Sizing the drive system - Propulsion Systems for Hybrid Vehicles - page 172

and from this using a post-processing calculation of the Maxwell shear force at the
rotor surface (after averaging over the pole pair area).
The machine design is further constrained by a mechanical limit - the rotor
burst condition. For this constraint it is common design practice to limit the
machine rotor tangential velocity to < 200 m/s. Surface speeds in excess of this lead
to retention issues of various sorts, windings, magnets etc. It is interesting that the
mechanical limit is linear with angular velocity and not quadratic as application of
material stress analysis would reveal. The following summary of large electric
machines in which rotor diameter, power rating and surface tangential speed are
listed supports the engineering practice of limiting rotor speeds according to a
linear velocity constraint [23].

Table 4.9 Mechanical constraint: large electric machines

Machine rating (MW) Cooling method Rotor diameter (m) Rotor surface

speed (m/s)

25 Air 0.75 141

120 Air 0.95 179

150 H 2 1.1 207

320 Water 1.15 217

757 Water 1.06 199

932 Water 1.25 235

Note :H 2 means hydrogen cooling. All machines are 2-pole.

Table 4.9 supports the engineering practice of limiting electric machine rotor
tangential speeds to less than 200 m/s. At higher speeds the issues of critical speed
flexing, rotor retention and eccentricity become major concerns.
When the electric machine fundamental sizing constraints are applied to a
hybrid propulsion M/G, it is found that magnetic pole pairs become a strong
function of the machine aspect ratio.
In Figure 4.18, the three ragged hyperbolic traces are stator outer diameter,
D so , rotor diameter, D ro , and rotor inner diameter, D ri . The rotor inner diameter
defines the hub OD. In this plot the stator winding aspect ratio, z h t , of lamination
stack length, h , to pole pitch, t p , is confined to the range, 1 < z h t < 1.5. In this
example z h t = h / t p = 1.1, so that circumferentially a pole pitch is somewhat shorter
than the stack length. This puts more of the stator copper in slots as active material
rather than in the end turns as a loss contributor. The two limit lines in the chart
define the package and mechanical constraints. Rotor mechanical burst limits based
on maximum shaft speed is labelled as D ro_lim , whereas the stator package limited
OD is listed as D so_lim . This analysis shows that for the power level given, only
stack lengths greater than about 50 mm are admissible in order to meet the package
limitation. If the limitation had been due to rotor burst limits, then stack lengths
down to about 34 mm would have been admissible. The pole number increases
from 2 up to > 20 by reading right to left in the plot in Figure 4.18. For example, the
minimum length, package OD constrained M/G will have 10 or 12 poles. If fewer