Fundamentally, the properties of rarefied gases must be deduced from the Maxwell-Boltzmann equation. We will treat the problem of steady one-dimensional heat transfer between two parallel plates in the rarefied gases. H. Grad expressed the distribution function of the gas molecules in the Hermite polynomials. This method, however, cannot satisfy the boundary conditions that the distribution function is discontinuous between incidental molecules and reflecting ones. Then we will divide the distribution function for incidental molecules and for reflecting ones separately, which have different coefficients. Using these distribution functions, we get four equations of the moments of distribution function and three equations can be obtained from the Maxell-Boltzmann equation. From these seven equations we can solve the temperature distribution between two parallel plates in the rarefied gases as the function of the distance from the wall. And we get the relation between wall temperature and heat flux vector.

View full abstract

In the previous paper, we solved the problem of the heat transfer between two plates in the rarefied gas. The equation obtained in that case contains some constants such as L^±, A^±, and B^±. We executed an experiment about the heat transfer between two plates and from the results determined the constants. The experiment consists of the measurement of the coefficient of heat transfer using the transient phenomena. To determine the constants, we simplified the original equation under some assumptions.

View full abstract

The authors have worked out a new air-micrometer having an air chamber which is partitioned from wall to wall with a corrugated diaphragm and in the centre of which a small aperture is bored to serve as inlet or outlet throttle depending on the direction of air flow. The characteristics of such an air-micrometer will represent the combination of the characteristics of an ordinary air-micrometer and deflecting characteristics of the diaphragm. If a large magniflcation is provided for the air-micrometer, the non-linearity of its characteristic may be ignored. As a results, there will be a linear characteristic over the wide range of measurement.

View full abstract

This paper describes the experimental results about the relation between the physical properties and the life of ceramic tools, the cutting performance of trial products in comparison with a carbide tool of a steel cutting grade, and optimum tool geometry and cutting condition of ceramic tool, at machining 0.4% carbon steel. The results are as follows : (1) The cutting performance of ceramics is greatly affected by the physical properties of ceramics. (2) The type of failure of ceramic tool is essentially the same as that of carbide tool. (3) It is necessary to choose proper tool geometery and cutting condition of ceramic tool for the increase of tool life.

View full abstract

In this report, the operating characteristics and the mechanism of lubrication of high speed tapered roller bearing under lubrication by atomized oil i. e. oil fog lubrication are investigated experimentally and theoretically. As the experimental results about the influence of oil supply, air supply, viscosity of oil, load and rotating speed, it has been clarified that the lubrication by atomized oil lessens remakably the friction and the temperature rise in the suitable condition and the atomized oil lubricates mainly as hydrodynamical lubrication. According to the above mentioned character, the hydrodynamical theory concerning the frictional moment and temperature rise of tapered roller bearing has been deduced, and it is confirmed that this theory coincides with the results of experiments moderately well.

View full abstract

The cylinder liner materials were tested for the reduction of wear in high speed diesel engine. The test cylinder liner containing Mo and Cu was cast by centrifugal casting. Addition of Mo 0.65% and Cu 2.0% was the most suitable, and through this the wear was reduced to 76% of the liner used hitherto. The author made precision measurement of the liner wear in relation to the running kilometers and could make the profile of the liner wear clear that was different from the typical one when chromium plating ring was adopted as the top ring. The author surmises that the structural change of matrix might be effective for improvement of wear resistance and advocate about the liner materials that attention should be taken not only to the properties of casting state but also to the hardenability and other properties at elevated temperature for cylinder wear.

View full abstract

Casting of wheel center of rolling stocks was experimented as an example for studies of sound steel castings. Risering considering the fundamental experiments of risering steel castings for simple shapes developed by Pellini and others was provided for this experiment which aimed both to study the thermal analysis of riser and to measure feed metal flow in mold. Casting process in the mold was analysed and thermal gradient promoting the directional solidification in molten steel comprehended which was needed for sound casting. The conclusions from this experiment are as follows, considering the result of γ-ray inspection. (1) Casting designs for complex castings considering Pellini's experiments for simple castings can give optimum or minimum adequate riser only under the correction which is given when the influences of molding conditions and of the delayed solidification at corner are fully investigated and taken into consideration. (2) Based on (1), the better casting design with riser dimensions enlarged by 15% was determined for wheel center when any exothermic compound was not used. (3) Through the author's analysis of the feed metal flow and the thermal gradient of metal in mold, further casting experiments applying chills to promote directional solidification will become easier to execute.

View full abstract

In recent papers, various methods of analysis, the so-called Bussinesq's problem⁽¹⁾, were given for the distribution of stress in a semi-infinite elastic medium deformed by the pressure of rigid body on a part of the plane boundary, while the remainder of the plane was free. In these papers, a friction on the contact surface in neglected or directly expressed⁽²⁾⁽³⁾. In this paper, the author proves that the stress distribution and displacements on the surface of semi-infinite elastic solid indented by a rigid sphere are given by applying the Hankel Transform, and that the approximate solutions under the influence of friction on the contact surface are reduced by suitable use of above solutions. An assumption of friction is made from the well-known fact that u_γ of the contact surface decreases by the friction.

View full abstract

As a fundamental experiment of ultrasonic techniques to be applied to the nondestructive testing of heavy steel forgings, ultrasonic reflection from simulated discontinuities and bottom surfaces were studied in water. Equivalent reflection surfaces of three each simulated discontinuities and bottoms were investigated and the nomograms for the size of discontinuities were established from the ratio of flaw-to-bottom indications and the distances from the transducer to them. The results obtained will not be applied immediately for heavy steel forgings but will be of future value and aid for analysis of reflection phenomena in steel and for the compilation of inspection data.

View full abstract

A new theory of plasticity was advanced. The experiments on the stress relation between plastic pure shear and plastic tension conform closely with this theory. Moreover, the hysteresis loops and the anisotropy due to plastic deformation will be accounted for by this theory. The relation between the yield point of mild steel and the plastic deformation beyond that can be also accounted for.

View full abstract

In this paper, the effects of a pair of symmetrical semicircular notches on the transverse flexure of an infinite strip under the state of plain bending are investigated by use of the Poisson-Kirchhoff theory of thin plates. The unknown coefficients included in the solution are determined by the method of perturbation. In order to clarify the effect of making the semicircular notches, the distributions of bending couples and the stress corcentration factor k_b are calculated and plotted versus the ratio of notch diameter to strip width and Poisson's ratio of the plate material. The deflections of the strip are also calculated and shown graphically.

View full abstract

In a previous paper, the author has reported "Stresses in a Circular Disk with an Eccentric Circular Hole under Radial Forces." In this paper, the stresses in a circular disk containing an eccentric circular hole fixed at its center and under the action of a tangential force were analysed. The method of solution was the same as that used in the previous paper, and the bipolar coordinates were used in the solution. The complete stress-function in the disk with a hole is constructed in the form, in which the basic stress-function is added to the auxiliary one. From the results obtained, the solution of the problem in a semi-infinite plate under a concentrated tangential force on its straight edge and containing an unstressed circular hole was derived.

View full abstract

As a means of reducing the circumferential stress concentration in a plate, in the preceding report, we took up the case of stiffening with a coaming plate around the edge of the hole to supplement the doubling plates. Further, to reduce such concentration of stress, stiffening flanges are attached on the coaming plate or double stiffening plates are used. This paper deals with the effect produced by the coaming plate having the stiffening flanges (namely, the flanged coaming plate), and the effect produced by the double stiffening plates on the stress distribution in an orthogonally aeolotropic plate under uniform tension. In the case of the flanged coaming plate, the circumferential stress around the edge of the hole dcreases in proportion to the increase of the area of the cross section of the stiffening flanges. But, if the stiffening flanges are not attached within an effective distance from the plate within the distance of about five times of plate thickness, there is hardly any reduction of the circumferential stress concentration, even if large stiffening flanges are used. Next, in the case of the double stiffening plates, we assume that the displacements are zero at the junction of the base plate and the coaming plate. Thus, the use of the double stiffening plates is the most effective of the various methods for reducing the circumferential stress concentration.

View full abstract

The strength of the wheel disc of a newly devised wheel in order to lighten rolling stock is discussed on the basis of an approximate bending theory for a flat spherical shell, since this wheel disc consists of two discs having the form of a flat spherical shell which is made up into a wheel together with boss and rim by welding. In this theory, unbalanced traction is supported only by the stresses deduced from the membrane theory and the boundary condition is satisfied by the sum of solutions of membrane and bending theories. Some approximations are utilized in order to derive the solution of bending theory. The stresses due to the force fit of axle and the shrinkage fit of tyre (i. e. initial stresses) and also those due to axle load and side thrust are considered. As the latter is a non-symmetrical problem, the boss and rim are assumed to be rigid, for simplicity. This assumption will entail larger errors than those due to approximations made in bending theory. A numerical example and comparisons with the experimental results and the other simple calculations are shown. The initial stresses are considerably large and the type of spherical shell is especially disadvantageous, as it causes very large bending stress. For the axle load, the calculation assuming the rigid rim and tyre does not agree with the experimental value which is concentrated in the direction of loading. But, the stresses due to the axle load will be small even if the load is unequally divided between discs. On the contrary, the assumption is reasonable for the side thrust and the calculated values agree with the experimental result. As the stresses due to axle load and side thrust are superimposed in the inside disc, the design is desirable in which the axle load is supported mostly by the other disc.

View full abstract

The accurate solution of bending of a clamped or a simply supported elliptic plate subjected to a concentrated load at the arbitrary point is given in the form of infinite series. The similar method in the previous report⁽¹⁾ by one of the authors is utilized in this paper. The arbitrary constants in the plane biharmonic function are determined by expanding the particular solution expressed by elliptic coordinates into Fourier series. As a numerical example a clamped elliptic plate under a concentrated load at the center is treated.

View full abstract

The author performed rotary bending fatigue tests on a bar of S40C with a rectangular cotter hole. Results of the tests are as follows : 1) The cotter hole had better be made up of a rectangle and two semi-circles, and the notch-factor is about 1.45. 2) If we make a rectangular hole, the fillet radius at the corner must be more than one-tenth of the width of the hole, or else the fatigue crack is liable to occur at the corner of the hole in the bar. 3) If the length of a hole is more than twice its width, the notch-factor is scarcely affected by the size of the hole.

View full abstract

In this paper, we analysed the motion effected by harmonic disturbing displacement of the system which has two masses suspended by two springs and a constant friction between masses or between the mass and the supporting ceiling, and obtained an analytical solution in the domain of vibrations with or without stops. Some experiments were carried out, showing close agreements with the theoretical analysis. By these studies, the following results were obtained : (1) In the resonance, when the friction is smaller than a certain definite value, the amplitudes of masses become infinitely large, and the friction which is larger than this value causes a motion with stops or a motion without the relative displacement of masses. (2) At 1/3, 1/5, 1/7, …… of natural frequencies, any smallest friction causes a motion with stops. (3) At infinitely high frequency, in the case that the friction between two masses is larger than a certain definite value, a motion with stops or a motion without relative displacement will occur, and in the case that the friction exists between the mass and the supporting ceiling, any friction does not cause a stop motion.

View full abstract

This paper deals with the natural frequency equation of the mechanical system shown in Fig. 1. As a numerical application the critical speed of a mixer shown in Fig. 5 was studied and it is found there is a zone having no critical speed for any value of K_φ. Comparison of analytical with experimental results of the mixer is presented. The natural frequency equation of a floating or flying body is obtained. For the problem of calculating the critical speed of a jet engine mounted on an aeroplane this theory may be applied.

View full abstract

The author deals with a one-dimensional power-transmission system having an angular clearance excited by a static torque and a cosine torque simultaneously. Although the system has symmetrically combined linear elasticities, the mean torque puts the characteristic asymmetric, therefore the system vibrates either "unilaterally" or "bilaterally", besides symmetrically. The author solves rigorously the harmonic or subharmonic vibration of the system without damping and discusses stability discrimination, then solves approximately the maximum amplitude state of the system under velocity-proportional damping, and as a result he is convinced that the latter approximation not only is easy to calculate, but also serves as stability discriminant. This approximation method gave practically coincident solution compared with the ones computed by Y. Yoshikawa with an analogue computer. Finally the author approximates the maximum amplitude state of the unilateral ultraharmonic vibration of the above system, and he verifies that velocity-proportional damping retards the vibration of the higher order the less effective contrary to the subharmonic mode, and the retardation characteristic resembles the one of the subharmonic mode of the order 1/2.

View full abstract

The author solves approximately the maximum amplitude state of one-dimensional systems retarded not only by linear damping, but also collision damping, which takes place at the clearance parts losing energy in the instant of their collision. In the first section a one-mass one-stiffness system is mentioned but later a two-mass one-stiffness system, of which the author performed an experiment that will be described in the next paper, verifying that the theory given in this paper is pracically true. A series of numerical diagrams is presented, making use of which the above calculations can be performed easier. Then the estimation of collision velocity may be given practically as well as of frequency and amplitude at the maximum amplitude state, if the data of the system dimensions and velocity-proportional damping coefficient are given. The estimated collision velocity may be a useful key of the problem about the fatigue failure of clearance parts.

View full abstract

To examine the approximation of collision damping in the former report, Part 2, here a two-mass one-stiffness system is checked experimentally, and as a result the author verifies that the theory gives practically sufficient accuracy of the order of 1st approximation. The experimental system is made up of an electrical dynamometer, an intermediate shaft, a variable clearance joint, and a fan, excited by a piston crank mechanism. The author reads the torque and r. p. m. at the maximum amplitude state, besides detecting electrically from the revolving system its fluctuating torque, collision velocity and touching of clearance parts.

View full abstract

Displacement excitation by errors of gear shape or by eccentricities of gear axes gives a one-dimentional shaft system substancially the same behaviour as torque excitation does, but in approximate solutions it is necessary to change the expression of excitation term. As stiffness fluctuation of gear teeth also excites vibration, the author solves the vibration of unilateral, symmetrical mode without damping, supposing the fluctuation as rectangular. The solution appears different from the one in the former cases, difficult to calculate, and is not yet numerically treated. The author thinks that this excitation gives rather high frequency, then the damping would act more effectively and this mode probably disappears. The author presents an approximation method to solve by hand a two-dimensional system at its higher resonance state solving rigorously an equivalent one-dimensional system and approximating the damped maximum amplitude state. Though the solution from this approximation method does not sufficiently agree with the one derived by Y. Yoshikawa with an analogue computer because of inadequate data, the method gives a new solution of the equivalent system, which is a limit case of clearance systems.

View full abstract

Recently, relay control systems have been studied from a new standpoint, to obtain an optimum nonlinear control, i. e., utilizing the maximum available power of actuating elements. In this paper, the author treats an optimum nonlinear control for the system with a dead time and shows that the optimum performance can be obtained by adding one more switching action to the case for a system without a dead time. If there is no integrating element, it is impossible to obtain an optimum performance with the same switching-curve. However, this defect can be avoided by the use of two controlling elements in parallel. The author also shows that the switching-curve can be obtained easily by using a transient response.

View full abstract

At high speed of train operation the air resistance dominates over the other elements of running resistance and additionally arise various aerodynamic problems to be considered. The authors established through a model test in the wind tunnel that streamlining of the head and complete coverage of the gap at connections of cars with outer diaphragms could substantially cut the air resistance ; and proved that the wind tunnel test results would in general be applicable to real cars designed on these test results. Reference is also made to the test results on a spoiler type air drag brake and the air force characteristics of a train exposed to side winds.

View full abstract