The Purpose of the present study is to obtain a condition which determines the forming limit for bending. In this report, the factors, affecting the bending limit which depends on the rupture are investigated, and it has been found that the ratio of minimum radius of bend to material thickness varies as the thicknesses, and the outer surface of thinner materials can be stretched to a certain extent where the strain induced is more than the elongation in tensile test. Then it has been also found that the condition of the bending limits may be revealed, if a condition determines the limit of forming in general having strain inclination.

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The experiments of the enlarging the circular hole in sheet metal with a conical mandrel are carried out in order to investigate the effect of strain inclination on the forming limit, and it has been found that the forming limit is not determined by the local stress or strain but it varies as the stress distribution. The idea that the forming limit may be determined by applying the condition of instability of force is introduced, and the forming limit calculated has been found in agreement with the experimental data.

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In this report, the criterion that the forming limit of bending is determined by the process of instability in bending moment is proposed. And in consequence of the introduction of the conception that the pure bending is accompanied by a shearing strain, when the tensile strain in bending exceeds the uniform strain limit, it may be explained that the bending limit varies with different thicknesses, and the factors concerning material properties which affect the bending limit are clarified.

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Shearing resistance of sheet materials has been evaluated to confirm the conception introduced in the previous report that the forming limit in bending is affected by shearing resistance. The ratio α=2τ₆/σ where σ : actual tensile stress at the uniform strain limit in pre-tension of shear specimen. τ₆ : proof stress in shearing test of pre-strained specimen in tension, is used to evaluated shearing resistance. The experiment has revealed that the forming limit in bending is affected by this ratio, and the forming limit of material which has small value of this ratio varies extremely with different thicknesses, and for thick material the forming limit approaches toward the value calculated under the condition that there is no shearing resistance, while the forming limit of material which has large value of this ratio is estimated under the supposition that the bending is not accompanied by shearing strain.

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Beginning with the pioneer work of Siebel, many attempts have been made to obtain a satisfactory solution of rolling pressure distribution over the arc of contact. But because of the complexity of the problem, all the theoretical solutions have been based on the plane strain problem without lateral spread. In hot rolling, it has been done under the condition that any variation in the width of plate is permitted. The author assumed the mean slipping angle α between the plate and rolls and developed the three-dimentional distributions of rolling stresses. According to the theoretical result, the decrease of rolling pressure to the edge during the rolling process was explained by taking the new factor of plate width.

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As the author previously mentioned both the theory and experimental results of method for measuring curved surfaces by regarding them as a series of curves or straight lines, in the present paper, he gives both the theory and experimental results of the method for measuring curved surfaces by regarding them as a series of planes and by using a simple instrument with one indicator, and examines whether it is to be practically applicable.

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We frequently observe the walking phenomenon of the conventional twjst drill in drilling operation. The mechanism of the phenomenon is not yet well known. The object of the present research is to observe various phenomenon about the walking. The main results obtained are as follows : 1. The chisel edge angle seems to have a considerable effect on the walking. 2. When the drill begins to walk, the thrust of the drill begins to decrease. 3. The drill point makes an elliptic motion due to walking.

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This paper deals with the experiment carried out by the author under a condition as cose to the actual situation as possible, wherein regarding the dispersion of equilibrium point, the knife edge and V shape bearing are used as the fulcrum of the lever. The inclination of the lever being relatively trifle, the weight working virtically upon the normal component during the weighing process, and the tangential component working instantaneously as a shock on the balance when the weight is added, are made the objects of the present experiment. As a result, two essentially different causes have been discovered for the dispersion of the equilibrium point. One of them is produced due to the variance of the stress distributions resulting from the roughness of the contact surface. The other is, it is believed, that when the shock is given to the balance and the lever moves in the tangential direction, the contact point of the knife edge and bearing geometrically moves, because the bearing is of the V shape. In view of the above, it is believed that the quantitative relations have been made almost clear.

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Limiting conditions of chip breaking with a parallel type chip breaker are found to be determined by only the following three items : the radius of chip flow circle, the material to be cut and the thickness of chip. The larger the radius of chip flow circle, the steeper the slant of chip breaker and the thinner the chip, the smaller is the force acting on a chip breaker due to chip curling. The yield stress of chip becomes about twice that of the same material before cut. From these results, a very simple method for finding the optimum shape of chip breaker is established. In this method, a proper radius of chip flow circle is found directly by measuring the thickness of chip which is obtained under the given cutting conditions and by the use of a diagram presented in this paper.

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Fundamental characteristics and the cause of the thermal crack which appears in the carbide face-milling cutter have been investigated. The observation of thermal crack has revealed that it appears nearly perpendicular to the cutting edge at a point apart from the cutting edge in the tool-chip contact area of the tool face. And a lot of other interesting features of the initiation and growth of the thermal crack have been also revealed. The cause of thermal crack of the carbide face-milling cutter has been considered at the view-point that, as generally said, it is due to the thermal shock accompaying the intermittent cutting. Next, the influence of cutting conditions on the thermal crack has been investigated and sometimes found explainable by the above consideration. At last, several grades of carbide have been examined experimentally in respect to the occurrence of the thermal crack.

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For the purpose of calculating the bending stress of gear tooth theoretically and finding the bending strength of spur gear the present study was carried out. Using the two-dimensional elastic theory and the transform function, the authors introduced equations for the calculation of the stress at the fillet curve of gear tooth. Investigating the stress calculated by these equations in various loading conditions, the authors reached a conclusion that it was reasonable to take the shearing force into consideration for the calculation of bending stress of gear tooth. Then the authors introduced equations for the calculation of the inner stress, and obtained the following result : the inner stress shows smaller value than the stress at the fillet curve, so it is resonable to determine the bending strength of gear tooth by calculating the maximum stress at the fillet curve.

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In the present paper the authors studied the position of the weakest section of gear tooth and the stress concentration factor at the tensile-side fillet of tooth. Then the authors calculated the stress concentration factors for some components of the force on the tooth profile, and found the relation among these factors. Consequently the following formula has been introduced for the bending stress of gear tooth : σ_t=(1+0.08 S/ρ){0.66σ_Nb+0.40√(σ_Nb²+36τ_N²)+1.15σ_Nc} By this formula the authors calculated the bending stress of gear tooth of some shapes, and compared the result with that of photoelastic experiments.

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For the purpose of calculating the bending strength of the gear tooth in general use, the authors studied theoretically the position of the weakest section of gear tooth and the point of the worst loading, and consequently definited the calculating method of nominal stress. Then by using the calculating equation of bending stress reduced above, authors calculated bending stress and stress concentration factor of gear teeth of various shapes in general use at present, and studied these relations.

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In order to investigate the pitting phenomena that arises on the surface of the power transmitting gears, a four-square-type gear testing machine was built. The heat treated gears of 0.35% carbon steel were tested with the induction hardened pinions of 0.40% carbon steel, being lubricated by No. 180 turbine oil, whose temperature was kept at 50°±2°C, under various load conditions. It was observed that, when the tangential force was beyond 146 kg/cm, the pitting grew rapidly with the cycles of load repetition, and the involute errors, the dynamic loads of gear teeth and the noise of gears increased along with the growth. However, when the tangential force was 124 kg/cm, the pitting grew very slowly and even showed the tendency of limiting of the growth, which was attributed to the equalization of load by wear and to the work hardening of surface materials due to the repeated load.

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Up to the present, the maximum pressure between two rolling rollers has been calculated by hydrodynamic theory on the assumption that the rollers are rigid bodies, or using a method devised by Hertz which ignored the oil film. But these two methods are the extreme cases and unresonable points arise in general case. In this report, a hydrodynamic lubrication theory between two rollers, taking into account the elastic deformations of the rollers, is presented. It was difficult to obtain analytical solutions of the equations, so the author used a digital computer to obtain numerical solutions. As a result, it was shown that under a light load the hydrodynamic pressure calculated by this theory was very close to that calculated by the hydrodynamic theory neglecting deformation, and that under the heavy load the pressure calculated by this theory approached the Hertzian elastic stress. The maximum pressure calculated by this theory was lower than the one calculated by either of the two classical theories.

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The exact or approximate solutions of the equation of tooth load distribution in marine turbine reduction gears have been developed in these fifteen years. On the other hand there have been many qualitative considerations from the empirical data about the factors which affect the load distribution. Also, some approximate formulae have been used to obtain the maximum concentrated load which generally arises at the torqued end of a pinion. Nevertheless, it is still necessary to consider the important factors theoretically in detail, and to assure the theory on the basis of proper experiments. In this paper the theory of load distribution in the case of a spur gear is presented describing the shape of the pinion as exactly as possible. The experimental results are also included. And it is shown that the theory agrees very well with the experimental load distributions.

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In the first report the load distribution along the axis of the pinion in turbine reduction gears in the case of spur gears was treated both theoretically and experimentally. It was demonstrated that the solution by infinite series of an integral equation showed excellent agreement with the experimental data. The present paper deals with the case of double helical gears by means of infinite series as in spur gears, considering the effect of the axial components of the load distributed along the pinion teeth. However, the effect is not so serious and therefore may be disregarded in practice. It is shown that the misalignment of bearings and the error in helical angles affect the load distribution greatly. Especially the difference in temperature rise in the pinion and the gear is important. A difference in temperature by a few-degrees in centigrade changes the maximum load by some 30% or so, increasing or decreasing its value depending on the direction of rotation.

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The lubricating condition of the cross head pin bearing of a 2 stroke cycle engine is considerably unique, because the direction of load acting on the bearing is limited to one direction in addition to the incomplete revolution of the bearing. Therefore, the writers studied the lubricating mechanism of the bearing, and estimated the frictional coefficient of the bearing of a large bore engine experimentally. As a result, we came to the following conclusions. i) It is recognized that a greater part of load carrying capacity is that of the fluid film pressure, because the frictional coefficient was found as low as 0.002∼0.003. ii) The ratio of maximum sliding angle of the bearing to the pitch angle of the oil grooves 2φ/α is to be less than 1, but if 2φ/α is raised much higher than 1 the load capacity is reduced.

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In the previous reports of this series, it was assumed that the piston-ring was pushed out by the force of back pressure, and the experiments were carried out by the rubber tire method. In the actual condition, however, the pressures of gas act on the surfaces of the back and side of the ring and between the ring and the cylinder at the same time. In this report we have obtained the ratio of the pressure in the rubber tire to the pressure difference between the upper and lower sides of ring in order to equalize the lubricating properties in both cases, through the theoretical and experimental studies. This ratio is influenced by the shape and thickness of the oil-film and also by the moving direction of the piston-ring and etc., however, the approximate value is 0.5 for all conditions.

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It is known that, although the wear of Polytetrafluoroethylene (P. T. F. E.) is not good, the material which is made of a porous metal impregnated with P. T. F. E. has good wear properties without any lubrication. In this paper the friction and wear behavior of the material is cleared using the method of measuring the electric contact resistance. Film of P. T. F. E. deposited on the surface of a metal does not show breakdown of resistance so far as the specimen is loaded statically up to 135 kg. It wore out, however, in a short time at the beginning of sliding even if the load and velocity are low. As a result, metallic contact takes place simultaneously throughout the experiment of the resistance. The phenomena can not be explained only by the suggested conceptions of "difference in expansion of P. T. F. E." by Mitchell and Burke⁽¹⁰⁾ and of "continue to feed the plastic as an action of bearing metal alloy" by Bowden and Tabor^(18e). It is concluded that the actual mechanism of anti-wear properties of the material depends both on the oxide film of bronze and the anti-wear properties of P. T. F. E. produced at a high temperature (200°C∼300°C) without impregnation as already reported by the author, and that, if either one of the two is lacking, it would easily fail. In this paper the temperature (T-T₀) of frictional heating is also described as follows : T-T₀=PV^0.85 (P : kg/cm², V : cm/s) This formula can be effectively used in a wide range of load and velocity.

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A magnetized ball rolling in a ball bearing induces an alternating current in the coil wound on the outer race. The period of the current shows one revolution of the ball. The slip of the ball is found by measuring the deviation of the period from the theoretical value. The variation of the axis of rotation relative to the magnetic axis of the ball is easily estimated from the variation of the amplitude of the current. Under the radial load an appreciable amount of the slip occurs at the unloaded side. It decreases exponentially with an increase in shaft speed. The variation of the axis of rotation is quite regular and is closely related to the slip. The cause of the variation is supposed to be due to the skewing motion of the ball at the moment of the slip.

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Operating a single row radial ball bearing under the pure thrust load, both the rolling friction due to the rolling motion of balls and the sliding friction due to the spinning motion of balls occur between balls and bearing races. The retainer is in sliding contact with balls. The rolling friction of ball depends upon both the elastic hysteresis loss of the materials and the differential slip friction on the contact surfaces. Analysing those causes of friction losses, auther gives the general formula of the friction moment of the bearing under the thrust loading. On various conditions of groove radii of inner and outer races, thrust load, number of balls, radial clearance, size of bearings and weight of retainer, the friction moments of the bearings are measured. Agreements of the experimental results with the calculated values from the formula are fairly well.

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In this paper, a new theoretical relation between the life and the load of a ball bearing is proposed basing on the same meaning of that of a roller bearing previously reported. The new equation obtained is based on the Heltz's equation and the empirical formula determined by "Degree of Fatigue" which is caused by the repeated stress on the contact surface and the frequency of the contacts. It has been confirmed by this calculation that the curvatures of the contact points are more effective than the other factores for bearing life.

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The noise of the ball bearing can be divided into two cases ; one is the case of the simple ball bearing, the other is the case of the fitted one. However, the noise of the latter case has not been researched systematically. So, the auther measured the noise of three kinds of the fitted ball bearings, analyzed about the peak values of the frequency spectrums, and obtained the results as follows : -(1) The noise of a fitted ball bearing has the frequencies above 1 kc/s. The frequencies of the noise do not change at many rotating speeds, but the sound pressure level increases with the rotating speed. (2) The principal noise of a fitted ball bearing is due to the vibrations of the race ring, and the other noise is due to the vibrations of the cage. (3) The noise of a fitted ball bearing and the noise of a simple one are identical in essence.

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In the hydrostatic journal bearing which requires an external resistance such as capillary or orifice, the load may be maintained on fluid film under pressure even though there is no relative movement between mating surfaces, and the fluid under pressure is supplied from external source to the load carrying fluid film as in the case of hydrostatic thrust bearing. This paper describes the characteristics of such a bearing having four rectangular pockets around the circumference. Particulary some theoretical investigations concerning the resistance, pocket throttle ratio and rigidity (i. e. stiffness) of this bearing are also reported to find out the designing factor of hydrostatic journal bearing under optimum operating condition.

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