The authors have made two kinds of fatigue test on shoulder fillet specimens (one is 135 mm dia. at the testing part and 15, 25 and 40 mm in fillet radius, the other is 14 mm dia. having proportional sizes to the large one), for the purpose of obtaining fatigue notch factors on shoulder fillet by comparing their fatigue limits with those of 125φmm and 10φmm plain cylindrical specimens described in Part 1. On the other hand, the stress concentration factors have been determined on fillets of the large specimens by taking into account the effect of the ratio of gauge length to fillet radius. Furthermore, the authors have studied the relationship between the stress and the propagating speed of fatigue crack by analysing shelly patterns on fracture surfaces of shoulder fillet specimens. It has been disclosed from these tests that ; (1) The correcting factors are 1.06, 1.018 and 1.006 where the above ratios are 0.60, 0.36 and 0.225, respectively. Stress concentration factors given by R.E. Peterson are equal to the author's ones without correction. (2) Fatigue notch factors of large specimens are nearly equal to those of smaller ones, and coincide with the corrected concentration factors of equivalent stress besed upon Mises'criterion. (3) Fatigue crack decreases remarkably its propagating speed as the stress concentration factor on the fillet part becomes larger.

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In this paper, the free vibration of a one-degree-of-freedom system with an elastically supported viscous damper and with arbitrary stiffness ratio k of the springs is considered. The interesting facts that the system has an optimum damping value for the free vibration and that the value is nearly equal to that for the displacement of forced vibration, have been derived from the study. In addition, the transient vibration of a vehicle equipped with a damper adjusted adequately for the steady motion in passing over a raised or sunken place, has been investigated, comparing the result with that of a vehicle with the conventional type of suspension consisting of a spring connected in parallel with a damper, and it has become clear that the former has considerable advantages over the latter in softening shocks.

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The forced vibration of a one-degree-of-freedom system with an unsymmetrical viscous damper was analyzed theoretically by a rigorous method, and the calculation was made for the following two cases : a) c₁=0.2 c_c, c₂=0.8 c_c, b) c₁=0, c₂=c_c, where c_c is the critical damping coefficient. The numerical results obtained show (1) that the neutral line of the vibration of such a system has a tendency of shifting to the direction in which the damping is weak, and also a tendency of the amount of the shifting growing with the frequency of the forced vibration as well as with an increase in the ratio of damping on rebound stroke to that on compression stroke, and (2) that the acceleration warps considerably in the shape of its wave These results were also ascertained by an experiment carried out with a system equipped with a damper which works on the stroke in one direction only.

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A phase plane method of analysis of the on-off control system with relation to sinusoidal input is proposed. The behaviour of a representative point in the phase plane is broken down into two separate movements, one of which is its rotation around the circumference of the ellipse, and the other is the travelling of the ellipse along a curve. This method is very useful especially in the analysis of on-off control system by reason of the fact that such an ellipse can be treated similarly to the representative point in the phase analysis of the system with relation to the step input. Several numerical examples are given to make this clear.

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The author has studied "summed and differential harmonic" oscillations occurring in rotating shaft systems, i.e., vibratory systems with gyroscopic terms. In the present paper, the author treats "summed and differential harmonic" oscillations appearing in rectilinear vibratory systems, the nature of which is quite different from that of systems with gyroscopic terms. By analytical discussion, it is concluded that summed types only can take place in rectilinear vibratory systems while both summed and differential type can occur in rotating shaft systems. Further, experimental results for two experimental apparatus having different construction from each other verify that "summed and differential harmonic" oscillations actually appear in rectilinear vibratory systems, and summed type only can take place.

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A theory is presented for the calculation of unsteady laminar boundary layers in an incompressible fluid about a two-dimensional body. Fluid velocity in the main stream just outside the boundary layer, expressed as a power series of the distance x measured along the body surface, is assumed to fluctuate about its mean value. The magnitude and frequency of the fluctuation are assumed to be small. Velocity fluctuation in the boundary layer is also expressed as a power series of x, whose coefficients are functions of the non-dimensional distance measured normal to the surface. These coefficient functions are universal and can be tabulated once and for all. Functions corresponding to the main stream velocities of third order polynomial and frequencies up to second order are actually computed and tabulated. As an example, the movement of the boundary layer separation point on a circular cylinder is calculated. The movement, although it increases with frequency, is rather small.

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Based on the analytical treatment of boundary layer, the author revealed that the frictional resistances of a rotating disk in a non-Newtonian fluid of infinite extension are approximately found by using the momentum equations in both cases of a laminar and a turbulent boundary layer flow. As a result of these analytical treatments, it has also been revealed that the relation between the Reynolds number R₆^* and the resisting moment coefficient C_M of a rotating disk in non-Newtonian fluids having different values of the rheological constant n is identical with the relation between R_s and C_M of the rotating disk in a Newtonian fluid.

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Continued from the 1 st Report, in which the combustion gas flow through a single chamber was analyzed, this paper presents the theory of gas flow through a typical annular combustion chamber of a gas turbine or a jet engine by using the thermo-aerodynamical analysis. By one numerical calculation, it was quantitatively shown that : (1) the cooling air which flows the outer space of annular combustion chamber enters naturally into the inner space through the mixing holes by the pressure difference between outside and inside and (2) it prevents the increase of temperature of combustion gas and it promotes the increase of gas velocity, while it causes a large pressure drop by mixing in addition to that by friction and expansion.

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The following terms are necessary for a theoretical quantitative study of gas leakage through the piston-rings of internal combustion engine : (1) the discharge coefficient through the narrowest gas passage, (2) the temperature of gas in the space between two rings. So at first the former is measured by letting a high temperature compressed air flow out through a gap of piston-ring set in the experimental apparatus. Next, the latter is studied using the apparatus provided with a stationary piston and a reciprocating cylinder. As a result, the following conclusions are obtained : (a) the discharge coefficients are 0.8∼0.9 and its mean value is about 0.86 when the states of leakage gas are near to those of an actual working engine, (b) the temperature of gas flowing out around the piston-rings almost is equal to that of gas on the surface of piston.

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The measuring values of the discharge coefficient and the temperature of a gas flowing through the piston-rings which were obtained in 1 st Report, are used to calculate the amount of the leakage gas and its pressure distribution under several conditions of the piston-rings. And comparing these calculated results with the previous experimental ones, the following conclusions are reached ; (1) The calculation and experimental values are consistent in results, (2) the mechanism of gas leakage through the piston-rings corresponds to that of a gas flowing through the labyrinth, changing rapidly its properties, (3) especially, the unsteadiness of leakage flow produces an interesting effect upon the gastightness, (4) and it is also proved that the leaking gas hard y contains combustion gas when estimated from the theoretical calculation.

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This paper reports the results of an investigation on the scavenging process in a model cylinder having a cross-scavenging system. The movement of the scavenge front in the cylinder and the short-circuiting of fresh charge were investigated by an electronic method. The profile of the scavenge front was made clear. The port arrangement investigated here gives a flat scavenge and an early short-circuiting occurs at the exhaust ports located near the scavenging ports. A poorly scavenging region exists above the exhaust ports.

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Dynamic loads on spur gear teeth are measured by a high speed gear testing machine at a periphery velocity of 80 m/sec and below. The ground gears (some of them have pressure angleerrors) are tested as reduction gears and also as speed-up gears respectively. The maximum dynamic loads occur at a critical speed, at which the meshing frequency is equal to the natural frequency of the vibratory system consisting of a pinion, a gear and a combined tooth stiffness. At a speed over the critical one, the magnitude of the dynamic load approaches a certain constant which is determined by the tooth errors. When the errors are repeated in each meshing as in these cases, the dynamic loads of the gear tested as a follower are nearly equal to the ones tested as a driver.

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To manufacture folding-less gears by hot-rolling method, the author experimentally investigated the rolling conditions. The results of a preliminary experiment by using soft materials revealed that the raise-up of the metal varied with the plasticity of the material which was to be rolled, the rolling speed, and the sliding action on the respective faces of the teeth at the moment of the generating motion. Applying these results to the hot-rolling of steel gears, module m=2∼3, rolling conditions such as the heating temperature, the depth of the heated zone, the pressing speed of the die-roller and the rotating speed of the gear blank, have been obtained. The metal structure of the gear rolled hot under these conditions is satisfactory without showing any crack or folding on the rolled teeth.

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The results of investigations on the accuracy of hot-rolled gears reveal that the accuracy is controlled by the shape of gear blanks, heating time, finishing rotations and the pressing method of die-rollers besides the accuracy of die-rollers and rolling devices and gear blanks. The results of investigations on the collapses found near the pitch circle of rolled teeth reveal that these collapses are caused by the sliding friction and the variation in the contacting pressure on the tooth face.

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In order to investigate the structure of the gear rolling machine which is suitable for manufacturing practical gears, the author made experimentally various gear rolling machines, and compared their performances. The results reveal that the most accurate gears are rolled by using a double-side-pressing type hydraulic rolling machine. Referring to these results, the author made a full automatic gear rolling machine, and examined the performance of the gear rolling machine. The results show that the performance of the gear rolling machine is stable, and the accuracy and the size of the hot-rolled gears hold uniformity during mass production.

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The author investigated the metal structure, bending strength, and the deformation caused by heat treatment of hot-rolled gears. The results reveal that the fibrous structure of material lies along the tooth form, and the crystal structure is of minute structure. The results of the bending test show that the hot-rolled gear is apparently stronger than the cut gear in the impact bending strength and almost equal or slightly stronger in the static bending strength. The deformation of hot-rolled gears as a whole and of their tooth form, when hardening, is made clear by the experimental results.

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Some experimental studies are made on the oil film thickness of the piston-ring which was obtained theoretically in the 1 st Report. The same apparatus as in the 2 nd Report is used, and the 1 st method of this work is a measurement of the electric resistance between the cylinder and whole body of the piston-ring or its certain local parts, and the 2 nd method is a measurement of the circumferential displacement of the gap of ring. From these experiments, it is shown that the appearance of variation and the absolute value of the thickness of oil film measured against the phase of a stroke and a μU/W which is determined by the running condition coincide approximately with the result of theoretical calculation.

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