The free vibrations of a bar bent to L-type (both ends built-in) are discussed. The method used is to minimize Lagrangian which is expressed in terms of the unknown functions and the known and unknown boundary values which describe the vibrations. In the case when there are lateral, twisting and longitudinal vibrations at the same time, the vibratory functions are obtained in general forms, and Lagrangian is expressed in terms of the boundary values. Using the known boundary conditions and the conditions of continuity, Lagrangian is expressed in terms of unknown constants. Then, Lagrangian is again minimized about the unknown constants and these constants and the frequency equations are obtained. In the case of an L-bar, the frequency equations of both vibrations in the plane of L-bar and perpendicular to that plane are obtained and the numerical calculations are carried out, and the comparison with the contents of papers already published is made.

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The analysis on the forced vibration of a system with elastically supported viscous damper whose damping is accompanied by the Coulomb friction is a very complicated one, for the reason that its every cycle is composed of two different kinds of motions and that seven boundary conditions are needed to solve it. In this paper, the author presents certain characters of the vibration of a system with optimum damping and Coulomb friction, the calculation of which is carried out by a digital computer. It became clear from the results of the analysis and the experiments that, while the Coulomb friction is smaller than the disturbing force, the amplitude seems to grow larger continuously from infinite damping curve to the optimum damping one as the frequency increases, but in the case where the friction overcomes the disturbing force, a jumping phenomenon of the amplitude occurs at a fixed place corresponding to the amount of friction.

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The large deflections of a circular-arc cantilever spring of trapezoidal profile subjected to a concentrated force at the free end in the lateral direction have been studied. A solution of the nonlinear beam equation is obtained in the form of power series. However, the power series used yields poor convergency as the shape of spring approaches the triangular profile and it diverges lastly. An approximate solution is also derived from the nonlinear beam equation after approximated appropriately. In comparison between the results calculated from the series-form and approximate solutions, respectively, it is seen that the approximate one gives practically satisfactory results. Numerical results according to both the series-form and approximate solutions are also presented.

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This paper is succeeded by No.2 and No.3 reports of the same title in which propagation of fatigue caracks on large smooth surface and fillet specimens has been dealt with. In this paper, the author has studied the following two problems : (1) The fatigue strength of large smooth specimens having a diameter of 130 mm with fine cracks artificially produced beforehand by sea water corrosion. (2) The influence of size on the fatigue strength of cracked specimens and propagation speed of fatigue cracks. The test results have revealed that the fatigue limit of steel specimens, 130 mm in diameter with fine corrosion cracks on the surface is about ±11.0 kg/mm². This limit coincides with the result assumed by studying the crack propagation of specimens, 120 mm in diameter. Analytical investigation of the propagation speed of fatigue cracks of 60 φmm and 20 φmm specimens has shown that the fatigue limit of these specimens are assumed to be about ±12.0 kg/mm² and ±15.0 kg/mm² respectively, when fine cracks may previously exist on their surfaces. From the above results, it may be stated that the fatigue limit of smooth specimens having fine cracks on their surface will tend to increase as the diameter decreases. On the other hand, from the analytical studies on the shape of shelly patterns on the fracture surface, the propagation of fatigue crack may be given approximately by the following formulae in connection with the diameter of specimen : σ_o≤ν_bσ_n<σ_o+σ_s, [numerical formula] where : υ_c is propagation speed of fatigue crack μ/c, ν_bσ_n : stress on the edge line of fracture surface kg/mm², σ_n : stress on the specimen having no crack, ν_b : stress magnifying factor due to crack, σ_o : fatigue limit of cracked specimen kg/mm², σ_s : yielding point of the material kg/mm², K and k : constants varying according to the properties of material and range of ν_bσ_n, d : diameter of specimen mm.

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The author has proposed a new measuring method of Rockwell hardness which is measured by an indenter with a conical angle different from 120° or by a minor load larger than 10 kg. The conversion formulae between this hardness and Vickers hardness Hv and the equations of errors were induced theoretically and checked experimentally. This new hardness has many merits. For example, using the conical angle larger than 120°, the hardness range of 60<Hv<1000 can be expressed by a single indenter continuously and thin sheets are measured without employing any special superficial tester. The conical angle smaller than 120° is effective to raise the sensitiveness of measurement for very hard specimens. For rough surfaces, we can get reliable results which have small scattering ranges by larger minor load.

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It is observed that human behavior is much more complex and reasonable than that of conventional servomechanisms, when one controls one's own action or drives an automobile. The author thinks that it is very useful for the improvement of the performance of servomechanisms to introduce such characteristics into the construction of servomechanisms. Prediction is a characteristic of the human behavior, but it is usually difficult to introduce prediction into servomechanism construction just as it is. The author introduced prediction into servomechanisms so far as servomechanisms are constructed easily. The author investigated three kinds of prediction servomechanisms ; the first is an error-prediction-servomechanism, the second is a prediction servomechanism in which manipulated variable is computed continuously, and the third is a prediction servomechanism in which the following velocity varies automatically. It is confirmed that these prediction control servomechanisms have superior performance to that of the conventional servomechanisms.

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An analysis of self-excited vibrations of hydraulic control-valve pipe-lines is presented taking the influence of the fluid column in the pipe-line into consideration. The pressure difference across the port v.s. the flow rate characteristics of the valve is found to have effect on the stability of the system. Analytical results are confirmed by a series of experiments.

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Bagley and others showed that the additional loss at the entry of a capillary tube, through which a viscoelastic fluid flows, was a strong function of the apparent shear rate. However, no one has ever attempted to treat analytically the entrance additional loss, as far as the author's knowledge is concerned. In this paper, assuming that the elastic energy is stored in the flowing fluid, this problem is approximately analysed. Then, the extrudate swelling (Barus'effect) and the extrudate irregularities are qualitatively explained. Moreover, the drag of a sphere placed in the viscoelastic fluid flow is calculated roughly.

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A theoretical method to estimate the effect of axial velocity change through a cascade was investigated. The change of axial velocity was reproduced by distributing sinks and sources within the blade passages, and the conclusions are set forth in some simple formulae. Some graphs for the numerical evaluation of the performance of NACA 65 series cascades were prepared, and several examples were compared with experimental data.

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A method of calculating unsteady laminar boundary layers is presented. Two-dimensional flow of an incompressible fluid is assumed. The case of an oscillating outer flow, about a time-mean value, with a small amplitude and at relatively low frequency, is considered. By the use of a power series expansion method, the boundary layer around a body with an arbitrary shape and with a wedge-shaped nose of arbitrary angle, can be calculated. The solution is obtained as a linear combination of a set of universal functions. Velocity fluctuations in the boundary layer, of second order in magnitude, are taken into account. The time-mean velocity at a point in the boundary layer shifts as the amplitude of outside flow oscillation is increased. At the same time, the second harmonic fluctuation is produced. The method of calculation is applied to the boundary layer of a circular cylinder, and it is found that the influence of the second order velocity change is rather small, even at the outside velocity fluctuation 0.5 times the mean velocity.

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The motion of solid particles within a hydrocyclone is analysed by solving dynamical equations in two dimensions, and with the aid of these equations the method of calculating the fractional recovery of particles is presented. Separation data by various previous experiments are in satisfactory agreement with the theoretical curves obtained by this method. Moreover the characteristic equations for cyclone as well as the formula for imaginary separation size are also presented. On the basis of these equations, effects of the relative size of inlet nozzle to cyclone diameter, and of the form of its cross-section on the accuracy of classification are discussed. Finally collection efficiency and thickening ratio are calculated by the use of fractional recovery already obtained. These theoretical values seem to confirm the experimental data.

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In pumping stations several pumps having different characteristics often are installed in parallel and operated partially or totally depending on the demand for water, in order to maintain better efficiency of the plant. This paper presents a method of analysis of water hammer in parallel operation of different pumps. As one example for this analysis the parallel operation of two pumps is chosen, and the transient phenomena of each pump following power failure are calculated. By these calculations a result as follows has been confirmed : When power failure occurs in parallel operation of two different pumps and there is a certain difference in the speed drop of each pump, the discharge of one pump, of which the speed reduces more slowly than the speed of the other pump, does not decrease but increases for a short time after power failure.

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The effect of the impeller entrance profile upon the velocity distribution just before the vane entrance edge was investigated, and experiments were conducted to examine the effect on the cavitation of centrifugal pumps. The results were as follows. (1) The velocity distribution just before the vane entrance edge, differed according to the difference of the impeller entrance profile. The flow was considerably one-sided in case of profile A whose cross-sectional area varied suddenly. However, the velocity distribution was uniform in case of profile C whose cross-sectional area varied little. (2) Irrespective of the velocity distribution, the static pressure distribution at the point just before the vanes was almost the same for all profiles. (3) In comparison of the cavitation occurrence of profiles A and C, no distinctive difference was observed except that the head drop due to cavitation in the large flow-rate range was smaller in case of profile C.

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Continued from the 1st Report, this paper deals with the effects of subcooling, tube diameter and air content under the transient boiling caused by step heat input. The experiments were carried out under the condition of a natural circulation of the water under atmospheric pressure. The results obtained are as follows : 1) Until a burnout occurs, the surface temperature of heat generator (nichrome wire) is independent of subcooling, the tube diameter or the air content, and the characteristics of heat transfer are similar to those under steady boiling. 2) The time lag to the burnout caused, which increases with the decreasing of the power input, is proportional to the subcooling or the tube diameter, but it has no relation to the air content. 3) When the value of subcooling, the tube diameter or the power input is large, a burnout is caused by the partial film boiling, while it is caused by the bubble blocking when that value is small. In the case of the subcooling of 0°C, especially, a burnout occurs owing to the film boiling without being affected by the tube diameter. 4) The critical heat flux, which does not cause a burnout, depends on the subcooling or the tube diameter, but it is independent of the air content.

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It is easy to determine the mechanism of time average eddy diffusion of fuel gas in a flame. But it is very difficult to determine the instantaneous movements of fuel gas in the flame. In the experiment described in this paper the fuel jet was ignited at various positions in the fuel jet by electric sparks, and the spreading of the flame was observed. Ignition probability was measured at various positions of the fuel jet, being determined by the mixture ratio and mean velocity of fuel jet and the velocity of secondary air. It seems that the ignition probability chiefly depends upon the fluctuation of the fuel concentration. It was found that, for an ignition for obtaining a steady flame, a spark must be provided immediately behind the burner tube wall.

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This paper deals with a theoretical analysis of one dimensional steady flow in a combustion chamber of gas turbine. The following assumptions were made : (1) The liquid fuel_spray and combustion gas stream have an equal velocity. (2) The law of combustion of single droplet is adopted for the combustion rate of fuel spray. (3) The combustion is not affected by the condition of combustion gas stream. (4) Both the air and the combustion gas are perfect gases. By using above four assumptions and the analysis which is analogous to Shapiro and Erickson's method⁽⁷⁾, the total heat release rate, the local heat release rate, the temperature-and velocity-distribution in the direction of gas flow were calculated. In this study, it is found that the local heat release rate rapidly increases but the temperature and velocity of combustion gas do not increase so rapidly as the local heat release rate and these values decrease after they attained the maximum. And the local heat release rate obtained has a similar form to the assumption that was treated to analyze the pressure drop in the previous papers^{(3) (4)}.

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To obtain the characteristics of turbine blades in the moving state, a turbine test was carried out using an experimental turbine of low pressure ratio and double rotation type. The testing method used in this research consists in the measurements of the torque and thrust acting on the row of nozzle blades and the row of rotor blades. The advantages of this method are as followings : (a) the state of flow before the rotor blades can be measured exactly, (b) the measurements are simple as compared with other testing methods, for example, Pitottube traverses.

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In the low pressure parts of a steam turbine, the annular flow areas are made diverging towards the downstream. In such a case, the fluid behaves with the radial velocity which cannot be neglected in calculation. Presented at the beginning of this paper are a method of calculating the velocity distribution through such stages and also descriptions of some examples of application for the concrete flow pattern. Then are described some results of the measurement of the flow through the last stage of the actual turbine, which show good agreement with theoretical prediction.

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The influences of direction of fuel injection and the temperature of the combustion chamber wall upon the ignition and the combustion process in the swirl chamber of a Diesel engine were investigated by means of high-speed photographs with indicator diagrams synchronized. The summary of results are as follows : (1) Ignition of fuel is delayed by the cooling effect of the wall when the wall temperature is low, and this trend grows more remarkable as the direction of injection gets nearer to the wall. (2) Duration of combustion is prolonged by increasing the concentration of fuel particles in the middle part of the chamber and by shortening the delay as well as by the increase of fuel adhering to the wall, which mitigates the rate of pressure rise due to combustion. (3) When the fuel is injected along the wall, several features of combustion such as blue flame combustion, ignition from several positions and an abnormal shortening of the ignition delay were observed.

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In order to clarify the effect of rolling conditions on the fatigue strength of rolled screw threads, the V grooves were rolled on cylindrical specimens and the rotating bending fatigue tests were carried out on these specimens. For this purpose a simple rolling attachment was designed and manufactured. The rolling pressure in the case where the V grooves were rolled by this attachment, was measured. This rolling process was analysed, and compared with the process of thread rolling. In the experiment the rolling conditions of the V groove were changed by varying the number of revolutions of the specimen during rolling process. The specimen materials were medium carbon steel cold worked and Cr-Mo steel quenched and tempered. As a result it was found that the endurance limits of the specimens with a rolled V groove were 2.5∼2.8 times higher than those of the specimens with a cut V groove. Statistical analysis has shown that there exists a definite relationship between the rolling condition and the endurance limit.

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Previously, K. Ogawa made an exhaustive survey on the synthesis of a four-bar linkage in which the locus of a point on the connecting rod was described systematically in a wide range of link dimensions. In this paper, the displacement characteristic of a six-bar linkage in the range of operation was analysed, when the driving crank made a complete revolution while the follower crank oscillated. As a result, the relationship between the form and its displacement became clear, when various forms of the six-bar linkage were given. It is expected to provide direct aid for designers in selecting a mechanism to produce a desired motion.

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In the last report, an unsolved problem in the analysis of six-bar linkage mechanisms was studied. In this paper, as the result of the investigation on the synthesis of C-type, the author found a new type of the thread take-up lever used for the sewing machine, employing six-bar linkage which has turning pairs only and whose free end performs an ideal thread take-up motion. Thus a most noiseless operation has been attained.

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For the purpose of improving lubricating performance on the gear-tooth surface, the authors investigated the relationships of lubrication properties to the driving conditions and the lubricating methods with back-to-back type gear testing machine with which the frictional moment and the oil-film thickness between gear-teeth were measured. The lubricating characteristics have been classified by the values of the dimensionless parameter ηυ_r/P^^^-_n as follows : boundary lubrication ≤5×10^-6≤ semi-fluid lubrication ≤5×10^-4≤ fluid lubrication. Owing to the effects of the discontinuous contact, the dynamic load, the variation of frictional direction and the surface roughness on the gear-tooth surface, the frictional coefficient is larger and the oil-film thickness is smaller than those obtained respectively on the roller surface which was considered in the equivalent condition to the gear-tooth surface. The stirring resistance in the oil-bath lubrication is much influenced by the oil viscosity, the rotating speed, and the oil amount.

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