Crack energy density concept is newly proposed as one of the most important parameters in fracture mechanics, and the role of it is discussed. This parameter represents the state of the work absorbed (strain energy in case of the continuum) at crack tip per unit area of crack plane generally, and it should be called, as it were, strain energy area density especially for the case of the continuum. The introduction of the concept enables us to make a unified smooth description of the fracture condition from completely elastic (brittle) fracture to ductile fracture with large scale yielding, and also to solve some ambiguous problems in fracture mechanics. For example, the physical meanings of G₀(K₀) criteria ; J_c criteria and COD criteria on fracture are explained clearly through the concept.

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The axisymmetric elastic contact problems of a plate pressed onto a rigid base with a cylindrical protrusion or pit are considered analytically. The problems are three-part mixed boundary value problems with unknown contact border. In the analysis, a general representation of the displacement of the contact surface is given by a term of infinite series, and the problems are reduced to the solutions of two infinite systems of simultaneous equations, by considering the smooth contact conditions on the contact border. Numerical results are shown for the distributions of contact stresses and surface displacements and for the relations among the pressure, the plate thickness, the annular contact region and the magnitudes of the protrusion or pit.

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Nature of the unsteady small perturbations observed in a sheared mean flow with linear velocity profile is examined. Results are applied to the actuator-disk analysis of a rotating stall in three-dimensional blade rows subjected to the spanwise shear flow. An example of numerical calculation is given, which shows the effect of the shear flow on the occurrence point of the rotating stall, the propagating velocity, and the distribution of velocity disturbances.

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The effects of compressibility on the flow losses at the high sub-sonic speed in piping systems with junctions are investigated experimentally in this report. Experiments were carried out varying the angle between the axes of pipes, the size of the radius of the edge at the joining corners and inner surface roughness of the pipe junctions as well as the flow Mach number. The effects of compressibility on Kc are expressed by the following empirical formula, Kc/Ki=1.0+α Mβ where Kc is the compressible flow loss coefficient at junctions, sub-script i refers to an incompressible flow and α, β are experimental constants. Furthermore, the flow patterns at junctions were visualized by means of Schlieren techniques, and loss characteristics were discussed on the basis of the photographic records. Finally, a practical computing method of the flow losses in a high speed pipe flow is described.

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The performance of a supersonic air ejector in the case of zero-secondary flow was studied by varying the Mach number of the primary nozzle and the throat area ratio of the mixing tube to the primary nozzle. As the result, it has been shown that an optimum throat area ratio exists for each Mach number of the primary nozzle in which case the vacuum performance of the ejector becomes maximum with a minimum stagnation pressure of the primary flow. The physical meanings of the optimum throat area ratio and other ejector characteristics have been clarified from the results of pressure measurements and optical observations. Furthermore, modifying a previous method in the case of a constant-area mixing tube, the ejector performance was calculated for a variable-area mixing tube in the case of a larger throat area ratio than the optimum one. Calculated values agree well with the experimental results.

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In the present experiment augmentation of forced convection heat transfer in single-phase flows was investigated using a channel whose parallel walls are bent perpendicularly at two locations. Heat transfer characteristics in both laminar and turbulent flow situations were observed by varying the pitch. Visualization of the flows revealed the formation of separation bubbles in the corners of the bends and the reattachment of the flows in downstream regions. It is accordingly concluded that augmentation of heat transfer occurs as a result of the reattachment and acceleration of the flows.

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Forced convection film boiling heat transfer from a horizontal cylinder to saturated liquid cross-flowing upward is analyzed based on the two-phase boundary-layer theory. Numerical solution of the conservation equations is determined by means of the integral method of boundary-layer for water, ethanol and hexane under the atmospheric pressure. The velocity profile, separation point of the boundary-layer, thickness of the boundary-layer, distribution of the heat transfer coefficients and average Nusselt numbers are discussed and the effect of the approaching velocity on them is also examined.

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The non-linear free vibrations of stepped beams under gravity are analyzed by using the transfer matrix method. By using the harmonic balance method, in which a constant term and a sinusoidal harmonic term are assumed as time functions, the governing partial differential equation reduces to simultaneous ordinary non-linear differential equations for the corresponding spatial functions. The transfer matrices are derived from these equations. The numerical results for simply supported and clamped, one-stepped thickness beams with rectangular cross-section are presented and the effects of gravity, the beam geometry, the concentrated mass, and the boundary conditions on the non-linear vibration characteristics are discussed.

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In this paper, we analyze the axisymmetric vibrations of a cylindrical shell of which the thickness varies in the axial direction by using the thin cylindrical shell theory and an improved thick cylindrical shell theory. We solve the equations of vibration exactly by using a series solution. As numerical examples, we obtain the natural frequencies and the mode shapes of cylindrical shells with both ends clamped, simply supported and free and examine the variations of the natural frequencies and the mode shapes for the variations of the thickness. And also, we make clear the influences of the shear deformation and the rotatory inertia upon the natural frequencies and the mode shapes.

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A shaft carrying an asymmetrical rotor is supported by upper and lower flexible bearing pedestals each of which has a directional inequality of stiffness ε=0∼1 and a concentrated mass. The analysis of this problem is carried out on the assumption that ε is either negligibly small or not so. The positions, width and number of unstable regions are analytically determined. The analytical results show a good coincidence with results obtained by an analog computer. Two sorts of unstable vibrations result due to the inertia asymmetry of the rotor. The mechanism of the unstable vibrations can be explained. The conditions for the occurrence of the unstable vibrations can be obtained, and all vibratory solutions obtained by an analog computer satisfy these occurrence conditions.

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Natural frequencies, natural modes and dynamic response of a crank shaft of an internal combustion engine are analyzed by the reduced impedance method the author proposed. A crank shaft is divided into the straight shaft parts and the arm ones. The dynamic behavior of the straight shaft part is expressed first by the transfer matrix, which is transformed into the reduced impedance matrix. Meanwhile the arm part is divided into the tetrahedral elements by the finite element method, and the degrees of freedom of their boundary surface parts are reduced to six. The equation of motion of the arm part is reduced to form a reduced impedance matrix with respect to the boundary parts. The reduced impedance matrices of all components are combined to give a global equation of motion of the crank shaft, and this equation is solved to get natural frequencies, natural modes and dynamic response. The calculated results agree well with the experimental ones.

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Thermally induced acoustic oscillations in a pipe in which two or more heat sources are closely installed have been studied analytically and experimentally. The analytical model used in the first report has been improved to describe the effect of the air current temperature change due to the variation of heat flow rate from the upstream source upon that from the downstream source. If there is a certain phase relation between the pressure variation and the heating rate, thermal energy is converted to acoustic energy, therefore an oscillation is induced. The condition in which the oscillation grows has been clarified as a function of heat generation rate, stream velocity, distance between the heat sources and so forth, which is different from that in case of a single heat source. Experimental results using nichrome heaters agree well with the calculations.

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In the locked condition of a oneway clutch, high stress will be generated at the contact surfaces between rollers or sprags and the races of the inner and outer wheelings. A study on the characteristics of self-locking can not go without regard for the effect of the deformation caused by these stresses in each part of the clutch. In this study a unique way to derive mapping functions has been developed and each part of the clutch has been analysed by using the two-dimensional theory of elasticity. Furthermore, on the reflection of the contact surfaces, the behavior of the sprag which rotates under the locked condition is analysed here by using the finite element method.

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Three dimensional numerical analysis of a spherical foil bearing used in a rotating head recording device is presented. Reynolds equation is solved simultaneously with the representative Green function of plane or cylindrical foil deformation, which includes bending stiffness. Calculated pressure, spacing and foil deformation are illustrated and typical trends are discussed for small bearing penetration. The calculated results are found to be in good agreement with the experimental results under submicron spacing conditions.

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The stability characteristics of outwardly pumping spherical spiral groove bearings lubricated with incompressible liquid are investigated. The resultant bearing forces induced by small vibrations of a rotor under radially unloaded conditions are obtained. The bearing parameters have been optimized in search of the maximum axial load capacity, and then in search of the maximum radial stiffness. The stability characteristics of outwardly pumping spherical spiral groove bearings are compared with those of inwardly pumping ones. Experimental results are in good agreement with the theoretical ones. The conclusions are as follows. Although the maximum axial load capacity of outwardly pumping bearings is a fraction of that of inwardly pumping ones, outwardly pumping bearings are as stable as inwardly pumping ones. Generally, the stability threshold when a grooved member is rotating is higher than when a smoothed member is rotating.

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This paper describes an investigation about the possibility of producing a fiber-reinforced plastic gear which is light, self-lubricated and of high strength, by taking advantage of the characteristics of the unidirectionally reinforced lamina. A fiber-reinforced plastic spur gear was molded by arranging long carbon fibers along the tooth shapes and then filling up inside with composite of glass fiber chops and epoxy resin. Bending strength of the tooth of the gear was studied experimentally and analytically. Availability of the fiber-reinforced plastic gear thus made was confirmed by the investigation.

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When the steel gear meshes with the nylon gear, the advantages are no lubricating operation and low noise. But a deddendum of nylon gear meshes strongly with a corner of tooth crest of steel gear when the nylon gear is a driving gear. This is the principle cause of tooth form transformation, tooth face seizure, abrasion, etc. In this report, for the purpose of eliminating this cause, a load test of nylon gear and steel gear was made. The steel gear was one cut by semitopping hob. Examination of the results confirmed usefulness of the steel gear which had been cut by semitopping hob.

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There are many reports on fundamental experiment of "Nylon-Steel" abrasion. But these are a little used for actual gear. This report discusses a nylon gear meshing with a hobbed steel gear and a ground steel gear. The load test of nylon cylinder was performed using a steel cylinder which has a different surface finishing. The abrasion, the allowable limit load, the surface temperature, the modes of breakage of nylon cylinder owing to a difference of a surface finishing of steel cylinder were investigated and useful data for design of nylon gear were collected.

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There are very few studies which deal with force-fitted helical gears hitherto. Considering such a present condition, stresses at the root fillet of gear tooth and safety for slipping at the force-fitted surface were chosen as subjects of this study. Some kinds of force-fitted helical gears were chosen, and stresses at tooth and rim, casued by force-fitting, were examined. Moreover, these experimental results were compared with theoretical ones by the finite element method. The following conclusions were obtained. (1) A practical formula to determine the fillet stresses at Hofer's weakest section and at the center of tooth space of a force-fitted helical gear can be introduced, and these stresses can be easily calculated when gear dimensions and force-fitted conditions are given. (2) Calculation method of dynamic slipping torque has been established.

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Practical design methods of cylindrical gear pairs with 2 to 4 pinion teeth for higher gear ratios were investigated to obtain higher load carrying capacities. Using a conventional hob with a pressure angle of 20°and a conventional hobbing machine with special made attachments, the authors designed and made test gear pairs with gear ratios of Z₂/Z₁=41/2 and 38/3. These gear pairs were tested beyond 10×10⁶ pinion rotations using the power circulating gear-load-testing-machines made by the authors. The tooth surfaces of large gears were very likely to pit although the load cycles were appreciably smaller than those on the pinion teeth. It was clearly indicated that a gear with higher hardness than that of the mating pinion had a greater load carrying capacity. The test gear pairs produced much higher sliding due to greater profile shifting than that of gear pairs with numbers of pinion teeth of greater than six, but they showed a comparatively good efficiency of about 93% in the case when the test gear pairs with 3 pinion teeth were used under normal running conditions.

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The hobs are theoretically reconsidered on their peripheral taper and their rough cutting mechanism. The taper angle under a fixed length of hob varies according to the helix angle of gear and the setting angle and the cutting feed direction of hob. A method of determining the optimum taper shape is described on a calculation example. Additionally, in order to relieve the cutting load concentrated on the side edge of end tooth, a new type side taper hob, whose tooth thickness is gradually reduced in the rough cutting teeth, is proposed. Design example is given and satisfactory result is obtained in a hobbing with the trial hob.

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In order to obtain friction-welded joints with enough strength under static and cyclic loads the friction coefficient at the contact surfaces being welded was measured during welding process. It was found that the heating pressure and the heating time which brought about a friction coefficient of μ=0.13 corresponded to the lower limit of welding conditions for producing joints with enough strength in the case of a standard rubbing speed of about 3m/s. From the measurement of the temperature and the shear flow stress at the rubbing surface, it was found that the temperature was in the range of 1100°C to 1200°C for an S35C-steel when μ=0.13 was achieved. Rubbing virgin-surfaces of the steel under this temperature could be joined completely at an upsetting pressure of about 59 MPa (6 kgf/mm²). The welding conditions obtained using a carbon steel would be applicable to other carbon steels and alloy steels because these steels show much the same flow stress at temperatures by about 200°to 300°C lower than their melting points.

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Some investigations have been reported about a structural design considering the characteristics of the machine tool joint. From these reports, it may be concluded that the joint is represented by mathematical models consisting of springs and dash-pots. It may, therefore, be said that the problems on the treatment of joints in the computer aided calculation of the structural stiffness are how to decide the spring and damping constants. However even if the basic mathematical model consists of springs and dash-pots, different joints will give various concrete models. It is necessary, for above reasons, to make clear a systematic method of treating the joints. In this report, results of previous studies were accumulated and analyzed to determine the governing factors and propose thereby concrete mathematical models of joints subjected to static load. In addition, some experiments were done to verify their characteristics. From these results, one determination methodology of the mathamatical model for joints was proposed.

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