In the preceding papar, vibrations of twisted rod, whose centroid lies on a straight line and does not coincide with elastic axis, are treated by the assumed-mode method. But, actual turbine blades are twisted about the straight line, called Twist-Axis, and centroidal axes are not always straight. In this paper, vibrations of twisted rod, as shown in Fig. 1(b), are studied analytically. The influences of the position of Twist-Axis, elastic axis and centroid on the natural frequencies are discussed.

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Lateral vibrations of rotating shaft are recorded, and response curves of sub-harmonic and "summed and differential harmonic" oscillations are experimentally obtained. Summarizing, the amplitudes of sub-harmonic oscillation of 1/2 order increase with the magnitudes of eccentricity of rotating body. Shapes of response curves of sub-harmonic oscillations of forward precession are those of hard spring type, and the response curves of soft spring type are obtained for backward precessional whirling motions. For one critical speed of "summed and differential harmonic oscillations, the height of peak decreases as eccentricity increases. The other critical speed has a constant amplitude, even if the magnitude of eccentricity is changed. Shapes of response curves of "summed and differential harmonic" oscillations are either discontinuous response curves with jump phenomena or continuous, according as the nonlinear spring characteristics of shaft are changed.

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Vibrations caused by a ball bearing are complicated because a ball bearing has many moving elements. In this first report, the authors deal with the radial vibration of a shaft caused by balls passing the bottom of the shaft, the frequency of which is given by the product of the retainer speed (in rpm) and the number of balls. The authors calcutated the statical radial displacement of a shaft caused by the passing balls in the bearing, and carried out its measurement which actually showed the existence of the displacement of this sort. From the analytical and experimental results, it was found that if the outer race was distorted in an oval form, the amplitude of the displacement due to the passing balls becomes generally larger. Furthermore, the authors investigated the shaft vibration caused by the passing balls. Experimental results concerning amplitudes and phase differences of the vibrations of the shaft and its pedestal, agreed with the analytical results.

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On the basis of the well-known equation of strain quadratic surface, we discuss the relations between the stress and strain components in the present problems, from which we find the states of stress at a given point, provided that we have the strain components [e_xx, e_yy, e_xy] at the point. Here, we propose curvilinear strain gages with such types as their basic domains are small ring ones surrounding the given point and show that the present problems are solved, if only we measure the curvilinear strains of the gages after having been deformed. As an actual example, we take foil gages of circular type. These gages are fairly smaller than usual Rosette gages and we have generally experimental results with high accuracy.

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In this report we treated the stiffness of bellows type air springs, and obtained the following [numerical formula] where A_s, p_s and V_s : effective load area, pressure and volume of air spring at normal state, respectively. V_a : volume of air chamber. p_a : pressure of atmosphere. m : polytropic index. δ : elongation of air spring bellows par unit pressure in air spring. α, β, γ, and ζ : coefficients which depend on the shape of air spring bellows. and then, we calculated the values of α, β, γ, and ζ of tyre type of bellows. The results applied to air springs for railway cars and models of air springs, show close agreements with experiments.

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In the previous papers the author represented a method to calculate the most proper clamping forces under the repeated loads. In that case, he calculated the stiffness factor ratios between the stiffness factors of bolts and those of abutments by Mr. F. Rotscher's " Effective Cone Method " etc. As those of the practical bolt-connections, however, varied in accordrance with the clamping forces, he has obtained the stiffness factor ratios in various cases of dimensions, materials and clamping forces. And also, he has established an empirical formula of the stiffness factor ratio suitable for the practical bolt-connections.

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In the previous papers the author reported the strength of bolt-connection under repeated load in the case the external load acted only along the axis of bolt. But in the case of practical bolt-connections, it may be well said that all of the external loads acting on bolt-connections may contain the bending stresses besides the tensile stresses, and that the stiffness factor ratios of practical bolt-connections may have very small values as 2 or 3. The author did not treat the bolt-connections having such smaller stiffness factor ratios as related above. In this paper he has obtained the stiffness factor ratios on the connecting rod used in the motor car, as a practical example, and established a new empirical formula of stiffness factor ratio suitable for such a practical connecting rod as this.

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Flat bar specimens of Phenolite with V notches on both edges were subjected to pure bending and the stress concentration factors under various conditions were measured by the photoelastic method. To determine the fringe orders at the base of the notch, several bending moments were applied. The effects of the root radius, the notch angle and the depth of the notch on the magnitudes of stress concentration factor were investigated. Experimental values were compared with Neuber's theoretical values and Nishida's experimental values with a single notch. The results obtained were as follows : (1) As to the effect of the root radius, stress concentration factor decreases steeply until ρ/♭ is nearly 0.3, and thereafter its diminution becomes rather slow. (2) The effect of the variation of the notch angle is little until the notch angle reaches 90°. For the value of the notch angle larger than 90°, the stress concentration factor decreases gradually till it reaches unity. (3) With respect to the effect of the depth of the notch, the stress concentration factor has its maximum value when τ/♭ is 0.15 to 0.25. (4) In all cases, the experimental values obtained were smaller than Neuber's theoretical ones.

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We studied on the following items : 1. The detect range of strain figures. 2. The relations between Luders' line and strain figure. 3. The equivalency of strain figures between strain caused by mechanical stress and that caused by thermal stress. As results, the following conclusions were obtained. 1. The yielding of steel or Fe-C alloy is due to slip failure of one phase in two phases, such as ferrite and pearlite or pearlite and cementite. In adequate structure, we detected the strain figures of steel, which carbon contents from 0.05 % to 3 % and some special steels. The strain energy of yield disperses at the temperature of A₁ point. 2. At low temperature, Luders' line relates equally to strain figure, but not at high temperature. 3. The strain energy of mechanical stress is equivalent to that of thermal stress. Note : -The details of their characteristics were explained with photographs.

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In general, the hardness of material is defined technically as the degree of resistance met by an indenter when it penetrates into the specimen. Understanding it mechanically, the penetration would come to an end when the load balances with the sum of stress component in the axial direction integrated upon the whole contacting area between the indenter and specimen. From this point of view, the author found the theoretical relation between the indenting load, conical angle, the radius of spherical apex of indenter and the depth of indentation. Stress distribution on the contact surface was solved by the slip-line theory. To check this relation, the depths of indentation for many kinds of specimen with different hardness, the indenter and load were measured by a special type of displacement gauge and compared with the calculated results. From that equation, both the theoretical conversion between H_R C, D, A, H_R 45N, 3ON, 15N and H_V and the equations of errors of H_R arised from the errors of load, conical angle and radius of spherical apex were induced. The calculated values by these equations were compared with the experimental results found by many workers. At last, the hardnesses of curved surfaces measured by the indentation method were studied from the same point of view. As a result, the Rockwell hardness can be explained as the function of yield stress of material similarly with the other types of indentation hardness.

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We measured the micro-Vickers hardness of 0.26 %-carbon steel, which had been subjected to rotatory bending stress at a high temperature. The fatigue test was conducted at the room temperature, 300°C and 550°C mainly, and hardness testing was held under 1000 gram load. Summary of the results is as follows : (l) At 300°C, the increase of the hardness number is greater and the hardening layer is deeper than that at the room temperature. But at 550°C, the hardness change is little or nothing. (2) Moreover, this hardening layer is caused by the repeated stress above about 0.8 σ_ω at the room temperature, but about 0.65 σ_ω at 300°C, where σ_ω is the endurance limit at each temperature.

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The 0.35% carbon steel specimens with crack, whose diameter is 50 mm, were made, and some of them were induction-hardened. The results of comparative tests on them show that the fatigue limit, which is only about 6 kg/mm² in case of no heat treatment, rises nearly to 40kg/mm² through induction-hardening. These induction-hardened specimens were rather overheated, so that the rapid heating effect could not be expected, nevertheless their fatigue limit did not remarkably fall. This is presumably due to the residual compressive stress on the surface of specimens. Strain gages were set across the crack and strain variations were measured under both compression and tension loads, respectively. When it is suspected that residual compressive stress is present, the strain is approximately equal under either load, but, when it is not, the strain becomes much larger under tension load. Such phenomenon must originate from the fact that strain at the tip of crack becomes smaller, due to the existence of residual compressive stress and seems to explain one of the main reasons for the increased fatigue limit in the above mentiones results.

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The authors have conducted fatigue tests on induction-hardened V-notched specimens with C=0.18% steel and C=0.38% steel. The experimental results are summarized in the following. (i) At C=0.18% steel, there is a great difference between σ_ωκ1 and σ_ωκ2, the former being 17kg/mm² and the latter 45kg/mm² ; however, at C=0.38% steel σ_ωκ1 is equal to σ_ωκ2, the value being about 46kg/mm². (ii) After a stress between σ_ωκ1 and σ_ωκ2 was repeated 10⁷ times, the authors examined the relation between the applied stress and the length of arrested cracks on C=0.18% steel, V-notched specimens. It was found that the length of crack became larger when the stress increased. (iii) The authors examined the relation between the number of repetitions and the length of crack. The crack initiated after about 10³ repetitions ; and after 10⁶ repetitions, the growth of crack stopped. (iv) The authors discussed the reason why there is a difference between σ_ωκ1 and σ_ωκ2 at C=0.18% steel, and why the value of σ_ωκ1 is very great and why there is no difference between σ_ωκ1 and σ_ωκ2 at C=0.38% steel.

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It is generally recognized that the plastic deformation always precedes the fatigue failure and the plastic region in the matrix palys an important role in the nucleation and propagation of fatigue cracks. The mechanisms of fatigue phenomenon, therefore, might be clarified by obtaining some correct information concerning the behaviors of the plastic region. From this standpoint, the experiments of fatigue failure of both the mild steel and the brass tubes under repeated finite strain and some other relevant experiments were performed. By these experiments several interesting phenomena and some relations among the factors concerning the fatigue phenomenon have been found.

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The problems of the fatigue of materials have been studied by many investigators, but there still remain many unknown factors, especially on the damaging effects due to the repeated stress with varying amplitude. In this study, we carried out the fatigue tests on the medium carbon steel by superposing the higher stress reversals upon the fundamental repeated stress levels in order to discuss the process of fatigue stressing, and investigated the effect of the cycle ratio of the primary stress, the effect of the secondary higher stress level, and its reversals on the cumulative cycle ratio to failure. As a result, it has been found that the more the cycle ratio of the primary stress amplitude is and the lower the secondary stress level is, the greater the cumulative cycle ratio to failure amounts. Besides, we have interpreted these test results by the use of the cycle ratio-damage curves (D-R curves).

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This paper contains an exact solution for the stress distributions in an elastic infinite plate under the two equal and opposite concentrated forces, or the two equal and same directional concentrated couples, applied at the points in the neighbourhood of a circular hole, an elliptical hole or two circular holes. The circular, the elliptical and the bipolar coordinates were used in the solutions, and the basic stress functions were expanded in the Fourier series. The complete stress functions in a plate with the hole were constructed in a form, in which the basic stress function was added to the auxiliary one. The parametric coefficients involved in the solutions were adjusted so as to satisfied the conditions at the hole. The formulas of the stress along the edge of the hole were derived, and the stress distributions were computed by them.

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This paper describes an approximate theory determining stresses and strains in a fully plastic rotating disc having a uniform thickness and a solid center, without any aid of trial-and-error method of calculation. In the first place, the approximate equations showing stress-distribution, strain-distribution and the relation between the number of revolutions and deformations of the disc were derived, assuming linear distribution of nominal strain and using some approximations. Then, this theory was examined by making use of the experimental results in discs of brass, aluminum, and mild steel. As the result of the examination, it was considered that this approximate theory might be applicable to the calculation of plastic deformations in such a disc as mentioned above.

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A method of optimalizing control proposed in this paper can be adopted to the systems, in which the static input and output relation has desirable maximum or minimum values at several load conditions. A sensing signal is applied continuously to such a system, in order to decide whether the output is of maximum value or minimum, by the output of the correlator which supplies cross-correlated value between output and sensing signal. The sensing signal using here is sinusoidal, rectangular, triangular, or random signal. The relation between dynamic characteristics of the system and the characters (i.e. frequency, amp1itude etc. ) of each sensing signal is determined. And then, when noise exists, the control action might be incorrect with a probable error. Therefore, if the output of correlator is smaller than a critical value, the control action should be stopped. This critical value is decided for a permitted probable error.

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In the preceding paper, we have already discussed a relay servomechanism operating on sampled data. In this paper is treated the cycling phenomenon of on-off control operating on sampled signals of a process, whose characteristic is approximated by a first-order system with a dead time. Such a system has been practically used as a chopper bar galvanometer type control system for a long time. The experiment was carried out using a water level control system and the result of the analysis is shown to be in very good agreement with that of the experiment. Optimum performance of this system is defined and a method to obtain it is considered.

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