This paper deals with an approximate theory of airfoil cascades in subsonic flow. The theory was developed by the so-called "Interference Method" and Prandtl-Glauert's approximate theory of airfoil. The calculated results of some airfoil cascades coincide well with the ones calculated by the "Hodograph Method". The Inverse Problem is also discussed in this paper.

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The authors carried out the experiments on a regenerative pump systematically, changing the dimensions of flow channels, impellers and clearances. And they propose a "characteristic dimension of flow channel" for a parameter. Then the following results are obtained through above experiments. (1) The influence of the clearances on the pump performance depends on the characteristic dimension of flow channel. The allowable clearance is decided by the value of the characteristic dimension of flow channel. (2) The pump efficiency is high in the adequate range of impeller dimension and characteristic dimension of flow channel. (3) The influence of number of vanes on the pump performance depends on the width ratio of vane. (4) The pump performance depends on the combinations of characteristic dimension of flow channel, width ratio, thickness and length of vane. (5) The upper and lower limits of characteristic dimension of flow channel are fixed by the values of clearance and dimension of impeller.

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According to the author's preceding research on a regenerative pump, in which the flow channel and the impeller dimensions were widely changed, the pump performance is influenced by their relations. Then, it is obvious that the analysis of performance can not be considered without taking their relations into account, when they vary with each other. The author's analysis consideres their effects on the performance. And he shows that the theoretical equations for performance are available for the practical purpose.

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This paper describes the behaviour of the chip in steel cutting by the lathe tool with the parallel type chip breaker, which is the most fundamental type of the chip breaker. The first half describes about the curling radius of the chip bent by the chip breaker. We present here a new equation about the curling radius. The latter half describes about chip breaking by the chip breaker. Using the above equation of the curling radius, we succeeded in an equational representation of the conditions in which the chip is properly broken. On the basis of this equational representation, a chart was drawn up for the design of the chip breaker.

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The displacement of the relative position of the grinding wheel and the work at grinding operation is investigated. The true and the equivalent wheel depth of cut, the decrease of work radius, and the cutting residue are computed under the following assumptions : (1) The effect of the vibration can be ignored. (2) The relative displacement between the grinding wheel and the work is elastic and proportional to the grinding force. (3) The parallel movement of the work and the grinding wheel is caused by the grinding force. (4) The wear of the grinding wheel can be ignored. The analysis shows that the equivalent wheel depth of cut is equal to the amount of the wheel-head advance at each pass of grinding wheel when the number of passes is increased.

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The lubrication theory on substances of rheological behaviour as grease is a recent theme. In particular, as the grease is often used for the lubrication of roller bearing, it is important to establish a theory of grease lubrication for roller bearings. In this paper, considering grease as a Bingham plastic, a theory of grease lubrication for cylindrical roller bearing has been advanced. The special core formation in grease film, the frictional resistance of roller bearing, the pressure distribution and the load capacity of grease film entrapped between roller and race of cylindrical roller bearing have been investigated.

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There are many researches on the noise of a ball bearing, and their conclusions about noise source can be divided into two main opinions ; one attributes it to elastic vibrations of the outer ring, the other to vibrations of the cage or ball. However, these conclusions are only based on a hypothesis. So, in the first place, the author measured the noises of three kinds of simple single row deep groove ball bearing, analyzed the peak values of their frequency spectrums, and obtained the results as follows : (1) The noise of a simple ball bearing is due to vibrations of the outer ring. (2) In the above vibrations, there are radial and axial bending ones which have the first and the second modes. (3) In the case of axial load, another vibration exists, and its vibratory system which was found by Mr. Tanaka, consists of a mass of outer ring and an axial stiffness of ball bearing.

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The three kinds of characteristic functions in the deformation theory of the authors, i.e. strain rate function, work hardening function, and rate of recovery, were determined for 0.14 percent carbon steel from the results of the constant strain rate tension tests at a temperature of 450°C. These functions were compared with those determined from the data of the constant stress creep tests. It was found that the agreement between them was satisfactory. The relations of strain rate to elapsed time in the constant stress creep tests under several stress levels were predicted by the theory using the three characteristic functions determined independently of the results of the creep tests. The predicted relations were in good agreement with the experimental ones. The characteristic functions determined were discussed on the basis of metal physics, and were interpreted from the knowledge of behavior of both dislocations and vacancies. It is concluded that the behavior of the mild steel at high temperatures could be predicted by the present theory, if a proper form of each characteristic function were given.

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Rotating bending fatigue tests under constant strain amplitude were carried out with a 0.55 percent carbon steel and a 13 chromium steel to study the influence of frequency of stress repetition on the fatigue strength of materials. The test temperature was from 450°C to 600°C and the frequencies of stress cycles were 170 and 1500 c.p.m. Both the 0.55 percent carbon steel and the 13 chromium steel showed the fatigue behavior characteristic to the elevated temperature above a critical temperature. That is, at a large amplitude, the specimens fractured at a definite number of stress cycles irrespective of frequency and, at a smaller amplitude, specimens tested at lower frequency fractured at less cycles than those at higher frequency. These characteristics are the same as those of low carbon steel studied previously, and suggest that the fatigue at elevated temperatures is a sort of rate processes and is closely related with the plastic deformation of material under alternating load. Interpretations were made on the common basis with the dynamic creep rupture.

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Experiments were carried out with a low carbon steel to study the influence of rest in stress alternation on the fatigue properties of a low carbon steel at elevated temperatures. The test temperatures were 450 and 300°C and the frequency of alternating stress was 1500 c.p.m. The tests were performed under the condition of constant strain amplitude in the rotating bending fatigue test. The rest in stress alternation was realized according to two sorts of programs. In the one, a rest of 0.5∼30 hours was given after the stress alternation of one half of the number of cycles to fracture, and in the other, rests of about 8 and 16 hours were given alternately after the stress alternation of every one fifth or one tenth of the number of cycles to fracture. The temperature during the rest was maintained at the test temperature. As a result, it was found that the influence of rest on the fatigue strength of a low carbon steel was little and the distribution of hardness through the cross section of specimen showed little difference between the two cases with and without rest.

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It was next to impossible to solve numerically the plane problem of elasticity having discontinuities composed of straight lines e.g. rectangular notches or projections, etc. But if we use the technique of expanding the series and the method of convergence of the series because the convergence is not good, we can solve numerically such problems though the terms of the series are quite numerous. That is by using the Schwarz-Christoffel's conformal transformation we represent such shape's domain by the unit circle, and we treat the plane stress boundary value problem by the method of Goursat-Kikukawa. In this way we can solve such problems. This paper deals with the problem of the belt having a rectangular projection with sharp corners and rounded off corners on one side and the results of these numerical calculations are pretty good as compared with the results of the experiments of the photo-elasticity and the wire strain meter.

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The tension problem of an infinite strip containing a square hole with rounded corners is treated by the method of perturbation, convenient formulas for the stress are given and numerical results are examined. The concept of "equivalent elliptic hole" given by F. Hirano in problems of perforated infinite plates is found to be not so valid for the present strip problem. On the other hand, the approximate method proposed by the author for the case of an elliptic hole is still applicable to this problem. In this connection, the author gives an advice on applying this method to other problems of multiply-connected domains.

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The tension problem of an infinite plate containing an infinite row of circular holes was first solved by R.C.J. Howland. In the present paper, the author treats other important plane problems of the same plate, that is, uniform tension, tension in arbitrary direction, uniform shear, bending in plate, uniform internal pressure, cos-type internal pressure and sin-type internal pressure. Formulas of the circumferential stress are given in forms of power series and the numerical results are examined.

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In this paper, the tension in an orthotropic strip with a circular hole, which has practical importance, is treated. The solution of the same subject for isotropic material, has been presented by R.C.J. Howland and lately improved by M. Isida to study the stresses in a strip with an elliptic hole by the use of orthogonal co-ordinates. In this paper, the same methods are adopted to express the free edge conditions at the rim of the strip and of the circular hole and the stresses are given in the form of the power series of λ which is the ratio of the radius of the circular hole to the half breadth of the strip.

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In this paper, the bending of an orthotropic strip with a circular hole is treated in the same way as in the previous report in which the tension in an orthotropic strip with a hole has been studied. Numerical examples are worked out for the plate of oak. They show that the existence of a circular hole in a strip decreases the stress at the straight edge of the minimum section, especially in the case of a strip bounded by lines orthogonal to the wood fiber.

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Fatigue lives under cumulative stresses were investigated under double and triple stresses on carbon steels (0.07%C, 0.25%C, 0.47%C). The results were as follows : (1) In a low carbon steel (e.g. 0.07%C, 0.25%C), the fatigue life was prolonged by secondary and tertiary stresses regardless of whether they are higher or lower than the primary stress. (2) In a high carbon steel (e.g. 0.47%C), however, the fatigue life was shortened by the secondary and tertiary stresses when they were lower than the primary stress. But the fatigue life was prolonged by the secondary and tertiary stresses when they were higher than the primary stress.

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In this paper, we tried to predict the fatigue strength of carbon steels which are subjected to multiple repeated stresses from the results of ordinary fatigue tests. The new relation is based on the already reported equation derived from the assumption that fatigue is caused by the accumulation of the distortion of atom lattice. We considered the effects of the access ratio of stresses, cycle ratio and carbon content of materials, from several experimental data. On the basis of this consideration, we derived an equation expressing the relation between the rotary bending stresses and the number of stress repetitions under multiple repeated stresses on two stress levels. The values calculated by the equation have been found in good agreement with those obtained from the experiment.

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Problems of lateral vibrations and the dynamic loads produced in a beam struck by a falling ball have been treated by many authors ; but in their studies only the impact caused by a sphere moving at a given velocity was discussed. The problem of impact by a falling body with a cylindrical contact surface has not been treated for the reason of its complexity. The relative approach in a cylinder-contact has a complicated mathematical form as compared with the case of a sphere-contact, but it is a very important problem in practice. In this paper two methods are developed to treat the problem : (a) step-by-step integration used by Timoshenko and (b) collocation method. The collocation method leads to a reasonable and sufficiently approximate solution without difficulty. Numerical examples and the effects of non-dimensional characteristic coefficients (k₁, k₂, k₃, and k_M) are discussed and the time dependency of deflection of the beam is given in order to compare the impact of a sphere.

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An experimental study was made on the dynamic theory of piston-ring lubrication, which was introduced in the 1st report. The apparatus used in this investigation had a stationary piston and a moving cylinder, the speed of which could be accelerated to 2000 r.p.m., and a constant or varied load was applied to the piston-ring by means of a rubber tire, which was pushed out by the compressed fluid. With the speed, load, temperature, and the phase of the varied load being changed, a frictional force of the piston-ring is measured by an electronic device which consisted of an elastic diaphragm, movable anode tube and oscillograph, These experimental results gave a good agreement both qualitatively and quantitatively with the theoretical value.

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