In this research, a numerical method for treating two-dimensional elastic, plastic problems is presented, in which the region of any given body is mapped into a lattice region by means of conformal mapping, and then the finite-difference method is applied. In this first report, the elastic problem of a circularly notched strip under tension is treated. To this problem, H. Politsky has once applied a method similar to the method in this study. Therefore, the authors try to improve his method in accuracy and extent of its applicability. The calculated results coincide well with Kikukawa's experimental data in maximum stress values as well as in the stress distribution, and also with Wolf's approximate solutions with regard to the stress gradient at the notch bottom.

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The problem of the stress waves propagation of an elastic semi-infinite plate subjected stepwise to concentrated impact load at a point on the free boundary is analized. By using Fourier integral and Laplace transformation, the theoretical impact stresses are given by expressions which contain real integrals. The variations with time of the stresses and the stress distributions are calculated numerically. The stresses vary discontinuously at the arrival of the dilational and the distortional waves. In the neighbourhood of the symmetric axis, the radial and the circumferential stresses are nearly always compression and tension respectively. The maximum radial stress along the symmetric axis is about 1.6 times as large as the static one. In the neighbourhood of the free boundary, all stresses vary complicatedly with time, because of the reflected wave from the free boundary.

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To enable the calculation of member stresses in a three-dimensional truss column under torsion, we examined the way in which each element in a matrix equation of equilibrium obtained as a result of statically indeterminate calculation could be expressed in a general manner. To be more precise, by automatically forming equations of equilibrium in a computer by repeated calculation, we formed a calculation program for working out these equations. In order to verify the practicability of this program, we made a comparison between experimental results obtained by means of using models and that of calculations under this program, ascertaining that these two results were in close agreement under various load conditions. In addition, we examined the characteristics of member stress in a three-dimensional truss column under torsion by this program. As a result, there was a clarification on the relation between the number of three dimensional framework stories and member stress, the effect of horizontal diagonal members, the distribution of twisting moment to joints, and other points. Also, it was proven that the conventional Japanese Standard JEC-127 furnishes a very different result from actual conditions.

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Fatigue tests under direct stress of killed steel, austenite stainless steel and high-strength steel were carried out at room temperature, -55°C and -195°C. The endurance limits and the fatigue reduction factor for notched specimens increase with a decreasing testing temperature. Very sharply notched specimens of killed steel and high-strength steel have also at low temperature such as -55°C two types of endurance limits relating the occurrence of fine non-propagating crack at the root of notch, whilst in the austeinte stainless steel they can not be obtained. A remarkable difference in Charpy impact values between killed steel and austenite stainless steel at low temperature has little influence on the fatigue strength. It can be concluded that the high strength steel quenched and tempered is more advantageous than the steel as rolled concerning the fatigue strength properties of notched specimens at low temperature.

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In this paper, we deal with the vibrational phenomena of a ball bearing of which the diameters of two adjoining balls are larger than those of the other seven balls. As a result, we make clear that the axial stiffness of test bearing varies chiefly with twice the angular velocity of a retainer. In addition, if the outer race being slightly inclined toward a shaft is fitted on a pedestal, a magnitude of the variation of the stiffness becomes the same as that of a normally mounted test bearing subject to a small thrust load. Furthermore, it is clarified that the resonant phenomena appear at certain rotational speeds at which i times, i=1, 2, 3…, of the angular velocity of retainer is close to a natural angular frequency of the system of a bearing having the diameter differences of balls.

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In this paper the circulation distributions caused by secondary flows occurring in the cases of flows with nonuniform velocity profiles passing through an axial flow compressor or a turbine cascade, are treated theoretically. It is assumed that this nonuniformity is small and the threedimensional flow is divided into two parts, that is, the two-dimensional fundametal potential and the perturbation flow. Starting from the equation of motion, Smith's equation⁽³⁾ which relates the span-wise velocity with the circulation variation is derived. Secodary-flow vortices which are parallel to the main outlet-flow and cause span-wise velocity confined in the rectangular flow passage, are determined to satisfy Kutta's condition at the trailing edge, using the relationship between the span-wise velocity and the secondary circulation. The curves of coefficients which relate the circulation with a velocity profile, are calculated and the comparison with author's experiments is made with fairly good agreement.

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Fourteen thermodynamic and electrical properties, including isentropic exponent, viscosity and thermal conductivity, of combustion gas and its plasma, which contain C, H, O, N, S and K, as elements, are calculated by IBM 7090, assuming the system is in equilibrium. Petroleum (C_nH_2n) and coke (C) combustion gases and their plasmas are treated. The conditions of calculation are : temperature ; 0∼4000°K, pressure ; 0.2∼8.0 atm, equivalence ratio ; 0.8∼1.5, N₂/O₂ ratio ; 0∼79/21 (air) and K₂SO₄ seeded ratio ; K/C=0.02∼0.4. K₂SO₄, K₂CO₃, K₂O, KO are considered in addition to KOH, K and K⁺ which have been treated in the previous papers as the potassium compounds caused by the dissociation of the seeded potassium salt. The results are compared with those of only KOH, K and K⁺ being considered.

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The theoretical analysis of a model of contact which is idealized in one of our test specimen shows that the convergent and divergent heat flows at the metallic contact spots on account of poor thermal conductivity of medium become strong contributory causes for thermal contact resistance. The experimental data on the contact of same metals agree fairly well with the exact solution obtained on the above-mentioned model of contact, assuming that the metallic contact spots are uniformly distributed and their equivalent radii are all of a size and approximately equal to 30μ.

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In the previous report, we have analyzed the heat flow in an infinite unit column as a model of contact, assuming that two metals in contact are of same material and very thick. But in practice, heat is often conducted through thin and differnt metals in contact, as is seen in the case of uranium fuel and canning material in a nuclear reactor. Thermal contact resistance between the different and thin metals is analyzed and compared with the previous analysis. And this leads to the conclusions as follows : (1) If the thickness of a metal is larger than about 1 mm, the metal can be regarded as semi-infinite in the direction of heat flow. (2) If the conditions of two metals in contact, such as thermal conductivity, surface roughness, etc., are greatly differnt from each other, the calculation should be performed on a model which will be shown in this report.

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The effect of the oxidation of surfaces on thermal contact resistance is investigated. If the surface of a metal is oxidized, the thermal contact resistance becomes greater and its change with the increase of contact pressure is slower than in pure metal contact. From the theoretical analysis these phenomena are explained only by the fact that the oxide of a metal has poor thermal conductivity compared with the pure metal.

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The effect of the waviness on thermal contact resistance is examined. The experiments performed on a simplified model of waviness show that the thermal contact resistance is roughly said to be the sum of the resistances for roughness and waviness in series. Long before investigating the theoretical analyses shown in the previous reports, we have obtained experimentally a practical method of estimating the thermal contact resistance. That is, on the assumption that the thermal contact resistance is the resultant of resistances to metalmetal and metal-medium-metal parallel heat flows and the additional resistance attached in series to the metal-metal heat flow, this additional resistance may be taken to be constant for each metal. This fact will be verified theoretically.

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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.

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By the flow visualization study, it was shown that the flow in a heat exchanger was quite different according to the tube arrangement, and the flow between the fin plates in the vicinity of the tube was three dimensional one including the vortex street. A comparison between the observed results and heat transfer data was discussed. By the naphthalene sublimation study, a particuler distribution of local mass transfer coefficient on the fin surface was discovered, which was due to the vortex street generated in a boundery layer. With a comparison between the heat transfer and mass transfer data, it was shown that the naphthalene sublimation technique was applicable to the heat exchanger.

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In this paper, the mechanism of the oscillatory combustion is studied by applying the equation of continuity, the equation of motion and the equation of energy to the unsteady flow in combustor. Main results obtained are as follows. (1) The driving force of oscillation is the fluctuation of heat adding rate, so the magnitude of both pressure and velocity fluctuations is proportional to the fluctuation of heat adding rate. (2) The frequency of oscillation has a similar dependency on the combustor length with an acoustic resonance frequency. But, since the phase shift of the velocity fluctuation at x=x₂ occurs through the interaction between the combustion field and the acoustic field, the frequency is always shifted, more or less, from such resonance frequency and the amount of such frequency shift depends on the flame type and the burning condition. (3) The amplifying conditions of oscillation are made clear and are classified by the distribution diagram of the pressure amplitude.

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This paper deals with the oscillatory combustion occurring in the diffusion flame of liquid fuel spray burning. Main results obtained are as follows. (1) Major part of the fuel burns as the droplet flames. Most of these droplets burn penetrating the surrounding gas and with the flame type of a wake flame. (2) Fluctuation of burning rate that is the driving force of oscillation is brought about by the transition phenomenon of the flame type of droplets. From the above result, the magnitude of the pressure fluctuation can be correlated with the burning condition by using a parameter f. (3) Dependency of the frequency on the combustor length agrees well with the prediction obtained in 1st Report and the dependency of that on the burning condition can be explained quantitatively by examining the relation between the burning condition and the parameters |B| and ∈ which are the synthetic parameters representing the burning condition.

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The local combustion efficiency and the local heat release rate in an upright cylindrical combustion chamber having a diameter of 100 mm and a length of about 1000 mm, were experimentally determined from the contents of combustion products. The burnt gases sampled from ten positions in the combustion chamber were analyzed with gaschromatograph. The experiments were carried out under the following conditions : Initial mean diameter of atomized fuel=40∼140 microns, air excess ratio=0.8∼1.6 Oil for a jet engine (JP-4) whose chemical compositions were known, was used as a fuel. In addition, the local combustion efficiency and the local temperature of burnt gas were determined theoretically and compared with experimental results. The theoretical results were in good agreement with experimental ones.

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In this paper, the authors investigated the relationship between case-hardening conditions and the bending fatigue strength of a gear tooth from the view points of the residual stress generated on the root fillet and the increase of the materials strength (hardness) by case-hardening. The main results obtained from this experiment are summarized as follows. (1) By proper selection of case-hardening conditions, the endurance limit of a gear tooth can be raised by about 100% of that of an unhardened gear. (2) The contribution of the residual compressive stress generated on the root fillet to the fatigue strength reaches 40∼50% of the increment of the endurance limit by case-hardening. (3) There exists an optimal case thickness for the bending fatigue strength of casehardened gears and an excessively large case thickness causes a decrease in the endurance limit. (4) A formula for the calculation of the endurance limit of a gear tooth is developed, assuming that the residual stress influences on the fatigue strength of metals as mean stress and H_V-σ_u (hardness-endurance limit under pulsating stress) and H_V-σ_T (hardness-ture breaking strength) diagrams are presented on the basis of the existing data. And the calculated values according to this formula and the diagrams show a good agreement with the experimental results.

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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.

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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.

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By deep-drawing sheet metals of aluminium which have various grain-sizs, the friction occurring in the flange part is measured under different lubricating conditions. It is found that the material with a larger grain-size has a higher coefficient of friction, and this phenomenon becomes noticeable at high tool pressure. As to the surface texture, the roughness of deformed material increases with grain size. The high coefficient of friction observable in a large grain size seems to originate in the fact that, on account of the relatively large space occupied by the surface pits, a lubricant previously applied on the metal blank becomes insufficient to fill up that pit-space, and so can not be squeezed and pressurized. It has been concluded that the difference in the lubricating conditions according to the grain-size is attributable to the hydro-static pressure generated in those trapped lubricants.

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In order to put electrospark forming method to practical use, generalized informations are necessary. Present paper is concerned with the analyses on the deformation of a cylindrical shell and a circular diaphragm in electrospark forming. The analyses are based on the Newtonian equation of motion, the maximum shear stress theory and a few assumptions. The applicability of the analyses was confirmed by the experiments with specimens of aluminum, copper and steel. Finally, the laws of similarity which can predict the deformation of the cylindrical shell and the circular diaphragm are obtained on the basis of the analyses and the experimental results.

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