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Modular PM Machines Based on Soft Magnetic Composite (SMC ). Prof. T.A. Lipo Wen Ouyang (Ph.D Candidate) University of Wisconsin-Madison April, 2006. Introduction.
Prof. T.A. Lipo
Wen Ouyang (Ph.D Candidate)
University of Wisconsin-Madison
Electrically Insulated Fe-powder Particles
Typical SMC micro-structure
Technology improvement narrows the gap between steel and SMC.
Core Loss (W/kg) Measurement from Ring Sample (OD55 ID45 H5 mm)
(according to CEI/IEC 60404-6)
Although the hysteresis loss of SMC is higher than conventional lamination, better eddy characteristics makes it suitable for applications with high frequency excitation.
Two phase (virtual 4 phase)
With higher γ, which means larger slot opening, the fundamental suffers with increased harmonic components.
With a rectangular design (χ=0), the fundamental reaches maximum while the same occurs for the harmonic components.
Note: scale is different
Comparisons of two phase and three phase design with trapezoidal pole shape
Comparisons of two/three phase design with trapezoidal/sinusoidal pole shape
PRrated output power
K = Ar /As, ratio of electric loading on rotor and stator. In a machine topology without a rotor
m number of phases of the machine
m1 the number of phases of each stator (if there is more than one stator, each stator has the same m1).
Keemf factor that incorporates the winding distribution factor Kw and the ratio between the area spanned by the (salient) poles and the total air gap area.
Kia current waveform factor in order to indicate the effect of the current
the current i(t) and Iphmax are the phase current and the peak phase current, Irms is the rms current.
Kpwelectrical power waveform factor,
where fe(t)=e(t)/Epk and fi(t)=i(t)/Iphmax are the expressions for the normalized emf and current waveforms. e(t) and Epk are the phase air gap EMF and its peak value. T is the period of one cycle of the emf.
KL , defined as the aspect ratio coefficient
o , the diameter ratio
the machine efficiency,
Bgmaxflux density in the air gap
A total electric loading, including stator and rotor loading
Nt the number of turns per phase,
f the power supply frequency
p number of machine pole pairs
Finally, the machine power density for the total volume can be defined as:
where Lt is the total length of the machine including the stack length and the protrusion of the end winding from the iron stack in the axial direction.
Machine assembly and module profiles
Two main design methodologies are applied in this project: 1) Analytical. 2) FEA.
The analytical method is based on a closed form analysis of the machine equations.
Advantages: 1) Concise formula for the machine performance.
2) Explicit dependency of machine design parameters.
3) Easy for optimization.
Disadvantages:1) Errors associated with nonlinearity and complexity of
FEA method is based on the numerical method analysis derived from Maxwell equations.
Advantages: 1) Very accurate solution for the machine performance.
2) Direct geometry modeling and analysis.
1) Computation cost, especially for 3D.
2) Difficulty to achieve global optimization.
pros: 1) Simple algorithm.
2) Global optimization.
3) Parameter impact information can be obtained.
4) Practiced quite a lot from aerospace engineering, such as plane wing
shape design. But few reports on machine design in IAS since 2000.
cons: 1) If the parameter number is 10, the sampling points
for the initial solution space will be 3^10=59049, which is 41 hours
CPU time if each point FEM simulation takes 1 minute.
2) Data analysis method is necessary to reduce the polynomial error.
3) High number of parameters (over 15) will take too much time on the
solution space construction, resulting in an unfeasible approach.
The coefficients are evaluated by regression.
The error of the model is less than 1% of the FEM prediction in most cases.
Stator side: (1) Stator outer diameter (2) Stator inner diameter
(3) Yoke thickness (4) Slot width (5) Slot opening
Rotor side: (1) Rotor outer diameter.(rotor inner diameter does not matter much)
(2) 2~4 parameters for surface PMs or 4~6 parameters for IPM.
Air gap: This is a very sensitive parameter, can be fixed based on
mechanical suggestion. Thus, the rotor outer diameter is
dependent on the stator inner diameter if air gap is selected at the
very beginning, which reduces the rotor side parameters!
The machine stator module can be defined by six main parameters:
1) Stator out radius. 2) Stator yoke thickness. 3) Stator inner radius.
4) Tooth span angle. 5) Tooth body width. 6) Tooth tip thickness.
The PM span and PM thickness are key parameters, with extra 1 or 2 parameters necessary if the PM is not a regular shape.
The bridge width is fixed due to the saturation and stress consideration.
5 parameters are necessary for the definition of a typical IPM rotor structure.
Optimization for maximum torque and acceptable efficiency
Optimization for limited field weakening capability and torque capability
Due to large tooth piece design, the machine inductance is inherently dependent on
rotor position, the associated energy variation produces cogging torque.
Optimization of module structure to minimize the back EMF harmonics is one of the optimization objectives.
SPM and IPM Rotor Concept Comparison
Back EMF waveforms
Back EMF Harmonics
where v, e, i, λ denotes the vector of phase terminal voltage, back emf, current, and flux linkage:
Adjacent phases out
Non-adjacent phases out
Speed & Torque
MOSFET Drive Circuit