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RESEARCH PAPERS

J. of Lubrication Tech. 1983;105(1):1-9. doi:10.1115/1.3254535.

The finite element formulation for regular cylindrical bearings is extended to include irregular (noncylindrical) bearing surfaces. The optimum bearing shape is sought for a specific duty cycle with a constant load and sinusoidal angular displacement. The optimization is done with a view to maximizing the minimum film thickness. For the purpose of optimization a one-dimensional cylindrical bearing is considered. The optimum among all elliptical shapes is found to combine a specifically elliptical sleeve and a perfectly circular journal. For this optimum noncylindrical bearing the absolute minimum film thickness is about a factor of 36 higher than that for the corresponding regular bearing. The absolute maximum pressure for the optimum bearing is about a factor of 5 lower than that for the regular bearing.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):13-21. doi:10.1115/1.3254530.

An analytical solution to the energy equation is provided for oscillating squeeze film flow, such as that which occurs in squeeze film damper bearings. Assumptions are: (a) the usual lubrication conditions for two-dimensional flow, (b) small oscillations, and (c) constant viscosity. Specific conditions are established for the latter assumption, which may be in force for stably operated squeeze film bearings. Relatively simple expressions are presented for the thermal performance variables (temperature field, average temperature, Nusselt number) for a variety of cases. The results are interesting from a heat transfer point of view in that the proper energy balance consists of dissipation, conduction, and storage terms, rather than convection terms as is usual in lubrication studies. Thus inferences drawn from other thermal analyses may be in error. Both average cross-film temperature rise and heat transfers are seen to increase from zero Péclèt number and asympotically approach constant values. Due to the negligible convection conditions, the conventional definitions of bulk temperature, Nusselt number, and Péclèt number are not appropriate. As a result of the thermal storage effect, interesting temporal phase-shift and temperature swing effects are exhibited.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):22-28. doi:10.1115/1.3254538.

A solution technique is developed whereby the problem of determining the synchronous unbalance response of general multi-degree of freedom rotor bearing systems is reduced to solving a set of as many simultaneous nonlinear equations in damper orbit eccentricities are there are dampers. It is shown how, in the case of a single damper, the resulting nonlinear equation may be solved directly to determine all possible orbit eccentricity solutions as a function of the rotor speed and bearing parameter, thereby ensuring completeness of solution, eliminating convergence problems and clearly indicating all multistable operation possibilities. Design maps portraying the effect of the relevant damper design parameters on system response may be conveniently obtained, allowing for optimal damper design. The technique is illustrated for the case of a simple squeeze film damped symmetric flexible rotor.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):29-38. doi:10.1115/1.3254539.

The dynamic behavior of rigid rotors as affected by the use of liquid-solid biphase lubricants in the supporting hydrodynamic bearings is studied theoretically. Two categories of dynamic behavior viz (a) unbalance response at low rotor speeds, and (b) half frequency whirl at high speeds, are studied. It is shown that the use of liquid-solid biphase lubricants causes considerable reduction in the size of journal orbit of an unbalanced rotor. The influence of particle size and dispersion concentration is studied. It is observed that an early reversal of journal surface velocity in the trailing half of crushing zone reduces the efficacy of the crushing action of the solid phase to some extent and results in periodic pulses applied by the solid phase on the journal. At higher journal speeds at which the operating point of the journal becomes unstable and the phenomenon of half-frequency whirl sets in, the use of biphase lubricants with small and medium-size particles causes a reduction in the size of whirl orbits. The journal, however, keeps whirling in a manner such that the whirl ratio crosses the value of + 1/2 twice in an orbit and thus the bearing loses its rotational load bearing capacity twice in an orbit. The use of large particles with heavy or medium weight rotors results in a significant qualitative change in the nature of whirl orbit. The journal center in such cases does not encircle the bearing center and the whirl ratio of + 1/2 is never reached. The liquid phase retains rotational load bearing capacity and shares the major part of rotor weight throughout.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):39-45. doi:10.1115/1.3254540.

This paper compares three different lubricant supply methods—pressurized supply (flooded), spray feed, and leading edge distribution groove—and analyzes their influence on the performance of tilting pad, equalizing thrust bearings. The paper presents experimental data on 267 mm (10-1/2 in.) o.d. bearings, operating at shaft speeds up to 13,000 rpm with loads ranging up to 3.45 MPa (500 psi). The data presented demonstrate the effect each lubricant supply method has on bearing power loss and temperature. Conclusions are drawn, based upon the effectiveness of each design, to guide the potential user.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):48-63. doi:10.1115/1.3254546.

The effect of the film shape on the load carrying capacity of a hydrodynamically lubricated bearing has not been considered an important factor in the past. Flat-faced tapered bearing and the Raileigh’s step bearing of constant film thickness have been the primary forms of film shapes for slider bearing studies and design data developments. This article, by the computer aided numerical solution of the Reynolds equation for two dimensional incompressible lubricant flow, investigates hydrodynamically lubricated slider bearings having different film shapes and studies the effect of the film shape on the performance characteristics of finite bearings; and it shows that optimized bearing with film shapes having descending slope toward the trailing edge of the bearing has considerably higher load carrying capacity than the optimized flat-faced tapered bearing of the same properties. For example the truncated cycloidal film shape yields 26.3 percent higher load carrying capacity for Lz /Lx = 1 size ratio, and 44 percent higher for Lz /Lx = 1/2. The article then presents charts for the optimum designs of finite slider bearings having tapered, exponential, catenoidal, polynomial, and truncated-cycloidal film shapes, and illustrates their use in numerical bearing design examples. These charts also furnish information on flow rate, side leakage, temperature rise, coefficient of friction, and friction power loss in optimum bearings. Appended to the article are analytical solutions for infinitely wide bearings with optimum bearing characteristics. The computer aided numerical solution of the Reynolds equation in most general form is presented by which finite or infinitely wide hydrodynamically or hydrostatically lubricated bearings, externally pressurized or not, can be studied. A digital computer program is made available.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):67-76. doi:10.1115/1.3254551.

Hydrodynamic sector bearings, which were arbitrarily oriented and tilted over a plane surface rotatng at constant angular velocity, were theoretically and experimentally investigated for thrust, pressure, friction, and lubricant flow. Such bearings have application in the positioning of circular saws and are termed saw guides. Four fundamental guide inclination states were defined, and a class of quasi-optimal designs, maximizing thrust intensity, were determined for each state. Experiments were conducted to support the theory.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):77-83. doi:10.1115/1.3254552.

In this work the authors give a method to determine the influence of the inertial terms, in the case of a lubricated slider bearing, based on the solution of the “inverse problem.” That is to determine the geometry of a slider bearing given the pressure distribution, the lubricant flow rate and the slider velocity. Unlike other methods till now proposed (i.e., the Slezkin and Targ, Kahlert, Constantinescu methods), in this work no simplifying assumptions have been made. A sensible influence of the inertial forces, already at the value of the modified Reynolds number Re* = 0.1, has been shown. At the same load capacity, the minimum thickness of the film decreases because of the inertia (at values of the parameters Re* = 0.1 and a = 0.2 the decreasing is about five percent). At a given geometry of the lubricant film, the inertial forces increase the load capacity, the friction forces and the friction coefficient if they are compared with the linear case. A comparison between the results of the present study and the results obtained solving the “direct problem” with approximate methods shows a good agreement relating to quality.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):84-89. doi:10.1115/1.3254553.

The phenomenon of cavitation in bearings is often studied under the assumption that the pressure and the pressure gradient both vanish along the unknown boundary of the cavitation bubble. However, such conditions (often named after Swift and Stieber) may be inconsistent with mass conservation. The discrepancy is particularly striking when the case of long bearings is studied within the so called Sommerfeld approximation. Therefore a complete analysis of the Sommerfeld case is carried out here again (in particular condition of starving feed are examined) under a hypothesis which allows mass-conservation and leads to a boundary relation of the Jakobson type.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):90-95. doi:10.1115/1.3254554.

The stochastic theory of hydrodynamic lubrication of rough surfaces is used to study the effect of surface roughness on the response of a squeeze film between two circular plates when one plate has a porous facing. An exact solution is given for the film pressure and pressure in the bearing matrix, valid for arbitrary wall thickness. The results are presented in tabular form and a comparison is made with an earlier approximate analysis to determine the range of influencing parameters for which the approximate solution is acceptable.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):96-104. doi:10.1115/1.3254555.

A noninertial theoretical model for the dynamics of film rupture has been formulated. Under the transient condition, movement of the rupture boundary is governed by the condition of flow continuity between the film flux and adhered film transport in the cavitation domain. The traditional Swift-Stieber condition for film breakup is shown to be valid upon reaching steady-state. Generalization is extended to allow consideration of two sliding surfaces and the pure squeeze-film. The possibility of subcavitation film pressure is shown to result in dry regions in the cavitation domain.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):105-112. doi:10.1115/1.3254519.

The micropolar fluid theory, a possible non-Newtonian model for fluids with rigid particle additives in which the average molecular size may be comparable to the material characteristic length, is applied to a two-dimensional problem of squeeze film of a ball in a spherical seat and to some three-dimensional noncyclic squeeze film problems, assuming the characteristic coefficients to be constant, in an effort to study the effects of rigid particle additives for the three-dimensional micropolarity model. Increase in effective viscosity due to the presence of additives is established theoretically. It is also shown that the theoretical effects of the additives on three-dimensional lubrication are identical to the two-dimensional problems, at least qualitatively.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):113-119. doi:10.1115/1.3254521.

The load capacity and stiffness of double-pad circular and rectangular porous gas bearings are analytically studied. Design curves for load capacity and stiffness versus static bearing numbers, for different supply pressures and eccentricity ratios, are given. The load capacity and stiffness of both bearings reach a maximum value at some bearing numbers and then decrease. A comparison between the load capacity and stiffness of single and double-pad gas bearings is made.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):120-129. doi:10.1115/1.3254526.

The experimental investigation discussed here gives experimental confirmation of the slip-flow theory for modeling hydrodynamic gas bearings with clearances below 0.25 microns. An interferometric technique employing two CW lasers is used to measure the small clearances with an accuracy of 0.025 microns. The effects of molecular rarefaction are studied by operating the slider bearing in different gas media of different mean free paths. Bearings operating at extremely high local Knudsen numbers are studied without approaching excessively high bearing numbers. Experimentally measured trailing edge clearances and pitch angles are compared with theoretical predictions using the modified Reynolds equation with velocity slip boundary conditions. Excellent agreement between experiment and theory is found for clearances as high as 1.60 microns to as low as 0.075 microns with corresponding ambient Knudsen numbers of 0.04 and 2.51, respectively.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):131-137. doi:10.1115/1.3254528.

The influence of two sided striated surface roughness on bearing load carrying capacity is analyzed for very low clearance gas films. As was done for the case of stationary surface roughness [1], a model lubrication equation appropriate for extremely high gas bearing number films is solved analytically for several simple geometry bearings. The analytic solution provides information on the exact relationship between pressure and roughness which makes it possible to ensemble average the lubrication equation before solution, greatly simplifying the solution procedure. It is found that the translating surface roughness has an influence on load similar to that caused by the stationary surface. Exact solutions with the current method are compared with those of the theory attributed to Christensen and To̸nder. The results are strikingly different and serve to bring attention to the fact that for high bearing number compressible lubrication, the Christensen-To̸nder theory is inappropriate. The results reported here should find application in the computer peripherals area where read/write heads now routinely hover over a spinning disk at clearances of 0.25 micron.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):138-142. doi:10.1115/1.3254529.

This paper describes a theoretical model for the prediction of the spacing profile between a wide flexible magnetic tape tensioned around a rotating drum and a protruding read-write head mounted on the drum. The model is based on the coupled equations controlling the elastic deformation of the tape and the hydrodynamics of the gas film which separates the tape and the head. Typical results are presented.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):143-146. doi:10.1115/1.3254531.

A theoretical analysis for the static characteristics of an aerostatic porous rectangular thrust bearing with an offset load, for both open and sealed end configurations, is presented considering three-dimensional flow in the porous matrix. Static characteristics for different operating parameters are calculated numerically and presented in dimensionless form as design charts. The effect of tilt is discussed.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):147-152. doi:10.1115/1.3254532.

The dynamic pressure in a squeeze film and the air flow through the film were analyzed experimentally and theoretically. The dynamic pressure was measured in a squeeze film between two rectangular plates with a small pressure transducer. Approximate solutions for the rectangular squeeze film were obtained analytically. The results were valid for small excursion ratios. Next, a squeeze film between nonparallel plates (wedge film) was examined. In this case, steady air flow occurred due to the unsymmetry of the pressure distribution. To investigate this fact, the air flow was measured in a spherical squeeze film. The values showed good agreement with the theoretical results.

Commentary by Dr. Valentin Fuster
J. of Lubrication Tech. 1983;105(1):153-158. doi:10.1115/1.3254533.

Efforts within the Materials Laboratory of the Air Force Wright Aeronautical Laboratories to develop seal materials for a nonflammable aircraft hydraulic fluid are discussed. Candidate materials are identified and the laboratory efforts to compound these materials for optimum performance are reported. Candidate seal performance is summarized from dynamic performance tests conducted at temperatures of 135° C and system pressures of 10.35 MPa in the laboratory’s “Chew Tester” and “Rod Seal Tester.” The drastic effect on long term seal performance caused by slight material formulation changes is noted. The value of performance testing of seal materials data to the material compounder is discussed.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

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