The relation between tangential force and relative slip displacement under fretting fatigue is analyzed by using a model of a spring system, and is compared with the experimental results. And the correspondence of the damaged layer of a carbon steel due to fretting fatigue with the stress conditions near the contact surface is studied. When slip amplitude Δy is small, it is proportional to tangential force T because of elastic adhesion which exists within contact surfaces partly. Both the wave forms of T and Δy are sinusoidal. When Δy becomes so large that macro-slip occurs, T shows a peak value and then decreases with progress of cycles. The wave form of T is trapezoidal and that of Δy is not sinusoidal, agreeing well with the analytical results. The frequency effect appears under Δy showing macro-slip, coefficient of friction being smaller under higher frequency due to the lubricating action of more oxidized debris. The depth of the damaged layer due to fretting fatigue is measured in several tens of microns. This depth is nearly equal to the depth where the combined maximum repeated shearing stress reaches the fatigue strength of materials.

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Elastic stresses of a thick plate under bi-axial uniform tension, weakened by a symmetrical conical hole, is considered. The solution consists of a linear combination of elastic solutions which satisfy always the boundary conditions on the upper and the lower surfaces of the plate. The coefficients of the linear combination are determined numerically to satisfy the boundary conditions on the surface of the conical hole by using the least square method repeatedly. By this method, the solution is obtained without solving a simultaneous equation. The circumferential stress on the conical surface is always tension and becomes maximum at the minimum diameter of the hole. This maximum stress varies in terms of the zenithal angle of the conical hole and the ratio of the minimum diameter of the hole to the thickness, but is always greater than the maximum stress of the plate with a circular hole.

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In the present paper, the deformation and stress state and their time dependent variation of a strip with circular hole of an elastic-viscoplastic material are investigated experimentally by using the photorheological method in the period from the instant of application of a constant compressive load to the static equilibrium state under the same load. As the result, it is made clear that the effect of viscosity of the material in the transient period is remarkable, and thus the deformation and stress state in the equilibrium state are quite different from those at the instant of loading. Deformation of the hole is measured in relation to time, which shows that the deformation during the transient period is far larger than that at the instant of loading. Moreover, the stress distribution in the minimum cross section of the strip and its time dependent variation are discussed in detail comparing with the existing data obtained by elastic theory or photoelasticity.

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Many investigations have been performed on the accuracy of the X-ray stress measurements from a physical point of view. However, in the X-ray stress measurements the individual stress values exhibit an intrinsic variability. The variability of the X-ray stress value and a precise estimation of the accurate stress value must be dealt with from a statistical point of view. The error distribution of stress values is expressed in terms of that of 2θ_i. And the statistical meanings of the X-ray stress values by various methods are clarified. Furthermore, it is proved mathematically that the stress by the double 0°-45° method proposed by the author, which can be obtained by four measured values like the most commonly used sin²Ψ method, has the least variance of stress for arbitrary value of variance σ_i² of 2θ_i among stresses by four methods described in this paper.

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In the last report the behavior of sliding wear of steels at ambient temperature was studied in summer and winter in Tokyo making use of various carbon steels as specimens that were melted in air or remelted in vacuum in author's Institute. But the effects of both seasons on the behavior of sliding wear could not be made clear from the above study. In this paper the behavior of sliding wear was studied at ambient temperature, 200°C, 400°C, and 600°C making use of the same steels as in the last report to explain the above mentioned effects. The results in winter had been obtained in the last report, then the experiment in summer was performed in this study. It was found from the above mentioned results that the oxidation tendency on the new clean surface created by breaks of contact points over the friction surface may change due to the difference of the relative humidity in air between summer and winter so that the changes of the oxidation tendency may have influence on the vehavior of sliding wear. Namely a coarse oxide film can be created on the new clean surface of steel in smmer while a thick oxid film can be created on it in winter in Tokyo.

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Analysis of vibration of a flexible rotor driven by limited torque through its critical speed is an important subject as rotating machines speed up. But a method of this analysis has not been established. In this study the method of the vibration analysis on a linear asymmetrical flexible rotor having an arbitrary distributed mass is presented. Equations of motion are written in the form of partial integro-differential equations. They are transformed to nonlinear simultaneous ordinary differential equations by the method of series expansion by eigenfunctions. These equations are solved by application of the asymptotic method and the averaging method assuming that asymmetry of the rotor, internal and external resistance coefficients, eccentricity and angular acceleration are small. The results of numerical calculation show that the amplitude through the critical speed increases as (1) the moment of inertia of the rotor is larger, (2) the incline of the torque-angular velocity curve is smaller.

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There are many reports in regard to oil film properties in the journal bearing, most of them based either upon infinitely long bearing approximation or upon infinitely short bearing approximation. Experimental results obtained by using full journal bearings with length-diameter ratio λ equal to unity did not show a good coincidence with analytical results derived by infinitely long or short bearing approximation, but they were found to agree well with exact solutions of finite bearing. Here is introduced a finite bearing approximation which depends on a simple assumption for axial pressure curve. This approximation can take less time for digital computation than the exact solution. Stationary properties of oil film bearing given by this approximation coincide well with the exact solution for a finite bearing with a wide range of λ=0∼∞.

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Although the optimal control theory has been much developed in recent years, the theory requires assumption that all the components of state vector are detected, but detection of all components of state vector is not always possible. The usual application of optimal control theory of incomplete feedback control system leads us to the inconvenience such that the optimal control law varies depending upon the initial point. this paper proposes a design method of incomplete feedback control system, where only the detected components are used to feedback. In order to get rid of dependence of optimal control law on the initial point, the method to optimize incomplete feedback control system in the sense of mini-max is contrived. The design method is explained in detail.

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The incompressible turbulent wake close to a flat plate (near wake) was theoretically analyzed with an inductive theory of free turbulence attributed to Reichardt, considering the influence of the velocity distribution at the trailing edge and the condition for smooth connection of the solution near the plate to the similar solution in the far down stream. In our experiment which is carried out in order to confirm the theoretical results, turbulent boundary layers (the shape parameters of which are equal to 1.45) on both sides of the plate join at the trailing edge. The experimental results show that the value of the momentum transfer coefficient at the center of the near wake agrees with taht which Townsend measured in a fully developed wake, and the theoretical results agree fairly well with the experimental results. The position at which the velocity defect distribution becomes similar is found to be predictable.

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In this paper the velocity distributions along the blade contour are calculated by the singularity method and computed values are compared with experimental ones. The contour of a blade is divided into 38 line segments and vortices are distributed on midpoints of each segment. Then the contour is divided especially finely at the vicinity of the leading edge and trailing edge, and Fredholm's type of integral equation obtained as a basic equation is substituted into simultaneous linear equations which can be solved with the digital computer easily. In this work, elements of simultaneous equations at the vicinity of the singular point and trailing edge are calculated most carefully and smooth velocity distributions are obtained.

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Two methods are presented for the theoretical analysis of the centrifugal impeller whose width changes and whose blades have an arbitrary aerofoil section. The first method is an approximate one which is available when the change in the impeller width is small. In the second method there is no restriction to the extent of the change in the impeller width. In both methods the velocity distributions on the blade surface are calculated by the singularity method presented in 1st Report. The errors in the approximate analysis are investigated in comparison with results of the second method and the limit of its application is given. In order to investigate errors in numerical calculation, the velocity distributions on the blade surface are compared with those by Eckert's method. Experimental data are included.

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In the pseudo-shock of duct flow, the static pressure at the wall surface increases gradually along the duct. This phenomenon has been explained by the well known Crocco's shockless model. His model, however, has some problems as follows : (1) It cannot present the distribution of various quantities related to the distance along the duct and the length of the pseudo-shock, since all the quantities are calculated as the functions of the ratio of the flow rate of the dissipative low velocity region to the total flow rate. (2) There is a discrepancy of velocities between the high and low speed regions at the final section of pseudo-shock. In order to correct these defects, a diffusion model for pseudo-shock has been presented in this paper by reforming his shockless model. The theoretical values of the length of pseudo-shock and the pressure distribution along the duct obtained by this model are able to explain the experimental data by the authors and other researchers quantitatively. Closer agreements are obtained in the case of higher Mach number at the initial section.

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The energy separation measurements were made of a vortex tube with a bend. The results are summarized below. (1) The influence of the bend may be neglected, for a bend with R=γ_w and α≤15°, and for a bend with R≥5γ_w and α≤90°, where R, γ_w and α are the radius of curvature, the inner tube radius and the turning angle of the bend respectively. (2) For α>15° and R=γ_w, the tangential velocity and the total temperature gradient of a spiral flow decrease remarkably at the bend, therefore the energy separation in the spiral flow drops suddenly. (3) The larger the value of α, the larger the total enthalpy of air in the central reverse flow near the nozzle openings and also the mass flow rate of air passing from the nozzle openings directly to the cold end orifice. These facts decrease the energy separation in the bent vortex tube with a small radius of curvature.

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A nonequilibrium, partially ionized stagnation point flow of a biased blunt-body in a supersonic flow is described. Electron temperature distribution from a free stream to wall has been computed for the case where electrons are in thermal nonequilibrium with heavy particles in the free stream. Immediately behind a detached shock, the solution of electron temperature in inviscid and boundary layers has been matched with that in the free stream, by using the relation for the jump of the electron temperature gradient across the shock. The method of matching is described. The effect of wall potential on the electron temperature distribution has been investigated, and a current-potential characteristic has been obtained.

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In order to obtain the necessary data for the development of magnetic pumps, MHD generators and so forth, the investigation of a magnetohydrodynamic (MHD) entrance flow seems to be important. There are many investigations of the MHD entrance flow, but all of them are concerned with a plane channel flow and we can not find any investigation of a rectangular channel flow. The present report is an analytical and experimental investigation of the MHD entrance problem in which a hydrodynamically fully developed flow in the rectangular channel with a finite aspect ratio flows in the magnetic field. In the analysis, we assumed the velocity profile in the rectangular channel appropriately and elucidated the phenomena of the MHD entrance region by using the momentum-integral equation. Through comparison between the analytical result and experimental one, the present analytical method is considered to be appropriate for the elucidation of the phenomena of the MHD entrance flow.

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In part 2 of this series it is attempted to describe how the slip velocity in vertical lines depends on the tube diameter the transport air velocity and the particle property. The slip velocities were determined by direct measurement of particle velocities at a comparatively small concentration of solids, using combination of a rotating shutter and a photographic measurement of particle trajectories. From these experimental results of other investigators could satisfactorily be represented by the authors' expression and that the friction factors in both horizontal and vertical conveying prove to be almost the same at high air velocity.

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In accordance with the recent developments in refrigeration engineering, the necessity to utilize the fluorocarbon refrigerants has increased. Hence it becomes quite essential to establish the thermo-dynamically consistent formulations in wide ranges of state parameters of these substances. For this purpose, new correlations of the saturation pressure and of the saturated liquid density have been devised for six typical different fluorocarbons such as R-12, R-13, R-21, R-22, R-23 and R-C318. Using these devised correlations with an aid of Cailletet-Mathias law, a set of most probable critical property values with their estimated uncertainties have also been derived. Additionally the necessity to derive the rational expressions for the thermodynamic consistency which have to be satisfied by the proposed formulations at the critical point is stressed and those expressions could be derived taking into consideration the estimated uncertainties of the critical property data.

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Following the results obtained in the first report, a set of the equations of state with respect to Those six different fluorocarbon refrigerants of practical importance have been formulated. The newly proposed equations of state can be determined mainly depending upon the second virial coefficient calculated from the available P-v-T data and they have the identical functional form for six fluorocarbons respectively. The calculated and compared results have shown a quite satisfactory coincidence with the experimental data used for the extended ranges of the state parameters. It was also examined and confirmed that the proposed equations of state could satisfy well the thermodynamically consistent conditions necessary to the pure substance at the critical point.

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Internal combustion engines are affected in their performance by varying atmospheric conditions, namely the atmospheric temperature, pressure and humidity. For gas turbines, however, performance correction formulae are not available as they are for gasoline engines. The purpose of this paper is to analyze the effects of atmospheric conditions on the performance of gas turbines, and to develop a theoretical correction formula by which gas turbine performance can be corrected from arbitrary atmospheric conditions to standard atmospheric conditions. In this paper, first, as a standard for comparision, the author shows the performance characteristics of three types of gas turbines under standard conditions at standard atmospheric temperature, pressure and humidity. Then he considers the performance of gas turbines under varying atmospheric conditions and, from the thermodynamic point of view, analyzes the effects of various atmospheric factors. Finally, the theoretical values obtained are compared with practical gas turbine performance data.

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This is a series of researches which aim to make fundamentally clear the effects of the bulk plastic deformation of work metals on the frictional mechanism at tool-work interface. In the first report, the contact ratio R and the frictional shear stress τ_f are measured on metal surface of blank-holder side in the sheet metal drawing and U-bending of strips. The bulk plastic deformation occurs together with the frictional sliding in the former, but does not occur in the latter. By comparison of the results in both cases, the effects of the bulk plastic deformation on R and τ_f can be examined. The following have been concluded. (1) The values of R in the case of the sheet metal drawing are 2.5∼3 times greater than those in the case of the U-bending. This is due to bulk plastic deformation. (2) Within the limits of this experiment, the frictional shear stress τ_f is approximately proportional to the real contact pressure, irrespective of presence of the bulk plastic deformation.

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In order to make clear the effects of the bulk plastic deformation on the frictional mechanism, a two-dimensional drawing-type friction testing machine has been designed and made. Using this Apparatus, it is possible to measure simultaneously and continuously the frictional and normal forces on both metal surfaces of the die side and the blank-holder side during the process. The apparent surface area of metal increases notably on the die side only, although the microscopic surface texture varies notably on both the sides. It has been confirmed by a calibration of the measuring devices that all the forces shown above can be precisely measured without mutual interference. Some preliminary experiments on aluminium and copper sheets have been carried out by this apparatus. As the result, it has been found that the frictional coefficients on the die surface are larger than those on the blank-holder surface.

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This report relates to two kinds of vibrationless geared devices according to the basic theories in the 1st report, that is, internal geared device and eccentric geared device of crankshaft rotary motion system. Design and construction of the above-mentioned two devices are described and it is ascertained that constructional defects in the eccentric geared device of crankshaft planetary motion system are eliminated by means of these devices, and that these devices are practical. Theoretical analysis of load on each portion, friction loss and equivalent moment of inertia in these devices is made and the results of their numerical computations are shown, and from the experimental results of vibration and torque, it is proved that the inertia forces and torques are perfectly balanced and that their vibration sources are only pressure torque and friction loss torque. Generally speaking, between the two, the internal geared device a more practical one, but in the case of utilizing these devices under special heavy load, the eccentric geared device is more suitable.

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A planetary differential reducer using internal gears with small tooth number difference is described : Essential points of the design are considered and an example of the reducer is manufactured. The idea is used that an internal gear with small tooth number difference has theoretically a contact ratio less than unity owing to trochoidal interference, but it is practically available under suitable condition. In case that the tooth number difference of the input-side gears is not the same as that of the output-side, such an especially high reduction ratio as 1/10, 000 is obtained. The calculation methods for strength and efficiency are given and the experimental value of efficiency is shown to agree with the theoretical one. The cost down of reducers with high reduction ratio is expected from using the above reducers which can be easily manufactured with standard pinion cutters of pressure angle 20°.

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Various kinds of boring bars to prevent chatter in boring operations have been developed, but they are not successful enough. This paper deals with a new boring bar which is composed of a body on which a tool is mounted and an internal plate fitted in a slit of the body. Its structure and dimensions are determined, based on the theoretical analysis in order to achieve the highest performance, and the stability limits of the new boring bar are compared experimentally with those of the conventional bar with the circular solid section of the same diameter and length to diameter ratio. The experimental results show that the new bar can perform stable boring operations in a wide range of cutting speeds.

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