In the present paper, the influence of temperature history on transient stage creep is discussed. The experiments were made employing a 0.15 per cent carbon steel and the results were interpreted by analysis. When the temperature is elevated quickly during a creep test, there appears a temporary increase in the strain and its increment is slightly larger than the value estimated by neglecting the influence of temperature history, in other words, from the concept of "mechanical equation of state in solid". On the contrary, when the temperature is lowered quickly from a certain value, we see a temporary retardation of creep which is called "incubation period"or "induction period". When the temperature variation is periodic, the both effects cancel each other and the combined influence is not so serious as to defy application in mechanics problems.

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In the present paper, the analytical relation of creep under temperature cycling to static creep under steady temperature is presented and is examined by the creep tests under step-wise temperature cycling on a low carbon steel, a 13 chrominum steel and an AISI 304 type stainless steel. It was found that temperature cycling does not give a serious influence on creep. The creep under cyclic temperature can be predicted by introducing the idea of the equivalent steady temperature for creep, which is determined from the data of usual creep tests at steady temperature combined with the prescribed program of temperature cycling. The analytical results are in good agreement with the experimental results under periodic stepped variation of temperature.

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In the present paper, the influence of temperature cycling on the accelerated stage creep and the rupture life is discussed by employing AISI 318 type stainless steel. In this discussion, the strength of material under temperature cycling was compared with that under steady temperature by introducing the idea of the equivalent steady temperature for the rupture life of material under temperature cycling. Embrittlement of a creeping material subjected to temperature cycling is significantly larger than in the case of steady temperature. It would probably be because of a difference in the metallographic structure change occuring during the tertiary stage of creep, for both series of tests.

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Dynamic creep and fatigue tests were carried out with an 18-8 Mo-Cb steel at a temperature of 650°C. The results were discussed from the standpoint of the analysis, which had been proposed by the authors previously, concerning the prediction of dynamic creep and fatigue strength from the information on static creep and creep rupture tests together with reversed stress fatigue data. The prediction by the analysis showed a satisfactory agreement with the experimental results as for a practical purpose, although a little discrepancy was observed due to the acceleration of the precipitation hardening by alternating stress. In order to contribute to clarification of the relation between the precipitation hardening characteristics of the material and its strength characteristics, the electron-microscopic observation of structure, hardness test and creep rupture test after the dynamic creep were carried out. Their results were discussed in connection with the discrepancy between the analysis and experiments.

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In this report, the compression of a wedge by a rigid flat die when the initial condition is symmetrical has been investigated. Ten modes of deformation of the wedge are expected depending on the friction at the die surface and the thickness of the wedge but the complete solutions have been obtained for seven modes of them. Some considerations have been made on the extremum principle taking into account the energy dissipation at the frictional surface and applied to the kinematically admissible field to estimate the load in the modes for which the complete solution is unknown as yet. It seems that the kinematically admissible field which satisfies the stress boundary condition on the frictional surface gives an estimation of the load nearly the same as that of the exact solution. It has been shown that the method to estimate a mean value of strain from the work of deformation is convenient.

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The load on and deformation of a wedge compressed by a smooth rigid flat die were investigated. Seven types of slip line field have been predicted for the wedge which has any inclination to the die face. These fields are classified into three modes of deformation where (a) the material flows separately on the contact face, (b) dead metal zone is in contact with the die and (c) the material flows only on one side of the wedge. Four of the seven fields are complete solutions. The width of the contact face, load or its upper and lower limits and the mean strain of the wedge were compared with these modes of deformation, and it has been revealed that the mode (a) exists in a very narrow range of the inclination and thickness of the wedge and is hardly realized and that the load of the mode (b) is larger than that of mode (c) but as the mean strain is small, mode (b) will be realized rather than mode (c) when the inclination of wedge is small and the thickness of wedges moderately large and when the material is in the state of strain hardening.

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The author has studied the lateral vibration of an L-bar with one end built-in and the other free. Two kinds of vibration can be considered, viz., the vibration perpendicular to the plane of the L-bar (including a twisting vibration), and the vibration in the plane (including a longitudinal one). To find the frequency equations, we give some unknown constants to the boundary values, and determine such vibration function and unknown constants as to minimize the Lagrangian. The results are given by the nondimensional frequencies in the table and diagrams. Further, in this paper, the author compared these experimental data with the Rayleigh method and strict solutions, and explained the combined vibrations caused by the inter-relation of some ratios and angles between the legs of the L-bar.

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In this paper, the fundamental differential equation of vibration of a cylindrical shell in a single displacement is discussed on utilization of the fundamental differential equation of a thin cylindrical shell for the statical problem introduced by the present author. This fundamental equation may be utilized to discuss the problems of general forced vibrations, of pressurized cylinders, or of vibrations of short wave length, etc.

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Experiments on the fluid friction of a rotating disc which has protuberances on its surface are performed. The author arranged blades radially or concentrically on the disc and on the vessel, and carried out experiments on same combinations of the disc and vessel which have blades or smooth surfaces. The main results obtained are as follows : 1) The relation between C_f and R₆ can be expressed by C_f=α·R₆^-0.1575. 2) The value of α increases first rapidly with the number of blades and then gradually approaches to a minimum value. 3) The shapes of blades (logarithmic and straight) have little influences on C_f for small clearance. 4) The increment value of C_f induced by the blades on the disc is nearly twice as large as the value by the blades on the vessel. 5) The boss ratio smaller than 0.5 has little influences on the value of C_f.

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Unsteady boundary layers, caused by a fluctuating circulation, are investigated theoretically. Incompressible, two-dimensional, laminar flow is assumed. Further assumption is made that the magnitude of velocity fluctuation is small compared with the mean velocity and that the frequency of fluctuation is low. Blasius'series method of solution of the boundary layer equations is extended to the unsteady flow. Detailed calculation is shown of the flow around a body symmetrical, with velocity fluctuation outside the boundary layer antisymmetrical, with respect to the undisturbed stream. As in the steady flow problem, the solution of the unsteady boundary layer equation can be expressed as a linear combination of a set of universal velocity distribution functions. Four of the functions are actually computed, by use of which boundary layer separation from a circular cylinder with circulation fluctuation is discussed. The separation point movement is found to consist of a quasisteady and an unsteady components, the latter increasing with frequency.

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A method of calculating the fluctuating boundary layer on a circular cylinder, performing rotational oscillation in a uniform flow, is presented. Two-dimensional, laminar flow of an incompressible fluid is assumed. Equation of motion is linearized on the assumption that the velocity fluctuation in the boundary layer is small. The frequency of the fluctuation is also assumed rather low, thus retaining terms up to the first order in frequency. By extending the Blasius'series method to unsteady flow, solutions are expressed as linear combinations of a family of universal functions. As an example, the torque fluctuation of the cylinder is calculated. Streamline patterns near the separation point of the boundary layer are calculated, by observation of which a new criterion of the separation of the unsteady boundary layer is proposed. It is based on the asymptotic behavior, at a large distance from the solid wall, of the streamlines.

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Boundary layers of a flat plate located parallel to the mean flow in the downstreams of a cylinder row in motion were empirically examined, in order to obtaine fundamental knowledges concerning the mutual interference between blade rows working in a viscous incompressible fluid. Influenced by the fluctuation in the main stream velocity, a unique turbulent boundary layer, which may be called "forced turbulent boundary layer", was developed at a distance from the leading edge of the flat plate. This boundary layer has several properties different from those of ordinary turbulent boundary layers. The characteristics, such as mean and fluctuation velocity distributions, of the forced turbulent boundary layer as well as of the boundary layer under transition to this type were investigated. With increased fluctuation velocity in the main flow around the leading edge, the thickness of the boundary layer in the reg on near the leading edge increases. Factors influencing this phenomenon were studied.

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A unique turbulent boundary layer-forced turbulent boundary layer-which is found on a flat plate, located at zero incidence angle in the downstream of a cylinder row in motion, as dealt with in the 1 st Report, was investigated theoretically in this report. As the result ; 1) An unknown function in the experimental formula of velocity distribution in the boundary layer under transition to forced turbulent flow was calculated by means of the equation of mean motion. 2) The mean friction coefficient in the transition region was calculated by means of the equation of momentum. 3) The position where the transition completes was estimated theoretically. 4) In the region where the forced turbulent boundary layer is fully developed, the mean friction coefficient was estimated theoretically.

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In this report, a method is presented for the calculation of a potential flow through straight cascades of thin wings. The calculation of the flow has been based on the singularity method : normal velocities v are cubic functions of abscissae x, and tangential velocities u, corresponding to normal velocities v (=0, 1, x, x², x³), are determinable by a conformal mapping of the cascade into a unit circle. As the author has introduced the recurrence formulae for velocity functions, an improved accuracy has been obtained by using the velocities u of higher degree. This method will be applied to the calculation of the flow through a centrifugal pump impeller in the following reports. In this report, the author has applied it to the calculation of the flow through a straight cascade of thin wings, comparing with the results hitherto published in numerical examples.

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In this report, the author has applied the thin wing lattice theory mentioned in 1 st Report to the two-dimensional flow through a centrifugal pump impeller with logarithmic-spiral blades. Compared with other methods, the calculation by this method is comparatively easy and accurate, even if the blade angle is small and the number of blades is large. Numerical examples of the performance curve and velocity distribution on the blade agree with the exact solutions obtained by Busemann and Shirakura respectively. Equations and numerical examples are also shown for the blades of approximately logarithmicspiral forms.

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Usually, the breadth of a centrifugal pump impeller is not constant, but a function of radius. A method for the calculation of the flow through such impeller is presented in this report. The author has treated such case by applying the method of series expansion, the method of generalised displacement flow mentioned in 2nd Report, and the thin wing lattice theory presented in 1st Report. Compared with other methods, this one has no limitations for the number of vanes and the vane angles.

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In the semi-axial pump impeller, the fluid flows on the conical surface and the breadth of the flow path is not constant usually. In this report the author has treated such cases in which the inclination of the flow path and the variation of impeller breadth are small, and the shape of blade is nearly flat. In such cases the flow can be analysed by taking the flow of an axial pump impeller with flat plate blades as a basis, and adding together the effects of the inclination of the flow path, the effect of the breadth variation, and the effect of blade camber. The author has analysed these effects by applying the method of complex velocity function presented in 1st Report, the method of generalised displacement flow introduced in 2nd Report, and the method of series expansion mentioned in 3rd Report.

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In this paper, the radiant heat transfer from a luminous flame is treated theoretically and experimentally, from the view point that the radiation from a cloud of carbon particles is most effective. In the case where only the cloud of luminous carbon particles under uniform temperature and uniform volume fraction is concerned with radiation, the relation between the total emissivity and X has been found, where X is the function of volume fraction, thickness and temperature of flame. And the calculated value agrees well with the Schack's results. Next, in the luminous flame, the relation between the total emissivity and X, has been found. Moreover, experimentally the relation between the emissivity of a luminous flame and X in the luminous flame which was formed artificially by inserting the carbon particles in a nonluminous flame, has been made clear by means of an optical pyrometer and a radiation pyrometer. The result of studies showed that the experimental values agreed with the above mentioned theoretical analysis.

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This paper deals with the burnout and meltdown caused by step-input to a fine nichrome wire (0.2 mm diameter) which is vertically supported at the center of a glass pipe (annulus) and cooled by natural circulation of water of 80°C subcooling at atmospheric pressure. The results obtained are as follows : (1) For the transient nucleate boiling which exists between the beginning of boiling and the burnout point, the correlation between the heat flux and the superheating of surface temperature shows the same tendency as obtained in the results by Nukiyama or McAdams, even if the heat flux is higher than the burnout critical heat flux. (2) The time interval until the burnout occurs is given by the following equation : τ_B=C (q/10⁶)^-1.7 sec where C is a constant, which is dependent on the pipe diameter, and q is the heat flux (kcal/m²hr). (3) The burnout critical heat flux, namely, maximum heat flux which does not cause the burnout is 5.3×10⁵, 8.2×10⁵, 1.33×10⁶, 2.4×10⁶, and 2.4×10⁶ kcal/m²hr, respectively, in the cases of 2, 3, 4, 6 and 8 mm of pipe diameter. (4) There are four different types of change in the temperature of a nichrome wire, until it is melted down after the burnout point.

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A method for obtaining the fluid and metal temperatures in a plate-fin type heat exchanger is presented. The method is general and can be applied to any configuration operating at any specified conditions. The method is illustrated by its application to recuperators of the cross-flow and cross-counter flow Z types for small gas turbines. It is concluded that the Z-type is more compact and will be least affected by thermal stresses.

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In the conventional design of slag-tap boiler furnaces, certain complicated procedures based on experience have been required because of their variety of construction. A new comprehensive design is explained here, being deduced from the thermal theory, so that a simplified design method may be introduced from the relation between the furnace heat-release and the form factor, and determined by the statistical data. Further, from the latest experimental information, a general viscosity equation of molten coal-ash slag is derived and the thickness of a fluid slag film is determined by the author. In particular, a simplified equation for calculation is deduced from the inherent operation conditions of the slag tap boilers.

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In this paper a new analysis of pressure distribution in hot rolling is made. For complexity of the problem, past investigations on the pressure distribution during the rolling are restricted to two-dimensional consideration. Then, the author develops a three-dimensional consideration of pressure distribution during the rolling by adopting the following two premises, namely the mean slipping angle is constant between the rolls and plate, and the rolling stresses states are expressed by partially approximating the yield criterion of Von Mises. Consequently, the author can explain the pressure decrease toward the plate edge by taking the new factor of plate width.

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Limiting condition of chip breaking with a parallel type chip-breaker has been found to be determined by only the follwing three items : the radius of chip flow circle, the material to be cut and the thickness of chip. The larger the radius of chip flow circle, the steeper the slant of a chip-breaker and the thinner the chip, the smaller was the force acting on a chip-breaker due to chip curling. The yield stress of chip was found to become about twice that of the same material before cut. From these results, a simple method for finding the optimum shape of a chip-breaker was established. In this method, a proper radius of chip flow circle is found directly by measuring the thickness of chip which is obtained under the given cutting conditions and by the use of a diagram presented in this paper.

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Fundamental characteristics and cause of the thermal crack which appears in the carbide face-milling cutter have been investigated. The observation of a thermal crack has revealed a lot of interesting features of the initiation and growth of the thermal crack. The cause of a thermal crack of the carbide face-milling cutter has been considered from the view-point that, as generally said, it is due to the thermal shock accompanying the intermittent cutting. Next, the influence of cutting conditions on the thermal crack has been investigated and sometimes found explainable by the above consideration. At last, several grades of carbide have been examined experimentally in respect to the occurrence of the thermal crack.

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The present study was carried out for the purpose of calculating the bending stress of a gear tooth theoretically and finding the bending strength of a spur gear. Using the two-dimensional elastic theory and the transform function, the authors introduced equations for the calculation of the stress at the fillet curve of a gear tooth. Investigating the stress calculated by these equations in various loading conditions, the authors reached the conclusion that it was reasonable to take the shearing force into consideration for the calculation of the bending stress of a gear tooth. Then they introduced equations for the calculation of the inner stress, and obtained the following result : the inner stress shows a smaller value than the stress at the fillet curve, so it is reasonable to determine the bending strength of a gear tooth by calculating the maximum stress at the fillet curve.

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In the present paper the authors studied the position of the weakest section of a gear tooth and the stress concentration factor at the tensile-side fillet of a tooth. Then they calculated the stress concentration factors for some components of the force on the tooth profile, and found the relation among these factors. Consequently the following formula has been introduced for the bending stress of a gear tooth : σ =(1+0.08S/P) (0.66σ_Nb+0.40√(σ<SUB)Nb<SUP2>+36τN²>+1.15σ_Nc) By this formula the authors calculated the bending stress of gear teeth of some shapes, and compared the results with those of photo-elastic experiments.

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For the purpose of calculating the bending strength of the gear tooth in general use, the authors studied theoretically the position of the weakest section of a gear tooth and the point of the worst loading, and consequently defined the calculating method of nominal stress. Then by using the calculating equation of bending stress and stress concentration factor of gear teeth of various shapes in general use at present, they studied these relations.

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Noise of ball bearing can be divided into two cases ; one is the case of a simple ball bearing, the other is the case of a fitted one. The noise of the latter case has not been researched systematically. The author measured the noise of three kinds of the fitted ball bearings, analyzed the peak frequency in the frequency spectrums, and obtained the results as follows : (1) The noise of a fitted ball bearing has the frequencies above 1 kc/sec. The frequencies of the noise do not change at many shaft speeds, but the sound pressure level increases with the shaft speed. (2) The principal noises of a fitted ball bearing are due to the vibrations on the race rings, and the other noises are due to the vibrations on the cage. (3) The fitted ball bearing noise and the simple one are identical in essence.

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This paper presents an experimental investigation about the spline shaft by the threedimensional photoelastic method. The results are as follows : (1) The stress distribution of the spline shaft was measured by Dr. Nisida's wedge method, and the stress concentration factor was obtained. The results were coincident fairly well with those of other methods. (2) The accuracy of the wedge method was checked and its value was about 5%. (3) The stress distribution of the meshing spline shaft was investigated, and it was shown that the maximum bending stress of the tooth was comparable with the maximum torsional stress.

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Because of difficulty in measurement and recording of the motion of running motor-cycle, the quality of its stability has so far been discussed merely through the feeling test. In this paper, by using a new test equipment for in-door test, the stability, especially "hands off" stability, of motor-cycle is quantitatively examined as are the effects of several factors such as longitudinal and vertical positon of center of gravity, amounts of trail, caster and moment of inertia about the steering axis. And also, the authors succeeded in confirming the results of indoor test by comparing with those of practical road running test. Finally the basic principle for designing motor-cycles from a view point of stability is established.

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