This paper contains an exact solution for the stresses arising in an elastic circular cylinder with an oblate spheroidal cavity or an internal penny-shaped crack under tension. The solution is represented by a combination of the solution which is regular in the outside of a cavity and the solution which is regular in an infinite circular cylinder, and is deduced with the aid of Dougall's stress functions. Two sets of harmonic stress functions are given by simple expressions referred to the cylindrical and oblate spheroidal coordinates. The boundary conditions on the surfaces of the cylinder and of the cavity are satisfied by using the relations between the cylindrical and oblate spheroidal harmonics. And the solution for the internal penny-shaped crack is given for a limiting case of the solution for the oblate spheroidal cavity. Numerical results for stress distributions, stress concentration factors and stress intensity factors are shown graphically.

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Considering a physical phenomenon of contribution of the internal stress in definite subsurface layer of metal to the X-ray diffraction, the authors derive a general fundamental formula existing between measured stress and internal stress. Then they propose the exact theories of residual stress measurement for the Front Surface Method and the Back Surface Method by successive thin layer removal in a plate, and show an example of application by characteristic X-rays of Cr and Co.

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Flexible tape deformation under a concentrated load is investigated theoretically and experimentally. The deformation solutions are obtained for both plane and cylindrical tapes under a concentrated load. From calculated results, design philosophy for a head scanning mechanism against a plane or cylindrical magnetic tape is discussed comparatively. It is also found that the theoretical results are in good agreement with the magnetic tape deformation in a practical rotating head mechanism.

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Pseudo-shock waves in a divergent channel were optically observed by a schlieren method, and the lengths of the pseudo-shock region as well as the static pressure distributions were obtained from pressure measurements. The dimensionless length of pseudo-shock in the divergent channel divided by the mean equivalent diameter before and behind the shock is nearly equal to that in a constant area duct. The static pressure ratio and Mach number across the pseudo-shock in the divergent channel were compared with those in a constant area duct, and the effect of the divergence on the characteristics of the pseudo-shocks was discussed. Assuming a one-dimensional flow and using the experimental pressure distributions in the pseudo-shock region, the flow variables such as the static and stagnation pressures across the pseudo-shock in the divergent channel were calculated. The calculated results agree well with the experimental values.

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Frequency characteristics of a plug-train system for infinitesimal sinusoidal waves are investigated experimentally by using an air-water system at rest in a pipe and theoretically by proposing a one-dimensional linear model. The characteristics are found similar to those of a bandpass filter. A high frequency cutoff occurs owing to the inertia of liquid plug and the compressibility of gaseous plug. The cutoff frequency increases with a decrement of plug length and a difference from 0.5 in void fraction. The low frequency cut off is due to the surface tension of liquid and the inertia of liquid plug. The cutoff frequency increases as the plug number increases and the liquid plug length decreases. The phase velocity of wave agrees with the analytical prediction based on the liquid inertia and the gaseous compressibility within the passband except in the neighbourhood of low frequency cutoff frequency.

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Discharge coefficients of venturi meters and nozzles employed in swirling flows were measured and the change of the coefficients due to swirling components was discussed in relation to the distributions of velocities, pressures and energies measured across sections before and after the constriction meters. Formulae of the discharge coefficients to correct the swirling components were given for the swirling flow range which will be expected to occur in pipe lines in engineering use.

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Change of discharge coefficient of elbow flow meters due to swirling flow component was analyzed. The theory based on a potential flow model shows that even a weak swirling flow component which will be found in the flow in actual pipe lines has a considerable effect on the discharge coefficients of elbow flow meters. Experimental verification for this result is also given.

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The cobra-type yawmeter is generally used for simultaneous measurement of by the null-reading method, but these are some special cases in which it is necessary to use it by the fixed direction method. Based on the experimental results on yaw characteristics of yawmeters of various head shapes and observation of flow on the probe-heads by tests with magnified scale models, the head shape suitable for the fixed direction magnified scale models, the head shape suitable for the fixed direction measurements is discussed in this paper. The results are summarized as follows. (1) A cobra-type yawmeter of semicircular head shape is preferable to the conventional trapezoidal head yawmeter for flow measurements by the fixed direction method. (2) A head shape modification by chamfering the front sharp edges of the trapezoidal head results in an appreciable improvement of both yaw characteristics and sensitivity of the yawmeter. (3) The semicircular head yawmeter is also superior to the trapezoidal head yawmeter in sensitivity for flow measurements by the nullreading method.

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The authors have published the numerical and experimental studies of heat transfer in parallel nozzles with two-dimensional critical flows in their previous 1st and 2nd reports. In this report, the studies are extended to the case of convergent nozzles. The compressible laminar flows are considered for convergent nozzles at the critical state, and heat transfer characteristics are calculated numerically. According to the results, the critical flow rate increases with a decrease of convergent ratio, and the variation of local Nusselt numbers along the flow direction becomes small by the effects of accelerated boundary layers. Furthermore, the experimental values of mean Nusselt numbers of the critical flow "Numc" agree well with the numerical results calculated on the basis of a laminar flow in the long-size convergent nozzles. From the comparison between the experimental and the analytical results, the range of nozzle characteristics numbers where laminar flows occupy the whole length of the nozzle is determined. Beyond this range described above, a turbulence arises and a turbulent flow is predominant in the critical nozzle, therefore, an experimental expression of mean Nusselt number is presented.

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This paper discusses forced vibrations in an unsymmetric piecewiselinear system excited by general periodic force functions. The system has no damping. The superharmonic resonances up to the second order are analysed by means of a perfect Fourier series method. As the simplest example, the exciting forces are assumed to be of even function with the second higher harmonics only. The theoretical resonance curves are computed by a digital computer and are compared with the results obtained by an analog computer. They show a fairly good agreement.

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The free vibration of radially stiffened annular plates is studied by the Ritz method using a spline function as an admissible function for the deflection of the plates. The transverse deflection of the plate is written in a series of the products of the deflection function of a sectorial beam with small angle and the trigonometric function of angular coordinate. The frequency equation of the plate is derived from the conditions that the Lagrangian takes a stationary value. The deflection function of the sectorial beam is approximately expressed by a quintic spline polynomial, which satisfies the equation of flexural vibration of the beam at all points dividing the beam into smell elements and also the boundary conditions at both ends. The present method is applied to annular plates with radial stiffeners located at equal angular intervals on both surfaces of the plates. The natural frequencies and the mode shapes of the plates are calculated numerically, and the effects of the stiffeners on them are studied.

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A transformation method with two parameters is described. A new correction of the Lagrange multiplier is presented and its theoretical results are proved. Based on the results one modified algorithm to improve the rate of convergence and make the existence of the saddle point possible is proposed. The present method is an efficient one for nonconvex function problems with constraints, does not suffer from numerical difficulties and has a rapid convergence rate. The method is applicable successfully to many nonlinear programming problems with a variety of nonconvexities and nonlinearities.

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This paper presents the inertia effects on the turbulent lubricant film of the thrust bearings. The stream lines for the sector bearing of constant film thickness are observed. The influence of centrifugal acceleration on the lubricant flow flow is found to be considerable, but in the turbulent regime, the radial deviation of the stream lines is smaller than in the laminar regime. The velocity distributions of a three-dimensional turbulent shear flow are analyzed. The calculated results of the pseudo-stream lines agree well with the experimental data.

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For the sake of quantitative evaluation of the local state of oil-film-formation in spur gears, the authors tried to analyze statistically the voltage between meshing teeth which was measured by electrical resistance method, using an analog-digital converter and an electronic computer. The local state of oil-film-formation at every meshing position on the line of action or no a pair of gears was evaluated as the distribution of the voltages between meshing teeth. It is shown that the local state of oil-film-formation in gears is affected significantly by the dynamic load and the surface defect of gear teeth. These analyses will be useful for elucidation of the mechanism of pitting in gears.

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The effect of module on scoring resistance of the Vau-Null gear pairs of the same gear ratio at the constant centre distance was examined from the point of view of the flash temperature. It was revealed from the calculated results of the flash temperature and the experimental results on scoring tests that the effect of module on scoring resistance is complicated. When the module of the gear pairs is comparatively small, the flash temperature is approximately proportional to module. Further, when the module is large, the effect of module on the flash temperature remarkably increases. Therefore, the scoring resistance will remarkably decrease. The above cited facts well coincide with the experimental results on scoring.

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By means of experimental rolling of screw-like and gear-like components, shapes which blank cylinders come to develop in a process are observed in detail and processes of forming their functional profiles are examined. In order to realize the characteristics of deformation, a method was taken in which experimental processes were examined comparatively by establishing a model process under some simple assumptions accepted as plausible. By this means, chief controlling factors of the process have been pointed out. A distortion observable in the cross-sectional figure of a workpiece is important. This distortion which affects considerably the forming of profile features cannot completely be represented by the proposed model. It is also important to realize that the material undergoes different cumulative amounts of reduction according to its peripheral position occupied when the rolling starts.

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In the experimental rolling of screw-like and gear-like components with flat dies the split plug devised by one of the authors is employed for detecting the deformation of material during the process. By examining a distorted grid of the plug, buried in the workpiece, a three dimensional pattern of the material flow has become clear for the first time. In has been proved that the central portion of the blank cylinders does deform so as to proceed the rolling action and this central deformation affects drastically the formation of functional features of the component surfaces. Efficacy of forming depends solely on the balance of these exo- and endo-deformations. On the basis of this deformation analysis, the mechanics of a rolling process was clarified, and the fundamental controlling factors pointed out.

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Using a power circulating type gear testing machine for straight bevel gears, the dynamic load of gear teeth, the torque variation and the bending vibration of gear shaft are measured under a constant torque with the speed of gear varied, and the results are discussed. The results are as follows : According as the speed of gear increases, the dynamic load factor varies in accordance with the contact position on a tooth trace and the load. The dynamic load factor is influenced more at the toe or center of bevel gear tooth than at the heel by the torque variation and the bending vibration of gear shaft. And the torque variation and the bending vibration of gear shaft are influenced considerably by the torsional vibration at the natural frequency of meshing gear.

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Weldability and bending fatigue strength of rim materials for welded structure gears were examined and the recommendable materials were indicated. Effects of rim and web thickness on root fillet stresses were investigated experimentally. The root fillet stress shows the highest value at the middle of the face width and it increases as the rim and web thickness decrease. Welded gears with different rim thickness were tested using a pulsator of hydraulic type. It was found that the bending fatigue strength of gear teeth decreases with a decreasing rim thickness and that the rim part may break when rim thickness is smaller than one module. The minimum allowable rim thickness for welded gears is also suggested, from the viewpoint of bending fatigue strength, on the basis of experimental results.

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The impact force is measured usually with the split-Hopkinson-bar method. However, in this method, the measuring time is restricted by the length of the bar. Therefore, one of the authors suggested formerly a new measuring method of the impact force based on the theory of propagation of longitudinal elastic stress wave. In this method, the impact force acting on the end of the bar can be estimated from the measured stresses at two suitable points on the bar, and without any restriction of its time range. We designed and completed a new measuring system based on this method. Using this system, we measured the blanking force in the high speed blanking test. As the result of the test, we confirmed that the measuring system is considerably effective for the purpose.

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