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Optimum stiffness of externally pressurised thrust bearings in turbulent regime
SYSTEMATIC
224
geometries considered, conical instability was not observed. Thus the threshold of the cylindrical mode together with calculated upper limits for dynamic unbalance provide a measure of the speed range in which operation will be satisfactory. The case of a symmetric rotor suspended on two, identical, rigidly mounted, self-aligning, finite-length, fluid-film journal bearings is considered. Equations and methods developed for the unbalance investigation are adapted to a variable speed analysis. An Augmented Small-parameter Equation for the Squeeze-film Journal Bearing. C. L. Strodtman, JOLT, 92 Ser. F, (3) (1970) 442-450; 4 figs., I table, IO refs. The asymptotic gas-film equation for the squeeze-film journal bearing is solved for the quadratic and cubic terms in the series expansion in terms of the radial displacement. The load support calculated shows good agreement to exist for large values of the radial displacement calculated from an all numerical procedure. A method of treating non-uniform excursion of the driving member by a root-mean-square amplitude and a shape factor is also given. Optimum Stiffness of Externally Pressurised Thrust Bearings in Turbulent Regime. F. A. Shen, JOLT, 92 Ser. F, (3) (1970) 457-465; II figs., 5 refs. _4 study to establish the optimum dimensionless stiffness and pressure, or pressure ratio functions of each of the various types of externally pressurised thrust bearings operating in a turbulent Couette flow regime. The shows that the dimensionless analysis optimum stiffness of the thrust bearing using any of the several types of geometricall) restrictive compensators such as capillary and orifice, decreases with increasing Reynolds number. At high Reynolds numbers, the effect of varying Reynolds number on the stiffness becomes quite small. In contrast, the the dimensionless stiffness of a constant flow bearing design increases strongly with increasing Reynolds number. Pivoted Plane Pad Bearings : a Variational Solution. A. Szeri and I>. Powers, JOLT, 92 Ser. F, (3) (1970) 466-472; II tables, 7 refs. The solution of Reynolds equation for the plane pad bearing presents no theoretical but much computational difficulty. A classical separation of variables is effected, the eigenvalue problem that arises is replaced by a Rayleigh-Ritz matrix and the design variables of the bearing, all of which depend on integrals of the pressure, are calculated quite accurately from inner products involving two vectors and a function of the W&WY,17
(1971)
ZI$,--2’27
ABSTRACTS
OF
CURRENT
I>ITERXTUHE
Rayleigh-Ritz matrix, without solving any eigenvalue problems. The use of the new solution is shown on a plane pad bearing but it should be possible to extend the solution to other bearing types. The Maximum Principle Approach to the Optimum One-dimensional Journal Bearing. C. J. Maday, JOLT, 92 Ser. F, (3) (1970) 482-489; 8 figs., L table, 12 rcfs. I’ontryagin’s maximum principle is used to determine the journal bearing which supports the maximum load for a given minimum film thickness and a specified load direction. The one-dimensional configuration which uses a constant-viscosity, incompressible lubricant is considered. The optimum bearing carries a load about ~3.5 per cent greater than the maximum carried by the usual full Sommerfeld bearing and about I 21 per cent greater than that carried by the half Sommerfeld unit. The actual extent of the bearing is determined in the optimisation process. This is 300 degrees. Further the bearing is stepped with only two regions of different but constant film thickness. Practical considerations indicate that the material for the hearing at the step must he selected carefully in order to reduce possible galling of the journal durin:: start up. On Fluid Inertia Effects in Infinitely Wide Foil Bearings. .\. Eshel, JOLT, 92 SW. I;, (3) ( I 970) 490 -495 ; 4 figs., 3 refs. Equations for a foil over a lubricating film in which the effects of fluid inertia are taken into account are derived. Xpproximate solutions showing the effect of inertia and fluid compressibility arc obtained. The effrct of inertia is to increase considerably the fluiclfilm thickness. The results obtainctl, in spite of their limitations, are consitlrrcd adequate for many purposes. The Optimum One-dimensional Hydrodynamic Gas Rayleigh Step Bearing. (;. M. Wylie and C. J. Maday, JOLT, 9z Sur. 1;, (3) (1970) 504-508; 7 figs., I table, 8 reis. The optimum Rayleigh gas slider bearing is determined for a range of bearing numbers Numerical methods are used to calculate step location, step pressure and load capacity for given values of step height ratio, bearing number and flow parameter. ‘1s many data points as desired are determined to obtain the optimum configuration dimensions to a very high degree of accuracy. ?\t low bearing numbers it is found that the optimum Rayleigh bearing has only slightly lower load-carrying capability than the optimum gas slider hearing. For bearing numbers of 50, IOO and 500 the optimum Rayleigh slider bearings were 5.8, 8.3 and 15.3 per ctnt lower
224
geometries considered, conical instability was not observed. Thus the threshold of the cylindrical mode together with calculated upper limits for dynamic unbalance provide a measure of the speed range in which operation will be satisfactory. The case of a symmetric rotor suspended on two, identical, rigidly mounted, self-aligning, finite-length, fluid-film journal bearings is considered. Equations and methods developed for the unbalance investigation are adapted to a variable speed analysis. An Augmented Small-parameter Equation for the Squeeze-film Journal Bearing. C. L. Strodtman, JOLT, 92 Ser. F, (3) (1970) 442-450; 4 figs., I table, IO refs. The asymptotic gas-film equation for the squeeze-film journal bearing is solved for the quadratic and cubic terms in the series expansion in terms of the radial displacement. The load support calculated shows good agreement to exist for large values of the radial displacement calculated from an all numerical procedure. A method of treating non-uniform excursion of the driving member by a root-mean-square amplitude and a shape factor is also given. Optimum Stiffness of Externally Pressurised Thrust Bearings in Turbulent Regime. F. A. Shen, JOLT, 92 Ser. F, (3) (1970) 457-465; II figs., 5 refs. _4 study to establish the optimum dimensionless stiffness and pressure, or pressure ratio functions of each of the various types of externally pressurised thrust bearings operating in a turbulent Couette flow regime. The shows that the dimensionless analysis optimum stiffness of the thrust bearing using any of the several types of geometricall) restrictive compensators such as capillary and orifice, decreases with increasing Reynolds number. At high Reynolds numbers, the effect of varying Reynolds number on the stiffness becomes quite small. In contrast, the the dimensionless stiffness of a constant flow bearing design increases strongly with increasing Reynolds number. Pivoted Plane Pad Bearings : a Variational Solution. A. Szeri and I>. Powers, JOLT, 92 Ser. F, (3) (1970) 466-472; II tables, 7 refs. The solution of Reynolds equation for the plane pad bearing presents no theoretical but much computational difficulty. A classical separation of variables is effected, the eigenvalue problem that arises is replaced by a Rayleigh-Ritz matrix and the design variables of the bearing, all of which depend on integrals of the pressure, are calculated quite accurately from inner products involving two vectors and a function of the W&WY,17
(1971)
ZI$,--2’27
ABSTRACTS
OF
CURRENT
I>ITERXTUHE
Rayleigh-Ritz matrix, without solving any eigenvalue problems. The use of the new solution is shown on a plane pad bearing but it should be possible to extend the solution to other bearing types. The Maximum Principle Approach to the Optimum One-dimensional Journal Bearing. C. J. Maday, JOLT, 92 Ser. F, (3) (1970) 482-489; 8 figs., L table, 12 rcfs. I’ontryagin’s maximum principle is used to determine the journal bearing which supports the maximum load for a given minimum film thickness and a specified load direction. The one-dimensional configuration which uses a constant-viscosity, incompressible lubricant is considered. The optimum bearing carries a load about ~3.5 per cent greater than the maximum carried by the usual full Sommerfeld bearing and about I 21 per cent greater than that carried by the half Sommerfeld unit. The actual extent of the bearing is determined in the optimisation process. This is 300 degrees. Further the bearing is stepped with only two regions of different but constant film thickness. Practical considerations indicate that the material for the hearing at the step must he selected carefully in order to reduce possible galling of the journal durin:: start up. On Fluid Inertia Effects in Infinitely Wide Foil Bearings. .\. Eshel, JOLT, 92 SW. I;, (3) ( I 970) 490 -495 ; 4 figs., 3 refs. Equations for a foil over a lubricating film in which the effects of fluid inertia are taken into account are derived. Xpproximate solutions showing the effect of inertia and fluid compressibility arc obtained. The effrct of inertia is to increase considerably the fluiclfilm thickness. The results obtainctl, in spite of their limitations, are consitlrrcd adequate for many purposes. The Optimum One-dimensional Hydrodynamic Gas Rayleigh Step Bearing. (;. M. Wylie and C. J. Maday, JOLT, 9z Sur. 1;, (3) (1970) 504-508; 7 figs., I table, 8 reis. The optimum Rayleigh gas slider bearing is determined for a range of bearing numbers Numerical methods are used to calculate step location, step pressure and load capacity for given values of step height ratio, bearing number and flow parameter. ‘1s many data points as desired are determined to obtain the optimum configuration dimensions to a very high degree of accuracy. ?\t low bearing numbers it is found that the optimum Rayleigh bearing has only slightly lower load-carrying capability than the optimum gas slider hearing. For bearing numbers of 50, IOO and 500 the optimum Rayleigh slider bearings were 5.8, 8.3 and 15.3 per ctnt lower