The present paper deals with the fundamental vibrations of simply supported but partially clamped square plates. The energy method is applied, which was proposed in the previous paper for solving the general problems of statical deflections, stationary vibrations, bucklings, etc. of rectangular plates. Numerical calculations are carried out for fourteen cases, and five diagrams are obtained which give the fundamental frequencies of the square plates under typical boundary conditions.

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In the lateral vibrations of a shaft mounted by an unsymmetrical rotating body, a free vibration of frequency p_i always appears with another free vibration of frequency p_i=2ω-p_i. When the bearing pedestals are somewhat flexible, e.g., in y direction, there are small differences in spring constants between x and y directions. Coexistence of p_i, p_i and small dissimilarity in spring constants result in new zones of instability. These zones appear at the rotating speed ω where the relation p_i=-p_i or p_i=p_i=2ω-p_i holds. In the zones, the motions are dynamically unstable, and the amplitudes of the vibrations with frequencies p_i, p_j, p_i, p_j grow up exponentially.

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A shaft carrying an unsymmetrical rotating body is statically unstable near its major critical speeds, and the unstable regions become smaller as damping forces are larger, and they vanish when the damping coefficients reach critical values. These critical damping coefficients c_c1, c_c2 are given in the present paper. Then, the amplitudes and phase differences of forced lateral vibrations are studied ; they are found to depend very much upon angular positions of static and dynamic unbalances. The characteristics of the response curves and phase differences are very different from those of a usual vibratory system. Furthermore, comparison with a flat shaft system is made.

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In the present paper, the authors obtain theoretically the response curves of summed and differential harmonic oscillations induced by symmetrical and unsymmetrical nonlinearities of spring forces, and they investigate the influences of nonlinearities and damping force of those vibrations. Further the stability criteria of vibrations are analytically studied. The conclusions obtained are as follows : (1) The charcteristics of summed and differential harmonic oscillations are analogous to those of subharmonic oscillations in the order of 1/2 and 1/3. (2) There are the critical values of damping coefficients, and summed and differential harmonic oscillations cannot take place, when the magnitudes of damping are larger than these values. (3) The loci of vertical tangent of the response curves divide the response curves into two parts, and the upper parts of the loci constitute a stable range, the lower ones an unstable range.

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By annealing and electro-polishing technique it was shown that the fatigue damage of 6-4 brass specimens is confined to within a thin surface layer of the specimens. The thickness of the damaged layer becomes greater when the applied stress is high and the number of stress repetitions is large. The rate of growth of the thickness of the damaged layer begins to increase rapidly, when the thickness exceeds some threshold value (in the present case, 30 to 50 microns). The fatigue damage occurring beneath the surface layer of the specimen seems to be of strain-hardening character and it disappears by stress relief annealing. It seems from this work that the fatigue limit is the stress under which the thickness of the damaged layer remains within certain limit, even if the number of stress repetitions is infinitely large.

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Theoretical and experimental studies were conducted in order to establish a method of computing the strength of hoisting drums for windlasses. It was assumed that external pressure is the only external force applied to a hoisting drum. Further, the strength of the hoisting drum was discussed in terms of the strength of the cylindrical parts and the strength of the stiffening rings. Each of the 16 model drums failed due to the yielding of either the cylindrical parts or the stiffening rings. As a result of the research, it was made clear that the initial deflection of the hoisting drum has a considerable effect on the strength, and formulas were obtained for computing the strength of the drum. Finally, applicability of these results to actual design of hoisting drums was discussed.

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In this paper, the strength and deformation of a cylindrical shell fixed at one end and supported at the other under the weight of lining is discussed, utilizing the fundamental differential equation introduced by Dr.K. Mizoguchi. The method of solving and the results here obtained can be applied to the design of a rotary kiln.

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The discontinuous motion of a body sliding at low velocity is known as stick-slip. In this paper, stick-slip in hydraulic driving mechanisms is analyzed quantitatively on the bases of the characteristic of flow control valve, the equation of continuity for oil flow and the equation of motion for the sliding element under the assumptions that the characteristic of flow control valve is linear and the friction between sliding surfaces is composed of static, Coulomb and viscous friction. An experimental verification of the theoretical analysis is made using the model table which is the same size as a table of No. 2 1/2 milling machine. Then it is shown that the motion of a table in stick-slip can be described by the pressure-flow characteristic of flow control valve, the friction-velocity relation between sliding surfaces, the compressibility of working oil and others.

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Forming a simple but sufficiently good analog computer model for each element of a process plant is a technique of great practical import in designing and analyzing a large system. A novel way to the solution of this problem was suggested by Paynter and Takahashi in 1956. In practice along this principle, however, one faces the following two immediate questions : i) Given a particular process element, how can one select the most appropriate type of transfer function to simulate it? ii) How can one conveniently determine the numerical values of the parameters when the number of such parameters is more than three? The technique developed here will nicely answer the questions and allow one to make a unique choice for the required model as the result of a straightforward process of model-forming.

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The experiments were performed on three flat-seated disc valves, having diameters d of 28.0, 30.2 and 38.8 mm, discharging water into the air under a constant head H which was varied from 194 cm to 9 cm. The discharge Q and the lifting force P were precisely measured at each valve lift l. The results show that ; (1) discharge coefficient ∝Q/l√(H) is more markedly affected than the non-dimensional lifting force ∝ P/H by the effective head H ; (2) if the lift l is not so small, the influence of H on Q/l√(H) and P/H becomes very small when H is greater than 194 cm ; (3) four special points are marked on a characteristic curve for H greater than 49 cm. Besides this many unexpected relations are observed.

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The centrifugal blower of a diesel engine super-charger operates under pulsating flow at 10 to 70 cycles per second, therefore if the scavenging system is not properly designed, the flow through the blower decreases remarkably and so does the power of the engine. The pulsating flow test with the rotary valve has proved that the characteristics of a centrifugal blower under steady flow condition are also available in pulsating condition. And we find that the graphical methods, taking into account the boundary conditions using steady flow centrifugal blower characteristics can be conveniently used. The equivalent length of the centrifugal blower is also determined by this test.

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In this paper similarity conditions of the three dimensional boundary layer flows over bodies of revolution are examined and very general forms of the distributions of the main stream velocity, the radius of the body and the scale factor are found. First, when the fluid at infinity is axially symmetric and the body is rotating about its own axis, the distribution of the outer velocity and others which fulfill the similarity conditions are found to be of the power or the exponential forms. Secondly, when the body is at rest and the main stream has both the meridional and the circumferential velocity components, the general solutions are found to be entirely different from those of the rotating body and are not restricted to the power and the exponential forms. Moreover, it is found that several different flow patterns correspond to one set of similarity constants.

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This paper deals with an analysis to determine the heat transfer characteristics of the thermal entrance region for an established laminar flow of a heat generating Bingham plastic through a circular tube with wall heat transfer. The conditions of wall heat transfer treated in this paper are both the case of prescribed uniform wall heat flux and that of uniform wall temperature. In this analysis, eigenvalues and eigenfunctions are evaluated by means of a digital computer KDC-1. The heat transfer characteristics approach those of a fully developed region which were calculated in the previous paper by one of the authors. The results for a Newtonian fluid flow which were analyzed as a special case agree very well with those by Nusselt and Siegel et al.

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In order to know the temperature gradient and heat flow in boiling heat transfer, Schlieren photograph technique is used and some of the observed results are shown here. The main features that have been found are ; (1) at low heat flux, each bubble is followed by a beautiful hot liquid tail ; (2) bubbles are ejected into liquid regardless of the direction of gravity by the inertia force of motion of the surrounding liquid ; (3) at high heat flux, a secondary "bubble cloud"covers the original bubbles which become smaller and greater in number and the bubble tails become smaller or vanish ; (4) transition boiling has much similarity to nucleate boiling and the former would be explained as an extension of the latter into the region where the heat flux shows a decrease in spite of an increase of wall temperature because of the decrease of the area of the liquid thermal boundary layer.

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In the previous papers the temperature rise due to throttling was applied as a starting aid for a four stroke cycle diesel engine and a crankcase scavenged two stroke cycle diesel engine. In the present paper the same process has been applied to a two stroke cycle diesel engine with a scavenging blower. By releasing the cylinder pressure on the compression stroke with an automatic valve, pressure drop under the ambient can be obtained at the end of an expansion stroke. When the exhaust ports open, the air rushes into the cylinder with a considerable temperature rise. After scavenging, the charge temperature is lowerd, being, however, higher than the scavenge air temperature at the beginning of compression. The calculated temperature rise reached 80°C before scavenging. However, when the delivery ratio was unity in the scavenging process, it was reduced to 24°C at the beginning of compression, while the observed one was 19°C. In the starting test the minimum cooling water temperature at which the engine can start can be lowered by 30°C in the range of small delivery ratio.

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The authors of this paper studied on the tracer gas method which had already been suggested for application in measuring the trapping efficiency of two stroke cycle engines. And in consequence, the superiority in both accuracy and reproducibility of measurement under the following conditions was recognized : The use of anhydrous monomethylamine as the tracer gas ; gas concentration being 0.1 to 0.3% ; the use of 10 cc of 0.02 normal solution of sulfuric acid as the absorbing liquid ; a mixture of bromcresol-green and methyl-red as the neutralization reagent. The type of sampling tube, the gas sampling points and the gas sampling apparatus are also selected. The accuracy are compared with the results obtained by the gas sampling valve method. Under these conditions, the errors are within the range of ±2%.

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The author studied the scavenging of crank case compression type two stroke cycle diesel engines, and examined the influences of engine speeds, delivery ratios, fuel injection quantities, crank case compression ratios and guide angles of scavenging ports upon the scavenging performance. Furthermore these engines were remodeled into the type with a scavenging pump and compared with the former. Thus the scavenging characteristics of crank case compression type two stroke cycle diesel engines were made clear.

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The hydraulic instability is one of the impermissible evils in the operation of BWR. And there has been no effective way of preventing it, because its mechanism is not clarified yet. The authors made many experiments with an electrically heated natural circulation loop which has electric condenser type void meters. As a result, they conclude that the hydraulic instability is a kind of non-linear oscillation caused by the combination of the fluid kinetics in the heated section and the non-linearity of the friction loss of the two-phase flow. They also derive analytically a block diagram of the circulation loop, in which the kinetics of fluid are simulated with simple linear transfer functions except the term of friction loss. The solutions, calculated by an analog computer, coincide well with the experimental results.

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An investigation is carried out on the hydrodynamic instability which has been observed in two-phase flow systems, such as boiling water reactors and once-through boilers. In this paper a system having a single boiling channel is treated. The equation of oscillation for the circulation flow rate is derived from the laws of conservation of mass, energy and momentum. The damping coefficient in this equation is given as the inclination of the characteristic curve which represents the relation between pressure losses and circulation flow rate. As the result, it is found that, when the equilibrium of the hydrodynamic system lies in the range of negative inclination of the characteristic curve, the system is unstable and a hydrodynamic oscillation is generated. In the case of forced circulation, the system is expected to be more stable than the natural circulation system, owing to the positive damping caused by the pump included in the circuit.

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Based on the preliminary research of one of the authors, a new and practical feed-back controlled gear hobbing machine for fine pitch gears was built at a low cost. The average and minimum of the maximum angular position errors so far obtained with the gears hobbed by this machine is 20 sec and 11 sec, respectively, when the module is 1 and the pitch circle diameter is 72 mm. Such accuracy is obtained by virtue of the special design of the machine, which makes use of an electro-hydraulic servomechanism to correct the error of the driving worm wheel. The servomechanism is actuated by the relative displacement of the driving worm wheel and the master worm wheel as well as the signal from the cam shaped to eliminate the inherent error of the master worm wheel. This paper presents the basic analysis, the design of the machine and the experimental result.

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In this paper, the author applied the theory of limit analysis to a theoretical investigation of the blanking process. In Part I, the statically admissible stress field in a sheet material was analysed on the assumptions : (1) The sheet material is a non-hardening plastic-rigid body. (2) The material near tool edges is approximately in the state of plane strain. (3) The stress field consists of several regions of constant stress separated by straight lines of discontinuity. In Part II, the deformation process of the sheet material was devided into four stages, and the kinematically admissible velocity field was analysed in each stage. Furthermore, comparing the solution of the stress field with that of the velocity field, an exact solution of the blanking force was obtained for blanking with smooth punch and die.

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Up to this time, the accuracy of gears has been expressed in terms of individual errors such as the pitch error, the tooth profile error, the eccentricity ett., or in terms of the total error from the single or double surfaces meshing test. Each of these methods, however, is not satisfactory ot express the accuracy of gears. The authors present a new method to measure the error of a gear. Two feelers contact simultaneously on two adjacent surfaces and draw error curves in the same way as in the case of a usual profile tester. The center distance of the two feelers is set equal to the normal pitch of the gear. Consequently, two curves of profile errors are recorded on the paper. The entire error curve around the gear teeth is obtained by superposing these individual curves. By this new method, the accuracy of gear is more adequately expressed than by any of the conventional methods. This method is convenient in other respects, for example, the analysis of the cause of error becomes easier, the testing procedure less laborious and the whole apparatus less expensive.

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A new type hourglass worm gearing is presented in this paper. In this new type, the worm is a conventional Hindley type, but the number of teeth of the worm wheel and the center distance are smaller than the corresponding figures of the Hindley worm gearing. In this paper, the principle of the new worm gearing, the derivation of the basic equations and their applications to the new worm gearing are given. For comparison, the lines of contact on the tooth surface are obtained with examples of various types of worm gearing. The conclusion is as follows. The cylindrical worm gearing or the Hindley worm gearing can be regarded as a special case of the new worm gearing. The new worm gearing can be properly designed to circumvent the defects of the Hindley worm gearing and expected to have good performance.

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Uber die Losung fur die Beschleunigungen beim ebenen Gelenkgetriebe sind wenige Methoden, wie zum Beispiel die Abbildungsmethode und das Verfahren durch den geschlossenen Vektorkreis, nur gekannt worden. Weil diese Methoden unterwegs die komplizierten Ordnungen begleiten, fehlt man leicht die Konstruktion und kann nicht deutlich die Ordunung der Konstruktion bezeigen. Die hergebrachten graphischen Methoden erklaren nur fur den Fall, daΒ das Antriebglied gleichformig rotiert, aber nicht fur den Fall, daΒ es Winkelbeschleunigung hat. Die Verfasser haben bereits das graphische Verfahren fur die Beschleunigungen in der Analysis uber die komplizierte Bewegung des Daumengetriebes vorgeschlagen. Die Verfasser haben es auf das Gelenkgetriebe angewandt, und haben das Verfahren, wovon sehr einfach die richtigen Werte der Beschleunigungen gewonnen werden, erfunden. Im Falle, daΒ irgendein spezielles Glied bei den Sechsgelenkgetrieben aller Arten gegebene Geschwindigkeit und Beschleunigung hat, ist das einfache, neue, graphische Verfahren, um die Winkelgeschwindigkeiten und-beschleunigungen der andren Glieder zu losen, vorgeschlagen worden.

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A theoretical research on externally pressurized journal gas-bearing has been reported by T. Sasaki and H. Mori. In their paper, the experimental data employed in comparison with the theoretical results were for the bearing with a single gas supply hole without restriction. It is common to use externally pressurized gas-bearings with multiple gas supply holes arranged circumferentially and axially. In this paper, a gas-bearing with multiple gas supply holes is designed theoretically and the pressure distribution, flow rate and optimum restriction are examined and compared with the complex potential theory. The experimental results show good agreement with the theoretical results.

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