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Hydrodynamic lubrication plays an important role in mechanical engineering, although not very many books have been published on the subject. This book was written with graduate students, researchers and designers in view. The first four chapters are preparations for the following five chapters, where several most important subjects in hydrodynamic lubrication are discussed in detail, based on the author’s own researches. Examples are oil whip (stability of rotating shafts), foil bearings in connection with magnetic tape storages, squeeze film between rigid surfaces and visco-elastic surfaces, theoretical and experimental analyses of temperature rise in bearings, those of turbulent lubricating film using the k-epsilon model.
E-Book Content
0 A1 A3
(5.58)
(5.59)
(5.60)
In other words, all the coefficients A0 , A1 , · · · must be positive and the two above determinants of these coefficients must also be positive. In the case of Eqs. 5.52 and 5.53, the coefficients of the characteristic equation Eq. 5.57, A0 , A1 , · · · will be as follows: 1 P1 2 ω2 ω1 4 mc 1 P1 2 1 P1 = B1 − B 2 ωω1 4 mc ωω1 2 mc 2 P1 1 1 P1 2 1 P1 = 2B0 2 2 + B3 4 − B4 2 +1 ω ω1 mc ω1 mc ω1 mc 1 P1 2 1 P1 = 2B1 − B 2 ω mc ωω1 2 mc P 2 1 P1 1 P1 2 1 = B0 2 + 2B3 2 − B4 mc ω mc ω1 mc P 2 1 P1 2 1 = B1 , A6 = B3 ω mc mc
A0 = B0 A1 A2 A3 A4 A5
where B0 , B1 , · · · are as follows: B0 = C xxCyy − C xyCyx ,
ω1 =
k/m
B1 = K xxCyy + KyyC xx − K xyCyx − KyxC xy B2 = C xx + Cyy , B3 = K xx Kyy − K xy Kyx B4 = K xx + Kyy When K xx , · · · C xx , · · · are given by Eqs. 5.37 – 5.42, the actual calculations show that Eq. 5.58 of the Routh–Hurwitz criterion always holds, and if Eq. 5.59 holds, Eq. 5.60 always holds. Therefore, only Eq. 5.59 need be considered as a stability condition. If the determi