Showing papers in "Jsme International Journal Series B-fluids and Thermal Engineering in 1968"

Application of Optimization Theory for Bounded State Variable Problems to the Operation of Train

Abstract: Finding a train operation which minimizes energy consumption for leading the train from one station to the next at the specified instant and stopping it there is dealt with in this paper. Since speed limit is observed strictly in the train operation, the problem should be considered as a bounded state variable problem. It is true that solving a bounded state variable problem is universally considered extremely troublesome, but the author has recently developed a very simple and clear method. The method is applied to this problem and the optimal control law has really been obtained straightforward and definitely. The author's is again confirmed to be very convenient to solve a bounded state variable problem. The research is believed to be the first scientific research on the economization of train operation.

Fundamental Investigations of Fretting Fatigue : (Part 5, The Effect of Relative Slip Amplitude)

Abstract: The fact that the fretting fatigue strength is significantly influenced by the relative slip amplitude was confirmed experimentally and reported in the previous paper. In the present paper, in order to make clear why the relative slip has a marked influence upon the fretting fatigue strength, the relation between the frictional force and the relative slip is investigated experimentally. As the result, the alternating stress amplitude, σfw1, which is the fatigue limit based upon the initation of fatigue cracks under the condition of fretting, could be expressed in the following equation as a function of relative slip, S, σfw1=σw1-2μp0{1-exp (-S/κ)}, where σw1 is the fatigue strength of plain specimen, μ is the coefficient of friction, and k is a constant.

The Two-Dimensional Stress Problem Solved Using an Electric Digital Computer

Abstract: In this paper, the author has developed a new method for solving the two-dimensional stress problems using a digital computer. As examples, he calculated the stress distribution of a rectangular plate subjected to symmetrical loading and the stress concentration factors of a semi-infinite plate having a circular notch or a V-notch under tension. The stress distributions of an infinite plate subjected to a point load are used as a fundamental solution in this method. To satisfy the boundary conditions, the body force distributed on the boundary curve imagined in an infinite plate is used.

Fundamental Investigations of Fretting Fatigue : Part 3, Some Phenomena and Mechanisms of Surface Cracks

Abstract: It has been known that the fatigue strength related to fretting is significantly reduced and that non-propagating fatigue cracks are often observed in the superficial layer of fretted area. In order to clarify the causes of such phenomena, the initiation of fatigue cracks is investigated in relation to the contact stresses caused by fretting. The main results obtained are as follows. (1) The reduction of fatigue strength is mainly attributed to the stress concentration caused by the frictional force due to fretting. Fatigue cracks are located at the stress concentrated area. (2) The fatigue cracks show inclinations to the surface, and the direction can also be explained by the contact stresses.

Fundamental Investigations of Fretting Fatigue : (Part 2, Fretting Fatigue Testing Machine and Some Test Results)

Abstract: In the present paper, the construction and features of a fretting fatigue testing machine designed by the authors are explained, and the experimental results obtained by using the testing machine are stated concerning mainly the relative slip which is considered to be one of the most significant factors affecting the fretting fatigue strength. The following are known from this investigation. In fretting fatigue, many shallow micro-cracks which seem not to propagate to a complete fracture are formed and develop somewhat obliquely from the surface of specimen because of the effect of frictional force due to fretting. Fatigue strength is reduced significantly by the effect of fretting, and the strength reduction factors, concerning both nucleation of fatigue cracks and fatigue fracture, are greatly influenced by the magnitudes of relative slips. The fatigue strength is most significantly reduced when the relative slips are about 0.015∼0.020 mm, and reduced to less than 1/5 of its strength without fretting, and if the relative slips could be kept less than 0.005 mm, a marked improvement would be expected.

Fundamental Investigations of Fretting Fatigue : Part 4, The Effect of Mean Stress

Abstract: A series of investigations is proceeding to clarify the phenomena of fretting fatigue. In the present paper, the effects of mean stresses on the initiation of minute fatigue cracks in superficial layer and on their propagation to complete fracture, under controlled conditions of fretting slip amplitude, are investigated using the fretting fatigue testing machine described in the previous paper. Annealed specimens and induction hardened specimens made of carbon steel are employed in the experiment. The following are the main results obtained. (1) The range of alternating stress amplitude at which no fatigue cracks initiate is not affected by the mean stresses, but is a constant value depending on the materials. The fatigue limit can be raised by induction hardening. (2) A fatigue limit against propagation of minute cracks (maximum alternating stress amplitude at which the minute fatigue cracks do not propagate) is cosiderably affected by the mean stresses, and it decreases with the increase of mean stress.

On the Characteristics of Divided Flow and Confluent Flow in Headers

Abstract: Formulas for calculating the flow rate ratio of each branch pipe are derived taking the diffuser effect on divided flow and the nozzle effect on confluent flow which is caused by branching streams in a header into consideration. Effects of the divided flow factor σD and of the confluent flow factor σo in those formulas on the flow rate ratio of each branch pipe are evaluated from the experimental results for water. The factors σD and σo are dimensionless numbers given by [numerical formula] where ησ is the diffuser factor which represents the pressure recovery factor due to branching of the fluid from a header, ψn is the nozzle factor due to adding of the fluid from branch pipes into a header, (ζ+λι/d) and m are the resistance coefficient of branch pipe and the ratio of crosssectional area of the header to one of the branch pipe respectively. A method for calculating the flow rate ratio of each branch pipe in the case where the inlet or the outlet of header is placed between both closed ends of the header is also presented.

Effects of Size on the Fatigue Limit and the Branch Point in Rotary Bending Tests of Carbon Steel Specimens

Abstract: The effects of size on the fatigue limits and the branch points of electropolished notched specimens were investigated. To clarify the effect of work hardened layers due to machining, the specimens having work hardened layers were also investigated. The main results obtained are as follows. 1) The necessary condition of non-propagating cracks is to take the root radius of a notch under a critical value ρ0 which is a material constant. ρ0 is about 0.5 mm for the 0.23% carbon steel. 2) The repeated maximum stress at the root of a notch at the fatigue limit based on crack initiation is determined only by the stress gradient x=(1/σ) (dσ/dx) at the root of the notch. 3) The size effect of the fatigue limits based on fracture in the range of existing of nonpropagating cracks is explained by the fact that the fatigue limits are determined from the stress concentration factor at the branch point α|ρ=ρ0.

A Magnetic Journal Bearing

Abstract: This report is related to the development of a magnetic journal bearing which can support a rotating shaft without any mechanical contact. A complete levitation is successfully achieved by means of a combination of permanent magnets and servo-controlled electromagnets. The principle and the characteristics of this bearing are as follows. The greater part of the rotor weight is supported by repulsion forces of like-poles of permanent magnets (barium ferrite) which are magnetized in the axial direction. Therefore, as indicated by the Earnshaw's theorem, there appears a strong unbalance force, but this can be prevented by attractive forces of direct current electromagnets which are servo-controlled. Owing to the use of the two control circuits which drive the two electromagents independently, the influence of current drifts of electromagnets upon the stability is made extremely low. The brake torque induced by eddy currents is made negligibly small by the use of ferrite.

The Mechanism of Lubricant Trapping under Dynamic Compression

Abstract: In the deformation processes in a pneumatic high speed hammer, friction is very low. This is due to the fact that much liquid lubricant is trapped between the tool and the specimen. In this paper, the mechanism of lubricant trapping under dynamic compression is analyzed with hydrodynamics and flow stress of the specimen material. The pressure distribution and the thickness of trapped lubricant film are calculated. The film thickness (h) is affected by compressive velocity (V), viscosity of the lubricant (η), diameter of the specimen (R), and flow stress of the material (p0). These are correlated as hocV1/3η1/3R2/3p0-1/3. Compression tests are carried out using a high speed hammer in order to ascertain the analysis. The experimental results agree well with the analytical results. It is found that most of the trapped lubricant remains entrapped even after a large deformation.

Fundamental Studies on Cavitation Erosion

Abstract: Cavitation erosion has been considered the fatigue failure of the surface due to repeated collapse pressures of cavitation bubbles. The present paper deals with severe erosion tests using the magnetostrictive oscillator vibrating in water, and gives the results. Cavitation damages consist of pitting by impact fracture and falling off by fatigue failure of the surface. The weight loss in the initial period is due to small pits, while the large particles due to fatigue predominate in the weight loss in the stationary period. The small pit is made by a single blow of large collapse pressure of some bubbles which produces the maximum shearing stress beneath the surface, and the falling off of large particles is due to the propagation of fatigue cracks by repeated smaller collapse pressure of numerous bubbles. The frequency distribution of collapse pressure depends on the cavitation conditions and the distribution curve is obtained by using simple hypothesis. As the surface tension of water is decreased by an active agent, the distribution curve shifts toward smaller collapse pressure, and the erosion damage also decreases.

Vibrations of an Infinite Beam on an Elastic Foundation with Consideration of Mass of a Foundation

Abstract: An analysis of wave propagation in an infinite elastic beam on an elastic foundation is presented, considering the effect of the mass of a foundation. The foundation is represented as a base consisting of closely spaced, independent bars or linear springs. The frequency equation is derived and the spectrum of frequencies for real, imaginary, and complex wave numbers is investigated. The phase velocity and group velocity versus wave number are also calculated for various ratios of the mass of a foundation to that of a beam. Results from the present method of solution are compared with those obtained under the assumption that a beam is supported by a massless elastic foundation whose local restoring force per unit length depends only on the local deflection.

Problems on the Finite Hollow Cylinders under the Axially Symmetrical Deformations

Abstract: In this paper, the authors consider three-dimensional elastic problems on a circular hollow cylinder under the axially symmetrical deformations. The problems on the cylinder are classified into twelve fundamental cases according to boundary conditions. The general solution to various problems was obtained by expanding each elementary formula to the condition in a form of a Fourier and Bessel series and by superposing the stress systems. As numerical examples, the stress distributions and deformations of a finite hollow cylinder subjected to uniform band pressure were calculated by the digital computer of Kanazawa University (NEAC-2230). This pressure is distributed circularly over the end-surface and over the middle zone of the inner or outer-surface.

Friction and Lubrication in the Deformation Processing of Metals : 1st Report, Quantitative Assessment of the Surface Texture of Materials being deformed under Rigid Tool

Abstract: Utilizing the plastic deformation occurring in the flange part of semi-formed cups of aluminium being drawn into the die, the authors investigated the mechanism of lubrication in metal forming processes. A model of lubrication is proposed, at first, on the basis of the observation of the surface. By means of a light reflectivity method, percentage of the surface areas occupied by the micro-plateaus (which were depressed and flattened by rigid and smooth tool surface) of the asperities on the deforming flange is estimated. The percentage varies according to the hold down pressure and the included lubricant. It is ascertained that the areas of the micro-plateaus being virtually in contact with the tool surface are responsible for the frictional resistance of the flange part. Then the mean hydrostatic pressure self-generated in the lubricant trapped in the pits of the surface is estimated, and the frictional shearing stresses acting on the plateaus are found.

A Microscopic Study of Metals Fatigued at Ultrasonic Frequency

Abstract: This paper is devoted to the microscopic observation and hardness tests on the surface of metals fatigued at ultrasonic frequency (17.8 kc/sec). It was found that, in iron and steel, microcracks were initiated at the boundaries of pearlite and ferrite without any accompanying slipbands. This is in marked contrast with the surface structure seen in those metals fatigued at conventional frequency. In copper, however, no marked difference between both was observed. Micro-hardness of iron failed by fatigue at such a high frequency remained almost equal to that of the annealed state, while that of copper increased as seen in the specimens fatigued at conventional frequency. Results observed above are discussed from a point of view of the strain rate dependence of unidirectional deformation behavior of b.c.c. and f.c.c. metals.

Transient Thermoelastic Problem for a Transversely Anisotropic Hollow Cylinder with Temperature-Dependent Properties

Abstract: This paper is concerned with an axisymmetric transient thermoelastic problem for a transversely anisotropic hollow cylinder, the boundary of internal surface being subjected to a sudden temperature rise. The problem is treated on assumption that the thermal and elastic properties of the cylinder are dependent on temperature. Basic equation is solved with the aid of perturbation method. The particular boundary value problems are carried out, and the corresponding displacements and stresses are clarified. For numerical examples, calculations are performed for the cases of anisotropic cylinders made of grades ATJ and ZTA graphites respectively. In these treatments, the variation of conductivity and thermal expansion is taken to be linear according to the temperature rise, but that of the Young's moduli is taken to be quadratic. The solution for an isotropic cylinder is also derived as a particular case of the present problem.

Nonlinear Free Vibration of Beams with Clamped Ends and with One End Clamped, Other End Simply Supported

Abstract: In this paper, an approximate solution is given by the use of Galerkin's procedure for the large amplitude free vibration of a beam with immovable clamped ends, subjected to an initial axial load. The results of the vibrations of a beam with one end clamped and other end simply supported are known from those of the vibrations of the antisymmetric modes of a clamped beam. Numerical calculations are carried out for cases of the fundamental vibration of both beams. Finally, a comparison of the increasing rate of the fundamental frequency with the amplitude is made among the beams having different end conditions : both ends clamped, one end clamped and other end simply supported, and both ends simply supported.

The Semi-Infinite Body Subjected to a Concentrated Impact Load on the Surface

Abstract: The problem of the semi-infinite body subjected step-wise to a concentrated impact load on the surface is treated by using the dynamical theory of elasticity. By using integral transformation, the results are obtained in forms of dual integrals which involve Laplace inverse-transforms and infinite integrals. The infinite integrals are evaluated by introducing a new variable. Laplace inverse-transforms which are separated from the static results are integrated numerically along the Bromwich integral path. As the result, the variations with time of the displacements and stresses are presented. The displacements and stresses begin to fluctuate suddenly upon arrival of a dilatational wave. In the neighbourhood of the symmetric axis, their absolute values increase till the arrival of a distortional wave. After this arrival, they decrease discontinuously and tend gradually to static results with an increasing time. On the symmetric axis, the radial stress is always compression and becomes maximum just before the arrival of the distortional wave. The circumferential stress is tension except for a short time just after the arrival of the dilatational wave, and becomes also maximum just before the arrival of the distortional wave. The magnitude of the maximum radial stress is about 3 times as large as the static one. The ratio of this stress to the static one in this case is considerably greater than the corresponding ratio in the plane stress state.

Studies on the Heat Transfer of Fluids at a Supercritical Pressure : 1st Report, A Proposition of Reference Values of Thermal Properties and Experiments with Supercritical Carbon-Dioxide

Abstract: A reference value of the thermal properties for a fluid at a supercritical pressure is proposed as, F=1/(tω-t∞)∫tωt∞F (t) dt where F : reference thermal property F (t) : thermal property as a function of temperature tω : wall temperature t∞ : bulk temperature. The heat transfer coefficient of a supercritical fluid can be determined by applying the reference value to an ordinary heat transfer formula for constant thermal properties. Experiments of heat transfer for carbon-dioxide at a supercritical pressure were made for three types of heat transfer, viz. (1) natural convection from a horizontal pipe, (2) natural convection from a vertical plate, and (3) forced convection from a circular pipe. The experimental result agrees with the proposed calculation.

Study on the Generating Process of Machined Surface

Abstract: Metal cutting process was investigated from the view point of generation of new surface and hence in association with machined surface characteristics. Discussions were made on the ploughing force on the extreme cutting edge, the depth of the distorted surface layer and the work absorbed in its generation in order to reveal the relation between generating process of ploughing force and surface layer. Following conclusions are drawn from the present study. 1. A part of the ploughing force consists of the force exerted in generation of distorted surface layer. 2. The work done by cutting edge is from 4 to 7 per cent of the work of all cutting operation under normal cutting conditions. 3. The depth of distorted surface layer in actual cutting is nearly equal to that of theoretical plastic zone which is calculated on the assumption that the ploughing force acts as a concentrated force on the semi-infinite surface of work-piece.

Friction and Lubrication in the Deformation Processing of Metals : 2nd Report, Surface Texture and Coefficient of Friction

Abstract: This paper is one of a series of investigations about the mechanism of friction and lubrication in metal forming processes. The friction occurring in the flange part of the cup being deep drawn is directly measured and the result is associated with the surface texture which is assessed by means of the light reflectivity method described in a previous paper. It appears that the frictional shearing stresses acting on the micro-plateau-areas of the asperities virtually in contact with the tool surface are independent of the tool pressure. Values of the frictional shearing stress per unit area of the plateau are found in accordance with the sort of lubricant, e.g., mineral, vegetable or animal oils, as well as soap suds. These stress values, to a considerable degree, seem to be associated with the coefficient of friction obtained by the four-ball-oiliness test.

The Mechanical and Optical Characterization of Polyurethane with Application to Photoviscoelastic Analysis

Abstract: The main requirement for practical photo-viscoelastic analysis is optical and mechanical characterization of the material, which has a strong time and temperature dependence of mechanical and optical properties. It is assumed that polyurethane is a linear-photoviscoelastic material and the correspondence rule for mechanical behavior proposed by Alfrey(1) can be also applied to optical behavior. The birefringence and stress or strain were measured simultaneously under two conditions, one being constant strain rate and the other being constant load. From experimental data, the stress-strain and the stress, strain-birefringence relations were obtained and the coefficients on the Laplace transformed plane of time were calculated. Based on this calculation, a new method of approximation of Prony series was proposed. The result calculated using abovementioned technique from constant strain rate data is well corresponding to the directly calculated result from creep testing. Therefore, it is found very good to apply the theory of linear-photo-viscoelasticity to this material.

An Experimental Determination of Transient Condensing Heat Transfer with Heat Absorption in Circular Cylinders

Abstract: Since the condensing heat transfer of steam on the container walls is one of the fundamental quantities for the safety analyses after the loss of coolant accidents of light water cooled nuclear reactors, the heat transfer was experimentally obtained in a model container. The temperature variations of a copper cylinder and a brass one installed in the container were measured, after the high pressure saturated water was injected and the heat transfer was calculated by analyzing heat conduction in the cylinders on the assumption that it is invariant in a short time interval Δt. The heat transfer increases to the peak value and then decreases in about 300 seconds to the stationary value which was measured with another expreiment done in the same container. The peak values depend on the energy injection rate into the container. The errors in temperature measurements and heat transfer calculations were examined, and the applicability of this method to similar cases was demonstrated.

Effect of the Superimposed Stress of High Frequency on Fatigue Strength

Abstract: The fatigue property of low carbon steel under the composite stress which was made by superposing the ordinary rotating bending stress and the vibrating stress of higher frequency was examined in this study. The experimental results were discussed by focusing on the effect of the ratios of the magnitudes and the frequencies of component stresses. It was ascertained that in some ranges of these parameters the fatigue life under the composite stress could be estimated by the criterion that the composite stress was equivalently replaced by the stress of constant amplitude whose magnitude was the sum of those of the component stresses. For the values of the parameters outside the ranges, the criterion did not hold and the fatigue life was reduced appreciably from the value given by the criterion. Another method for estimating the fatigue life by calculation was also presented, which was available for the latter case.

Dynamics of Compressible Saturated Two-Phase Flow : Critical Flow

Abstract: In order to establish a bridgehead for attacking the complicated phenomenon of the two-phase critical flow, an exact analysis is initially attempted on an idealized model of constant-area adiabatic two-phase flow. On the process of analysis, it is pointed out that there is a dynamical critical-state which is determined in a self-consistent way from the fundamental equations of dynamics concerned with the flow. With this universal principle of critical state, the afore-mentioned model is analyzed exactly, and the variation of entropy at the critical state is also examined. Although the simplicity of the model adopted poses a problem, not only the analytical results thus obtained show a good correspondency with the experimental results, but also it has various distinctive characters which have not been seen in the existing theories. The study is then moved to the examination of the general structures of logic concerned with the dynamics and thermodynamics included in the analysis, and the results are presented in a clear form discussing important items such as the mutual independency between the regulations of dynamics and the second law of thermodynamics ; the relation between the model and actual flow ; and the state of actual critical flow. In conclusion, it may be noted that the basic dynamic concepts connected with the two-phase critical flow have been clarified.