Journal Bearing Impedance Descriptions for Rotordynamic Applications

Abstract

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.

Use of nonlinear journal-bearing impedance descriptions to evaluate linear analysis of the steady-state imbalance response for a rigid symmetric rotor supported by two identical finite-length hydrodynamic journal bearings at high eccentricities

“…Childs, H. Moes, H. van Leeuwen [6], D. Childs [4] and H. Moes and R. Bosma [8] derived the journal impedance descriptions for rotordynamic applications, which consist of defining the bearing reaction force components as analytical nonlinear functions of the journal motion (displacement and velocity). They also derived the analytical bearing stiffness and damping coefficients by linearisation of the bearing reaction forces using Taylor series expansion, where second and higher order differential terms have been dropped.…”

“…where p 2 = Cω 2 g , and the 8 non-dimensional bearing coefficients are obtained according to [6] as follows:…”

“…Bearings with low L/D ratios in particular are more stable than others [6], therefore they will be the object of the present work, using L/D = 0.25. R.D.…”

“…The high nonlinear characteristics of bearing reaction forces at large eccentricities make both numerical differentiation and integration approaches less accurate to linearise the bearing reaction forces [6].…”

Investigations of mechanical behavior in gear pump using design of software

“…The mathematical modeling was developed for eccentricity of shaft and pump, with the aim of including all the important effects, as well as to get a rather simple mode [2] l. There are three main sources of noise, vibration and friction considered: Angular pressure variation and gear meshing. The model has been taken in to account for comparison with experimental vibration data, in a wide range of operational parameters condition [1] s for several profile errors.…”