thickness sei m Depth ss m Depth rs m 8 Wind and Water Power Technologies Office eere.energy.gov

9 Modeling Approach Parameterized models are very beneficial for rapid analysis, trades and optimization of different geometries. A motion component that included the rotor, two air gaps closest to the rotor tooth and the rotor air box enabled transient analysis with minimal remeshing for faster analysis times was critical for a successful analysis effort. Even periodic boundary conditions on the radial planes and a normal boundary condition on the mid plane were used to minimize problem size. For initial model validation, a preliminary coarse mesh and static solution using linear materials were generated at the tooth aligned and unaligned positions to verify model mesh integrity it Non-linear ferromagnetic material properties were also used in final design analysis. Ferromagnetic material conductivity was set to zero; eliminating eddy currents assumes that with proper lamination, eddy currents will be manageable. Traditional analyses are based on the weight of the iron, the electrical frequency and flux density (Steinmetz model) to account for core losses. 9 Wind and Water Power Technologies Office eere.energy.gov

10 Generic 3D Model Typical Static ti Solution, Linear Material, Unaligned (L) and Aligned (R) 10 Wind and Water Power Technologies Office eere.energy.gov

11 Model Geometry, Boundary Conditions & Mesh 11 Wind and Water Power Technologies Office eere.energy.gov

12 Modeling & Analysis Approach For initial model validation, a preliminary coarse mesh and static solution using linear materials were generated at the tooth aligned and unaligned positions to verify model mesh integrity. The mesh was refined, globally by setting a maximum limit to the size and a local limit was applied to the two gap regions closest to the gap midline. The following illustrates the Flux Density results for one design point. Subsequently, a nonlinear material (1010 Steel) was implemented and resulted in improved solution accuracy with an insignificant increase in solution time. The maximum gap mesh size value was varied to achieve acceptable solution accuracy without undue increase in problem size or solution time. The following two slides shows the torque accuracy improvement versus rotor position. Transient solver with motion was implemented next. 12 Wind and Water Power Technologies Office eere.energy.gov

13 Flux Density Plots Tooth Geometry Effects Parallel l Side (L) vs. Angular Side (R), Geometry & Flux Plots 13 Wind and Water Power Technologies Office eere.energy.gov

14 Mesh Refinement Sensitivity Torque Per Half Tooth vs. Position 56 Teeth A - 6 Turns mm Gap ue (Nm) Torq m Max Gap Element 1333NI m Max Gap Element 1333NI.0025 Max Gap Element 1333NI -600 Position (Deg) 14 Wind and Water Power Technologies Office eere.energy.gov

15 Trades & Mechanical Support With an acceptable torque accuracy obtained, parametric sensitivity studies were preformed. The nominal gap was varied first to obtain a method to evaluate axial stiffness. Three currents were evaluated at each gap. Force, torque and flux linkage were obtained and plotted for various gaps, A typical result for 2.5 mm is shown in the following slides. 15 Wind and Water Power Technologies Office eere.energy.gov

16 Axial Gap SRM FEA Results 1 Coil Per Phase 16 Wind and Water Power Technologies Office eere.energy.gov

17 Axial Gap SRM FEA Results 1 Coil Per Phase 17 Wind and Water Power Technologies Office eere.energy.gov

18 Typical Analytical Results 18 Wind and Water Power Technologies Office eere.energy.gov

19 Trades & Mechanical Support Note that the results must be multiplied by 2 times the number of teeth (NT) to yield a total t machine torque result; likewise i for the flux linkage. The y axis force must be multiplied by the number of teeth to yield a correct result and will cancel with the other half or mirror of the tooth geometry. Therefore, no axial force exists when the rotor is axially centered. However, these forces are present in the stator structure and must be considered in the structural and bearing designs. Parametric evaluations besides the gap and current studies included sensitivity to changes in the Mean Tooth Width to Height ratio (a - Alpha) Tooth Width to Valley Width ratio (b - Beta) Core Material (CM) and Number of Teeth (NT) 19 Wind and Water Power Technologies Office eere.energy.gov

20 Alternate Multi Coil Design Model The design and simulation of the single coil winding model showed that despite the benefits to winding only a single coil versus many individual pole coils the large thickness of iron in the axial direction as back iron to get the flux along to the teeth as well as the back iron channeling the flux around the coil increase the dimensions and weight to where desired benefits against the radial machine were not realized. The focus was shifted an axial flux design that does not require radial channeling of the flux along the radially directed teeth of the axial flux machine. Most of the simulation and trade-offs above are relevant to the dimensions of the rotor / stator pole / slot structure. The model geometry was easily modified and parameterized. 20 Wind and Water Power Technologies Office eere.energy.gov

21 Multi Coil Design Model The flux density plot in the following slide illustrates how the magnetic flux now travels axially through teeth and then splits, traveling circumferentially through two parallel paths in the disk of iron (top wedge in the FEA model shown in Figure 27) that supports the stator tooth. No flux path is needed at the ID or OD as was the case with the single coil configuration. The coil on each tooth structure has a lower mass of material than the single coil configuration. The lower weight comes at the cost of an associated increase in complexity of multi coil connections. This configuration is most similar to an axial embodiment of the baseline radial gap SRM. The value of taking time to parameterize the 3D FEA models facilitated the study of key parameter variations and led to the discovery of benefits of the straight tooth with a radially diverging slot taper in high tooth count configurations. 21 Wind and Water Power Technologies Office eere.energy.gov

22 Axial Gap SRM FEA Model 1 Coil Per Tooth Parallel Sides 22 Wind and Water Power Technologies Office eere.energy.gov

23 Axial Gap SRM FEA Results 1 Coil Per Tooth - Radial Sides 23 Wind and Water Power Technologies Office eere.energy.gov

24 Axial Gap SRM FEA Results 1 Coil Per Tooth - Radial Sides 24 Wind and Water Power Technologies Office eere.energy.gov

25 Negative Stiffness The axial forces also produce a negative linear and angular stiffness present between the rotor and stators. The rotor and stator mechanical structure and bearings must have net positive stiffness 5 to 10 times larger than the negative stiffness to insure the structure is stable and the gap dimensions i can be maintained. i The negative stiffness also has an effect on modal analyses, as it lowers the resonance of the axial mode. The parameter variation results show the axial stiffness is negative and decreases as the nominal gap increases approximately as the ratio of the gap. 25 Wind and Water Power Technologies Office eere.energy.gov

26 Negative Stiffness Model Multi-coil Machine 26 Wind and Water Power Technologies Office eere.energy.gov

27 Negative Stiffness The previous Figure shows the stiffness plot vs. current levels, on a per tooth pair basis for the aligned teeth case. The stiffness begins to roll off with NI at and above the 4000 AT range due to saturation effects. Based an approximate worst case -4E6 N/m stiffness result and multiplying by the number of teeth pairs (28) a phase stiffness of -1.1E8 N/m is calculated. Series combination of the stiffness of all mechanical elements in the structural path should have a resultant stiffness on the order of 1.1x10 9 N/m per phase. The negative stiffness must also be considered when evaluating structural resonances because the reduced stiffness lowers the resonant frequencies. 27 Wind and Water Power Technologies Office eere.energy.gov

28 Torsional Negative Stiffness Estimation In addition to the negative axial magnetic stiffness, the SRM machine also has a negative torsional magnetic stiffness that must be considered d in the machine design. Given the size limit on the FEA analysis, performing a torsional stiffness analysis of an entire rotor is not feasible. Therefore, the torsional stiffness is calculated from the tooth pair analysis results. 28 Wind and Water Power Technologies Office eere.energy.gov

29 Torsional Stiffness Estimation Formulation 29 Wind and Water Power Technologies Office eere.energy.gov

30 Negative Stiffness From the axial stiffness analysis, the peak forces and negative stiffness occur when the teeth are aligned; the same is true for the angular stiffness. For the maximum angular stiffness, the aligned tooth position is used and an angular displacement gamma (g) is assumed about any axis normal to thespinaxis(yaxis) (y-axis). The resulting change in gap (Dg) at the midpoint of each tooth is found. Using the Dg at each tooth, an estimate in the change in force for each tooth is calculated and using the distance from the axis of rotation the torque is calculated. Summing the resultant torques for all the teeth and dividing by the angle yields the estimated angular stiffness. Only one quadrant need be analyzed and the result multiplied by 4 times to obtain the total angular stiffness value between the rotor and stators of one phase. 30 Wind and Water Power Technologies Office eere.energy.gov

31 Typical Torsional Stiffness Result Parameter Value Unit No. Teeth 28 No. Teeth per Q 7 Mean Radius m Nominal Gap m Max Delta Gap m Angular Tilt radian Pole Span radian Force 823 N Torque 1325 Nm Torsional Stiffness 8.20E+06 Nm/rad 31 Wind and Water Power Technologies Office eere.energy.gov

32 Conclusions Parameterized models are very beneficial for rapid analysis, trades and optimization of different geometries but require some up front investment A motion components with adjacent regions for rapid re-meshing enabled transient analysis very fast analysis times. Boundary conditions significantly reduce problem size. Non-linear ferromagnetic material properties and effects easily included in the analyses. Global and local mesh refinement in the gap allow for tailoring of problem size versus solution time. Transient solver with constant velocity motion enabled easy data generation Exporting to Excel and MatLab/Simulink enabled seamless interface with power electronics and mechanical engineers. Infolytica s Magnet enabled the magnets analysis effort to be completed on time and on budget. 32 Wind and Water Power Technologies Office eere.energy.gov

33 Contact Information Jerry Foshage RCT Systems Inc. 1745A West Nursery Rd. Linthicum, MD Phone: Cell: Fax: Wind and Water Power Technologies Office eere.energy.gov

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