In the present paper, the acoustical effects caused by elasto-plastic finite deformations in slightly orthotropic materials are theoretically investigated using the theories of finite deformations and plasticity in which the plastic strain increments are expressed with stress deviations and their increments. From analytical results, it is found that the expressions for the elastic-plastic strain-velocity relations of acoustic waves propagating in slightly orthotropic materials can be derived skillfully with aid of Jaumann co-rotational rate and can be reduced to the theoretical results derived by Iwashimizu and Kubomura in the elastic state. Further in order to remove the previous discrepancies between the theoretical results and the experimental ones about the influence of plastic deformations upon the acoustoelastic effects, the author discusses the influence of the deviation of stress increments on the plastic strain increments.

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Concerning a symmetrical four-point bending, the nonlinear large deflection problem of a thin elastic beam in the presence of friction between beam and the loading supports is investigated analytically by applying Legendre-Jacobi form's elliptic integrals of the first and the second kinds. A reduction technique is proposed to estimate easily the maximum deflection, the end slope, and the maximum bending stress in large flexural states from the conventional linear bending theory. An experiment is also performed to confirm the applicability of the presented large deflection theory. The experimental results agree well with the solutions based on the large deflection theory.

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This paper presents a theoretical analyis for obtaining stresses of a spring of arbitrary cross section. In the analysis the stresses of a straight rod subjected to torsion, shear and bending are derived based on the two-dimensional theory of elasticity by means of the Fourier expansion collocation method which has been reported by the author. The results for a coil spring are derived by including the curved rod theory in the expressions for a straight rod. The present result is applicable to the problem of coil springs by merely including the geometrical data on the spring, whatever the shape. The numerical results obtained by this analysis are in very good agreement with the previously published ones for some typical cases.

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numerical calculations have been carried out for springs of irregular cross section by using the theoretical results given in the companion paper (1st report). experimental tests have been performed to clarify the accuracy of the theoretical results, and it is concluded that the theoretical results have sufficient accuracy. The paper proposes a new type spring which has an oval cross section. Stresses along the boundary of the oval cross section have been investigated in detail theoretically and experimentally. The results obtained are compared with those of a circular cross section spring, and it is shown that the oval spring has advantages over the circular cross section spring. This paper also discusses stresses in an elliptical cross section spring and a spring having a rectangular cross section with semicircular sides.

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A variational principle for impact contact of two bodies generally requires subsidiary contact conditions for the bodies on a contact area, because of the continuity of displacement between the bodies. Various Lagrange multipliers are used to include the subsidiary conditions in the principle. This paper presents an extended multiplier applicable to the subsidiary contact conditions for both contact displacement and contact acceleration of the two bodies in the principle. This multiplier can also formulate a hybrid type of virtual work principle for various impact contact states of two bodies. A finite element method (FEM) based on this principle is applied to a two-dimensional response for longitudinal impact of two uniform rods in order to check the validity of impact force based on this multiplier in the principle. The mean value of impact force by FEM agrees well with the value by the theory of propagation of one-dimensional elastic stress wave. Moreover, this paper illustrates the time variation of impact contact pressure distribution.

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A new approach to describing the Bauschinger curves for metals is presented on the concept of the field of the resisting force against the movement of dislocations. In a previous paper, it has been clarified that the cyclic plasticity model, proposed by the authors based on this concept, would be applicable to the quantitative descriptions of various cyclic deformation phenomena in the steady state, and the tensile stress-strain curves with a different type of yielding. In this paper, the Bauschinger curve can be expressed by applying this concept with some assumptions of the changes in the field of the resisting force caused by pre-loading. This has provided a satisfactory agreement with each experimental curve for a carbon steel and a brass with a wide range of strains.

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The flow between concentric cylinders both rotating in the same or opposite directions has been studied by flow visualization and velocity measurement. We used slit illumination for flow observation and pitot and hot wire probes for velocity measurement and obtained the following results. When the outer cylinder rotates faster than the inner one in the same direction, the flow is stabilized and the laminar flow region is fairly wide but there is a fluctuation which is too small to observe. The boundary beyond which a spiral turbulence occurs has marked hysteresis and changes with the fluid used. When the tow cylinders rotate in opposite direction s, Taylor vortices and spiral turbulence arise almost simultaneously and both exist together in the gap at some Reynolds number. Such situation is supported by velocity fluctuation and its power spectrum.

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There have been many papers on the experimental and theoretical investigations of the rotational flow characteristics of the standard forms of cyclone dust collectors, or of cylindrical vortex chambers. However up to this time, the experimental studies of the rotational air flows in the spherical forms of cyclone dust collectors or in the semisphere and cone combined cyclone dust collectors have seldom been published throughout the world. Therefore in order to recognize the fluid dynamic characteristics of the turbulent rotational air flow in the returned flow types of cyclone dust collectors, the spherical forms and the semi-spherical and cone combined forms of the cyclones were made of transparent acrylic resin. Then, the distributions of the tangential and axial velocities, and also the distributions of the static pressures were measured by the cylindrical Pitot-tube in the five kinds of cyclones. In this paper, the experimental results of the velocity index n of the quasi-free vortex, those of the maximum tangential velocities V_θM/V_o and those of the coefficients of the pressure drops which were related to the dimensionless time T=T₂/F were described in detail, where T₂ means the spin-up time and F means the reside time in the cyclones.

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An experimental study has been performed on the structure of a turbulent flow around a cylinder spinning in a quiescent fluid. The visualization using smoke wires and the method of thermal tuft have revealed that the reverse flow occurs not in the internal region but in the external regions of the layer. The reverse flow occurs in the same regions as the eddies which can be generated by scattering aluminum powder. It has been found that the eddies displayed in a picture of aluminum powder, which was taken by a rotating camera, grow larger and larger in proportion to the distance from the cylinder. Also the mixing length increases. The radial length of eddies almost agrees with the mixing length. Furthermore, the turbulent diffusion of the instantaneous spot of a dropped dye has been examined. The examination shows that the scale of diffusion has a strong correlation with that of the peripheral length of eddies.

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A model of a propulsion mechanism for a ship is proposed, using a novel and efficient lift generation mechanism found by Weis-Fogh. The model consists of a wing (or two wings) in a square channel, and the motion of the wing has three stages : opening, translating, and closing and their repeated cycles. Each stage of the motion of the wing is analyzed by assuming that the flow is a potential flow and using conformal mapping. The circulation around the wing in each stage are calculated. The conditions to make this propulsion mechanism work efficiently are established and the applicability of this mechanism to actual ships is predicted to be good.

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This paper presents a study on the flow characteristics of capsule transportation. Especially, a method is presented for predicting the pressure drop required to move cylindrical solid capsules steadily and to suspend them freely in pipeline. For this prediction, an analytical method based on a study of multi-phase mixtures is proposed and it is confirmed that the present method is very useful for both hydraulic and pneumatic capsules. During the experimental and theoretical work, we can derive a general formula of the required pressure drop which has an inherent value for each of various conditions of capsule pipelining. In this paper, a detailed comparison of capsule transport with hydraulic transport of solids is also made.

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An experimental study was performed on the mean flow properties of a two-dimensional impinging jet on a wedge whose included angle is 90°. The variations in static pressure in the streamwise and transverse directions are large near the wedge vertex, and should not be neglected in the calculation of these flows. The non-dimensional velocity profiles in the fully-developed-flow region far from the vertex do not coincide with the similar profile of the two-dimensional wall-jet. Also, the trends in the decay of the maximum velocities and in the growth of the half width of the present wall-jet are different from those of the two-dimensional wall-jet. The local skin friction coefficient is estimated and compared with the empirical formula proposed by several authors. The logarithmic velocity distribution is examined using the estimated skin friction coefficients.

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A statistical method is proposed to express the characteristics in interface on various sizes of liquid lumps appearing in both froth an huge wave flow regimes. Cross-sectional mean liquid holdup trances suggest that the interfacial structures fundamentally consist of base wave and liquid slug or huge wave. The determining procedures of the shape factors and probability density of wave crests are examined. In addition, typical examples of applying this method into air-water two-phase upward flow in a 18.0 mm inside diameter tube are presented.

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Experiments on flows of water and dilute aqueous solutions of polyethylene oxide are carried out in the Reynolds number range of 10³ to 5× 10⁴. Concentration of polymer solutions is varied from 1ppm to 100ppm. The ratios of curvature radius to pipe radius, R/a, are 18.7, 34.3 and 47.3. Measured pressure distributions along a bend axis are classified in three types by their patterns. Flow property of each pattern is clarified by using the method of flow visualization. Drag reduction in a bend flow is smaller than that in a straight pipe flow. Pressure loss coefficients are correlated with the Reynolds number, the ratio of radius R/a and the Weissenberg number. The empirical formulas presented for the bend loss coefficient are useful from an engineering viewpoint.

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Water hammer phenomena caused by a sudden valve closure are considered in two-component bubbly flows where the phenomena are more complicated than in single-phase flows because of the presence of a compressible component. Basic partial differential equations based on a one-dimensional homogeneous flow model are solved analytically by linearization and iterated Laplace transformation. As a result, the profiles of the pressure transients, the propagation velocity of a pressure wave with a small amplitude, and the effects of valve closure on transient pressures are found. Further, the effect of friction factor on pressure profiles is shown and approximated by a simple equation. It is also shown that reflection and transmission occur at the interphase where the void fraction changes.

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Experiments were performed on rectangular take-off branch ducts of three types and eleven different shapes. Change in shape of the ducts has a small effect on the coefficient of branch loss of the main flow, but has a large effect on the loss of a branched flow. Chamfering the upstream side of the branch edge has a larger effect of making the coefficient of loss small than rounding the downstream side. This corner modeling effect on branch duct loss was confirmed also by tuft method. Based on these results, rectangular straight branch ducts furnished with installation faces were developed for the purpose of rationalizing the production and as well as modernizing and facilitating the manufacture.

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From a view point of machine dimension, the axially curved mixed-flow diffuser has a large benefit compared with the purely conical of the radially curved mixed-flow diffuser. In the present study, the flow pattern and pressure recovery in the axially curved mixed-flow diffusers are experimentally examined and the results are compared with those of the purely conical diffusers. The pressure recovery factor and diffuser effectiveness of the axially curved diffuser were low compared with the purely conical diffuser, but the difference between them was small. By use of guide fences at the inner wall, the flow in the axially curved diffuser was rectified and a favorable performance was obtained.

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Diffuser performances for the two-phase flow of air-water mixture have been scarcely studied, though those for the mono-phase flow have been examined and the optimum diffuser profile is given. The diffuser performance for the mixture flow may be affected not only by the channel profile but also by the inlet velocity of the diffuser. Thus, this study aims to make clear the efficiencies of vertical diffuser with rectangular cross-section and to obtain the desirable channel profile and the inlet velocity, for the air-water mixture flow. The efficiency deteriorates as the air-water mixture ratio increases, and the desirable inlet velocity exists for each mixture ratio and channel profile. The highest efficiency is obtained when the diffuser length-width ratio l/W is about 7 irrespective of the mixture ratio. At l/W ≒7, the optimum divergent angle and inlet velocity are also determined from this result.

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A spiral grooved vacuum pump which works in the pressure range from 1 to 1000 Pa is studied theoretically and experimentally. The flow in grooves and ridges on the pumping rotor is treated as a slip flow, and Boon and Tal's "Narrow groove theory" developed for viscoseals is used. The theoretical predictions show good agreement with the experimental results. Suggestions are made regarding the choice of design parameters, i.e., aspect ratio, helix angle, clearance parameter and groove-width ratio.

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The slip of pump feet on the baseplate caused by piping loads was investigated. The test pump was axially-split, single-stage double-suction volute type with foot support. The static coefficient of friction between the pump foot and baseplate ranged between 0.15 and 0.35. The effects of dowel pins and jack screws on the slip were also investigated. Shaft displacements due to the deformation of pump casing and baseplate were measured. In the case test pumps, the proportion of the shaft displacement due to the casing deformation to that of pump assembly was 50% and more in most load conditions. Then, the rigidity of not only the baseplate but also the pump casing must be increased when large piping loads over API loads are specified.

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A mass transfer between recirculation zone and outside flow of an annular premixed propane flame was investigated experimentally using MgO powder tracing method and NaCl flame emission. The loacation of the stagnation point in the recirculation zone of the burning flow moved gradually from the nozzle exit with an increase of the gas exit velocity and became constant independently of the gas exit velocity in the very high velocity region. In the region of lower gas exit velocity, the average residence time of the fluid in the recirculation zone of the burning flow was evidently smaller than the time of the cold flow (air) at the same exit velocity, and both residence times decrease gradually with an increase of the gas exit velocity and became a same constant value in the region of very high velocity. Thus, the rate of mass transfer through the surface of the recirculation zone of a high velocity burning flow issuing from the annular nozzle was estimated by the data on the annular air jet.

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In order to ensure the efficiency of Diesel engines and to adjust the exhaust gas for environmental requirements, it is desirable to control not only the timing of fuel injection beginning but also the period or duration of the injection positively. With the conventional fuel injection systems however, it has been extremely difficult to carry out especially the latter control in all operation modes. The authors, based on a new idea of controlling the amount of fuel injection by means of injection pressure and thereby regulate the injection period freely and at its optimum value in principle, made some basic experiments and obtained satisfactory results on the whole. The results will be reported briefly in the following.

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The purpose of this study is to clarify the effect of liquid viscosity on the Sauter mean diameter and the spray angle. The spray injected by a diesel nozzle of hole type was observed by the laser diffraction technique system and the direct photography method. The tests were carried out over a wide range of injection pressures and viscosities of glycerine solution at ambient pressure of 3 MPa. With an increasing liquid viscosity, the spray angle decreases and the Sauter mean diameter gradually increases. With further increase of the Viscosity, the Sauter mean diameter suddenly increases. There is an upper limit of the viscosity to be atomized as a spray of fine droplets. At a high injection pressure, the effect of viscosity on the Sauter mean diameter still remains but the viscosity has no effect on the spray angle.

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The secondary movement of the piston within the piston-cylinder clearance was measured on a small automotive IDI diesel engine. A total of six inductive transducers were installed on the piston skirt to measure the clearance. Slap-induced vibration measurement was made on the liner, the cylinder block and the head bolt. The effects of the gudgeon pin off-set, the engine speed and the load on the piston slap phenomena are discussed. Some of the experimental results of the piston secondary movement are compared with the numerically simulated movement of the piston. It is suggested that the profiles of the piston skirt and the cylinder have also important effects on the impulse of the piston slap.

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Coupled torsional-lateral vibration of softly supported shafts in a spur geared system is investigated. Taking torsional flexibility and bearing stiffness into consideration, dynamic characteristics of a countershaft in a geared system are discussed. It is shown in this paper that the dynamic characteristics of a countershaft are affected not only by the angle between the two power transmitting directions on the shaft but also by the angle between power transmitting direction and elastic principle axis of the support. In this study, the relationships between these factors and dynamic characteristics including natural frequencies are discussed numerically and experimentally.

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Steady self-excited vibrations of a bowed string, which is perfectly flexible and subject to negative damping due to solid fractional force of general characteristic and to positive damping due to air resistance only, are studied by means of a Fourier series method utilizing series transformation. Contrary to the foregoing paper where the limiting case of air resistance tending to zero is investigated, in this paper it remains finite but small.

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Water (working fluid) lubricated bearings are used in various pump designs. This type of bearing has many characteristics different from usual oil lubricated bearings. This paper describes the following characteristics of the water lubricated bearings : (1) Turbulent flow (2) Full film due to high ambient pressure (3) Large additional mass effect Theoretical analysis by numerical calculation and model test using a special test system are performed for a cylindrical bearing. As a result, the characteristics of the water lubricated bearing are recognized and good agreement between theoretical and experimental results is confirmed.

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When a uniform beam is subjected to impulsive-like rotations, equations of motion in the axial and transverse directions of the beam are derived from Hamilton's principle, based on the Euler-Bernoulli hypothesis. By using of linear elasticity and other assumptions, they are simplified and decoupled. An impulsive-like velocity Ω(t) is given by Ω(t) = Ω₀ [1-exp(-ct)] The fundamental equation is transformed into a finite-difference equation and the later is numerically analyzed. The dynamic responses of the beam are obtained for various values of c in the above equation. The variations of the deflection at the beam-tip with time are discussed. The amplitude and period of the cyclic deflection at the beam-tip are obtained for c.

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As one of the promising methods to suppress sloshing in a liquid tank, a reversed U-tube is employed as a dynamic damper and its damping characteristics are studied theoretically and experimentally. It is found that, when the oscillation of liquid column in the reversed U-tube is so coupled to sloshing in the tank that the natural frequency of the former is nearly equal to the fundamental one of the latter, the total system exhibits the vibration characteristics of an inertia-coupled, two degree-of -freedom system, and that the reversed U-tube can play the role of dynamic damper. It is also confirmed experimentally that it could suppress the resonant amplitudes of sloshing to 1/6 - 1/10 of the undamped ones, even when such small values of the equivalent stiffness ratios are chosen as 3.5 - 4.5%

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Displacement, velocity and acceleration of a mechanism of an arbitrary type are analyzed numerically in order to simulate motion of an articulated robot. Uicker's method of analysis, based on the matrix algebra for a link mechanism of a closed loop, is extended to mechanisms of an opened loop and compound loops. How to judge a singular point of motion is explained. On each step of the iterative calculation for convergence by the Newton-Raphson method, a method is proposed to correct the angular displacement of the pairs. It is made clear that the proposed method of correction realizes the analysis with rapid convergence and high accuracy.

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Static and dynamic forces which have to be applied to input pairs of an arbitrary-type mechanism for many kinds of actions are analyzed numerically, in order to simulate motion of an articulated robot. Uicker's method of analysis, based on the matrix algebra for a link mechanism of a closed loop, is extended to mechanisms of an opened loop and a compound loop. The static forces necessary to compensate the forces acting from the outside are analyzed by the principle of virtual work. The static and the dynamic forces necessary to compensate the inertia force, the gravity force, the spring force, the spring force and the damping force are analyzed using Lagrange's equation of motion. The forces of two kinds of robot models are calculated numerically by the present method and the results are compared. Both results agree well with each other.

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The vibration of link mechanisms of a closed loop, and opened loop and compound loops is analyzed numerically, in order to simulate motion of articulated robots at the design stage. It is assumed that all parts of the mechanisms have linear characteristics against small displacement around the equilibrium positions. First, the equation of motion is composed of the inertia, damping and spring forces calculated in the authors' previous report. The natural frequency, natural mode and transfer function of the link mechanism are analyzed by this equation. Next, the displacement and the stiffness of the hand of an articulated robot are analyzed. The vibration of the actual robot for industry is calculated numerically by the present method under the assumption of structural damping. The damping and stiffness coefficients of each pair are determined by the basic experiment. The calculated results are compared with the results of the vibration test.

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We developed a practical computer program to calculate the stationary sound pressure level by using wall or machine surface vibration modes and frequencies. This approach is named the method of superposed sound sources. In this paper, we first describe the theoretical background of this method, and next show that the numerical results obtained by this method agree with the experimental or analytical results. We can predict the sound level by using this approach.

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A forced cooling heat exchanger constructed of many fins with slits causes a discrete tone equally-spaced in frequency, which depends on the air flow velocity. In order to calculate the natural frequency of the cavity, we made an analytical model, consisting of a main cavity, corresponding to the slits, and additional cavities attached to it at equal intervals, corresponding to the spaces between the fins. The boundary conditions at the branch points are the same pressure for each cavity and flow continuity. Wave equations and the boundary conditions define a difference equation. The natural frequencies and the modes can be determined by solving the difference equation. The frequencies and the modes deduced analytically agree with experimentally obtained results. We can predict the tone and make it quiet by using the analytical results.

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As one approach to noise problem of machinery, advantages of near field sound measurement are discussed for a resonating rectangular steel plate. A proposed technique after Acoustic Intensity Method was applied to measure the distributions of both intensity and particle velocity over a plane placed close to a sound source. Particle velocity in the normal direction of plate proved to be reliable for estimating the vibration of the plate surface. And far field sound pressure is calculated accurately from it. In addition, for the ease of calculating far field sound pressure form a known mode of vibration, a simple approximation by which the sound source can be replaced by the least number of point sources, is also proposed.

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In this paper, a theoretical method to analyzed dynamically planar link mechanisms with consideration of bearing clearances and link elasticities has been proposed. Applying the method to a planar four-bar mechanism having an elastic coupler link whose pairs have clearances, the dynamic characteristics of the mechanism have been analyzed with an experimental discussion, revealing the influences of the clearances of pairs and the flexural rigidities of elastic links upon the relative motions between pairing elements, the forces acting at pairs with clearances and the transverse vibration of the elastic link. Moreover, the dynamic characteristics have been improved by increasing the damping ratio of the elastic link.

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Dynamic characteristics of the planar link mechanisms with clearances have been theoretically and experimentally analyzed. The results of both analyses are mutually coincident, and it is shown that there exist at least three kinds of separations between pairing elements. It has been revealed that the three kinds of separations can be predicted from an exciting force of a model vibratory system with a mass, spring and dashpot which has been derived from equations of motion of mechanisms with clearances.

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For the development of mechanical systems of high-speed and high-precision, a dynamic design theory with consideration of bearing clearances which have a great influence upon the dynamic characteristics of the systems is strongly demanded. In this paper, about a crank-and rocker mechanism with clearances, three kinds of restraint methods of separations between pairing elements have been discussed with consideration of the conditions which the exciting forces of a model vibratory system with a mass, spring and dashpot which is derived from equations of motion of mechanism with clearances decrease or become constant. Especially, in order to obtain mechanisms with good dynamic performance, an optimum design method of the mechanisms with clearances has been discussed to determine directly shapes of moving links instead of their mass parameters.

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Using a two-disc machine scuffing conditions were investigated with a 0.45% carbon steel quenched which had high surface hardness and low ability to form oxide film compared with an annealed or a refined carbon steel reported in the previous papers. The following results were obtained. (1) It was confirmed that there were three critical surface temperatures with respect to incipient scuffing. In order to prevent scuffing at each critical temperature the film parameter must be kept above a certain value according to the operating condition represented by the product of the load and the sliding speed. (2) When the film parameter became below unity, the formation of oxide film effective in decreasing the coefficient of friction and enhancing the scuffing resistance was promoted unless scuffing took place. (3) The rotational ratio of a high speed disc to the mating low speed disc, integral or hunting, also affected EHL film formation and scuffing resistance.

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A double-row admission gas journal bearing with partially gas-fed slot restrictors is investigated. In this type of bearings, gas flow is mainly restrained by both the viscous resistance in the slot region and the inflow resistance at the inlets of narrow feeding slits. Therefore, the maximum load capacity of this bearing can be obtained easily in a small bearing clearance of less than 10 μm. Here, influences of various design parameters on the static characteristics are described and the optimum design conditions for the load capacity are theoretically determined. Furthermore, the validity of the theoretical predictions and the usefulness of this type of bearings are confirmed by comparison with the experimental data.

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In this paper, the effects of fluid inertia forces in annular parallel plate squeeze film bearings lubricated with pseudo-plastic fluids are investigated theoretically. The cubic equation obtained from the empirical flow curves for the pseudo-plastic fluids is used as the relation between shear stress and shear strain rate. Approximating the inertia term in the momentum equation by the mean value averaged across the film thickness, a lubrication equation for calculating the film pressure of annular parallel plate squeeze film bearings is derived. Applying the lubrication equation to the annular bearings under the sinusoidal squeeze motion, the effects of inertia forces on the film pressure are examined for various nonlinear factor.

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An analysis of the laminar squeezing flow of an incompressible viscous fluid between a rotating curved disk and a plane wall is presented in which a successive approximation technique is used to account for fluid inertia, curvature and centrifugal force effects. Assuming a small ratio of the film thickness to the radius of the disk, the Reynolds equations in first order approximation and second order one are derived and solved analytically for the case of the curved disk having an arbitrary profile. The forces and the moments acting on the disk and the wall are found in the form of a function of the film thickness. The forces depend on the acceleration of the disk, but the moments are independent of it. A force applied to the disk is completely transmitted to the wall, while a moment applied to the disk is partially transmitted to it. The transmission loss in the moment depends only on the velocity of the disk. The forces and the moments are concretely obtained for the case of the disk having a parabolic profile.

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Two prevention methods are proposed in the previous report as the prevention methods of tooth profile change in the course of operation of a nylon gear which transmits the power. And their effect is confirmed by experiments. In this report as a method simpler than those methods, a plus profile shifting of nylon gear is proposed. In the plus profile shifted gear, the tooth thickness of tooth flank increases and the tooth is less liable to deflect. Meanwhile the sliding of tooth is large. In this report the abrasion of tooth of nylon gear is investigated under several profile modification coefficients and this method is examined to see how useful it is as the prevention method of tooth profile change.

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The true root stresses of internal spur gears with various numbers of teeth and addendum modification coefficients were calculated by 2-dimensional elasticity theory and mapping function, and the position of critical section on tensile side of internal spur gear tooth was indicated. The stress concentration factors at the position of critical section were calculated under different loading conditions. A practical formula for true root stress of internal spur gear tooth was derived on the basis of these calculated results. Furthermore the root stresses calculated by this practical formula were compared with those by FEM and measured ones, and the validity of the practical formula was confirmed.

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In the present paper, the characteristics of surface durability of a tufftrided roller under uniform cyclic and two-step loading conditions were investigated. The surface durability of the tufftrided roller used in this experiment is found to be higher by 90 ∼ 100% than that of a normalized steel roller and shows a tendency to increase with an increasing hardened depth. The cumulative cyclic ratio S varies considerably according to the loading condition due to the strengthening or strength-reducing effect of prior load. Therefore, it is unreasonable to apply Miner's rule directly to the estimation of the surface durability of the tufftrided roller under varying load.

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Crank-length adjusting mechanisms are proposed in order to change input-output relations of arbitrary planar spherical and spatial mechanisms and also to stop output motions of crank-and rocker mechanisms during rotations of their crank shafts. Structures of the crank-length adjusting mechanisms are obtained by a number synthesis, after analyzing the relations between the crank length and the displacement of a moving pair on the crank in the case where the pair moves along a straight line or an arc fixed on a rotating plane of the crank shaft. Some applications of the mechanisms to adjustable path and function generators are shown.

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A simple queuing system with a queue-dependent server is considered. Assuming a finite waiting space in front of servers, we derive the system size distribution (the state probability) and the mean number of customers in the system for two servers. Furthermore, a method of diffusion approximation is applied for solving the system with general independent inter-arrival time and general service time distributions. Numerical examples for the mean number of customers in the system are given to compare an exact value with an approximate one.

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