The method of multiple scales in conjunction with the Galerkin method is applied to the analysis of multimode responses of thin, geometrically nonlinear rectangular laminated plates subjected to a harmonic excitation. Responses of simply-supported laminated plates are treated, and two symmetric modes of vibration are adopted in the analysis. In order to use the method of multiple scales properly, we introduced new detuning parameters which indicated the relationship of natural frequencies of each mode. It is found analytically that two-mode responses can occur at each primary resonance. The analytical results are confirmed by numerical integration of the equation of motion.

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An analysis is presented for the free vibration of a CFRP cantilever annular sector plate. Kinetic and strain energies are obtained in Cartesian coordinates and are then transformed into polar ones for the convenience of the following analysis. The Ritz method is used to derive the frequency equation, and power series are employed as admissible functions. Natural frequencies and mode shapes of symmetrically laminated plates are calculated numerically and are compared with those obtained by the finite-element method and experiments.

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An exact procedure is presented for solving free vibrations of a rotating thin laminated composite shell of revolution with meridionally constant curvature. Based on the classical lamination theory, equations of motion and boundary conditions are obtained from the stationary conditions of the Lagrangian. The equations of motion are solved exactly using a power series expansion for symmetrically laminated, cross-ply shells. Frequencies and mode shapes of the shells having both ends clamped and both ends freely supported are presented to show the effects of rotating angular velocity, number of laminae, stacking sequences and other parameters on the frequencies and the mode shapes.

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Forced vibrations of rotating anisotropic cylindrical shells are investigated. The basic equations, including the effect of the initial stresses due to the rotation, are formulated by the finiteelement method. The characteristic relations for finite elements are derived from energy principle by considering the finite strain. The equations of motion can be separated into the quasi-static and dynamic ones, i.e., the equations in the steady rotating state and those in the vibration state. Radial concentrated impulses and step forces are considered as external dynamic forces. The transient responses of circular cylindrical shells which have various degrees of anisotropy and lamination parameters are numerically calculated.

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Free vibration of thick rotating prestressed anisotropic cylindrical shells is investigated. Torque, external pressure and axial compression load are considered as prestresses. The basic equations are derived from Hamilton's principle based on the first-order shear deformation theory. The equations of motion can be separated into quasi-static and dynamic ones, i.e., the equations in the steady rotating state and those in the vibrating state. Using the modified Galerkin's method, frequency analisis is carried out for four boundary conditions. The general cases with anisotopy and prestresses are analyzed. Then numerical results are compared with those based on the classical shell theory, and the differences between the theories are examined.

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Dynamic characteristics of squeeze-film dampers which have an annular oil-feeding groove in the center of the width are tested experimentally. Measured values show that the damping coefficients can be roughly estimated by a short-bearing approximation of a classical lubrication theory in the case of a small clearance damper ; however, the inertia coefficients are large and entirely differ from the value obtained using Smith's well-known short-bearing theory. In this study, the influence of 0-ring end seals is also investigated by removing 0-rings. The test facilities, measurement method, and experimental results are presented and compared with well-known classical theories.

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After the investigation of the experimental results in the 1st report, an analytical theory based on a linearized Navier-Stokes equation is developed for the estimation of the dynamic characteristics of an annular center-grooved squeeze-film damper. In this theory, the center groove is treated as a damper with large clearance, and analytical solutions of land part and groove one are connected at their boundaries. This analysis illustrates that the pressure at the groove part is not negligible ; it arises in a 90-degree phase-shifted direction against journal whirl velocity, and causes a large inertia force even at small damper Re number. The results of the analysis show good agreement with the measured values in the 1st report

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It is well known that vibration is induced on elastic tube wall downstream of stenosis, but the mechanism of this vibration is not understood completely. In this research, displacement of wall vibration was measured to obtain knowledge about this vibration. Two gap sensors were installed at same longitudinal position to measure the displacements of opposite side. Differentiating and adding these displacements, components of flexural and wall bending vibration were separated. By this mensurasion, peaks observed in the frequency spectrum were deduced to be each vibration. The wall bending vibration was studied into detail, and the following conclusion was derived. Forming natural mode of wave length 2, the vibration is locally induced on elastic tube wall downstream of stenosis. The peak frequency depends on both character and transmural pressure of the tube, but not on Reynolds number, severity and geometry of stenosis. So the tube character of cylindrical shell is essential to the vibration on elastic tube wall downstream of stenosis.

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This paper deals with parametric vibration of an elevator caused by variable stiffness of the guide rail. The guide rail is lined with rail brackets which are arranged at equal intervals. The rail is stiff on the brackets, but soft between the brackets. That is to say, the elevator cab vibrates because the stiffness of the rail varies periodically. The elevator cab vibrates in the transverse and rotational directions. We calculated the stable and unstable regions of this two-dimensional vibration, and confirmed the results by experiment. The elevator cab vibrates with large amplitude when the frequency of stiffness variation of the rail is twice the natural frequency of the elevator cab. The softer the rail is, the more the cab vibrates. If the stiffness of the rail is at least three times as high as the stiffness of the guide roller, the elevator cab will hardly vibrate. We also examine the effect of damper. If there is a little damper, we can sufficiently prevent this parametric vibration. According to these results, we indicate a design method for prevention of the parametric vibration of an elevator.

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We present analytical and experimental studies on the stability of an axisymmetric body which vibrates with one degree of freedom of translational motion in a narrow annular tapered passage. The leakage models are three divergent passages and one parallel passage. For the divergent passages, the angles of the wall surface of the outer cylinder to the axial direction are negative, zero and positive. When the flow rate of water is gradually increased or decreased, `the damping ratio of the system and the critical flow rate at the stability boundary are measured under conditions of the variable natural frequencies. If the angle of the wall surface is negative, it is necessary that area ratio of the exit to the inlet used in the calculation be smaller than the designed passage because the leakage flow separates from the wall surface. From the agreement between the experimental and calculated results, we conclude that the theory on the damping ratio is reasonable. The calculated results for the nondimensional critical flow rate increase linearly with for increasing natural frequency. When the flow rate is decreased, the theoretical results for the critical flow rate agree well with the experimental results.

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Experimental studies have been conducted on the traveling wave mode of a liquid free surface in a cylindrical weir. Three test weirs, two types of inner and outer tank in which the test weir settled, and water were used in the experiment. The influence of the secondary overflow in the weir was found to be significant on the circumferential wave number of the traveling mode, and on the regions of vibration. A model which can be used to describe the continuity of the traveling mode is presented for the case when a secondary overflow exists.

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A middle-load thermal power turbine generator frequently exceeds its critical speed, and it must be balanced at the critical speed carefully. Also, it is desirable to thermally balance the generator rotor at a factory to reduce the shaft vibration stroke caused by a load change at rated speed. In particular, when the generator capacity exceeds 500MVA, the generator rotor shifts from the secondary mode to the tertiary mode, and the in-phase unbalanced sensitivity increases due to the thermal bending of the shaft and other causes. As a result, thermal balancing is required in addition to conventional mechanical balance. This study presents a method for adjustment in order to decrease the thermal vibration stroke. By analyzing the kind of thermal cause in vibration phenomena and diagnosing the rotor condition with a vibration measuring equipment, it was possible to predict the cause of the thermal vibration and decrease its stroke. By this method, a satisfactory vibration level was achieved for 600MW∼700MW class turbine generators.

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In this paper, a method of electromagnetic levitation control of a thin steel rectangular plate (length : 800mm, width : 600mm, thickness : 0.3mm) with free edges is prerented. To carry out fundamental investigation of the restraint of elastic vibration of the plate, the steel plate is reinforced by plastic beams at two opposite edges. This plate is supported in a contactless manner by attractive forces of five electromagnetic actuators which are controlled by feedback signals from five gap sensors to stabilize the levitation behavior. The optimal control theory and the suboptimal control theory are applied in this study. To verify the usefulness of these methods, experiments in which the optimal digital control theory was applied were performed. As a result, it was confirmed that these control methods were very effective in levitating the plate, and it was further observed that the spillover of residual vibration modes was restrained by applying the suboptimal control method.

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We report a hydraulic active mass damper (AMD) system based on the optimal control theory, combined with a Kalman filter. The study was carried out to try to improve the conventional optimal control AMD system by reduction of detected signals required, spillover prevention and reduction of the low frequency mass movement due to wind load. A design method using a Kalman filter was developed for the system. Simulations and experiments showed the advantages of the combined system. The effects of the Kalman filter design parameters and structure model errors on the performance characteristics were investigated and system design guide lines were established.

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To suppress the low-frequency vibrations of large space structures, the possibility of using a proof-mass-based actuator is discussed. In order to avoid instabilities caused by the effect of the actuator's own natural frequency on the low-frequency components of the structural vibration, it is proposed that the only control force be the electromagnetic force generated by the actuator and that there be no mechanical spring between the moving and the fixed parts of the actuator. In this configuration, it is easy for the moving mass of the actuator to exceed the stroke limit, so the actuator must be controlled to avoid these limits. Using the proposed actuator, three kinds of intelligent control methods are considered in order to achieve reliable control of the low-frequency vibrations : fuzzy control, dithered fuzzy control, and rule-based crisp control. Simulation and experimental results show the effectiveness of the proposed control algorithms.

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The theory of design optimization based on stability maximization of the passive gyroscopic damper (PGD) is discussed and applied to the stabilization of a ropeway carrier. The design formulae exactly maximize the degree of stability of the linearized model, which is defined as the negative of the maximum value of the real part of the characteristic roots. The new design is analyzed using the linearized model of the PGD and the nonlinear model in order to investigate the practical characteristics of the formulae. It is found that the transient responses are almost the same as those of numerical optimization designs. The new design formulae are very simple, but the response is improved compared to those obtained using previous linear designs. The formulae have been successfully used to design a V-gimbaled PGD for a full-scale ropeway carrier. The step responses of this test are presented.

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This paper deals with the active power flow control of a simply supported thin plate. Particular emphasis is placed on the vortex power flow pattern that has the potential of confining external energy, a cause of exciting vibration modes, into a restricted area and of diverting the power flow out of a specific region where vibration is to be prohibited. With a view to observing the power flow occurring in a plate, a wave visualization system has been developed. Based upon the visualization system, it is verified experimentally that the vortex power flow can be produced at an arbitrary position of a plate. An energy stream function as well as a vorticity function is derived in a general form. Furthermore, both the energy stream and vorticity functions are calculated as a function of vibration modes which are selected in the order of magnitude of their contribution to the total kinetic energy of the plate. As a result, as many as 100 vibration modes are found to be necessary to form a vortex power flow pattern.

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This paper concerns design methods of optimal placement for locating sensors and actuators on flexible beams. Recently, modern control theory, which is based on the LQ control or H_∞ control theory, has been applied to control the vibration of flexible strutures. However, most of reports are concerned with model reduction and spillover problems, but few reports have discussed whether located sensor/actuator of the flexible structures are suitably placed for the designed controller. Therefore, it is necessary to consider optimization through the entire design procedure including sensor/actuator placement. In this paper an iterative algorithm is proposed to search for the optimal sensor/actuator placement for stabilization of flexible beams. This method is based on the steepest descent techniques using sensitivity analysis and output feedback control. It is shown that the system controlled by the proposed method improves closed-loop performance in frequency domain,

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A new multi directional bending and expanding motion actuator for a microsystem is proposed, and the static and dynamic experimental results are reported. This flexible actuator is composed of multi layered PZT unimorph cells. These cells are arranged vis-a-vis alternately with three micro pillars. Each PZT electrode is divided into three sectors and the sectors facing each other are connected electrically. Multidirectional bending is realized by single, double or triple driving of the sectors. Dimensions of the 40-cell actuator are 12mm in diameter, 20mm in length and 6.4g in weight. Static tests showed that the bending angle was 2.1 degrees with no load. The expansion displacement was 700μm with no load when all electrodes were simultaneously charged with 150V. Dynamic tests showed that the characteristic frequency was 95Hz at 25V.

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We describe a postural stabilization of a unicycle which has a swinging arm to stabilize rolling motion. The equations of motion for a nonholonomic constraint system are derived, and the equations are linearized and separated into two subsystems which are associated with pitching and rolling motions. The control system is based on the digital optimal theory and the state variables are estimated with finite-time settling observers using the data obtained from the internal sensors. The deviations of the state variables and their estimation errors caused by the sensing errors are evaluated. Experimental results show that the proposed swinging arm system is useful for the postural stabilization of the unicycle, and the finite-time settling observers are effective for estimating the state variables.

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The driver's seat of a heavy-duty truck is usually supported by a spring-damper assembly on the cab floor. This passive suspension isolates the driver from vibration of the cab floor effectively except for a 2 to 3 Hz vibration, which still leads to an uncomfortable ride for drivers ; thus it is desirable to achieve isolation from this low-frequency vibration. To improve riding comfort of the driver's seat, we propose a newly designed active suspension system, where an actuator is installed in parallel with the spring-damper assembly. The actuator is constructed using a DC servo-motor and ball-screw mechanism. A dynamic model of the seat is represented by a two-degree-of-freedom system including a cushion, but influences between foot and floor, arm and steering wheel etc. are neglected. The control system is designed using optimal control theory to minimize rms acceleration of a driver's hip point (seat cushion surface). In this system, accelerations of the hip point, the seat frame and the cab floor are measured and integrated to obtain the state variables to be fed back and fed forward. An experimental study was carried out on a shaker realizing vibration of the cab floor of the truck, and the active seat suspension system achieved satisfactory performance for the human body.

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This paper presents a study on traction force control of an electric vehicle using fuzzy reasoning. The electric vehicle treated here is a motor-in wheel system, and it is regulated by the traction force at each wheel independently. The yaw moment of the electric vehicle is regulated by changing the right or left motor torque. The simulation study indicates that the handling and stability of the vehicle, and the slip prevention of tires are improved by the fuzzy reasoning.

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This study investigates, experimentally and analytically, the polygonal wear of truck/bus and car tires and elucidates the generation mechanism of polygonal wear caused by the first natural vibration mode of the tire in the vertical direction. In the analysis, the phenomenon is modelled as a time delay system accompanied by wear in which the amount of wear of the tire is fed back as forced displacement in the vertical direction after the time period of tire rotation. The progress of the polygonal wear of the tire is very slow and is caused by unstable vibration in the steady-state wear process generated in the limited regions where the products of polygonal numbers and the rotational speed of the tire are less than the natural frequencies of the tire system. The tire is deformed almost to the shape of a regular polygon when polygonal wear occurs. Good agreement between experimental and analytical results concerning the occurrence of polygonal wear of the tire was confirmed.

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To increase the reliability of a roller overlapping friction feeder, the paper traction forces created by the feeder have been estimated, and the paper double feeding mechanism has been studied. Paper traction forces depend on the position at which paper is delivered and increase in proportion to the number of sheets of paper which are fed into the roller overlapping mechanism. The ratio of the area of the double feeding papers to the overlapped area depends on traction forces.

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This paper is concerned with LMI-based H_∞ control and H₂/H_∞ control. We have designed an LMI-based control system for a milling AMB spindle, and compared its performance with that of conventional H_∞ control. The LMI-based control system for this AMB system is designed by taking into account unknown higher-order flexible modes and unknown disturbances of the plant. The state space model for the full-order system of the flexible rotor is derived using the finite element method. Also, the reduced-order model for the controller design is obtained by eliminating every flexible mode of this rotor because the operating speed of this rotor is below the first bending mode. After designing the continuous-time LMI-based controller with the eighth-order which is similar to conventional the H_∞ controller which is reported by us through adjusting frequency-dependent weighting functions. We digitized the continuous-time LMI-based controller to the discrete-time LMI-based controller using a bilinear transformation method. We have carried out a rotation test up to 45000rpm. We conclude that the LMI-based H_∞ control and H₂/H_∞ control systems for the milling AMB spindle has good performance and robustness compared with a conventional control system.

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We deal with motion planning problems for nonholonomic systems. Our approach is based on optimal control algorithms. First, we formulate motion planning problems for nonholonomic systems as trajectory optimization problems, which are (singular) optimal control problems. Next, we develop a new algorithm for (singular) optimal control problems, and prove its convergence property. Finally, applying the algorithm, we solve the motion planning problems for nonholonomic space robot systems, and show the efficiency of the proposed algorithm.

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Human reliability in a complex system has been studied to establish safety systems by analyzing the operator's performance in a control room of a nuclear power plant. In this paper, results of a mathematical model and a questionnaire given to plant designers and operators led to the proposal of a fuzzy tool for evaluating the quality of recent automated control systems. The first report described a method which is capable of calculating human performance by summing the weighted utility of attributes. The modified fuzzy measures learning identification algorithm (FLIA) reduces a set of attributes until human tasks are represented clearly. A change in the performance is illustrated on a two-dimensional map of the dominant attributes as a function of the automated level. The designers and the operators determined the balance of the manipulated/automated phase on the map after careful individual interviews. In the present paper, we attempt to interpret the boundary with a cluster-analysis theory, where the Euclidian square distance and the nearest-neighbor method are applied. The evaluated aspect of the boundary on the map can be divided into the manipulated/automated phase. It is shown that the calculated boundary is equal to the vertical bisector between the center of gravity of the clusters. The analytical boundary agrees precisely with the questionnaire result.

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This paper discusses an approach for detecting not only a contact point between an environment and a robotic finger, but also the local stiffness of the environment where the finger makes contact. We assume that the environment's stiffness is three dimensional with coupling terms, whereas most the conventional studies have assumed a one-dimensional spring as an environment model for simplification. When a finger confirms that there exists considerable compliance, the finger tip is pressed against the environment and starts several active pushing motions in various directions to eventually obtaining the stiffness matrix. After the stiffness matrix is obtained, the initial contact point can be evaluated by using the measured stiffness matrix. The overall concept is also verified by experiments utilizing a wire-driven robotic finger.

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Present electrical servo systems are sensitive to environmental hazards such as electromagnetic noise and radiation. To avoid such influences, it is effective to use laser beams and optical fibers. Our purpose is to develop an optical servo system in which an optical signal is used as a control signal in part or all of the system. In this paper, we describe the development of two types of optical servo system which consist of a photo-fluidic interface, two tested double-acting booster amplifiers, a pneumatic cylinder and an opto-optical encoder. One type is the cart position control system in which the optical signal is fed back directly, and the other type is that in which the optical signal is fed back indirectly. As the result of experiments on these systems, it is shown that the cart positioning in which an optical control signal is fed back directly can be realized by using dither generated in a booster amplifier. In the tested servo system in which an optical signal is fed back indirectly, the position control performance can be improved using a P-controller to compensate the friction, compared with the direct feedback type.

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This paper proposes a new system for analyzing the shearing process using the visioplasticity method. This visioplasticity method is well known as a method for analyzing the metal deformation processing. Drawbacks to the grid method such as large deformation cannot be treated, time-consuming, Processing procedure is complex when image processing by computer is performed, have been overcome with this newly developed method. This newly developed method consists of the following steps. First, images of materials at an arbitrary stage and the following stage are input into the computer. Next, the displacement between the two stages is obtained by a correlation methed based upon the inverse Fourier transform of the phase difference between two images. By repeating this process, the whole forming process can be analyzed accurately in a short time under a wide range of deformation. In order to verify this proposal, practical shearing tests and the analysis of these tests using this system were carried out. As a result, the distribution of displacement and strains until a very large plastic deformation of the material could successfully be obtained.

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We describe the improvement of a miniature two-dimensional optical scanner for wide-area optical scanning and low-voltage driving. First, the bending and torsional fracture stresses of a fine leaf spring made of single-crystal silicon were experimentally determined. They were 1 GPa for bending fracture and 0.3 GPa for torsional fracture, and a fatigue fracture tendency was also observed. Based on the determined fracture stresses, an improved two-dimensional fine leaf spring resonator, wherein the wing part of the previous resonator was removed to reduce air resistance, was developed. Also, an additional mass was put on the mirror to create torsioal and bending moments. Secondly, the shape of a moonie actuator, which magnifies the transverse strain of a piezoactuator more than 10 times, was optimized by FEM analysis to produce a large displacement with a low-voltage drive. Consequently, a miniature two-dimensional optical scanner 5mm×10mm×2.2mm in size was developed, which can scan from forty degrees to eighty degrees with a 15-volt drive.

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The ball bearings supporting an unbalanced rotating shaft have oblique inner rings as well as rotating radial load because of shaft bending and unbalanced force. The generating mechanism of the forces acting on the retainer of the bearings is analyzed theoretically and compared with the results of experiments. The forces act on the retainer when the difference in the excursion between the ball and retainer exceeds the sum of pocket and riding land clearances of the retainer. The method of controlling the forces using the retainer design is applicable under any operating condition of ball bearings.

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The present paper proposes a method of analyzing the motion of planar link mechanisms with revolute and prismatic pairs which have clearances and friction. In order to analyze the motion of mechanisms precisely while considering the influences of clearances and friction upon it, the contact state at each pair is discriminated in this analysis. Routines for searching the contact state at each pair are found, which are applied individually to each pair and utilize only the local information of geometric and dynamic states at the pairs. An algorithm for motion analysis of planar linkages is shown. The effectiveness of the proposed method has been investigated using an illustrative example of a slider-crank mechanism.

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A numerical method based on a finite volume approach has been proposed to estimate the rotordynamic forces on an eccentric labyrinth seal. The general orthogonal coordinate system is applied to the Reynolds averaged Navier-Stokes equations in order to accommodate the geometry of interest efficiently. The SIMPER algorithm and the low Reynolds number κ-ε turbulence model are used to compute the complex turbulent flow field within a seal. To verify the validity of the proposed method, the turbulence in a three-cavity labyrinth seal with an inlet swirl has been calculated. The results are compared with the experimental data in previous reports, and good agreement is found. It is shown that the details of the flow field near each labyrinth fin should be rigorously taken into account to estimate the rotordynamic forces accurately, and that the labyrinth fin has more effect on the tangential force component than on the radial one. The proposed method has been proven to be an effective tool for estimating rotordynamic forces.

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The behavior of oil films formed between two types of nitrile rubber seals and an oscillating glass plate is examined by means of optical interferometry. The friction force is also measured. The average oil film thickness takes a maximum near the center of the stroke and minima at both ends of the stroke, and their values increase with increasing reciprocation frequency. The friction force is markedly influenced by the thickness of oil film; generally, the thicker the oil film, the lower the friction force. In particular, the aeration produced at the oil side region near the end of the motoring stroke results in a large increase in the friction force in the succeeding pumping stroke. The results obtained are explained based on the inverse hydrodynamic lubrication theory and the observed oil film behavior.

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Lubrication in space machines is very important and is being developed world wide. However, to date, lubrication methods developed have not met with the requirement of the space industry. Many troubles of space machines have been caused by tribological problems in the past. In this study, therefore, we propose a new lubrication method called Tribo-Coating for space machines to answer requirments, and we prove its effectiveness from a view point of tribological properties such as low friction coefficient and long life. Optimum combinations of mating materials and lubricant for this method are selected using a pin-on-disk test machine with the tribo-coating system, and the effects of lubricant thickness and surface roughness on friction properties are investigated under optimum conditions. As a result, a minimum friction coefficient of 0.02 and a life-span of 350 000 cycles are obtained by tribo-coating film of 70 nm thickness in one application. Furthermore, using the tribo-coating method, the possibility of unlimited life method of low and stable friction coefficient are suggested. Finally, we propose an empirical formula for the design of tribo-coating of recommendable friction pair.

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Crossed helical gears are engaged geometrically in a point contact between two tooth surfaces, but this contacting point changes to an elliptic contact due to elastic deformation of tooth surfaces under applied load. Therefore the contacting area of two tooth surfaces is small, so that the Hertzian pressure on the tooth surface is high. Since the sliding speed is also very high, the limiting load for scoring is low and the amount of wear is comparatively high. Although crossed helical gears can transmit only light load, they have many advantageous features : e. g., crossed helical gears are easy to produce and mounting error has no effect on engagement. Therefore, in practice, on of the major problems is finding a way to increase the load-carrying capacity of crossed helical gears. In this study we examined the limiting load for scoring, specific wear and friction loss of crossed helical gears with various kinds of surface treatments. We found that the influences of surface treatment and lubricating oil on the limiting load for scoring are very strong, which is useful in practical applications, particularly from the viewpoint of power transmission.

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This paper reports on line contact skew gears, one of which is a spur gear, where the angle of the gear axes is free. Firstiy, characteristics and space image of limit normal of general skew gears are clarified. Secondly, characteristics and space image of limit normal of skew gears, one of which is a spur gear, are clarified. Thirdly, development expressions of directions of various lines and specific sliding of general skew gears are led. Finally, development expressions of directions of various lines and specific sliding of skew gears, one of which is a spur gear, are led.

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In the present tooth geometries, rotational motion of a gear pair with variation of angular velocities caused by errors and deflection cannot be analyzed because the ratio of angular velocities is always given as a premise. In the present models of dynamic load, rotational motion of a gear pair is not sufficiently approximated because the fundamental requirement for contact is neglected ; thus the calculated results are not reliable. To solve these problems, a new theory on tooth contact and dynamic loads is presented in this series of papers. This first paper introduces a new tooth geometry that can deal with rotational motion of gears with errors and deflection. Namely, the two axes and their common perpendicular determine the static coordinate systems in which a point of contact and its common contact normal are arbitrarily given and described as functions of angle of rotation by using the instantaneous planes of action that include the common contact normal and are parallel to each axis, and the ratio of angular velocities at each point of contact is obtained from the fundamental requirement for contact. When the points of contact and their common contact normals are transformed to the coordinate systems rotating with each gear at the obtained ratio of angular velocities which varies with the rotation of gears, a pair of tooth profiles is obtained.

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For a point of contact and its common contact normal given through the new tooth geometry, equations of motion and the bearing loads of a gear pair are presented. Analysis of the bearing loads clarifies that the conditions under which a pair of tooth profiles has no variation of bearing loads are as follows : (a) the path of contact must be a straight line which coincides with the common contact normal at the point of contact and must be fixed in static space, and (b) the ratio between angular velocities must be constant and coincide with that between input and output torques. This indicates that the variation of bearing load is composed of both the variation of static load due to violation of condition (a) and that of rotation due to violation of condition (b), the former of which has not been discussed in previous theories of dynamic load. Condition (a) indicates that the pair of tooth profiles corresponding to the straight path of contact must lie on involute helicoids and a pair of tooth surfaces must include the pair of tooth profiles and be modified to make contact along it, which explains why the choice of the tooth surfaces and the tooth bearing corresponding to the tooth profile greatly influences the noise and vibration of gears for power transmission.

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A dynamic model of a helical gear pair has been developed taking the kinematic properties of the shafts and bearings as well as mesh excitation into account. The model can be used to describe transverse, rotational, tilting and axial vibration of gears, that is, the gears are assumed to be vibrating in six principal directions, three for translational motion and three for swing motion. To introduce mesh excitation into the equation of motion, the properties of the shafts and bearings are considered to be concentrated at the center of the gear bodies and are modeled in terms of a suspending spring and an additional mass besed on Rayleigh's principle. Then the tooth mesh stiffness was modeled in terms of two parallel springs which varies temporally with a certain phase relationship due to the helix angle. The differential equations are numerically solved using the Runge-Kutta-Gill method. The results are in good agreement with experimental results with respect to the major resonance frequencies and amplitudes.

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The objective of this research is to develop a CBN (cubic boron nitride) hob that can finish medium-to high-hardness gears accurately and efficiently. The cutting performance of the CBN hob has been investigated by cutting tests using a fly tool. Fly tools with the chamfered cutting edges were used in previous experiments. The chamfer is effective to prevent chipping of the cutting edge. However, the chamfer has a tendency to accumulate dead metal and, as a result, the finished surface becomes rough. In this study cutting tests using fly tools with rounded cutting edges are carried out. The roughness of finished surfaces and the durability of cutting edges are compared with those obtained using the chamfered tools. A rounded tool with a radius of curvature of about 0.03 mm shows excellent cutting performance.

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The potential drop method is applied to the measurement of fatigue cracks in a gear tooth. First, the relationship between the direct current potential drop and the crack length is calculated by the boundary element method (BEM), and the influence of the positional errors of terminals, probes and crack on the potential drop is discussed. From this result, an expression is obtained for estimating the crack length a from the normalized potential drop V/V₀. The alternating current potential drop V is measured during fatigue crack growth in a gear tooth. The potential drop V is approximately proportional to the square root of the current frequency f. The normalized potential drop V/V₀, which is defined using the potential drop V₀ for an uncracked tooth after loading, is fairly close to the result calculated by BEM. The value V/V₀ slightly depends on the current frequency f.

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The complex variable integral equation has been applied by Hirano to solve plane stress problems. This paper presents a new mathematical approach to the formulation of integro-differential equations and simple formulae for analyzing the stress and displacement distributions at internal points in gears using a conformal mapping technique. In addition to setting up a system of linear equations for calculating the complex stress functions, we show how the conformal mapping function that transforms the gear domain into a half-plane is analytically obtained from the viewpoint of complex variable analysis.

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In recent years, the general trend is to minimize the carbon content of austenitic stainless steel for the enhancement of corrosion resistance and the restriction of the formation of carbides. Despite the wide use of low-carbon SUS 304, basic research on the machinability of these materials is rare. In order to clarify the effect of carbon content on the machinability of SUS 304, the relationships between the carbon content and mechanical properties, carbon content and cutting characteristics are investigated and the mechanism by which drill life is shortened with high-carbon SUS 304 is examined. The following results are obtained from this study. A sharp drop in drill life with increasing carbon content occurs for austenitic stainless steed. The tensile strength, the yield strength and the shearing energy of high-carbon SUS 304 are higher than those of low-carbon SUS 304. In addition, the work hardenability of high-carbon SUS 304 is larger, and as a consequence, the cutting forces and the cutting temperature increase, leading to drill wear and a higher propensity for chip adhesion and consequently, shorter drill life. Work hardening of the upper layer of the drilled surface of high-carbon SUS 304 is severe compared with low-carbon SUS 304. The shorter drill life associated with drilling high-carbon SUS 304 is attributed to the high hardness of the work-hardened layer over a greater depth.

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In the cutting process, chatter vibration greatly restricts the accuracy and efficiency. Establishment of an objective and practical method which can be used to estimate the commencement of chatter is necessary in the field of automatic manufacturing systems and dynamic performance tests of machine tools. However, qualitative estimation of excitation mechanisms of mingling regenerative with parametric vibrations has not yet been investigated. In this study, therefore, the estimation of transient vibration is investigated for the turning process, by a statistical method. Chatter instability is predicted by theoretical analysis. The results are confirmed by excitation and cutting tests. Furthermore, the generation mechanism of transient vibration is elucidated experimentally. The results obtained from this study are as follows : The excitation mechanisms of mingling regenerative and parametric vibrations are clarified qualitatively. The transient area between parametric and regenerative vibrations can be estimated qualitatively. The point of chatter vibration commencement can be estimated qualitatively in the turning process.

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We present the effects of a unique magnetic abrasive behavior on finishing characteristics in a new internal finishing process applying magnetic abrasive machining. In this process, the abrasive shows two kinds of unique behavior depending on the finishing conditions. One is that the magnetic abrasive adheres over the entire inner surface of a tube. Once this occurs, the relative motion between the magnetic abrasive and the inner surface of the tube ceases. This results in zero finishing force and internal finishing becomes impossible. This phenomenon occurs when the magnetic force of the abrasive is low and the tube is rotated at high speeds. The other behavior is that the magnetic abrasive moves spontaneously in the finishing zone. This behavior stirs the cutting edges of the abrasive, encouraging the metabolism of the cutting edges. It is experimentally verified that this behavior is indispensable for increasing the finishing efficiency in this process.

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A new deep drawing process for laminated sheet metal is developed to eliminate unfriendly environmental factors from a can manufacturing system. This new dry forming process is carried out without using coolant/lubricant and take advantage of the good sliding property of polyester film. The main purpose of the stretch draw forming is to reduce the thickness of the body walls by more than 20%. From Experimental results on wall thickness reductions, optimum regions of die radius and blank holder radius in the stretch draw forming are determined as 1.1 <Rd/to<3 and 4<Rh/to<12, respectively. As far as any wrinkling or breakdown occurs, a higher backward tension on the body wall, which can be controlled by the blank holding force, is effective to achieve a high reduction in cup wall thickness. The limiting reduction rate of wall thickness is related to the material strength.

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The multiaxis machining technology using a non-rotating cutting tool can produce a well-finished surface with little machining damage or roughness, and can be used to remove the remaining material in a concavity formed by the ball nosed end mill. This technique will extend the machining limits beyond the processing capability of the rotating tool. However, the single-blade non-rotating tool does not have a long life nor a flexibility for cutting various shapes. Therefore, a cylindrical non-rotating tool with long life and multiusability has been developed. This tool machines using a sharp blade having a wide curvature which gets shape by its inclination toward the feed direction. The cylindrical non-rotating tool can precisely machine a wide surface always with a sharp portion of the blade, because it can perform cutting at an arbitrary position on the blade due to spindle axis turn positioning. On the other hand, non-rotating machining with μm-scale cutting depth requires more precise CL data than is necessary with a rotating tool. If such CL data are generated by existing methods, a greatly increased quantity of data results, and more time is required to generate an offset surface. However, the copy simulation CAM method for multiaxis machining has been developed, which makes it possible to calculate highly precise CL data without offset processing. The imaginary stylus of this copy simulation CAM method traces on a surface of the defined shape while it self-determines the distance and course to the defined shape. Therefore, it is easy to determine the necessary tool axis vector for multiaxis machining, and the present method can generate highly precise CL data for non-rotating cutting. Results of machining experiments with this CAM method and the cylindrical non-rotating tool show that (1) it was able to get a good surface with approximate roughness of 2μmRy by smoothing machining, (2) it was able to completely removed material remaining in the concavity formed by a ball-nosed end mill, (3) the non-rotating tool and copy simulation CAM method for multiaxis machining can significantly extend the machining limits.

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