The main parameter to watch before proceeding with an analytical design is the magnet air gap flux density waveform. Samarium allows the user to control this as well as offering an automatic mechanism of generating the magnet waveform. The main reason the manual adjustment is provided is to take into account the magnetization, especially for multi-pole ring magnets. |
Once the number of poles has been set, the correct angle for the pole span has to be entered. Samarium offers three mechanisms of generating the air gap flux density waveform generated by the magnet. None of these methods take slotting into account as all three mechanisms assume the stator inner diameter to be a smooth cylinder similar to a slotless motor. The three mechanisms can be found in the Magnet page of the input property pages. They are
| 1. | Exponent: The magnet waveform is modeled using exponents and the waveform is built using the user supplied coefficients. The motor geometry is taken into account as well. |
| 2. | Harmonic: A Fourier series is used to generate the waveform. No user defined coefficients are used and only the geometry of the motor is considered. |
| 3. | Sigmoid: A sigmoid function is used and user defined coefficients define the shape of the waveform. |
It is important to check this waveform and model it correctly to enable the rest of Samarium to produce accurate results. Some examples of proper and improper waveforms are shown below along with the coefficients and method used to generate them. Once this waveform is being generated correctly, all other results like, flux densities in the stator lamination, back emf, cogging torque, and performance results follow automatically. Fine tuning the magnet waveform is made possible with these options.
Breadloaf- 4 pole rotor
Exponent: Frng = 3, Exp = 3 |
Harmonic |
Sigmoid: Frng = 0.1, Exp = 0.5 |
Incorrect waveform by Exponent: Frng = 0.1, Exp = 0.5
Ring- 8 pole rotor
Exponent: Frng = 0.3, Exp = 4 |
Harmonic |
Exponent: Frng = 0.3, Exp = 2.5 |
The above examples show three different waveforms generated for an 8 pole ring magnet. The waveform shown on the left is the actual waveform whose coefficients were adjusted after a prototype was built. The waveform in the center is generated by the Harmonic method and is not suited for ring magnets as the waveform generated may be impractical to implement. The waveform on the right is a modified waveform generated using the Exponent method that takes into account the magnetizing fixture capability. So the waveforms can be adjusted manually to fine tune an existing design and be used as a basis for new designs.
The air gap flux density patterns with ring magnets between analytical computations and finite-element analysis differ slightly in this version of Samarium as magnet shaping is not available in the FEA engine. The difference can be easily viewed after FEA as both the waveforms are plotted in the air gap flux density graph. This graph can be seen in the Multirun results page as well.