This paper contains a three-dimensional solution for the stresses and deformations arising in a semi-infinite elastic body with a spherical cavity, when the body is subjected to uniaxial tension. The solution is presented in integral form and infinite series and is deduced with the aid of six stress functions combining the Boussinesq, Neuber and Dougall stress functions. Numerical results are given for the stresses on the surface of a spherical cavity and along the z-axis and at the plane boundary corresponding to several values of radius of the cavity. The results obtained thus are compared with the axi-symmetric solution in the previous paper.

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A theory is developed in this paper to explain the effects of hydrostatic pressure on the deformation of cast iron. It is assumed that a graphite flake in an iron matrix acts as a penny-shaped crack. The external stresses necessary to induce a finite plastic zone near the crack tip are calculated with rough approximation. The analysis provides a qualitative explanation of the following experimental evidences : (1) Superposed hydrostatic pressure increases the flow stress of cast iron. (2) The increase of flow stress due to hydrostatic pressure is reversible with respect to the hydrostatic pressure. (3) Hydrostatic pressure decreases the anisotropy of cast iron usually observed in torsion tests.

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Rolling contact fatigue tests were conducted under pure rolling conditions using carbon steel and alloy steel rollers. Hardnesses of pitting rollers were in the range 160 ∼ 100 HB (mating roller hardness was 420 HB in the case of unequal hardness combination). The results obtained are as follows : (1) Theoretical limits of contact stress p_max allowable on the steel rollers are in the range 0.31 ∼ 0.52 HB (kg/mm²) when they are calculated under assumption that pitting does not occur until the reversed shear stress τ₂max in rolling contact reaches the endurance limit τ_w in reversed twisting. (2) In the cases of unequal hardness combination, pitting occurred at Hertzian stresses less than 0.3 HB when the roughness R_max2 of harder roller was greater than the theoretical oil film thickness h_min. For instance, many pits occurred at a Hertzian stres of 50 kg/mm² = 0.17 HB when a 300 HB roller with a roughness of 1μm R_max was combined with a 420 HB roller with a roughness of 3 μm R_max. (3) However, no pitting occurred at Hertzian stresses greater than the upper limit of theoretical pitting limit p_max = 0.52 HB when R_max2 < h_min. For instance, no pitting occurred until 10⁷ rotations even when loads corresponding to Hertzian stresses of 113 (=0.71 HB), 140 (=0.61 HB) and 165 (=0.55 HB) kg/mm² were applied on 160, 230 and 300 HB steel rollers respectively. (4) Appreciable increases in hardness were observed at the subsurface of pitting rollers when the rollers were rotated at Hertzian stresses greater than the theoretical pitting limit 0.52 HB (kg/mm²).

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It has been well known that the elastic constants and breaking strength of the spheroidal graphite cast iron are larger than those of the flake graphite cast iron, etc. But, the quantitative explanation on that has not been given. In this paper, the theoretical method to estimate stochastically the elastic modulus and Poisson's ratio of the spheroidal graphite cast iron is investigated by using the finite element method and the Monte Carlo method. The simulation model of the cast iron is composed of the elements (a) and (b), (a) being made of a matrix only, (b) of an element of the graphite grain enclosed by a matrix. These elements are disposed in the composed model by using the random unmbers and the finite element method on two-dimensional problems is used to analyze the deformation behavior of this model

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An incremental finite element method of the large elastic-plasic deformation of non-axisymmetric metal diaphragms which are edge-clamped and bulged by hydrostatic pressure has been formulated. The diaphragm is divided into a number of flat triangular elements and the behavior of a typical element is described in terms of the displacements of its nodes. The authors derive stiffness matrices, taking account of effects of shape change on the equilibrium equations, from a total differential of the equivalent nodal forces. In order to check the theory, numerical calculations were carried out for the bulging of a circular diaphragm under hydrostatic pressure. Theoretical results were in reasonable agreement with experiments for aluminium sheet and also with numerical solutions by means of a finite difference method.

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It is important to clarify how the propagation of a longitudinal wave in a visco-elastic bar is affected by the lateral inertia. This paper purports to clarify the coupling effect of the viscous force and the lateral inertia force on the propagation of the wave, especially in the vicinity of the wave front. It is assumed that the visco-elastic material is represented by a Voigt model. The equation of motion of the bar, in which the effect of the lateral inertia is taken into consideration, is obtained with Hamilton's principle. The solutions of the equation are presented for two cases. One is the case of one end of the bar being impacted at a constant velocity and the other is the case of the stress or strain at the impacted end being kept constant.

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The fundamental equations for the free vibration problems of pressurized axisymmetric shells are presented, and they are solved by the finite difference method. For numerical examples, the effects of internal pressure on behaviours of free vibrations of cylindrical and spherical shells are investigated. The results are compared with experimental data and with those obtained using Timoshenko's fundamental equations for cylindrical shells. From these examples, it is found that the results obtained by our method almost coincide with experimental data, but the results based on Timoshenko's fundamental equations are slightly different from our results.

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The experimental performance of a flat-plate cascade has not been clarified, although the theoretical one was calculated by Weinig about 40 years ago. Reliable two-dimensional cascade data for thin flat-plate profiles have been obtained by means of the porous wall cascade tunnel testing technique. These results have been compared with Weinig's classical theory. The cascade interference coefficient coincides with the theoretical value in the case of a space-chord ratio smaller than unity. Some potential theories with respect to the effect of blade thickness have been also discussed based on the experimental data. Lastly, the available design diagrams for a flat-plate cascade have been presented.

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Turbulent jet of a dusty gas in a fully developed region is studied using following assumptions; an interaction force between the dust particles and the gas stream follows the Stokes law; a mean velocity of particulate phase is equal to that of gas stream, but fluctuating components of particulate phase are negligible as compared with those of gas stream; and the settling velocity of particles is small compared with the characteristic velocity of gas stream. A similar solution of velocity is obtained under the uniform concentration of dust particles. It is shown that eddy viscosity is reduced due to the presence of dust particles, and that rates of the decrement of axial velocity and of the spread of jet of dusty gas are small compared with those of gas jet. An applicable range of the present analysis is determined by the assumptions. Results of the analysis well explain experimental results by M. K. Laats.

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In this paper the pressure losses of the symmetrical Y-branches in the horizontal flow of air-solid mixtures are treated. The branch angle is 30°, 45°, 60°, 90° and 120°. In case of air stream alone the pressure losses of the branches are given by a quadratic expression of air flow ratio and the experimental formulae, which give the pressure losses in branches, are obtained. By adding the additional pressure losses due to solids in the air stream to those of the air stream alone the equations for the pressure losses in the air-solid two-phase flows are obtained. The coefficient of pressure losses depends on the air flow ratio and the solids loading ratio. According to the experiment the solids are distributed into the branch pipes nearly in equal quantity independently of both air flow ratio and branch angle.

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In the previous paper, we presented the diffusion model of pseudo-shock waves, by which the time-mean static pressure distributions in pseudo-shocks could be explained. In the actual flow, however, the pseudo-shock wave is not steady, but oscillates about a mean position and causes the fluctuations of the local static pressures. In this paper the oscillation phenomena of pseudo-shocks in a straight pipe were experimentally investigated and the causes and the frequencies of oscillations were discussed. As the results, it was found that the oscillation of the pseudo-shock became stronger with the increasing Mach number and the maximum wall static pressure fluctuation induced by the oscillation amounted to about 60 per cent of the difference of static pressures before and behind the shock. Moreover, it was showed that this oscillating phenomena could be explained by the interaction of the shock with the small disturbances existing in the supersonic flow upstream the shock.

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To investigate the effects of the number of impeller blades on the pump performance under air admitting conditions, tests were carried out for semi-open impellers having three, five and seven blades, respectively. The flow patterns in the impellers were also observed. When the number of impeller blades is sufficient, namely, five or seven, the flow pattern in the impeller is not altered substantially by air admission, and the performance of the pumps is decreased in a similar tendency. An impeller with three blades, however, shows an abnormal tendency in a small air range 9_s/Q ≤ 0.03, namely, the head developed is increased by the admitted air, when φ₀ > 0.03. The admitted air improves considerably the unevenness of flow pattern due to the unreasonable form of the impeller passages, and causes an increase of the impeller work and the pump head. When the air quantity is increased further, all of the pump performances fall repidly and the pumps lose their prime. With knowledges of the test data under a pure water running, an assessment of the pump performance under the air admitting conditions is made.

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To clearify the flame structure of a spray burner, distributions of droplets, and those of temperature, flow velocity and gas composition were measured within the flame of an air-atomizing burner. The magnesium oxide method providing a shutter mechanism was adopted to detect the droplets. To measure the gas temperature, a suction pyrometer free from the effect of droplets was specially desined. The following were concluded. (1) The flame may be simplified as a model consisting of three regions. Designating them as A, B and C in order of distance from the burner nozzle, A is a region where a heterogeneous mixture containing many droplets is burning; in B, only a combustible gas fed from A is burning continuously; in C, its remainder is burning intermittently. (2) It can be assumed that the droplets in A do not burn individually, but fuel vapor evaporated from them collects and burns like a gas diffusion flame.

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A new combustion method for decreasing the emission level of nitrogen oxides is studied and developed. The combustion is divided into two parts, the primary and the secondary, and about 50-60 % of the stoichiometric air is supplied to the primary combustion to complete the 'partial combustion'. We found that considerable amounts of HCN and NH₃ are formed in this region and these are closely connected with the overall emission level of Nox. These primarily formed nitrogen compounds are converted to NOx through the secondary combustion at the rate of about 80 %. Completely premixed 'partial combustion' is effective to decrease these compounds, and therefore, the overall emission level of NOx. The effects of some catalysts are also studied.

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Studies were carried out on the high temperature corrosion of exhaust valve in a diesel engine, by the procedure of accelerative testing. The authors could, therefore, separate the effects of various factors which affect the corrosion rate every two hours of testing. As the result of experiments, the following conclusions were reached. (1) Effects of the temperature and the air factor on the high temperature corrosion are both remarkable. However, the effect of the temperature is greater than that of the air factor. Consequently, unlike the case of a spark ignition engine, a decreasing tendency of corrosion rate is observed as the air factor increases to a large value. (2) The effect of vanadium in the fuel on the high temperature corrosion is small compared with those of the temperature and the air factor. (3) The corrosion rate is proportional to the stress, though the effect of stress is comparatively small. (4) The corrosion rate is proportional to the product of impact energy and the number of impacts during the prescribed period.

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In the last reports, assuming that the surface irregularities of specimens were isotropic and had a form of similar truncated cone whose deformations were elastic, plastic and elasto-plastic, the analytical solutions of equivalent gap for the fluid leakage between contact surfaces were verified with the experimental results using a lapped carbon steel. In this paper, the specimens, which are finished by lathing and grinding, are axamined. The results obtained can be summarized as follows : (1) In the case in which the phenomenon of leakage was a radial and sector flow, the experimental values of equivalent gap obtained by assuming the surface roughness as anisotropic were in agreement with the analytical values with deviation about 8 %. (2) The characteristic curves of parameters a and b for the carbon steel listed in the 2nd report can be applied for the materials tested in this experiment.

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As the nonuniform motion mechanisms which constitute a function generator, the geared linkage mechanisms which are composed by adding the spur gears to each pair point of the planar four bar mechanisms were classified and analyzed. The mechanisms were divided into six classes, and the shapes of the displacement curves were made clear and the characteristic of each mechanism was investigated. And, the conditions and basis for designing the mechanisms of which the motions were swing and rotation were analyzed and made clear. Next the static and dynamic characteristics of the mechanisms were analyzed and, by comparing the theoretical values with the experimental ones, the characteristic of the geared linkage mechanisms as a function generator was investigated.

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This report presents the test results about bending fatigue strength of gear tooth under two kinds of repeated 16 steps program loads which are gradually increasing or decreasing. Load frequencies are gamma distributed. Materials of test gears are normalized S38C and carburized SCM21. Each of test gears has module 4mm, pressure angle 20 degrees, number of teeth 27 and width 8mm. Miner's cumulative damage theorem is statistically tested and the following facts have become clear : (1) Factor of loading sequence and load frequency distribution are not significant. (2) Factor of material is significant. (3) Fatigue life has a trend that the longer the program load cycle period is, the longer is the fatigue life in comparison with the values calculated from Miner's theorem. (4) Frequency of stress which is higher than fatigue limit strength has little correlation to C. (5) The scatter of Miner's constant C is mainly due to the scatter of fatigue life, and C itself is rather deterministic.

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This paper deals with the theoretical and experimental studies on the behaviours of a helical gear with the finite width under load transmission. The load distribution along the line of contact on the helical gear teeth was made clear. The stiffness of a pair of the helical gear teeth with the finite width during the whole engagment period was evaluated. The behaviours of a driven gear under loading were made clear with the use of the evaluated stiffness. The theoretical behaviours agreed well with the experimental results. The behaviours of a driven gear under loading were not found for a pair of helical gear with overlap ratio greater than 1.0. On one pair of teeth of helical gears, the behaviours of load transmission changed very gently during the contact in comparison with those of spur gear.

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Experiment of milling process, which is an unsteady cutting process with varying undeformed chip thickness, is carried out by using annealed and rolled aluminium, copper and 7 : 3 brass as work material. Effects of the strain hardening on the cutting process are discussed. When cutting the metals such as aluminium and copper having a low yield point and a high strain hardening characteristic, multiple patterns of cutting force variation may appear. This phenomenon is considered to result from the transitional period in an initial cutting process being very long for these materials, and cutting energy decreasing remarkably when the ratio of the depth of work hardened layer to the undeformed chip thickness exceeds the critical value. This becomes more conspicuous when a large rake angle tool is used. The above inference is confirmed by the measurements both of the cutting force of a special workpiece to eliminate the hardened layer by annealing, and of the hardness distribution on subsurface of workpiece.

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