The surface roughness of the case plate was 1.6 *μ*m. The surface roughness of the laminations was determined using the same technique and yielded 10.9 *μ*m and 11.8 *μ*m for the M15 and JFE materials, respectively. Any roughness tester could be used to measure the surface roughness provided it has the range needed. Measuring tan Θ is nontrivial, and motor designers are unlikely to possess the necessary equipment. As an alternative, tan Θ can be calculated based on the surface roughness correlations [15]. However, the surface roughness is outside the valid range for the correlation to be valid. Furthermore, the correlation assumes a Gaussian, random surface, which is not necessarily the case for this contact. Because of this, tan Θ was determined empirically to be 0.12. Typical values for tan Θ range between 0.03 and 0.18 [7,15]. Note that bulk properties for k are used (22 W/m K for both types of laminations), not the effective properties reported in Fig. 9, which are a function of the stacking factor and include a small amount of interstitial air. The aluminum thermal conductivity was measured to be 195 W/m K. The aluminum microhardness was estimated to be 930 MPa, derived from typical Brinell hardness for Al 6061-T6. Surface microhardness is dependent on the history of the surface, including how it was finished, heat treatment, or work hardening. The actual surface microhardness may differ from the estimated value and requires specialized equipment to measure. The gaseous fluid conductance (*h*_{g}) is described by Eq. (7) as
Display Formula

(7)$hg=kg/\delta $