In recent papers an analysis was given of the distribution of stresses in a thick elastic plate of infinite length on the smooth rigid boundary, loaded with the external pressure on a part of the plane boundary, the remainder of the plane being free^{(1) (2) (3)}. This paper is to find an approximate solution for the plane stress problem caused by a normal load on the free surface of a large thick plate in tight contact with rigid foundation. This problem is complicated too much, but a solution can be obtained by properly using an approximate calculation with the aid of the Fourier integral transformation. The significance of the stress distribution across the contact area and interior part of the plate is discussed. As an example, the contours of the maximum shearing stress τ_max are shown.

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Flat bar specimens of Epoxy Resin with two U notches of identical shape on one edge were subjected to pure bending. The effects of the pitch of two notches, the notch depth and also the root radius on the stress concentration factors were investigated. As to the effect of the pitch, the stress concentration factor of two notches decreased at first owing to the overlapping effect, and then showed an increase up to the value of a single notch. With respect to the effects of the notch depth and the root radius, the stress concentration factor of two notches showed a similar change to that of a single notch. In all cases examined, the stress concentration factors of two notches obtained were smaller than those of a single notch. This fact offers a possibility of reducing the stress concentration due to a single notch by a supplementary notch formed in its neighbourhood.

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This paper deals with the summary of the results of rotating-bending fatigue tests on shafts 10 to 100 mm in diameter of medium carbon steel of 0.39 per cent carbon content. Shafts were tested under a concentrated stress, as represented by both a shrink-fitted member and a fillet. The shrink-fitted specimen hardened by induction-hardening exhibited the same size effect as an untreated shrink-fitted specimen ; the reduction ratio 1.8 was obtained by comparing the endurance limit for a shrink-fitted specimen 10 mm in diameter with that of a specimen 100 mm in diameter and the value 1.6 was obtained for induction-hardened specimens with a shrink-fitted hub. The endurance limit of a large shrink-fitted specimen as well as a small one was increased 1.8 to 2.1 times by induction-hardening. By the photoelastic tests and the fatigue tests was obtained the critical ratio between the diameter of fillet specimen, in which the stress and the fatigue strength at the end of shrink-fitted portion is equal to that of fillet portion. Using this critical diameter has practically effective for increasing the fatigue strength of the fillet specimen with a shrink-fitted member.

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A lot of problems concerning the heat indication test were settled by the use of a model apparatus of heat indication test and by the application of some advanced techniques of metallurgical experiments. Main points are as follows. (1) Proposal of type C' deflection. (2) Two kinds of type C deflection which are caused by the non-uniform distribution of Mo dissolved in matrix could be eliminated only by heat treatments. (3) Types A, D and C' of deflection which are considered attributable to the non-uniform thermal emissivity of forging surface could be completely remedied by the coating of a mixture of flake graphite powder and heat resistance paint. Consequently, no heat treatment is necessary to eliminate these three types of deflection. (4) Introduction of a new specification concerning the heat indication test. At the heat indication test, only types B and C should be examined closely. The rotor forgings showing other types of deflection i.e. A, D and C' are not ccnsidered unsuitable as turbine or generator rotors.

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The free vibrations of rectangular frame works in two groups of mode moving perpendicular and coplanar to its own plane are studied by the Lagrangian-minimizing-method. In the former group, flexural and torsional deformations must be considered, and in the latter, flexural and extensional ones must be. The frequency equations for both groups of vibration are derived explicitly, and numerical results of nondimensional frequencies in some special cases are demonstrated in graphs. The natural fact that the center of gravity of the frame in free vibration does not move is certified analytically.

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In order to investigate the effect of the speed of stress reversal on the endurance limit, and to reduce the time necessary for a fatigue test, a high speed pneumatic fatigue testing machine has been developed. Ultrasonic siren (air interruptor) is used as an exciter for a plane bending type testing machine for the frequency range of 3 to 20 kc/sec. Specimen is a uniform bar of the rectangular cross section vibrating in the first free-free mode, and is supported by steel wires at the nodal points. Tests were made on normalized carbon steels at frequencies up to 18 kc/sec. In order to compare the endurance limit at high speed with that at ordinary speed, the same materials were tested by the ordinary plane bending machine and the rotary bending machine. Speed dependence of the endurance limit obtained from these tests is notable, and the endurance limit at the highest frequency was 43% higher than that in the ordinary frequency range.

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The writer measured the torque between co-axial cylinder walls exerted by the water flow when the inner cylinder rotates. Furthermore, the writer carried out experiments on the co-axial cylinders having circumferential grooves on its inner cylinder surface. The results obtained are as follows : 1) When grooves and an axial flow are absent, the torque coefficient C_f increases as the clearance between two cylinders increases, and when the peripheral Reynolds number R_w is large, the clearance has little effect on the value of C_f. 2) The axial flow extends the range of laminar state of R_w, where the value of C_f decreases, but when the axial flow increases beyond that range the value of C_f increases again. 3) When there are grooves on the cylinder, it becomes difficult to keep the flow laminar, so that the torque hardly decreases with an increase of the axial flow.

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The resistance of a flow through co-axial cylinders of which the inner cylinder rotates is studied experimentally, when there are grooves peripherally on the inner cylinder or on the outer cylinder. Results obtained are as follows : (1) When the Reynolds number R₆ is larger than about 200, the value of resistance coefficient λ of grooved cylinder is much larger than that of non-grooved one, whether the inner cylinder rotates or not. (2) When rotating Reynolds number R_w is large, the value of λ increases with the increase of clearance. (3) When the pitch of grooves is constant, the value of λ increases with the increase of breadth of the grooves.

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The Navier-Stokes equation is linearized for the steady flow in the laminar inlet of a pipe with annular space. This solution shows the family of velocity profiles defined by the modifled Bessel functions. By applications of this family to the momentum equation and the energy equation, respectively, the inlet length and the pressure drop are presented. Some examples of computation are given for the ratio of the inner and outer radii of annular space, m=1.2∼5. The results of computation prove that the relation between the dimensionless distance from pipe entrance σ=x/(R₂-R₁) R₆ and the pressure drop (p₀-p)/(ρu₀²/2) is almost unaffected by m, and the inlet length σ_L also unaffected. Practically, σ_L maybe evaluated to be 0.02.

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In connection with pneumatic micrometers, the outward flow characteristics of narrowly spaced radial-flow nozzles are studied with analytical methods. Assuming that fluids are incompressible and the velocity distribution in a boundary layer is parabolic, the momentum equation of a laminar boundary layer is solved approximately. Thus it becomes possible to calculate theoretically the inlet length, the velocity distribution in the clearance, the pressures at various radii or the pressure loss of any nozzle. As a corresponding value to the Reynolds number, in this case, R=Vh²/νr₁ should be used, where h is the breadth of a clearance, r₁ is the inner radius of a nozzle and V is a radial mean velocity at r₁. Then profiles of pressure and velocity distributions are determined by R only.

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The inward flow characteristics of radial-flow nozzles are studied by the similar procedure to the 1st Report. As a parameter, R=Vh²/νr₂ should be used to calculate velocity distributions in the clearance, pressure losses, etc., where r₂ is the outer radius of a nozzle and V is a radial mean velocity at r₂. When R is over 5.42, boundary layers cannot fill up the clearance, and if R is less than 5.42, the velocity distribution in the clearance becomes perfectly parabolic, that is, Poiseuille flow will be established. In either case, the thickness of the boundary layer reduces to zero at the center of the nozzle. Therefore, the pressure loss of the nozzle should be expressed by one of the three different equations according to the combination of R and the diameter ratio of the nozzle.

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This paper concerns the experimental results of the outward and inward flows in radial-flow nozzles. With an air source of 500 mmAq gauge pressure, the overall pressure losses and pressure distributions are obtained for various flow rates. It follows that the results of the theoretical analysis obtained in the 1st and 2nd Reports are applicable to the practical problems with reasonable accuracy in spite of simple assumptions. However, when the flow is outward and the inner corner of a nozzle is sharp, a severe contraction will occur and experimental results will not be consistent with theoretical values. Since the clearances of the nozzles dealt with are extremely narrow, the velocity distribution in the clearance cannot be obtained by the experiment.

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Characteristic equations of the low pressure pneumatic micrometers are derived from the results of the theoretical analysis obtained in the 1st and the 2nd Report. To prove these equations, experiments are carried out with respect to the characteristics of the outward and inward flows with a single nozzle and the push-pull and V shape characteristics with a combined nozzle. Experimental results show good consistence with theoretical values. The equation for outward flow in a single nozzle is compared with two typical equations of papers published previously, and it is found that the present one gives the values closer to the experimental results than others.

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To design a mixed-flow impeller, the impeller must be divided into partial runners by flow surfaces, which are determined usually without considering the action of blades. In this report, the following two methods established by the author to determine the flow surface are described. These methods are more reasonable than the usual one because proper considerations have been given to the action of blades. (1) In the 1st method, the author has solved numerically the fundamental partial-differential equations for the flow in the interior, in front, and in the rear of the impeller, which have been derived from the equations given by Lorenz and Bauersfeld. (2) In the 2nd method which is an approximate method, the author has solved graphically the fundamental equation for the flow in the interior of the impeller by transforming the coordinates. An example is shown comparing the 1st and the 2nd method with the usual one.

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As to the formula predicting the efficiency of prototype water turbines by their model tests, many formulas have been already presented by many investigators and are used practically. It seems, however, these formulas are not always exact as to treatment of hydraulic pressure losses. In this paper the authors show the method predicting the efficiency of prototype water turbines using the model test data at different speeds. By this method more precise values of the efficiency can be obtained. A similar calculating method is applied to the test data using the different size models also.

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The purpose of this paper is to present a method of simplifying those so far used in determining the cascade characteristics. Specially-designed probes, which swing through an amplitude of one blade spacing at a constant speed in the downstream of blade cascade, were used in order to obtain average values of spatial pressure distribution. A model measuring apparatus was built, and its applicability was examined experimentally. The results are : 1. This swing method is applicable, if the coefficient of the total pressure loss is smaller than 0.1. 2. The error in average outlet static pressures and outlet angles by the swing method is confined within the limit of measuring errors. 3. If the coefficient of the total pressure loss is known, the coefficient of the wake momentum loss, which is necessary for obtaining the lift and drag coefficients, can be calculated on a few suppositions. 4. The adoption of the swing method will save the time by 1/8∼1/10 of that needed by any conventional method.

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This report presents the results of high speed cascade tests on some turbine blades. The wind tunnel used for the cascade tests had the test section at the suction side of blower. For the sake of simplicity, the control of the boundary layer at the side wall was ignored. One typical impulse blade and one noz le profile were tested. In this test the effects of pitch-chord ratio were mainly investigated.

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In this report, new characteristic equations and tables of mercury vapour are shown, based on the results of our experiment on the relation between temperature and pressure of saturated mercury vapour, and using the experimental values of enthalpy of saturated liquid mercury by T.B. Douglas and others. The equation of state of mercury vapour obtained here is as follows : υ=RT/P-1.793×10^-2(100/T)+2.51×10^-2(100/T)²+1.071×10^-3 where, P is pressure kg/m², T=273.15+t is absolute temperature °K, t is temperature °C, υ is specific volume m³/kg and R is gas constant of mercury vapour 4.226 2 kgm/kg°K.

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Spontaneous ignition delay of fuel spray injected into a hot gas stream produced by burning of propane has been measured, using a test rig consisting of 200φ×3 m parallel duct. Results obtained were compared with those by Mullins, who had carried out the same experiment in the range of higher stream temperature and velocity, and with the delay obtained by other methods at atmospheric pressure. Conclusions can be summarized as follows : Controlling factor of ignition delay in a gas stream is considered to be of chemical nature judging from activation energy, 35 to 45 kcal/mol. It depends predominantly on the temperature and less on the physical factors such as velocity or spray condition. This is explained as follows : In spite of rapid formation of uniform mixture, velocity and concentration prevailing is outside the stability range of fuel spray and cannot lead to flame propagation against other ignition processes.

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The object of this paper which deals with the phenomena at the end of injection of Bosch pump injection system is to show the relation between the design of fuel injection equipment and the pressure drop at the pump side. It was found from experiments that the pressure drop had two features. Pressure at the pump side drops down along a fundamental pressure drop curve. The fundamental pressure drop is a function of cam angle, but not of engine speed. The pressure drop along this curve has a maximum value which is determined mainly by the design of the delivery valve of the pump. The theoretical equations of pressure change and flow through the delivery valve port are obtained after reasonable treatment. Assuming suitable factors, the solution of these equations coincided very well with the experimental results.

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There are two cases for measuring the roundness of a cylindrical work ; the one for the work with two centre-holes on its sides and the other for one without a centre-hole. For one of the latter cases, the author previously published both the theory and the experimental results of the method based on the chain rule in which he regarded the circumference of the work as a series of straight lines. In that case, measurement was performed with regard to a set of finite points on the circumference, not performed with regard to the other points, and so, if we take other sets of the finite points, we can expect to obtain more precise results. In this paper, he gives both theory and experimental results of a new measuring method developed from the above standpoint, and examines whether it is practically applicable, and makes it clear that a precise test of roundness can easily be performed by this method.

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A method of predicting the shape of an oil film cavity in the diverging region of a short journal bearing with a circumferential oil groove is presented. The first term of Reynolds' equation was neglected for mathematical simplicity, thus simulating a short bearing. The pressure distribution, load capacity and attitude angle were also discussed. Some numerical calculations were made to predict the shape of the cavity, and some experimental observations were made using transparent bearings to compare with the analysis.

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Under severe cutting conditions of carbide face-milling operation, cracks first come out almost perpendiculary to the cutting edge on both rake and relief surface of blades, and next, cracks parallel to the cutting edge appear according to circumstances. These cracks have negative effects on the durability of a cutter and especially when cutting fluids are applied, they occur remarkably and the cutter is damaged at an early stage. Situation and circumstances under which cracks occur have three characteristic features. (1) Cracks occur easily when the rate of cooling is better or the cutting condition is severe, namely the effect of thermal stress which depends on temperature difference of cutter surface is large. (2) Occurrence of cracks has size effect. (3) Cracks occur as a saturation curve. It is reported that probability Pv of cracks occurring by one thermal tensile stress σ_T is given by the following equation and the features of crack occurrence are explained qualitatively. Pv=1-exp [-r_mLdsecc/(K(m+1))(σ_T/(σ₀))^m 2r_m : thickness of carbide tip Ldsecc : size of chip contact area σ₀ : strength const. of tip K : const. depending on relative heat transfer coeff. m : material const.

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In operating the gear generating machine with a leading screw and a worm gear, which gives regular rolling motion to the gear blank, the minute errors of the leading screw and the worm in one revolution are called the cyclic errors. To what degree the cyclic errors are manifested on the profile of a generated gear tooth was studied, and the following results were obtained. The effect of cyclic errors on the profile of the generated gear tooth can be divided into two ; (a) the irregular motion caused by the cyclic errors appears comparable to the same degree as the profile errors of the generated gear tooth, and (b) the effect appears in a greatly decreased degree on the tooth. The author calculated the degree of the diminutive of the cyclic errors, and obtained graphs of nondimensional equations for general use.

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It is somewhat troublesome to handle the intermeshing equation of the involute crossed helical profile shifted gear. Prof. T. Nakada has constructed an approximate formula by means of approximate geometry, but it has not been hitherto successful to evaluate the errors of the approximation. In this paper, the author gives an analytical explanation of Nakada's formula and a more detailed approximate solution of the intermeshing equation. Hence we can evaluate the errors resulting from Nakada's formula and propose the more detailed approximate formula of the intermeshing equation. The numerical illustrations of how to use our formulas are also shown.

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The mechanism of formation of discontinuous chip in metal cutting was analyzed theoretically with the concept of regional plastic flow in the flow region instead of the conventional concept of single slip along the so-called shear plane. The relationship between formations of continuous and discontinuous chips was reasonably explained. Theoretical expressions for inclination angle of the ending boundary line of the flow region, i.e., fracture surface, the starting boundary line of the flow region, and the shearing strain in the discontinuous chip fragment were deduced and ascertained to be in agreement with the experimental results for carbon steel. Moreover, the shearing stress-strain diagram in metal cutting was discussed and compared with that in static material tests.

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The machinability of free-cutting leaded steel was investigated from the viewpoint of chip formation. Orthogonal and conventional cutting tests were performed on nine grades of leaded steel and three grades of non-leaded steel in order to determine the effect of the lead contained in steel. The addition of lead to steel was found effective in improving the machinability. The cutting mechanism of free-cutting leaded steels was analysed based upon the flow region concept. The effects of depth of cut and lead content on the cutting process were discussed. It was found that a smoother shear deformation occurs in the cutting process on leaded steels than on non-leaded steels, hence the inclusion of lead in steels improves machinability.

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