The fulcrum of single flexure used as the fulcrum of the lever of a scale, because of its construction in which the lever is hunging supported with the flexure, was unavoidably accompanied by lateral vibration of lever, rendering it extremely difficult to read the correct angle of the inclination of the lever, while, on the other hand, the lever could not be used where lateral force was applied to the fulcrum, as in the case of an upper-dish scale where the Roberval structure is adopted. Thus, for the purpose of eliminating such lateral vibration as mentioned above, and, at the same time, in order that the lever be used where lateral force is liable to be applied, the present author has conceived a construction in which two equal-size flexures, mutually crossing at the right angle, would be used before and after, the lever being hung at this very point. In the present paper, effort has been made to introduce a formula on the sensitivity of such an elastic fulcrum of cross flexure, and, at the same time, to ascertain that the dispersion of the equilibrium position of the lever will be drastically reduced as compared with the knife edge fulcrum, and, thus, the applicability of cross flexure as the fulcrum of the lever of a scale has been examined.

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Many researches on the dynamical properties of rubber vibration isolators have been made according to the theory of visco-plasto-elastic materials. As the result of these researches, it became possible to analyze theoretically those problems that were discussed experimentally. Getting such studies into the shape of rubber, a method to design rubber vibration isolators, in the cases of simple shapes, was reported formerly by the present author. But practically, their shapes are not simple, and, bush, truncated cone and truncated pyramid type rubbers are often used. So the study on a rational method to design such rubber isolators mentioned above has been continued, and using many nomograms as in the former report, it was made simpler and more accurate.

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Experimentally, a rubber cord seems to have characteristics of a string on one hand, and of a beam on the other. Equation of motion with a term of damping was introduced as for a rubber cord. Then the solution was compared with the results of experiments, and the dynamical characteristics of rubber obtained as rubber vibration isolators were taken into account. 1) Vibration of rubber cord with a concentrated mass. Linear vibration with one degree of freedom was assumed. Elastic modulus E calculated from this experiment was compared with static modulus. Values of E are thought to be adequate when the ratio between dynamic and static moduli is taken into consideration. 2) Torsional vibration of rubber cord. Shear modulus G^^- calculated in the same way was compared with the static shear modulus. 3) Free damped vibration of rubber cord. A term of damping was added to an ordinary equation of string. Results of experiments could be explained by an equation ∂²y/∂t²=a²(∂²y/∂x²)-2c(∂/∂t)(∂²y/∂x²), when an effective value of tension was taken into account.

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

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This report deals with the damping factor of herical compression spring with a constant pitch and presents studies for the calculation of the additional stress on the spring at thee time of surging, which is often a main cause of failure of the spring. The results of our experiments reveal that damping effects come from three major frictions, internal and external frictions of the coil itself, the contact friction of the both ends of the spring, and the friction when coils are driven home. If the logarithmic damping factor derived form the linear theory is taken into account for the clarification of experimental results, and if we consider the ratio ξ between the amplitude of the mth harmonics C_m and the geometrical minimum coil clearance a_T, the minimum damping factor is obtained as follows : ξmin≅0.015 whenζ≤0.003, ξmin≅1.6(ζ)^0.8 whenζ≥0.003

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In the lateral vibraticns of a shaft mounting an unsymmetrical rotating body, a free vibration of frequency p^^-_i allways 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 the small dissimilarity in spring constants result in the new zones of instability. These zones appear at the rotating speed ω where the relation p_i=-p_j or p_i-p_j=2ω. 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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The rotating shaft carrying an unsymmetrical body is statically unstable near its major critical speeds, and the unstable regions become smaller as the damping forces are larger, and they vanish when the damping coefficients reach the critical values. These critical damping coefficients are calculated in the present paper. Then, the amplitudes and the phase differences of the forced vibrations are studied. The angular positions of statical and dynamical unbalances have an influence upon the amplitudes and the phase differences, and the characteristics of the response curves and the phase angles are very different from those of usual vibratory systems. Furthermore, the comparison with the flat shaft system is carried out.

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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 forces of those vibrations. Futher the stability criteria of vibrations are analytically studied. The conclusions obtained are as follows : (1) The characteristics of summed and differential harmonic oscillations are analogous to those of sub-harmonic oscillations of order 1/2 and 1/3. (2) There are the critical values of damping coefficients, and the summed and differential harmonic oscillations cannot take place, when the magnitudes of damping are larger than these critical values. (3) The loci of vertical tangency of the response curves divide the response curves into two parts, and the upper parts of the loci are the stable range, the lower unstable.

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The stresses and strains are obtained by successive approximations for a heterogeneous plate whose elastic moduli vary periodically both in the x-and y-directions. Some numerical results are given for a plate pulled in the x-direction, when Young's modulus varies in the x-and y-directions with equal period.

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By annealing and electro-polishing technique it was shown that the fatigue damage of 6-4 brass specimens is confined within a thin surface layer of the specimens. The thickness of the damaged layer becomes thicker 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 its thickness exceeds some threshold value (in the present case, 30∼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 some limit, even if the number of stress repetitions is infinitely large.

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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 Prof.K.Mizoguchi. The method of solving and results here obtained can be utilized to the design for rotary kiln.

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In the present paper, the author analyses the temperature and the thermal stresses int the long hollow cylinder a<r<b, initially at zero temperature, which is heated by heat transfer at r=a from a medium at temperature T₁ and cooled by radiation at r=b into a medium at zero temperature. The rigorous solutions are represented by the form of infinite series. When the parameter κt/a² (κ : diffusivity, t : time) is small, the convergence of those series is unpleasantly slow. In order to avoid these, the author introduced the approximate formulas well suited to this region. It is shown that the solutions in the cases of the constant surface temperature may be obtained as the special cases of the above problem. Numerical calculations are carried out for three cases of b/a with various values of coefficients of heat transfer.

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The quenched and tempered steel, which has been subjected to a load below the yield stress, shows various residual strains after unloading, according to the condition of heat treatment. Especially, in the case it is tempered at 300°C, the residual strain appears in the opposite direction to the applied load. In this report, on the heat treated plain carbon steel subjected to tension, compression or torsion below yield stress, the dimensional change after unloading and the results of measurement of the residual stress in the specimens before loading and after unloading are explained. Also, the new method of measurement of the residual stress, which is suitable to apply to the heat treated cylinder with a small diameter, is explained.

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In the previous papers, the authors reported that the half-value breadths of metals read from X-ray diffraction lines changed with the application of alternating stresses at constant or varying stress amplitude, and it was found that the change of half-value breadth b/B (B and b are the initial and the current value of half-value breadth respectively)-logn/N (n/N is the cycle ratio) or b/B-logΣn/N (Σn/N is the summation of cycle rations under a varying stress amplitude) relations were expressed by a straight line irrespective of the magnitude of applied stress or stress history. Namly, the authors offered a certain method of nondestructive prediction of fatigue life. The studies carried out by the authors previously, however, did not treat the interpretation of the change in half-value breadth from the viewpoint of the mechanism of fatigue. In this connection, in order to reach a better understanding of the change in half-value breadth, they investigated the changes in half-value breadth of X-ray diffraction line, residual stress, microstructure, and micro-hardness due to stress cycles, and discussed on a change of half-value breadth.

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Flat bar specimens of Epoxy Resin with multiple V notches of identical shape formed on one edge were subjected to pure bending. The effect of the pitch on the stress concentration factor of each of the multiple notches was investigated, the depth of the notch being varied in three steps. In the range of smaller pitches, the reduction in stress concentration due to the overlapping effect was observed quited similarly to the case of the previous experiment on two notches, but its amount was found different between the central, intermediate and outside notches. As to the effect of the notch depth, an optimum depth was found to exist. For multiple notches with more than five, the stress concentration factors of both the central and outside notches showed nearly constant values.

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In the present paper, the problem of plastic yielding of notched steel plates subjected to pure bending is investigated experimentally. The test pieces examined are 0.34%C carbon steel plates which have a single wide notch with circular fillets. Six shapes of notches are examined. To clarify the effects due to the difference in the shape of notches, Lueders' bands and strain figures developed in the plates are observed in detail during the elastic-plastic stage of bending. The values of bending moment defined as the Limit or Collapse Moment are obtained for each notch. Constraint factor for each notch is given. They show the effects of the constraint of plastic deformation given by the neighbouring elastic regions.

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Some experimental studies on the aspects of surface layer of various steel specimens were carried out. The chief conclusions obtained are as follows : (1) The depth of the machined surface layer (on this expression, the author mentioned in the previous report⁽¹⁾) decreases as the hardness of the base-metal increases. (2) The depth of the machined surface layer of austenitic steels is more deeper than that of ferritic steel. (3) Two types of the distribution of the half value breadth of the X-ray diffraction pattern and the micro hardness in the surface layer existed. (4) Many forms of the distribution of the residual stress in the machined surface layer were observed. These distributions are explained qualitatively by a superimpose of the effects caused by four origins. (5) The half value breadth of the X-ray diffraction pattern is correlative to the hardness value.

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The authors have frequently pointed out the nonuniform thermal emissivity as the cause of type D deflection in the four reports previously issued. In the 5th report of the studies about the heat indication test, the thermal diffusivity theory which is generally believed to be a cause of type D deflection is fully discussd. Thermal conductivity of low alloy steels used for turbine and generator rotor forgings is accurately mesaured by the relative mthod. 1% Cr-1% Mo-V Steels tempered at 625°C and 675°C showed the difference of 5 per cent in thermal conductivity, and in case of 3%Ni-Mo-V Steels tempered at 600°C and 680°C the difference was 3.5 per cent. Timo and his co-worker have reported 2.5 per cent nonuniformity of thermal conductivity and explained it as the cause of the type D deflection. However, a model rotor which has the difference of thermal conductivity at diametrically opposite sides more than 5 per cent (twice the difference of thermal conductivity Timo and his co-worker refered to) did not show the type D deflection, but it showed only type C deflection (the heating and cooling rates were both 120°C/hr at the test). It was described in the 2nd report that an actual rotor forging with 2 per cent nonuniformity of thermal coefficient and model rotors with all sorts of metallurgical asymmetry revealed only the type C deflection, and never showed the type D deflection. In the authors' plant the type D deflections were all disappeared by mechanical improvement of rotor forging surfaces. Considering the above results, it is concluded that Timo and his co-worker's thermal conductivity theory about the type D deflection is not founded on fact.

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Experimental results which were described in the previous five reports have been ascertained by the tests using actual rotor forgings in works in this 6th report. (1) Type B deflection is attributable to the relaxation of residual stresses, and does not appear again, unless re-machining is applied. (2) Deflection for which it is necessary to perform the heat treatment to be eliminated is type C only. (3) Spray coating with a mixture of flake graphite powder and heat resistance enamel is one of the practical techniques to eliminate the deflection of types A, D and C' in works, Consequently, no heat treatments are necessary to eliminate these three types of deflection. At the heat indication test of turbine and generator rotor forgings, only deflection of types B and C should be examined closely, and the other types of deflection i.e. A, D and C'are generally considered harmless.

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To find out the prevention of defacement in case of deposited weld high manganese metal used for points of the railway, I have conducted experiments under the following conditions, i.e., lubricated and non-lubricated states and determinations made by using an Amsler type abrasion testing machine, employing slip velocities ranging from 0 to 15 cm/sec and contact pressures between 50 and 90 kg/mm². The test piece of tyre is about 0.7%C standard structure steel, and the other material of deposited weld high manganese metal. The results of tests indicated that : - 1) "Pitting" amount of the deposited weld high manganese metal is very little, and the effect of lubrication is very remarkable. 2) In case of austenitic structure, deposited weld high manganese metal, shows the same tendency of wear as cast high manganese steel.

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Stick-slip is sometimes observed in the sliding surfaces of machine tool. In this paper the Characteristic of 4-way valve, the equation of continuity for oil flow and the equation of motion for the sliding element are described. Stick-slip is analysed quantitatively under the assumptions that the characteristic of 4-way valve is linear and the friction is composed of static friction, coulomb friction and viscous friction. An experimental veriflcation of the theoritical analyses is shown, using a model table which is same size of the table of no. 2 1/2 milling machine. It has become apparent that friction-velocity relation and oil compressibility are two major factors for the growth of stick-slip. It is shown that the motion of table in stick-slip can be described by 4-way valve pressure-flow characteristic, friction-velocity relation, oil compressibility and the sizes of the hydraulic driving elements.

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For high-supercharging of diesel engines, we planned a blower with straight impeller of the radial type which we have never used before. The circumferential design speed of the impeller of this type is much higher than that of the ordinary impeller. Therefore, in order to confirm the strength of the impeller, we have theoretically analyzed the stress, using the digital computer and on the other hand we have experimentally analyzed the stress by stress freezing by revolution for the three dimensional photoelastic model. Thus, by clearly knowing the stress distribution in the blade and the disc, we could confirm the reliability of the impeller of the radial type. Also, from the view-point of the limit design, we could presume that the bursting-speed would be 30 000 rpm, which corresponds to 100% over-speed.

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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 to conveniently determine the numerical value of the constants involved in the transfer-function? 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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Finite-settling-time systems which are nonminimal have constants which can be arbitrarily assigned. This opens up the possibility of selecting the extra system constants with a view of optimizing the system under some criterion. An approach to this problem is to minimize the intergrated-square sampled error or the quadratic control area. This paper is concerned with the problem of synthesis of nonminimal finite-settling-time systems which have no ripples after a suitable transient period has elasped under these two criteria. The treatment of these optimization problems makes use of the z transform and the modified z transform methods. By representing polynomials by vectors or matrices and making use of the linear algebraic techniques, the synthetic studies can be systematically carried out. The design equations of the optimum systems and the evaluating formulas of the minimum integrated-square sampled error and the minimum quadratic control area are derived.

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Transfer function between the feed concentration change and the liquid concentration on any tray is derived here in a compact form for the binary distillation column. When the signal flow diagram is drawn from basic material balance equations and transformed into the equivalent simple diagram, the transmittances in the simple diagram take the form of continued fraction. The continued fractions thus obtained are reduced to compact forms by the use of hyperbolic function, and the transfer function is obtained from them. It is remarkable that the time required for calculating the frequency response can be much shortened than going throught the usual straightforward methods and is also independent of the number of trays.

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