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RESEARCH PAPERS

J. Basic Eng. 1960;82(2):251-256. doi:10.1115/1.3662563.

Although the purpose of this paper is specifically that of describing the Fluids Engineering Laboratory at the University of Michigan, it is clear that an understanding of the faculty philosophy underlying the planning of this unit is a necessary part of the document. This is an age of technological expansion, the rate-of-change of which exceeds any progress the world has hitherto known. The seeking of new knowledge and the application of that knowledge is the work of an ever-increasing number of competent scientists and engineers not only skilled in a technology but equally successful in the art of human understanding and relationships. Institutions of higher education are an integral part of this technological age and, because of this fact, find themselves confronted with the task of foreseeing the educational and research needs of the future. This is an immense task, one which is occupying many of the best minds of this generation. The technological and social progress of the coming generation depends upon the continuing flow of students emanating from our institutions of learning. They must be adequately prepared for the responsibilities which they alone can assume.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):257-264. doi:10.1115/1.3662564.

In the case of hydrostatic lubrication the designer of thrust bearings has to make decisions regarding the shape of pads, location of oil holes, and configuration of oil grooves. In this paper several pad shapes and associated oil inlets were investigated using conformal mapping techniques to obtain the total load-carrying capacity, flow rate of oil, oil-film thickness, pressure and velocity distribution. The results of these calculations permit the designer to approximate his chosen configuration by computed models in order to estimate the flow parameters.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):265-272. doi:10.1115/1.3662567.

The proper selection of an optimum labyrinth seal for a given application depends upon an accurate estimate of the seal leak rate. Suitable accuracy, particularly for straight labyrinth seals, can only be obtained from actual seal tests. Testing a complete series of seals is time-consuming and expensive. A method for correlating test data is presented which allows calculation of the leak rates for an entire family of labyrinth seals on the basis of tests of only two characteristic seals. Leak rates predicted by the method are within 3 per cent of the basic test data.

Topics: Leakage , Testing
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):276-285. doi:10.1115/1.3662571.

Orifice-regulated hydrostatic gas bearings offer significant advantages for instrument applications. In particular, gimbal bearings for inertial guidance systems can be designed with negligible starting torque and high stiffness, and for operation at extreme temperatures. A literature search revealed the lack of convenient and accurate data for the design of hydrostatic gas bearings of various configurations, taking into consideration the effects of compressibility, which cannot be neglected at higher pressures. Based on Euler’s equation, expressions for the significant parameters, i.e., pressure profile, gas-flow rate, gap height, and load-carrying capacity of pad and step bearings, are developed. These parameters yield results which are in excellent agreement with experimental data. The test fixture incorporates pneumatic loading by means of a bellows-suspended piston which is prevented from cocking by an air bearing.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):287-294. doi:10.1115/1.3662574.

The effect of hardness, surface finish, and grain size upon the compressive rolling-contact fatigue strength of M-50 bearing steel has been studied. Considerable testing on the RC Rig and statistical-treatment methods have been included. A mathematical expression relating these variables to life expectancy is presented and the optimization of these variables is discussed. It is shown that bearing fatigue of M-50 increases by increasing hardness, decreasing surface, and increasing grain size. The optimum life identified occurs at Rc 64 hardness, 1.5 rms surface finish, and a grain size of ASTM 2.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):295-300. doi:10.1115/1.3662578.

Experimental work was done rolling balls on flat plates and in V-grooves at loads and contact angles corresponding to usual thrust-bearing practice. It is shown that the spinning action of the ball with respect to the race should account for the major part of the over-all friction of a thrust-carrying ball bearing. Variables studied included contact angle, conformity, load, lubricant, and temperature. The results have been correlated and shown to follow theoretical predictions.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):302-306. doi:10.1115/1.3662583.

The rolling friction, contact plastic deformation, and elastic limit were determined for SAE 52100 steel structures with retained austenite contents from zero to 18.4 per cent. The force necessary to roll a ball on a plate decreased as the retained austenite was decreased. The contact stress necessary for the initiation of plastic deformation and the elastic limit of the material increased as the retained austenite content decreased from 18.4 to 3.9 per cent. No further change occurred when the retained austenite was reduced to zero. The extent of plastic deformation at very high contact stresses was reduced by the presence of retained austenite contents up to at least 7.4 per cent. These observations were applied to the problem of selecting the best steel structure for an instrument ball bearing.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):309-320. doi:10.1115/1.3662587.

A completely general solution is obtained whereby the elastic compliances of a system of any number of ball and radial roller bearings under any system of loads can be determined. Elastic yielding of the shaft and supporting structure are considered as well as centrifugal and gyroscopic loading of the rolling elements under high-speed operation. The solution defines the loading and attitude of each rolling element in each bearing of the system as well as the displacement of each inner ring with respect to its outer ring. For ball bearings the precise location of the load paths in each raceway are found. Life estimates can be more accurately made since the fatigue effects can be evaluated over known paths in the raceways. The solution, which is accomplished numerically by iterative techniques, has been programmed for an IBM-704 digital computer.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):321-326. doi:10.1115/1.3662589.

A method of solution is developed that circumvents the algebraic complexity in the solution of Reynolds differential equation applied to full journal bearings. The method leads to equations for journal-bearing characteristics that are in finite form. Salient features of the complete-oil-film solution are: As the eccentricity ratio b approaches 1, the load capacities of all finite bearings approach that of the infinite bearing; also, the friction curve intercept, (r/c)f, is 1 for all finite bearings when b equals 1. Results are compared with calculated values published by Muskat and Morgan for 0 < b < 0.6. Excellent agreement is found throughout the compared range.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):327-334. doi:10.1115/1.3662590.

A series of tests was made with rings ranging from 2 3/4 to 16 1/2 in. ID and at journal speeds up to 4000 fpm. Correlation of the results provides means for calculating ring speed for any journal speed. Oil viscosity, ring weight and diameter, ring immersion, and journal diameter are taken into account. From this calculated ring speed, oil delivery can then be estimated from equations incorporating the effect of oil viscosity and related operating factors.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):335-340. doi:10.1115/1.3662591.

A perturbation analysis is used to find the torque generated by a misaligned journal bearing (or, equivalently, to find the angular displacement of a torque-loaded journal). Results are presented graphically in terms of nondimensional parameters.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):342-345. doi:10.1115/1.3662595.

It is well known that the load of an ordinary friction slider is supported by a large number of surface asperities having a collective area that is small compared with the apparent area of contact. The metal in bulk beneath such surface asperities is elastically loaded. In many metalworking operations, such as wire drawing, extruding, rolling, and metal cutting, the bulk metal undergoes plastic deformation as sliding occurs. The influence of this subsurface flow upon the coefficient of sliding friction is discussed. A simple test procedure for studying the friction characteristics of sliding metal surfaces, one of which is being subjected to plastic flow in bulk, is described, and representative data are presented for both dry and lubricated sliding.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):347-359. doi:10.1115/1.3662598.

The effects of lead addition in alloy steel upon the metal-cutting process were explored over a wide range of conditions. In particular, a range of cutting speeds (from 50 to 800 fpm) and workpiece hardness (from 230 to 450 Bhn) were investigated on one work-piece material (4340) using principally a carbide (C-6) cutting tool. Orthogonal (two-dimensional) data was taken to describe the metal-cutting process, and tool-life data were obtained by running a typical production tool to failure at the various cutting conditions. Several mechanisms to explain experimental results, including lead acting as a lubricant, are discussed.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):360-366. doi:10.1115/1.3662599.

This paper presents a flow graph approach for analyzing multiloop sampled-data systems. Two techniques for finding the sampled output are examined. These are, first, construction of a “sampled” signal flow graph from the original system; second, a general gain formula which can be directly applied to the original system. The theorems necessary to establish the formula are rigorously proved. The first technique allows two possible modes of solution. The sampled output can be found directly from the sampled flow graph by the use of Mason’s formula, or in case of a more complicated multiloop system, the problem of enumerating nontouching feedback loops can be simplified by the use of topological matrices. Techniques developed in the paper are also applied to the solution of multirate systems.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):371-393. doi:10.1115/1.3662604.

The “second method” of Lyapunov is the most general approach currently in the theory of stability of dynamic systems. After a rigorous exposition of the fundamental concepts of this theory, applications are made to (a) stability of linear stationary, linear nonstationary, and nonlinear systems; (b)estimation of transient behavior; (c) control-system optimization; (d) design of relay servos. The discussion is essentially self-contained, with emphasis on the thorough development of the principal ideas and mathematical tools. Only systems governed by differential equations are treated here. Systems governed by difference equations are the subject of a companion paper.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):394-400. doi:10.1115/1.3662605.

The second method of Lyapunov is applied to the study of discrete-time (sampled-data) systems. With minor variations, the discussion parallels that of the companion paper on continuous-time systems. Theorems are stated in full but motivation, proofs, examples, and so on, are given only when they differ materially from their counterparts in the continuous-time case.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):401-410. doi:10.1115/1.3662606.

The basic relations which govern the behavior of titanium alloys in the presence of stress concentrations, as caused by notching, were investigated for cylindrical and prismatic tension test specimens. Notch tensile strengths were determined, at room temperature, for 4340 steel heat-treated to various strength levels, and for the titanium alloys 6Al-4V and 5Al-1.5Fe-1.4Cr-1.2Mo (Ti-155A). Some effects of notch geometry, specimen shape, type of loading, material history, and test temperature were included in the investigation. The information acquired from these studies leads to recommendations pertaining to the design of notch tensile specimens for evaluating the relative notch sensitivity of titanium sheet alloys.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):411-416. doi:10.1115/1.3662607.

Some observations showing the adverse effects of certain kinds of nonmetallic inclusions on the strength and fracture behavior of alloy steel test specimens are presented. The observations pertain to the effects in tests at low and high temperatures and under steady and cyclic loading.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):417-423. doi:10.1115/1.3662608.
Abstract
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):426-434. doi:10.1115/1.3662611.

A method is described which should prove useful in the study of strain distribution in a metallic member during plastic deformation. Regularly spaced lines are drawn on a test specimen of interest and on a glass plate. After exposure to strain the part is photographed through the grid of lines on the glass. The strain distortion on the part results in an interference pattern from which the amount of plastic deformation may be calculated.

Topics: Deformation , Glass
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):435-440. doi:10.1115/1.3662612.

In the application of various damage accumulation hypotheses to shock and vibration problems, a pattern of results was observed. A plot of allowable response (for the largest of a sequence of excitations) versus the number of excitations in the sequence produced straight lines on log-log paper for each value of damping. It seemed likely that a generalization could be found which would relate the allowable response to the largest excitations with a load-distribution factor, a material-and-structure factor, and the material constants from fatigue tests. One form of this generalization is presented, together with some numerical examples of its use, and a discussion of its possible significance.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):441-445. doi:10.1115/1.3662613.

The effect of temperature on the stress range diagram is discussed and the particular characteristics of the curves for unnotched and notched specimens are analyzed. Excluding metallurgical factors from consideration, it is suggested that relaxation is the principal mechanism which influences the behavior of polycrystalline metals under combined alternating and static stress. Two parallel nonlinear Maxwell units are used to represent the relaxation mechanism at elevated temperature. An analysis of this model shows that relaxation occurs to an asymptotic finite value of stress which is a function of the initial stress. The same model is applied for representing the behavior in the stress range diagram with the assumption that a linear relationship exists at low temperature between the fatigue strength and the normal stress acting on the planes of reversed slip.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):447-451. doi:10.1115/1.3662617.

An elastic-plastic analysis is developed for an internally cooled pressure tube with uniform heat generation. This analysis extends the method of calculating the location of the elastic-plastic boundary reported by Barrie [4] to account for the change in the plastic zone due to residual stresses which occur during cyclic operation. Numerical calculations are made for operating conditions expected to be encountered in a pressure tube in a loop through the Engineering Test Reactor Core. The numerical results show that the radius of the initial plastic boundary decreases during subsequent loading cycles. Also, for equal maximum pressure and volumetric heat generation, the total plastic strain per operational cycle on the inner tube surface and the residual tensile stress on the outer tube surface increase when the tube wall is thickened.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):453-461. doi:10.1115/1.3662621.

Creep rupture tests on tubular specimens of type 316 stainless steel were run at 1200 F and at pressures up to 24,000 psi. The specimens were tested under pure internal pressure and equal biaxial tensions. The results of these tests correlate favorably with those of uniaxial tension tests if a comparison is made on the basis of effective stress and effective strain rate.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):462-464. doi:10.1115/1.3662622.

It is shown that for a tube in bending the steady-state bending creep rate may be greatly increased by the addition of internal pressure. If the maximum bending stress is small compared to the pressure stress, a very simple expression is obtained for the ratio of bending creep rates with and without internal pressure. Experiments on lead tubes show good agreement with the theory.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):465-473. doi:10.1115/1.3662624.

Stress-rupture data obtained from tubular specimens stressed with internal pressure are compared with data from standard tension-bar specimens from the same heats of material. Agreement between the data of the two types of specimens is poor for thick-wall tubes when the hoop stress in the tube wall is calculated on an average stress basis. Better agreement is obtained with thin-wall tubes. These results show that any design formula that neglects the variation of stress through the thickness of a tube wall is unsatisfactory for thicker tubes. A dimensionless parameter method is presented which provides satisfactory correlation of the data for three materials, four test temperatures, and a wide range of wall thickness. Several areas in which additional research would be of value are discussed.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):477-481. doi:10.1115/1.3662629.

General equations for the stresses in a thick-walled cylinder in a state of plane strain are derived considering “steady-state” creep. A specific form of the creep-rate function is assumed and numerical examples are included to show the effect of geometry and material properties.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):482-488. doi:10.1115/1.3662632.

A first-order, first-degree, linear expression is developed to describe the transient behavior of a practical pressure-sensing system. The development is in terms of usual fluid-flow parameters. An experiment is described whereby the transient behavior is determined for a variety of pressure-sensing systems. Experimental uncertainties are determined. Comparisons are drawn between several published expressions, the proposed linear expression, and the experimental data reported herein, to indicate the validity of the proposed expression. Selected references to related work are given.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):489-500. doi:10.1115/1.3662633.

The author rejects, momentarily, actual experimentation with real heat exchangers for logical cogitation and arm-chair experiments. Observed as mental images or models, these heat exchangers reveal their basic characteristics—characteristics that will be partially obscured in an actual experiment by secondary effects inherent in the equipment. These basic characteristics, once perceived, may be used to correlate by means of frequency-response diagrams many results heretofore diverse and seemingly unrelated, that have been reported in the literature. Included among such results are not only the dynamics of various types of heat exchangers but also the thermal dynamic interaction between fluids and the confining pipe used for their transport. In addition, the author warns that all too frequently the use of the average temperature in heat-exchanger dynamics is based on faulty logic.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1960;82(2):285-286. doi:10.1115/1.3662573.
FREE TO VIEW
Abstract
Topics: Hydrostatics
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

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