PROCESS IMPROVEMENT

Process Improvement Technique

Process Improvement Technique

Pareto Analysis for Increasing the Efficiency

The geometrical characteristics of the generator are shown in the figure below

The bore radius rs is related to the fundamental value of the air gap magnetic flux density (B1g) and the slot depth/bore radius ratio Rdr (Rdr = ds/rs) as follows:

(7)

where Kr is the slot filling coefficient. B1g is computed from the magnet properties (relative permeabilityµr = 1.05 and remanent induction Br = 1.1 T for NdFeB magnet) and from the electrical half pole width am:

(8)

where lm/g' represents the ratio between the magnet thickness and the air gap corrected by the carter coefficient. In these two equations, the unknown variables are set to typical values, i.e. Rdr = 0.25,Kr = 0.5, am ˜ 1.31 (i.e. 75°) and lm/g' = 3.5 while the Carter coefficient is set to 1.05.

The magnet width wm can be deduced from:

(9)

The generator air gap g is calculated from the empirical relation:

(10)

Tooth and slot widths are then obtained from the bore radius and the number of slots per pole per phase Nspp:

(11)

and the slot depth dS is given by:

(12)

dS=Rdrrs

Finally, the yoke thickness is obtained as follows:

(13)

where the maximum magnetic flux density in the air gap is evaluated from the following relation:

(14)

The generator masses are obtained from the volume of each constitutive element and from the corresponding mass density. The rotor volume Vrotor can be approximated as:

(15)

where rrotor = rs - g - lm and dR = dy. The corresponding mass is given by:

(16)

Mrotor=Vrotor?iron

The stator volume Vstator is composed of yoke and teeth volumes

(17)

Vstator=Vteeth+Vyoke

which can be approximated as follows:

(18)

The corresponding mass is

(19)

Mstator=Vstator?iron

The total iron mass in the generator can be expressed by summing stator and rotor iron masses

(20)

Miron=Mstator+Mrotor

Similarly, the magnet volume is given by:

(21)

and the corresponding mass by:

(22)

Mmagnet=?magnetVmagnet

with ?magnet = 7400 kg m-3.

Finally, the copper mass is deduced from the copper volumes in the slots and in the winding heads

(23)

which implies

(24)

The total mass of the generator is then approximated by summing the masses related to each component:

(25)

Mmotor=Miron+Mcopper+Mmagnet

Electromagnetic parameters of the generator are computed from the previous geometric variables. In particular, leakage inductances Ll are obtained from [22] by considering a trapezoidal slot as shown in Fig. 3

(26)

where Ncs denotes the number of conductors per slot and where the ?s coefficient depends on the slot geometrical characteristics (27) and (28).

(27)

with

(28)

The main inductance Lm can be expressed as:

(29)

where the winding factor K1b is given by the following relation:

(30)

The corresponding stator inductance Ls is defined as follows:

(31)

It can be noted that these inductance values can also be computed from the generator geometric features with the Finite Element Method [17] and [18] for a better accuracy.

The magnetic flux Fs and the stator resistance Rs are defined as follows:

(32)

Fs=2K1bNsppB1grslrNcs

(33)

Finally, the generator current Is can be obtained from the current density Js:

(34)

To compute all parameters of the generator, the number of conductors Ncs in one slot has to be determined. It should be designed in order to fulfil the operating conditions at the base point. The permanent magnet machine must be able to provide the base torque Tm = Tb under the supply voltage Vm = Vb at the electrical pulsation ? = ?b. By setting Ncs = 1 in Eqs. (26), (29), (32), (33) and (34) circuit variables Ll1, Lm1, Ls1, Fs1Rs1 and Is1 can be obtained for one conductor per slot:

(35)

By considering the electrical diagram of the generator (see Fig. 4), operating at the base point (Tb, ?b), the number of conductors in one slot can be obtained by solving (36):

(36)

Thanks to the calculation of the circuit parameters (Rs, Ls, Fs), a circuit (a,bc) 3-phase model can be derived. This latter model will be considered as the “reference model” of the ...