A multilevel solver for the circular contact was extended to elliptical contact problems. After verification of its predictions by comparison with results presented in literature, it was used to study the variations of film thickness with varying operating conditions and aspect ratio of the contact ellipse. Detailed computational results are presented and observed tendencies are traced back to the modelling equations.Subsequently it is demonstrated how and when, for contacts with the entrainment directed perpendicular to the major principal axis of the contact ellipse, the pressure and film thickness on the centre-line of the contact can be predicted accurately from an equivalent line contact analysis. Finally, survey graphs of the minimum and the central film thickness are presented and a formula is given that predicts the central film thickness as a function of load and lubricant parameters, and the ratio of reduced radii of curvature of the surfaces. This formula incorporates asymptotic behaviour and as a result it can be applied for all conditions. In particular, its accuracy for contacts with the major principal axis of the contact ellipse perpendicular to the entraining direction is demonstrated in this paper.

57 to elastohydrodynamic 217, 7500 AE Enschede (Netherlands) A new method for deriving similarity solutions is introduced. The application proves to be very simple and straightforward. For any set of analytical relations, whether dimensionally homogeneous or not, the greatest possible reduction in the number of quantities may easily be accomplished. The method is introduced by means of simple applications and the results are compared with the results of conventional dimensional analysis. In elastohydrodynamic lubrication in particular, this method may readily be accepted as a very helpful tool when dealing with the extensive sets of analytical relations involved. Yet it is certainly not restricted to lubrication problems only. Furthermore, the results show that physical properties seem to have no place in similarity analysis. Similarity analysis is pure string manipulation. Consequently, the method has proved to be perfectly suitable for personal computer applications.

Wherever friction occurs, mechanical energy is transformed into heat. The maximum surface temperature associated with this heating can have an important influence on the tribological behavior of the contacting components. For band contacts the partitioning of heat has already been studied extensively; however, for circular and elliptic contacts only approximate solutions exist. In this work a numerical algorithm is described to solve the steady state heat partitioning and the associated flash temperatures for arbitrary shaped contacts by matching the surface temperatures of the two contacting solids at all points inside the contact area. For uniform and semi-ellipsoidal shaped heat source distributions, representing EHL conditions and dry or boundary lubrication conditions respectively, function fits for practical use are presented giving the flash temperature as a function of the Pe´clet numbers of the contacting solids, the conductivity ratio, and the aspect ratio of the contact ellipse. These function fits are based on asymptotic solutions for small and large Pe´clet numbers and are valid for the entire range of Pe´clet numbers. By comparison with numerical results they are shown to be accurate within 5%, even for the situation of opposing surface velocities.

Bearing impedance vectors are introduced for plain journal bearings which define the bearing reaction force components as a function of the bearing motion. Impedance descriptions are developed directly for the approximate Ocvirk (short) and Sommerfeld (long) bearing solutions. The impedance vector magnitude and the mobility vector magnitude of Booker are shown to be reciprocals. The transformation relationships between mobilities and impedance are derived and used to define impedance vectors for a number of existing mobility vectors including the finite-length mobility vectors developed by Moes. The attractiveness and utility of the impedance-vector formulation for transient simulation work is demonstrated by numerical examples for the Ocvirk “π”, and “2π” bearing impedances and the cavitating finite-length-bearing impedance. The examples presented demonstrate both bearing and squeeze-film damper application. A direct analytic method for deriving a complete set of (analytic) stiffness and damping coefficients from impedance descriptions is developed and demonstrated for the cavitating finite-length-bearing impedances. Analytic expressions are provided for all direct and cross-coupled stiffness and damping coefficients, and compared to previously developed numerical results. These coefficients are used for stability analysis of a rotor, supported in finite-length cavitating bearings. Onset-speed-of-instability results are presented as a function of the L/D ratio for a range of bearing numbers. Damping coefficients are also presented for finite-length squeeze-film dampers.

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