The influences of the internal resonance on the summed-and differential harmonic oscillation [p₁+p₂] and the ultra-summed-and-differential harmonic oscillation [(p₁+p₂)/2] in a nonlinear two-degree-of-freedom system whose natural frequencies, p₁ and p₂, are at the ratio of 1:2 are discussed. The resonance points of these oscillations do not coincide with those of other kinds of oscillations. These are the oscillations whose coexisting components do not have the frequency ratio of an integer when the relationship of internal resonance does not hold. In this paper, we investigated the relating nonlinear components, the variations in the shape of resonance curves, the change in the stability of the stationary solutions, the occurrence of the almost periodic oscillations, and the occurrence of new stationary oscillations by theoretical analysis. In the results, it is clarified that, due to the influence of the internal resonance, (a) other kinds of nonlinear components become influential, (b) the stationary oscillations which are observed in a system with no internal resonance change to almost periodic oscillations, and (c) stationary oscillations whose vibration components are at the frequency ratio of an integer become apparent.

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A strain wave gearing has been widely used as the reduction gear drive in industrial robots. Transforming the robot system, which had been investigated experimentally in the previous paper, into an equivalent vibration model, the vibration occurring in the robot system was analyzed theoretically to compare the theoretical value with the experimental on and to determine the cause of the vibration with the following result. The amplitude of the vibration occurring in the robot system was influenced by the variation of the torsional stiffness and by the composite error in meshing due to the machining and assembly errors of elements.

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Head assembly vibrations in flexible disk drive units (FDD) are discussed in this paper. The head assembly on a disk encounters unstable vibration in FDD which induce read and write malfunctions and decrease the life expectancy of the head assembly. In this study, vibrations are experimentally analyzed using an FDD unit modified to rotate at a variable speed. The unstable vibrations of the disk are measured by a photonic sensor. It was found that the heads vibrate in a pitching mode, while the disk vibrates in a wave propagation mode toward the head, and the both modes are couples. It was also found that instability occurs only in a certain speed range of speed, and that the frequency of the unstable vibrations increases as the rotational speed increases.

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A new type of the theory that solves the impact vibration problems is proposed here. The impact treated here is that a tube vibrates with the gap support, such as in a hole and to a flat bar. The theory is based on the modal synthesis analysis by using the fixed mode at the gap support. The results are compared with these of the usual modal analysis using the free mode at the support and the efficiency is proved by comparing the Rogers' previous paper and our test results.

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The authors used Mindlin's equation, and calculated the circular plate natural mode with a solid shaft under the boundary condition of a fixed inner diameter. As the result, the caclulated natural frequency of the low mode of the thick circular plate differed greatly from the one measured by model analysis. The causes were analyzed on the (1, 0) mode of vibration, which had the biggest error of 78 percent. It was revealed that the elastic deformation on the boundary between the circular plate and the solid shaft, and the bending deformation of the had a strong influence on the natural frequency. By taking both influences into account, the natural frequency of the (1, 0) mode was corrected to within a 5 percent error.

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Coupled liquid-structure oscillations of a container of pool-type LMFBR (liquid metal fast breeder reactor) subjected to horizontal excitations are studies for small motions. First, a variational principle is introduced for a perfect fluid and a linear elastic solid. Ignoring pumps and IHX's (intermediate heat exchangers), the container is treated as an axisymmetric structure containing liquid sodium considered as a perfect fluid. Discretized equations of motion are derived from the variational principle, using FEM for axisymmetric shell and BEM for liquid sodium. Free vibration analysis is worked to obtain natural frequencies and modes. Then, a modal analysis method is applied to give time history of the liquid-structure system subject to horizontal excitations resonant to the first bulging mode. Characteristic features of resonance are observed in deformations of an inner oblique wall.

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The steady state response problem is solved for cantilevered rectangular plates made of symmetrically laminated FRP (fiber reinforced plastic) composites. The bending rigidities are obtained by using the thin-plate laminate theory, and the governing equation of motion for generally orthotropic plates is solved by the Ritz approach. In numerical study, driving point impedance is calculated for three types of FRP materials, and the effects of various parameters (material, number of layers, fiber orientation) upon the responses are discussed.

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In this study, the seismic response and the reliability of elasto-plastic structures were treated by taking the stiffness degradation into consideration. The nonstationary seismic input was assumed to have not only a time-varied envelope but also time-varied spectral density. Effects of the nonstationary variations on the response and threshold-crossing probability of the structure were studied by taking the resonance frequency change due to the stiffness degradation of multi-component structure into account. The restoring force characteristics of each component was represented by a simplified Clough model and has various yielding levels. The covariance of response, the first passage probability, stiffness degradation rate and plastic deformation rate were computed using equivalent linearization techniques on the assumption of a narrow band response. These results were compared by digital computer simulation.

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The torque-induced transverse vibration of rotor systems driven by Cardan joints with with initial intersecting angles is analyzed. Three systems, MR2, MR4, SR4 models are analyzed. MR2 and MR4 are models for working machines such as the compressor and SR4 is for transmission shafts. The analysis proves that the initial intersecting angle induces parametric terms of frequency 4ν(νis frequency of shaft rotation) in addition to 2ν, which is induced when there is no initial intersecting angle. The 4νterms make the system unstable especially in the low-speed range. MR2 and MR4 models are shown to have quite different instability boundaries, depending on the sign of torque. The parametric tems of SR4 have no principal parametric instability region. SR4 is more stable than MR4.

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The vibration of a rotating disk restrained at a space-fixed point, such as a computer memory disk with a magenetic head, is theoretically analyzed. The frequency equation is derived by using the receptance method. The natural frequencies and the vibratory modes are discussed for the rotation speeds below the critical speed. The analysis indicates that the phenomenon of"curve veering"for a frequency-speed diagram is observed for the restraint with high receptance, and that"quasi-standing waves"are formed for the restraint with low.

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In the present paper, vibrations in a rotating disc with a clamped inner circle, a free outer periphery and a support on the outer periphery are analyzed. A characteristic equation is obtained without introducing the so-called Green's function, and relations between natural frequencies and an angular velocity of rotation are determined. Due to the existence of the support, these relations are more complicated than those of a disc without the support. Also, figures of eigenmodes are shown. Nodal radii do not remain during the rotation of the disc.

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Thin paper proposes a midget mobile robot in a thin tube using piezovibration. The principle of the robot movement is the use of a frictional difference against the wall between forward and backward fin movement through the piezovibration. Experiments have been carried out suing a trial model to comfirm its mobile characteristics. Experimental results show that a running velocity and a tractive force greatly depend upon an exciting frequency of piezovibration. These characteristics are analyzed by introducing equivalent coefficients of dynamical friction on the viewpoint of an approximate static model. This theoretical model clarifies these phenomna affected by the excitation frequency. Experimental and theoretical results show that the proposed mechanism excellently expresses robot motion in a thin tube.

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An analytical method is presented for free flexural vibrations of a cantilevered beam with a concentrated mass, introducing the new mode shape function to the Galerkin procedure. The mode shape function is expressed with the sum of the product of the trigonometrical function and the finite power series truncated with the fourth order. The trigonometrical function expresses the form of the higher mode of vibration. The coefficients of the power series are determined by solving the homogeneous equations for the boundary conditions of the beam. Applying the Galerkin method, the sets of differential equation in a time function are reduced. It is found that this method gives good accuracy to the natural frequencies and the natural modes of vibration within the limited number of terms for unknown time functions.

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This paper describes the general formulation for the in-plane flexural free vibration analysis of a multiple layered structure by the transfer influence coefficient method. The structure is modeled as a distributed mass system with lumped masses and lumped inertia moments, and massless linear and rotational springs. The present method does not require a change of fundamental algorithm but necessitates only substituting appropriately large values into the corresponding spring constants when intermediate elastic supports are many and very stiff. Boundary conditions are also easily controlled by the spring constants. Some devices are taken for high calculation accuracy and calculation speed. The occurrence mechanism and the simplified elimination of false roots involved in the frequency equation are discussed in the use of the bisection method.

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The authors apply the general formulation for the in-plane flexural free vibration analysis obtained in the previous report to a structure with two layers regarded as a distributed mass system. They state the effective method of numerical computations suitable for the remarkably stiff intermediate elastic supports between layers in detail. The results of the simple numerical computational examples demonstrate the frequency equation for all boundary conditions when the bisection method is used as a solution, and the flexibility for programming of the transfer influence coefficient method, compared with the transfer matrix method on a personal computer. The cancelling attributable to the sum and difference of the trigonometric and exponential functions is overcome by partition of the uniformly distributed beams.

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To analyze the three-dimensional vibration behavior of the crankshaft system, the crankshaft was idealized by a set of rigidly jointed structure consisting of rods and beams, the pulley and the flywheel by a set of lumped masses and moments of inertia, and the journal bearings by a set of springs and dashpots. The dynamic stiffness matrix for the complete crankshaft system was derived from the principle of superposition and the natural frequencies were calculated from compliance matrix. These modeling and calculation methods were applied to the analysis of two kinds of planar structure crankshafts, one for a single cylinder engine, and the other to a four-cylinder in-line engine; the calculated natural frequencies and mode shapes coincided well with the experimental results.

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The modeling method and calculating process described in the earlier report were applied to two kinds of solid structure crankshaft systems: one for a three-cylinder in-line engine; the other for a V-six-type engine. Again, good agreement was obtained between the calculated results and the experimental ones. The influence of oil film stiffness of the crankshaft journal bearings on the vibration behavior of the crankshaft system was examined. The vibration behavior of the crankshaft system was predicted by taking account of the influences for a four-cylinder in-line engine, mentioned above, and the results were compared with experimental values.

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n a railway vehicle, the wheel tread profile is one of the most important factors which have influenced running stability and safety. In current high speed railway vehicles, the wheel tread profile is compared to worn profiles, and is used for the improvement of running characteristics and to simplify maintenance and the control. The authors have theoretically analysed in detail the geometrical contact between the wheel tread profile consisting of compound circular arc-forms and the rail. Then, a describing function method is applied to the theoretical calculation for the SHINKANSEN truck hunting having six-degrees of freedom. Consequently, it is made clear that the truck hunting is influenced by many factors, such as non-linearity wheel tread conicity, clearance between the truck frame and the bolster anchor, non-linear characteristics of the turning moment of truck and the supporting stiffness of the axle and so on. Furthermore, the guiding principle for the improvement of the running capacity and the target values of the design for high speed trucks are presented.

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During a high speed running test of an actual car of the SHINKANSEN conducted by the Japanese National Railways, a severe truck hunting having a high frequency and a very short wavelength began to occur at a speed of about 180 km/h. It is already known that the main reasons for such a truck hunting are, among others, large clearances of the connecting positions between the truck frame and the bolster anchors, and inadequacy of the supporting stiffness of axles. Taking into account these facts, the authors made a theoretical analysis of the hunting stability of a one-half car model which is an eight-degrees-freedom system. In the analytical calculation, the repulsion of the rail against the wheel flange, the variation of wheel tread conicity due to geometrical contact between the wheel and the rail were taken into account. Consequently, in this basic investigation, truck hunting, which has been an unsolved phenomenon, is now clarified and its preventing method has been established.

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This paper is concerned with the problem of keeping the pantograph in contact with the overhead-line on a railway. A new system of wire and pantographs was proposed to which a dynamic damper was added in order to avoid sparking on the contact wire. The phenomenon of the system was analyzed and the effects by dynamic damper were were examined. Consequently it was demonstrated in the present paper that the natural frequency of the auxiliary equipment affects considerably the rate of the amplitude growth in the unstable region, and the best tuning condition for resonance lowers greatly the static amplitude in parametric excitation if the dynamic damper has a viscous damping element

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A power spectrum control technique for a shaking table system of response, which is excited by a pseudo-ramdom wave, is studied. By the experiments using a practical machine and a shaking table model with a single degree of freedom, composed on an analog computer, it is shown that the cause of performance reduction in the power spectrum control concerns a nonlinear friction force and a transient response of a low damping system. Concerning the transient response, it is proved that a good control performance is obtained by an improvement of the averaging method in the power spectra measurements. Concerning the friction force, it is proved that the magnitude influences the control perftrmance. As a result of the power spectrum control for an analog computer model of the shaking table in which the hydraulic servo system is considered, it is shown that the control performance of power spectrum for a response system with a friction force level of a practical machine can be put wdthin the target level ±3dB.

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A stepping motor has the drawback that vibration occurs because of an intermittent motion mechanism, although it has the advantage in the field of an open-loop control system. Concerning this problem, the application of the dynamic absorber to the beam rotated by the stepping motor is investigated in this paper. Optimum tuning design parameters of the absorber are obtained on the condition that the logarithmic decrement of the residual vibration for the single step input assumes a maximum value. From the transient response analysis, it is shown that beam tip vibration during the multiple driving signal input is suppressed, and the residual vibration is reduced rapidly. Numerical and experimental results are shown to be in good agreement.

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In the near future, many robots will be used in space for extravehicular tasks. Most of these robots will be structurally flxible reflecting the necessity for their light weight. In this paper, dynamic control for a two-link flexible SCARA manipulator, handling a large mass payload, has been studied. For real-time compensation, a simple dynamic model was derived using the static deflection model, to derive the system dynamics equations of a flexible manipulator. To investigate the effectiveness of this model, dynamic analysis was done by simulation and experiments. A two-link flexible SCARA manipulator system was constructed. This manipulator was 1.5 m long and was floating on a plate base using air bearings, handling a 100 kg payload. Its results showed that the model accurately reproduced the state of main deflection. Next, a dynamic control was done using this experimental setup. Its results using this model were compared to results using a rigid model, and the validity of the developed model was demonstrated.

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This paper proposes a new design concept that takes into consideration the construction of a mechanism that consists of a structural system and a control system. In order to obtain a fine mechanism with high performance, it is necessary to prepare the structural system with higher controllability in the design stage. The essence of the concept is to make practical lse of the nodes at the vibration modes of the structural system for the purpose of suitably arranging the controller and the sensor within it. Firstly, uncontrollability and unobservability, which correspond to the pole-zero cancellation, is realized on the vibration node. Next, it is shown that the controller located on the vibration node cancels any undesirable resonance peak of the structural system required for achieving higher controllability. The effectiveness of the design concept is demonstrated by the design of the optical servosystem.

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The optical servosystem requires a high degree of controllability. However, it is very difficult to realize a servosystem with higher controllability since the dynamic characteristics of an optical pick-up influence the stability of the servosystem. Therefore, both a control system and a structural system must be considered simultaneously in the design stage of the optical servosystem. The purpose of this paper is to determine the structural system in order to obtain higher controllability. Firstly, the authors investigate the structural characteristics of an optical pick-up model and explain the necessity of structural optimization to improve servo characteristics. Secondly, the structure of the optical pick-up model is optimized by using the Pole-Zero Cancellation Method proposed by the authors. The servosystem is comprised of the optical pick-up model with the phase-lead compensator. Finally, the characteristics of the servosystem are investigated and the improvements are confirmed. The practicability of this design method is verified by the experiments.

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The design method of an optical servosystem and its practicability were discussed in the first and second reports. In this paper, the authors develop a practical optical pick-up. Firstly, we propose a new type of optical pick-up which is a simple monobloc hinge-type structure and investigate its structural characteristics. As a result, it is confirmed that the structural characteristics of the optical pick-up influence the stability of the servosystem; accordingly, a structural optimization is necessary to obtain a high degree of controllability. Secondly, the optical pick-up is optimized by using the Pole-Zero Cancellation Method and the servosystem is comprised of the optimal pick-up with the phase-lead compensator. The results of both analytical and experimental investigations verify that the servo characteristics are improved and sufficient characteristics are satisfied such that the servo specifications are realized

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This study deals with a hydraulic actuator system operated by two 3-way solenoid valves in PWM-Digital mode. It has been often pointed out that there are practical problems to be solved in the PWM system. For example, (1) Accuracy of positioning control becomes considerably insufficient, because the system is affected by on/off action of the solenoid valves, and (2) Serious nonlinearity appears in the valve characteristics as a result of the switching behavior of the valves. As a method to overcome these defects, a new concept of PWM control, that is, a differential PWM method, is proposed in this study. In the method, the pressure difference for driving the actuator is method, is proposed in this study. In the method, the pressure difference for driving the actuator is given by pulse trains which are modulated by Duty-input to the valves. The dynamic characteristics of the system, controlled by the proposed method, are investigated by experiment and digital simulation. Consequently, the availability of the proposed method is confirmed.

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This paper discuses the linear-quadratic optimal control problem of a type-1 deadbeat servo system for single-input linear time-invariant discrete-time system with fixed terminal atate. The fixed terminal state condition is called the state deadbeat condition. The type-1 servo system is transformed into the deviation system. first, the general deadbeat input of the deviation system is expressed by constant gain state problem is transformed into the deviation system. First, the general deadbeat input of the deviation system is expressed by constant gain state feedback and arbitrary input. By using this general deadbeat input, the fixed terminal state problem is transformed into the free new terminal state problem. Then, the problem of minimizing the quabratic performance function is solved, and the optimal deviation input is obtained by using the special Riccati equation. This optimal feedback gain is made up by the variable gains and the constant gain, which are independent of the initial state of the controlled system, the step command signal and the step disturbance.

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Current robot manipulators are controlled by decentralized or independent joint controllers. That is, each joint is locally controlled using only local information. We discuss the asymptotic behavior of the closed loop eigenvalues of such systems when the high gain feedback is implemented. The high-gain feedback is an effective control method because of its robustness to parameter variations and disturbances. By using a theory of multivariable root-loci, we present three propositions about the behavior of the closed loop eigenvalues in the case that the constant gain controller is used. It is supposed that the obtained results are useful in the control system design of manipulators.

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An efficient algorithm for solving minimum time trajectories planning problem of manipulators is proposed. This problem is meaningful in the sense that shortening of traveling time is directly related to improving productivity in manufacturing plants. Although many algorithms for planning the minimum time trajectory have been proposed, an efficient method has not necessarily been obtained yet. In the present paper, the dynamical equation of the manipulator is expressed by a path parameter s which does not depend on time, and a two-point boundary value problem for an iterative equation represented by the parameter s is solved to obtain the near-minimum time joint trajectory. Finally, the proposed method is applied to a simple manipulator with two links and two degrees of freedom. Numerical results show that fairly good trajectories can be obtained by this method with less calculation time. Furthermore, this method is easily applicable to multiple joint manipulators because of the simplicity of calculation.

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A multifingered hand system for robots with a capability of controlling joint compliance has been developed. In order to drive each finger joint, a pulley-cable system with DC motor was introduced. Usual pulley-cable driving systems have friction and low rigidity, which make high quality compliance control difficult. To compensate for these undesirable characteristics, a small specially designed strain sensor was installed near the joint and was used to construct torque sensory feedback. Through experiments using the individual joint, the effectiveness of the feedback was confirmed. The system developed was a two-fingred hand, each of which has three joints. To evaluate the system, the joint compliance was measured at each joint and the compliance ellipsoid was measured at the finger tip. From these measurements, it was found that the developed finger system provides stable and fine compliance controle ability.

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A high resolution tactile sensor of pressure to-light conversion type is developed. An object is pressed on a white elastic sheet to make close contact with a transparent plate underneath. Then the side of the plate is irradiated. The sheet contact areas on the plate scatter the light which provides a tactile image of the object profile. This is based on the mechanism that the contact material at the surface of the transparent plate is changed from the air to an elastic sheet, and then the condition of total reflection does not stand any more. A CCD-camera is used to detect the images and microcomputer is used to convert to binary images with a fixed threshold. In order to get an optimal sensor system, how to design the parameters of each sensor assembly is discussed. Through the evaluation experiment for the sensor system, it is found that spatial resolution of measuring object profiles is about 2 mm and pressure sensitivity is about 2×10⁴ Pa.

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This paper deals with the method of the optimal configuration of a manipulator based on cell structurization, as one of the methods of determining kinds of cell and order in reconfiguration. The proposed methods can determine the joint location, the degree of freedom and the link length using the characteristics of cell structures of the DRRS. The method takes into account both cases of the fixed-type and the mobile-type of manipulators. The proposed performance index for the selection of both types under given tasks is based on the number of works, the accuracy of the manipulator in positioning, the required torque for keeping the attitude, the displacement between given works and the cost of cells in the configuration. The simulation results are also given to clarify the difference of performance for each task. Thus the DRRS can realize the idea of self-organizing system.

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Characteristics of a bipedal walking model consisting if eight rigid elements were simulated for a wide range of walking speeds. The simulation results are similar to experimental findings reported by other researchers in the following : changes of joint angles in the leg with respect to time : changes of magnitudes of floor reaction with respect to walking speed. Controllability of the body motion in the transient phase of walking, starting and stopping, is shown by the rank of Jacobian relating the body velocity with input velocities at joints. The dynamic equation is expressed by the spatial vector method, in other words, the screw coordinates, then a zero moment joint condition is formulated to simulate an abnormal walk. The resulting equations are easily modified to apply to general cases by adding appropriate terms.

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The lost function at zero moment joint (ZMJ) is compensated by the remaining normal joints. The compensatory actions are so great that a stable walking can not be realized in some cases. Methods to reduce the compensation are introduced as follows: walking velocity, lateral motion of pelvis, and inclination of legs at the instant of heel contact. A gait that is realized by a slower waling with wider step width and lateral inward motion of pelivis during stance phase can reduce the strength of compensations. The walking style resembles to that of men or infants. passive elastic elements attached at both ankles (ZMJ) contribute to make the upper torso almost upright. The passive elements are effective for the correction of abnormal walking. Some applications of results are, also, discussed with respect to the design of locomotive robots.

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Femoral chondrocytes of pigs were pressed against a glass disc to simulate and investigate the lubrication characteristics of a synovial joint under physiological conditions. The surface deflection of articular cartilage was measured by a laser displacement pickup through the glass. The following conclusions were reached through the experimental study : when cartilage is pressed by fluid, no creep deformation is detected; most of the applied load is supported by pressurized synovial fluid entrapped inside a slightly contacting circumferential zone; the external flow from the cartilage to the gap causes creep deformation, a reduction of contact pressure and an increase of fluid pressure in the gap.

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This paper is concerned with the reduction of the power loss of the thrust bearing. A thrust bearing with a disk floated by externally pressurized oil is proposed, and the static characteristics of the thrust bearing are investigated by experiments and simplified analysis in the laminar regime. As a result, the following conclusions are obtained: The power loss of the thrust bearing decreases by approximately one-half of the same-shaped hydrostatic bearing without any disk. The disk is floating nearly in the middle of the oil film. The rotational speed of the disk is about one-half of the shaft rotational speed. The floating position of the disk and the disk rotational speed do not influence the power loss very much.

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A conventional skew gear pair does not change its relative position of gear axes. On the contrary, one of the axes of the gear pair offered in this paper is able to be displaced one-parametrically on the space fixed to the other gear axis. At any relative position of the gear axes, the gears rotate at a constant speed ratio. The displaceable axis gear pair has three backgrounds as follows. (i) The gear pair is potentially a power transmission element. (ii) The motion of these gears can be applied to the generating motion of gear manufacturing. (iii) The gear tooth bearing problem is based on a deflection or displacement of the gear axis in loading. This paper discusses the relative curvature of gear tooth surfaces and the motion of the tooth bearing pattern.

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A conventional skew gear pair does not change its relative position of gear axes. On the contrary, one of the axes of the gear pair offered in this paper is able to be displaced one-parametrically on the space fixed to the other gear axis. At any relative position of the gear axes, the gears rotate at a constant speed ratio. The displaceable axis gear pair has three backgrounds as follows. (i) The gear pair is potentially a power transmission element. (ii) The motion of these gears can be applied to the generating motion of gear manufacturing. (iii) The gear tooth bearing problem is based on a deflection or displacement of the gear axis in loading. This paper discusses the relative curvature of gear tooth surfaces and the motion of the tooth bearing pattern.2145Three kinds of induction-hardened sintered powder metal gears were fatigue-tested using a power circulating gear testing machine in order to elucidate the fatigue strength and failure mode. The relation between the tooth profile change and the dynamic performance in the fatigue tests of the gears were also investigated. The fatigue strengths of three kinds of gears were almost the same. The failure modes in these gears were tooth breakage at the tooth fillet, tooth breakage due to pitting near the pitch point, and destructive tooth surface failure. Except for one case of the destructive tooth surface failure, the dynamic performace changed slightly during the fatigue test since the tooth profile deterioration was small. The occurrence of the destructive tooth surface failure influenced the dynamic performance of the gear.

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This study aimed to elucidate the fundamental characteristics of the composite plastics that adopt thermoplastic resin as the basic material, and in which various fibers are filled, when they are applied to gears. In this case, polyacetal was used as the basic material, and glass fibers, carbon fibers or potassium titanate whiskers were used to fill it in. Gears were made with these composite materials, and the wear of teeth, the change of the tooth profile, the temperature on tooth surfaces and so on of the respective gears were examined. In this way, the features were elucidated by comparing those with the case of polyacetal gears.

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Under severe lubricating conditions such as in a gear lubrication, the lubricating oil will be expected to behave as viscoelastic fluid. The Navier-Stokes equations cannot be applied to the fluid analysis when the fluid characteristics are obtained theoretically for the severe lubricating conditions mentioned above. The author constructed the models for viscoelasticity which can be applied to both the boundary lubrication and the elastohydrodynamic one, taking the viscoelasticity of lubricating oil into consideration. The basic equations were derived from the new model constructed in the paper.

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The elastohydrodynamic equation of a line contact is solved by using a finite element method for a range of Dowson's dimensionless load W=2.042×10^-5-1.5×10^-4. A lubricant model of limiting shear stress is introbuced in this calculation. The existence of the limiting shear stress greatly influence either the film thickness or the distribution of pressure, with the exception of the pressure spike. In the case of a small slip, the minimum film thickness in this calculation is almost the same as the film thickness based on a Newtonian model. The adoption of the lubricant model also has a remarkable influence on the traction force. An approximate formula, which is adequate for the estimation of the maximum coefficient of traction, is proposed based on the examination of the calculated shear stresses.

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The following two factors are newly considered in the prediction of friction force between the piston ring-like test piece and the cylinder liner-like test plate on the simulating rig in order to explain the discrepancy between the previous prediction and measurement. (1) The viscous shear force of the oil striation in the cavitated region is included. (2) The transition between the separation boundary condition and Reynolds' is considered, which seems to be caused by an oil film rupture releasing negative pressure. The prediction can be sufficiently improved by considering these two factors for the case of simulating rig. The difference of the ring profile and the effect of oil starvation must be taken into account additionally for the case of piston rings in real engines.

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In order to estimate the varying friction coefficients during the ring compression test, we have proposed new calibration curves which describe relative effect of friction on the extension velocity of ring diameter. Commercial pure aluminum specimens with several different surface appearances, which were made by various finishing methods, were tested, with paraffin oils as a lubricant. The change in the outer diameter of the testpiece was continuously meassured by means of clip gauge during compression. Transient friction coefficients in the stage while lubricant is trapped have been obtained clearly according to the proposed method. It is found that the new calibration curves are more effective than the commonly used calibration curves, particularly in small reductions.

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The authors have found that a lubricant which consists of boron nitride and boric acid (BN/BA lubricant) shows a very low coefficient of friction in isothermal forging of a Ti alloy with ceramic tools, i. e., AL₂O₃, SiC, Si₃N₄. To apply the developed lubricant to a practical forming operation effectively, frictional characteristics of the BN/BA lubricant are investigated in detail by carrying out ring-compression tests. The coefficient of friction is kept very low when the weight fraction of boron nitride is in the range of 20 to 40% for every ceramic tool, and is reduced with an increase in strain rate. The temperatures at which the BN/BA lubricant exhibits excellent frictional characteristics coincide with the temperatures at which superplastic property appears in the Tialloy and Ni base superalloy. It is concluded that thick lubricant film entrapped between the tool and the specimen reduces the friction in isothermal forging with BN/BA lubricant

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In cold forward extrusion, dimensional errors are caused in products by elastic expansion of the die exit and elastic recovery (expansion) of the billet after extrusion. To improve accuracy, an extrusion method using a ring-shaped die is proposed. Thc outer surface of the ring-shaped die is of a conical shape and is fitted to a conical holder. By the axial extrusion force, the die moves slightly in the direction of extrusion so that the die exit is reduced in diameter. The dimensional error due to elastic recovery of the billet after extrusion is canceled by the decrease in exit diameter during extrusion. The deformation of the ring-shaped die during extrusion is calculated using the elastic finite element method, and the effects of die dimensions on the degree of reduction in the diameter of the diameter of the die exit are investigated. Extrusion tests are carried out for dies with various conical angles of the outer surface. It is confirmed that the present extrusion method is effective in decreasing the diametral error of an extruded bar, especially the error due to fluctuation of the extrusion load.

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Recent developments in the electronics industries a piercing technique for many fine holes at a high production rate. The present research attempts to apply to such piercing a manufacturing process using a viscoplastic pressure medium process (VM Process) previously proposed by one of the authors. The appearance of the holes pierced through copper foils is observed microscopically, and the effect of the working conditions on it is examined. Although only for a specific condition, the process is shown to be successful in piercing the circular holes of 50 μm in diameter with 75 μm in pitch, unobtainable by the conventional shearing process. Besides, a new technique (AFM method) for precise piercing applicable to general working conditions is proposed.

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To measure the flow stress of metals under forming conditions, i. e., at large strain rates and elevated temperatures, a method based on the ring compression test is proposed. In this method, ring-shaped specimens are compressed between two flat tools with or without lubrication. The coefficient of friction between the specimen and the tool is determined from the change in inner diameter, and then the load and reduction in height measured in the test are converted into average flow stress are derived from the rigid-plastic finite element calculation. This method is simple to carry out and does not require control of the friction during compression. Ring compression tests for some kinds of lubricants, billet materials an strain rates are carried out. The method is confirmed to provide flow stress-strain curves within an error of 5%, and is effective especially for measuring the flow stress of heat-resistant materials such as Ti alloys and Ni base superalloys which are formed at elevated temperatures. As an example, flow stress-strain curves of Ti-6 Al-4V alloy measured by the present method are demonstrated.

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Recently, the thinning and strengthening of sheet metal is of importance for conserving natural resources and energy. In this paper, the effects of the thicknesses, lubricants and temper of metals on the pure stretchability of aluminum sheets are studied. The pure stretchability of sheet metals deteriorates with a decrease in thickness. The optimum frictional coefficient, which gives a maximum of critical forming depth, was found in this experiment. The thickness dependence of the critical forming depth was analytically calculated by means of Hill's diffuse neck criterion, Yamaguchi's method based on M-K theory and the criterion proposed by Gotoh, and results were discussed in detail.

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