This paper is a part of the continued study on the errors of measurement of Rockwell hardness number and reports the results of experiment and the caluculated results from Meyer's law to find the effect of the errors of preliminary and total loads. Both results obtained by observation and theoretical calculation respectively coincided very well with each other. The errors due to the error in the total load W₂ and the preliminary load W₁ are given as follows : [numerical formula] and [numerical formula].

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Regarding the error introduced into Rockwell hardness numbers by the error of form of diamond indentor, this paper reports the results of experiment and the calculated results from Meyer's law. Results obtained by observation and theoretical calculation respectively coincided well with each other. The errors resulted from the errors in the total load W₂ kg, the preliminary load W₁ kg (see the first report), the tip radius R mm and the angle of cone θ (rad) of diamond indentor will be as follows : [numerical formula]

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On the error introduced into Rockwell hardness numbers by the error of steel ball diameters, this paper reports the results of experiment and the caluculated results from Meyer's law. Results obtained by observation and theoretical calculation respectively coincided well with each other. Accordingly, the errors caused by the errors of total load W₂ kg, preliminary load W₁ kg and diameter D mm are shown as follows : [numerical formula].

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The authors have made two kinds of fatigue tests on shoulder fillet specimens (one is 135 mm in diameter at the testing part and 15 mm, 25 mm and 40 mm in fillet radius, the other is 14 mm in diameter, having proportional sizes to larger one), for the purpose of obtaining fatigue notch factor on shoulder fillet by comparing their fatigue limit with those of 125 φmm and 10 φmm smooth surface specimens described in Part 1. On the other hand the stress concentrating factor has been determined on fillet of larger specimen, by correcting the effect of the ratio of gauge length to fillet radius. This correcting factors are 1.06, 1.018 and 1.006, where the above ratios are 0.60, 0.36 and 0.225 respectively. It has been disclosed from these tests that : (1) Stress concentrating factor given by Petereon is equal to the measured value without correction. ( 2 ) Fatigue notch factors of larger sepcimen are nealy equal to those of smaller ones ; and coincide with the corrected concentrating factor of quivalent stress by shear strain energy theory.

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The author has studied the relationship between the stress and the propagating speed of fatigue crack by analysing shelly pattern on fracture surface of shoulder fillet specimens obtained by the tests described in Part 3. This analysis was based upon the assumption of the stress σ on the cros section of fillet as follows : [numerical formula] where η : distance from neutral axis for bending C₁, C₂ : constants given by stress concentrating factor. As the results of above studies, it has been presumed that the propagating speed of fatigue crack may be reduced due to coaxing effect and strain harding at the tip of fatigue crack, where the speed is smaller than 0.2μ/c. When the speed exceed 0.2μ/c, it may be obtained from the following formula ; [numerical formula] where υσ_n : stress on edge line of fracture surface kg/mm². υ_c : speed of fatigue crack propagation μ/c. σ_o : fatigue strength of specimen having fine crack kg/mm². Φ_r : stress gradient on surface layer of cracking part kg/mm²/mm.

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The authors have conducted fatigue tests on the force-fitted specimens 50 mm or 10 mm in diameter and the plain specimens, 65 mm or 10 mm in diameter. The experimental results are summarized in the following. (i) Even when there is a difference between the fatigue limits of the force-fitted specimens and the plain specimens, 10 mm in diameter, there is no difference between the fatigue limits of the force-fitted specimens 50 mm in diameter. (ii) The fatigue strength of the force-fitted specimens 50 mm in diameter, which were made of the wheel-axle of the car broken while running, is not lower than the fatigue strength in the former experiment (i) and the old experiment in 1950. Therefore, we could not understand from this experiment the reason why the running shaft have broken.

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The authors have conducted fatigue tests on the induction-hardened V-notched specimens, 50 mm in diameter. The experimental results are summalized in the following. In the normalized V-notched specimen (α is nearly 7.65), the value of σ_w2 is 6.5kg/mm² and σ_w1 is 1.5 kg/mm² (this is tredicted on Mr. Ouchida's data), but in the induction-hardened V-notched specimen, these values are very large, that is, σ_w2 is the fatigue limit causing the failure of a whole piece, and σ_w1 is the lowest of the stresses causing the start of crack at the bottom of V-notch after infinite number of repetitions. Lastly, the authors discussed the reason why σ_w2 and σ_w1 of the induction-hardened specimens are very large in comparison with those of the normalized ones.

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To find out the prevention of defacement in case of being used for the point or railway, I carried out an experiment under the following conditions, using an Amsler-type abrasion testing machine, at various slip speed of 0∼15 cm/sec, and contact pressures of 50∼90 kg/mm². The test tiece of tyre is about 0.7%C steel of standard structure, and the other material of High manganese steel and Chrome-mangan steel is from 1050°C water-hardning. The following are the findings result from the present test : 1. Hardness of High mangabese steel goes up to a certain extent at the beginning of the test. However, anti-wearing character can not be expected to increase owing to the growing of its hardness. 2. Satisfactory effect of wear resistivity can not be expected much in the sliding motion between C-steel and High manganese steel due to sliding friction. 3. From these facts, High manganese steel seems to be superior in anti-shock toughness than in wear resistivity. 4. Chrome-mangan, which somewhat covers for the effects of High manganese steel, in somecase must be used carefully within the limit of its application. 5. In this case, the actual amount of the wear can be estimated by this tests.

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In this paper, the free vibration of a one-degree-of-freedom system with viscous damper supported ellastically and with springs whose stiffness ratio κ is arbitrary, is studied. Some intresting facts have been derived from the study that the system has an optimum damping value for the free vibration and that the value is nearly equal to that for the forced vibration. In addition, the transient nature of a vehicle equipped with a damper adjusted adequately for the steady motion in passing over a raised or sunken place, has been investgated, comparing the result 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 in comparison with the latter in reducing shocks.

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The forced vibration of the one-degree-of-freedom system with unsymmetrical viscous damper has been analyzed theoretically in a rigorous method, and the calculation has been made for the following two cases : a) c=0.2c_c, c=0.8c_c, b) c=0, c=c_c, where c_c is the critical damping coefficient. The numerical results obtained have shown (1) that the neutral line of the vibration of such a system has a tendency or shifting to the direction, in which the damping is weak ana the amount of 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 wave figure of the acceleration warps considerably. These results have also been ascertained by an experiment carried out with a system equipped with the damper which works on the stroke of one direction only.

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In recent times, rubber is widely used as a vibration and shock isolator in the vehicle suspension of two-degrees-of-freedom such as railway cars or automobiles, solely at the damperrod hinges in the shape of rubber bushing or sometimes as the cushion seat for both the steel springs and the damper. It seems to the authors from a qualitative analysis of the system that such uses of rubber present no positive effect in isolating small vibrations, and to ascertain the above expectation some experiments were carried out using a model vibration system and a vibrating table. The response of the main mass to small harmonic excitation was measured by means of an unbonded type of strain gauge accelerometer and a new type of transistor D.C. amplifier, the result showing that the rubber bushing at the eye of the damper-rod did not serve as a vibration isolator in the case where either the rubber was loaded or unloaded with the main mass.

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The mechanical properties of rubber vibration isolators depend on the amplitude, frequency, temperature, inclination and mean stress, and have remarkable shape effect. When designing, not only such properties but also the kinds of rubber, the conditions of vulcanization, the influences of blending and coating of different rubbers as to the characteristics of materials have to be considered. Furthermore, the deformation of rubber under usual stress is not infinitesimal. The author has continued calculations and experiments in view of the theory of viscoplasto-elasticity advanced by Prof. Sawaragi and strength of materials. And now it becomes possible to calculate the apparent modulus and spring constant by the successive approximation method. From such results a rational method to design rubber vibration isolators is contrived, considering terms above mentioned as much as possible. In this method using nomographs, design can be expedited with a high accuracy.

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In press-fitting an axle into the hub of a wheel the part of the axle not yet in the hub must bear the total pressing force, while in the hub, the force is distributed along the fitting surface. As a result the amount of the axial contraction of the axle, due to pressing force, becomes different from that of the bore of the hub and, consequently, when the force is removed, large axial tensile stress will be induced on the surface of the axle near the portion just inside of the hub face. This stress will lower the fatigue strength of press-fitted assemblies. In this paper the effect of the stress stated above on the fatigue strength of press-fitted bars has been confirmed by calculating the said stress, as well as by measuring the fatigue strength of cracked bars with fillet or with a press-fitted part.

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In this paper, a problem of determining the stress distribution produced by an infinite series of equal and equally spaced circular holes in a thin plate subjected to bending or twisting moments is treated with the help of real variables. Here the plate is considered subject to the limitation of the Poisson-Kirchhoff theory of bending and a method of perturbation is adopted for the determination of the coefficients contained in the solution. For some special cases numerical results are given.

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A two-dimensional solution in series form is given for the stresses and displacements around an annular inclusion perfectly bonded to an infinite strip under tension. The known solutions for an infinite plate with a reinforced circular hole and a strip with a central hole are obtained as limiting cases. Numerical results are given for the variations of stresses for various values of parameters which define the geometry and the elastic properties of the strip and the inclusion. The effect of reinforcement with beads is also discussed.

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By experimenting on bars subjected to an axial impact by a rigid mass, the author has investigated effects which the initial curvature of a bar, the ratio of the rigid mass to the bar and the velocity of the impact that produces the axial stress or the lateral deformation of the bar. The larger are the value of initial curvature, the ratio of the mass to the bar and the velocity of impact, the larger the value of lateral deformation of the bar is, and when this deformation becomes larger than a certain value, the mass runs against the bar twice or more before one impact is over.

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A phase plane method for analizing an on-off controlled servomechanism to any sinusoidal input is proposed. In this method, the behaviour of a representative point is broken down into two separate movements, one of them is its rotation around the circumference of an elipse, whose radii are a and aω, where a, ω are the half amplitude and the angular frequency of the input respectively and the other is the travelling of this ellipse along a curve decided by the transfer function of the controlled element and the manipulated variable. The necessary conditions for generating the subharmonic oscillation in the output are stated as followed ; 1) The trajectory of the center of an ellipse is a closed curve. 2) The time for one cycle of the center of the ellipse is equal to an integral multiple of the period of the input. 3) The trajectory of the center of an ellipse converges into this closed curve as time goes on. 4) The representative point is always on one side of the switching line during a half period of the output. Practical examples of the first three conditions are calculated, where the on-off controlled servomechanism of the first or second order having symmetrical switching line is treated and some numerical results are shown through graphical figures. In these figures, the conditions that the output follows the input are indicated. These conditions are very valuable for designing on-off controlled servomechanisms so as to follow to given sinusoidal input.

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Recognizing that the probability distribution of input signal to the nonlinear element in a closed loop control system is not a Gaussian, the authors present, in this paper, a more precise evaluation of equivalent gains of various nonlinear elements in control systems subject to a Gaussian random input. The conception with respect to the Markov random process in statistics is introduced and the justification for assuming the response of a nonlinear control system as being a Gaussian process is considered in detail. The equivalent gains obtained in the previous papers are modified from the results of evaluating the probability distribution of the response of nonlinear control systems. Moreover, the statistical linearization technique is theoretically checked for the various important cases. The authors find that the results of these evaluations agree with the experimental results sufficiently.

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The author has studied on "summed and differential harmonic" oscillations occuring in rotating shaft systems, i.e., vibratory systems with gyroscopic terms. In the present paper, the authortreats "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 analitical discussion, it is concluded that summed type only can take place in rectilinear vibratory systems while both summed and differential types 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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It is ordinarily assumed that the superheater and the reheater in boilers, unlike the evaporating section, do not generate pressure by absorbing heat. In this paper it is proved that the boiler pressure increases or decreases by manipulations that tend to increase or decrease the total volume of contained water in evaporators as well as in superheaters and reheaters. A simple theoretical reasoning leads us to conclude that the transfer function from the heat absorption to the steam pressure is mainly affected by the fluid-volume increase in the section devided by the outgoing (and not by the in-coming) fluid volume. Thus the pressure-generating effect in the superheater and the reheater in modern high-pressure boilers is nearly as large as, and sometimes even greater than, the effect in the evaporator. Similar investigation on the feedwater indicates that the steam pressure in supercritical boilers can better be controlled by manipulating the combustion than by manipulating the feedwater flow.

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