Utilizing the physical meaning of the interference of notch effects, the author developed a simple calculating method of stresses introduced in an elastic body due to the effect of interference of many notches. Using the method, stress concentration factors were obtained for the cases of a row of elliptic holes in an infinite plate under tension, a row of elliptic rigid inclusions in an infinite plate under tension, a row of elliptic holes in a strip under tension, a row of elliptic holes in an infinite plate subjected to bending (flexure), two spherical cavities in an infinite body under tension and a row of spheroidal cavities in an infinite body under tension. When the elliptic holes become circular holes, the stress concentration factors obtained by author's method are always in close agreement with the exact values obtained by other investigators.

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The stress concentration factor, K, for the circular fillets under tensile load was investigated photoelastically for flat bars having a projection on both sides (i.e. a cross-shaped plate). The experiment shows that the values of K are given by the empirical formula as follows : [numerical formula] where D and L are the width and length of the projection respectively, r is the radius of the circular fillet, d is the width of the bar ; and the coefficient C and the exponent α are indicated as functions of L/d. Then, the values of K increase with increasing D/d, L/d and d/r respectively, but in a range of L/d>5, K agrees with the values of stress concentration factors of the shouldered plates which are the limiting cases when the value of L/d tends to infinity.

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The effect of hardness on the fatigue behaviors of Cr-Ni-Mo high carbon low alloy steel for a hardness range from H_v 350 to H_v 650 has been discussed here. From the test results the following were clarified. (1) The fatigue strength of unnotched specimen under rotating bending and torsion increases with the increase of hardness, but the maximum fatigue strength is obtained at hardness H_v 550 and above this hardness the fatigue strength decreases on the contrary. (2) The fatigue strength of notched specimen under rotating bending increases with the increase of hardness, but the fatigue strength reduction factar decreases conversely above H_v 550. The rate of growth of fatigue crack in the specimen above hardness H_v 550 is considerably larger than that in the specimen below hardness H_v 450. (3) The fatigue strength of cracked specimen under rotating bending decreases gradually with the increase of hardness. This is similar to the case where the impact value of steel decreases with the increase of hardness. The fatigue strength reduction factor of cracked specimen increases proportionally to the decrease of the impact value. (4) Fish eye was found only in the fatigue fracutre of unnotched specimen of hardness H_v 650 under rotating bending, and the fracture appearance is of intergranular one. On the other hand, the fracture of specimen below hardness H_v 550 was a fatigue fracture. It is presumed that the drop in fatigue strength of steel of hardness H_v 650 is due to the existence of stress-raising elongated carbide particles.

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In this paper, the characteristics of crack propagation in low cycle fatigue were studied using electropolished 7 : 3 brass specimens. The method of loading is reversed bending. The following results were obtained. 1) The parameter deciding the rate of crack propagation is hθa^1/2, where h is the minimum width of specimen, θ is the amplitude of bending angle and a is the effective crack length (the sum of crack length and notch depth). It is condidered that hθa^1/2 represents the amplitude of reversed plastic strain at the root of crack. 2) The mean strain (the mean of maximum tensile and maximum compressive strains) near the root of crack is positive (that is, the grains near the root of crack have been extended under alternate bending). 3) One spacing of the fatigue striations in low cycle fatigue corresponds to one cycle of reversed bending.

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The stress wave under service is generally non-sinusoidal. The fatigue test by non-sinusoidal loading was made and compared with the sinusoidal stress wave fatigue test. Wave forms selected are 5 c/sec sinusoidal, square and triangular and 11.5 c/sec sinusoidal. The test results show that, for test specimens of 0.3% carbon steel, especially for unnotched specimens, the fatigue strength differs significantly with different wave patterns, for the reason mainly of different amounts of repeating plastic strain. Then, an attempt was made to obtain an analytical expression of wave-form effect in terms of the relationship between stress and plastic strain during the fatigue test using a rheological model.

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In recent years it has been well known that the remarkable improvement of fatigue strength of carbon steel specimen which was induction-hardened, can be due to 1) an improvement of mechanical properties of material by rapid heating, and 2) prevention of the propagation of the fatigue crack by the residual compressive stress in the surface layer of a specimen. However, at the initiation stage of a macro-or microscopic fatigue crack, it is not yet defined what kind of role the residual compressive stress in the surface layer of specimen is to play, and what kind of effect the rapid heating has. In this paper, the fatigue behavior of induction-hardened microstructure which is free from the residual compressive stress, is investigated. Also the effect of the microstructural change of material due to induction-hardening on the fatigue strength, is observed.

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It is quite well known that a remarkable rise of fatigue strength of an induction-hardened, carbon steel specimen, can be attributed to the following : 1) Quenching after rapid heating may improve the mechanical properties of material. 2) The existence of residual compressive stress in the surface layer of the specimen may prevent the fatigue crack from propagating. However, it has not been clarified which of these has a more important bearing on the fatigue behavior of induction-hardened steel. In this paper, the mechanical behavior of retained ferrite was investigated, which was considered to govern the fatigue behavior of induction-hardened steel being free from the residual stress. Results obtained are as follows : the fatigue crack originates in the part of the retained ferrite in the quenched microstructures, and the final fracture seems to be governed by the surrounding quenched microstructures.

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In this paper, as an attempt at the quantitative representation of the behavior of fatigue cracks during thermal fatigue, the concept of "crack density"is proposed. This can be defined by n^^-=1/(2πr)∫^2πr₀ nds where n denotes the number of cracks intersecting a meridian line drawn on the surface of specimen, and r indicates the radius of cylindrical specimen. Experiments were carried out in two different temperature ranges ; 200∼600°C and 300∼700°C. The values of crack density on the surface of a specimen, after a certain number of repetitions of thermal load before failure, were measured by optical microscope. Then relations between the values of crack density and crack depth were investigated. The behavior of cracks at a certain stage is discussed also. It was found that the crack density n^^- is one of the appropriate parameters to represent the damaged state of specimen.

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Plastic strain fatigue tests have been carried out on high tensile steel specimens in saline to observe the plastic fatigue characteristics in corrosive media. Electrode potential was measured to explain the corrosion behaviours under cyclic strains. Corrosive media decrease the fatigue strength in terms of plastic strain range or total strain range, whilst the relation between the total amount of plastic work and cycles to failure is not affected by corrosive media. Plastic strain range is greater in corrosive media than in air under the same total strain range, and this is the cause for the decreased fatigue lives in corrosive media. Cycle frequency lower than 2.7 c/min has no effects on the corrosion fatigue strength, because the corrosion potential of specimens follows perfectly the strain varying at such a low cycle frequency, neither is observed the effects of cycle frequency on the potential variation with the progress of cycles.

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The absorbed energy which determines the impact strength of a material depends on the magnitude of deformation and the deformability of the material. In an impact fatigue test, the phenomena of fatigue strength may differ for the low-cycle fatigue region (where the plastic deformation acts mainly) and for the high-cycle fatigue region (where the fatigue crack propagation acts mainly). In this research, tensile pulsating impact fatigue tests were carried out on the carbon steels whose deformabilities were changed by the carbon contents (0.28∼0.89%), the notch forms (the stress concentration factor α=1.05∼3.00), and the heat-treatment conditions. The results obtained can be summarized that the impact fatigue phenomena in low-cycle fatigue region show quasi-characteristics in unit impact test, and at high-cycle fatigue range they do not depend on unit impact characteristics. The rolled material has a lower notch sensitivity factor than the annealed material, which is different from the conventional fatigue phenomenon.

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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.

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Based on a pressure solution for an infinitely long journal bearing clarified in the previous paper, the vibrations of a rotating shaft which is supported in oil lubricated journal bearings is investigated theoretically and experimentally. The results are as follows : 1) A system in which a rigid shaft is supported in oil lubricated journal bearings has in general an angular natural frequency slightly less than ω/2 (ω is angular velocity of rotating shaft). Although the free vibration with angular frequency about ω/2 is stable at low rotational speeds, it becomes self-excited when the rotational speed increases to a high enough value. 2) In the case of a flexible shaft, the system has three angular natural frequencies, one of which is slightly less than ω/2 and the others are nearly equal to Ω (Ω is a fundamental angular frequency of flexural vibration of the shaft). Only one of the vibrations with frequency Ω becomes unstable when the rotational speed increases above about twice the critical speed of the shaft.

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This paper analyzes spring property of a single-row, deep-groove radial ball bearing containing a large number of balls ; it is a continuation from the previous papers in which a fundamental consideration is made and a case with a small number of balls is treated. The analysis is carried out mainly for the characteristics in axial direction, with special emphasis on the state of zero contact-angle of ball, in order to contribute to research of vibration problem including the so-called abnormal oscillation. A complete expression of axial spring and associated characteristics, extreme characteristics corresponding to the case of an infinite number of balls which is applicable to almost all the cases in practice to express their fundamental properties, and a typical excitation form due to irregularity of raceways are presented. And numerical examples of axial spring, radial motion of inner ring under an average operational condition are demonstrated.

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This paper is concerned with the theoretical analysis of the optimalizing control system by a continuous correlation method. First, detailed studies are carried out on the patterns and the instability of the step response of the system to a displacement of the extremum depending upon the initial conditions, the parameters of the system, and the magnitude of the displacement. Second, the integral of the absolute error and the hunting loss are considered as the performance criteria for the transient and steady state, respectively, of the system contaminated by a noise. The contributions of each element of the system to these criteria are clarified. Finally, a reasonable design method is proposed on the basis of the results obtained.

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This paper is concerned with the theoretical analysis of an optimalizing control system by an improved peak-holding method. First, detailed studies are carried out as to the patterns and the incorrect action in the step response of the system to a displacement of the extremum of the controlled system. Second, the control actions disturbed by a noise are analyzed in detail. The frequency of the step response with the false action and the hunting loss are considered as the performance indices for the transient and steady states, respectively, of the system contaminated by a noise. The contributions of the parameters of the system to these indices are clarified. Finally, a reasonable design method is proposed on the basis of the results obtained.

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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.

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The statical fundamental equations for the dry system of nearly spherical granular materials were derived on the basis of the analysis of interactions between two particles. Compression tests were made and compared with the theoretically derived formula of compression. Moreover the aspects of the surface of particles were observed with a microscope. Then the following conclusions were obtained. 1. The interactions in the imagined models of particles hold for the actual granules. 2. The interactions are represented by ω=b_mP^1/m with the displacement ω and force P ; m changes as 3→2→1 for the actual granular systems. This is due to the plastic deformations of asperities and the bodies of particles. 3. The formula of compression derived here coincides with those proposed so far.

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This paper deals with a theoretical investigation on the effect of injection or suction from the disk surface on heat and mass transfer confficients. That is, the basic differential equations for the velocity and temperature (or concentration) fields are solved numerically by means of the electronic computer for a disk rotating in a uniform forced stream. Especially, referring to the applcation to the transpiration cooling, the following conclusion is considered to be of interest. The flow around a rotating disk has a character of three dimensional boundary layer. Therefore, the velocity relative to a rotating disk, i.e. u=λγ{λ=(α²+ω²)^1/2} may be used as the main stream velocity. Then, the mass transfer parameter H_w is expressed by H_w=(W_w/U) R_sr^1/2, R_er=Ur/V where ω is the rotating angular velocity, a the constant obtained for the three dimensional stagnation flow and λ the resultant angular velocity in the presence of an axial forced flow. This relation corresponds qualitatively to that for the flow in a boundary layer over a flat plate with injection which has been analized by Hartnett et al.

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The step function factor for laminar heat transfer from a disk rotating in uniform forced stream, with its surface temperature changing step-wise was analysed by the profile method based on the energy integral equation. The velocity profile in a laminar boundary layer changes complicatedly by the ratio of axial velocity to rotating one, but it was expressed by a single formula. On the other hand, the temperature profile was assumed by cubic polynomial. The step function factor was numerically obtained by HIPAC 103 electronic computer and then in view of the application of the technique of superposition, an empirical formulation of the step function factor was conducted. Its adequancy was confirmed by comparison with the exact similar solution for the case of the simple quadratic surface temperature distribution as a typical non-isothermal surface. Moreover, for the isothermal disk with an unheated part in center, the mean heat transfer coefficient was obtained by use of the step function factor.

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In the radiative heat transfer of gas bodies it often becomes necessary to estimate the emissivities of mixtures, because the gas body would exist in the form of mixtures rather than of pure constituents in the practical engineering problems of interest. The current study presents an evaluation procedure of the emissivities of CO₂-H₂O mixtures on the basis of the tentative physical models about the interactions of radiation embodied in the spectroscopic analyses of carbon dioxide and water vapour and also includes the results of the evaluation. The wavelength regions of important overlapping of vibration-rotation bands are substantially restricted to CO₂-2.7μ band versus H₂O-2.7μ band and CO₂-15μ band versus H₂O-10μ∼pure rotations. In consequence the comparison of calculation results of the interaction term Δε with the Hottel's data indicates a pertinent consistency. It facilitates the estimation of Δε under an arbitrary physical condition (say, temperature, optical length, mixture ratio, etc.) and these results are applicable to the various important problems in the radiative heat transfer.

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The test results of the comprehensive investigations, which are carried out by the Department of Public Nuisance, the Tokyo Municipal Government, concerning the influence of the type and design principle of incinerators, operation conditions and refuse properties on the nuisances due to smoke and ash, give synthetic informations to improve the present policy of incinerator design, from the point of view of the public nuisance and also of incinerator maintenance. For instance, the upper limit of the furnace outlet temperature, which is supposed 950°C at present, is found slightly too high, considering the content of NO+NO₂ discharged from the furnace, and the maintenance of air preheater located immediately behind the furnace. Further, it is found difficult to decrease the content of organic acids even through high temperature incineration. In order to prevent the nuisances of these gases to the environment and the furnace itself, the present furnace volume design or other factors effective to decrease the content should be discussed.

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In the peripheral milling process with a single straight cutting edge, two components of cutting force both in dry cutting and wet cutting are measured precisely corresponding to the undeformed chip thickness. On the basis of these experimental results, the effects of cutting fluid both in up milling and down milling are investigated. The main effects of cutting fluid obtained from the experimental results are as follows : (i) The effects of cutting fluid are generally remarkable in down milling. When the rake angle is large, however, the effects are almost nonexistant. (ii) The smaller the feed per tooth, the more remarkable the effects of cutting fluid. (iii) The effects are generally greater in thrust force than in normal force. This tendency is notable in smaller feed, too. On the basis of these experimental data, some considerations of the frictional behavior on tool rake face are made both for dry cutting and wet cutting.

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Chatter vibrations which occur after considerable grinding time are closely related to surface waves generated on the grinding wheel. Experiments are carried out using a surface grinding machine to make clear the general characteristics of waves. Influence of various grinding conditions such as grinding wheel hardness, workpiece speed, dressing conditions and others on chatter vibration is investigated. A close relation between the generation of waves and the characteristics of the grinding wheel wear is recognized. Influence of the disturbance during grinding on the generation of waves is also investigated with a specially designed grinding wheel.

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