In the present paper, vibrations in a rotating clampedfree disc under a static in-plane load and with constraint on the outer periphery are analyzed. A solution for the equation of motion is described by the series of orthogonal eigenfunctions of a nonrotating disc with the same boundary conditions. By the use of the orthogonality of the eigenfunctions a characteristic equation is obtained. The relations between the natural frequencies and an angular velocity are shown. Also, these between regions of instability of the free vibrations and the magnitude of the static load are shown.

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This paper presents a method for obtaining the frequency equation for a circular plate with a number of eccentric circular inner boundaries. In the analysis, the exact solution which satisfies the outer boundary conditions was applied, and the inner boundary conditions were satisfied by means of the point matching-method under consideration of the symmetry of the vibration modes. Numerical calculations were carried out for a clamped circular plate with two or four eccentric circular clamped edges and for the plate with two eccentric annular supports.

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A stability analysis for a uniform elastic rotor filled with incompressible, inviscid liquid is presented. The authors consider small dynamic perturbations in the asynchronous whirling of the coupled fluid-structure system. A complex eigenvalue problem is derived for the natural whirling modes in order to discuss the rotor stability criteria. As a result, the theoretical predictions show fairly good agreements with experimental results. The effects of the length-diameter ratio of the rotor on the stability criteria are also discussed on the basis of the natural modes of the liquid.

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The transient vibration due to imbalance of a lightweight rotor that comprises flexible blades, disk, shaft, and rigid bearings is analyzed by a finite element method. The dimensions of matrices used in the computation are reduced by representing the shaft and blades by beam elements, and the disk by annular elements. The computed results are compared with the experimental data obtained by a test conducted on a small model rotor with a blade loss simulator. A fairly good agreement was obtained between the computed and experimental results.

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The concept of the transfer influence coefficient method is extended and modified so that it is applied to the free vibration analysis of systems with variable parameters. In the present modified transfer influence coefficient method, four dynamic coefficient matrices are introduced to analyse the free vibration of a beam with a variable cross-sectional area. Since the solution of every differential equation for the dynamic coefficient matrices has poles in the domain of integration, the numerical integration of the field transfer rule is executed by selecting an adequate differential equation from among them, whose solution is not h pole at every integration point. The results of the simple computational examples on a personal computer demonstrate the validity of the present algorithm; that is, the high numerical accuracy and the high speed of the present method, as compared with the transfer matrix method.

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Nonstationary vibrations of a flexible rotating shaft with nonlinear spring characteristics during acceleration through a critical speed of a summed-and-differential harmonic oscillation were investigated. In numerical simulations, we investigated the influences of the angular acceleration λ, the initial angular position of the unbalance Ψ_o, and the initial rotating speed ω_s on the maximum amplitude. We performed experiments with various angular accelerations. The following results were obtained : The maximum amplitude depends not only on λ but also on Ψ₀ and ω_s. When the initial angular position Ψ_o changes, the maximum amplitude Varies between two values. The maximum and the minimum values of the maximum amplitude do not change monotonously for the angular acceleration. In order to always pass the critical speed with a finite amplitude during acceleration, the value of λ must exceed a certain critical value.

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The present report describes a theoretical analysis of the thermally induced bending vibration of the thin-walled boom with tip mass subjected to solar radiant heating. The governing equation and the time-dependent boundary conditions are formulated assuming that the boom is heated by the unidirectional solar radiation and that net absorption depends on the angle of incidence of heat radiation with respect to the boom. The methods of solution consist of applying the Laplace transform with respect to time to the equation and to the boundary conditions, and of obtaining the response by a numerical inversion of the transformed solution. Stability of the system is studied using the root locus, and the unstable boundary curves, which divide the parameter plane into regions of stability and instability according to the direction of radiation and four system parameters, are also studied.

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When a shaft rotates resisting a certain load, the rotating shaft must undergo bending and torsion simultaneously. The driving torque on such a rotating shaft influences the whirling motion of the shaft. This paper presents an analytical study of the effect of the load torque on the whirling vibration of the rotating shaft. Equations of motion are derived with an accuracy of the second order for the deflection and the torsion, and are analyzed by using the. asymptotic method. The analyses produced the following results. The effective damping coefficient for the whirling vibration can become negative when the viscous damping coefficient of the torsional vibration is larger than that of the lateral-reciprocal vibration. In this case, the whirling vibration of the rotating shaft assumes an unstable state. The damping coefficient for whirling vibration of the shaft in an accelerated rotation differs from that in a decelerated rotation.

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A new concept and method of vibration reduction of a rolling piston-type compressor for a room air conditioner is proposed. To suppress the compressor vibration due to the excit of the torque, the torque control method using a microcomputer control which makes the motor output torque nearly equal to load torque variation by means of gas compression of the compressor at each angular position through one revolution is applied. Theoretical analysis and computer simulation show that the control method in which the rotational variation (fluctuation of speed or acceleration) for one revolution caused by the load torque and transmitted to the motor output torque at the next revolution due to the cyclic characteristic of the compressor load, that is to say, "repetitive control" can be adopted. Thus reduction of compressor vibration is possible.

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The liquid in a liquid storage container, e. g. an oil, tank, starts to vibrate in earthquakes and other cases. This paper describes an active adaptive control method to suppress this liquid sloshing vibration avoiding the liquid container from being damaged. This study considers a nonlinear friction between the liquid container and the ground. We propose the usage of an adaptive observer, which is based on a basic model of the container. This model is considered the first order vibration mode of the liquid in a vertical plane. The efficiency of this control method for suppressing the liquid sloshing vibration has been shown by simulations and experiments.

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An antiresonance is formed by attaching a dynamic absorber to a vibratory system. Even if the exciting frequency shifts, the antiresonance can be retained by adjusting the parameters of the absorber. In this paper, the frequency, phase, and amplitude of the antiresonant point are theoretically investigated. The transient response is also investigated. For the actual use, the antiresonance is obtained by keeping the phase lag between the main system and the absorber to be tan^-1(1/2ξ₂), (ξ₂: damping factor of the absorber). Usually the damping must be small, but it should be increased only when the tracking has a delay and the sytem passes through the resonance.

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A method is presented to suppress an unbalanced vibration of rotors supported at both ends. In this method, only one end of the rotor is supported by a spring and a damper, and the bearing box mass m, the viscous damping coefficient c and the spring constant k in the support are determined in order to suppress the rotor amplitude by applying the theory of dynamic absorbers. In this case, the rotor supported by the spring-damper needs to be replaced by the equivalent two-degree-of-freedom system. Two approaches for the replacement, that is, an analytical and an experimental approach, are developed. It is found from the experiment and the numerical simulation that the spring-damper support with m, c and k obtained from both approaches suppresses the rotor vibration very well. The characteristics of both approaches are shown.

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This paper describes vibrationless acceleration control for hard-disk drive positioning mechanisms. This control accelerates a flexible positioning mechanism to a certain acceleration without the transient vibration that prolongs the settling time and decreases positioning accuracy. We first describe how we derive the solution to optimal acceleration control based on optimal control theory. We then discuss results, and apply this control to the operation of a practical 5.25-inch magnetic disk drive.

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This paper deals with the flexural wave control of a flexible beam. It is the purpose of this paper to present a new vibration control method, the active sink method, which makes it possible to suppress all vibration modes of the flexible beam. Unlike the conventional vibration modal control method, the active sink method is designed for making all the vibration modes of the beam asleep. First, this paper presents the principle of the active sink method and shows a means of realizing it. Then, in order to describe the principle mathematically, a transfer matrix of a beam using a progressive wave solution to the wave equation is obtained. Moreover, based upon the transfer matrix method, the optimal conditions for the active sink system are derived, the fundamental characteristics of the system being discussed. Finally, from the viewpoint of vibration intensity analysis, the validity of the active sink system is clarified.

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The stochastic response spectrum approach is presented for predicting the dynamic behavior of structures to earthquake excitation expressed by a random process, one of whose sample functions can be regarded as a recorded strong-motion earthquake accelerogram. The approach consists of modeling recorded ground motion by a random process and the root-mean-square response (rms) analysis of a single-degree-of-freedom system by using the moment equations method. The stochastic response spectrum is obtained as a plot of the maximum rms response versus the natural period of the system and is compared with the conventional response spectrum.

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In the stress analysis of sinusoidal vibration response under the base excitation, a modal analysis combined with an attached large mass called the large-mass method is widely used. The problems associated with this method are the truncation errors and evaluation of the arbitrary nature of the attached mass. The proposed method employs the modified mode acceleration method considering load equilibrium and the modal transformations. This method has no large arbitrary coefficients of mass and can estimate the excitation reaction force effects. Examined for a simplified Spacecraft model, the proposed method needs only 10 modes to achieve satisfactory accuracy; with the conventional method, more than 60 modes are necessary for the same.

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Evaluation of time-integration methods should be done from the viewpoint of the response to the external force as well as the response to the initial value. Only a few studies have been performed on the former, whereas many have been conducted on the latter. Thud, the objective of this study is to establish a theoretical method which can evaluate the accuracy of the solution when the response to a sinusoidal force is solved by time-integration methods. As the first step of this study, a method to evaluate the accuracy of the numerical solution to a sinusoidal input is proposed. Based os this method, some famous time-integration methods are evaluated; typical examples of evaluation results are shown in this paper.

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To find a numerical solution to the two-dimensional buckling equation, we use Richardson's second-order extrapolation formulae with the finite-difference methods. The two-dimensional buckling equation is treated and rewritten as follows : forth-order partial derivatives + unknown coefficient·second-order partial derivatives = eigenvalue·warp function. When the eigenvalues become zero by searching for the corresponding values of unknown coefficients, we can obtain the numerical solutions as the warp functions with arbitrary scale.

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In present-day experimental modal analysis, multi-point force excitation techniques, where structural vibration is considered as a multi-input/output process, are often used. This paper deals with the study of base excitation modeling by modal analysis. First, multi-point random excitation techniques and curve-fit algorithms for multi-directional base excitation data, are studied. These methods are then applied to the microtremor data of boiler plant structures in thermal power stations. The identified modal parameters are shown to be in good agreement with those of FEM. As a result of these investigations, this kind of modal analysis has proven to be an effective tool for seismic modeling of large-scale structures.

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In the typical structural optimization method, the structural eigenvalues or eigenvectors are modified in order to avoid various problems caused by the resonances. In this case, the optimization is done on frequency domain. However, in some cases the time history response is more important than the characteristics on frequency domain. In this paper, the optimizations of both natural mode and impulse reponse are performed by modifying the thicknesses and the nodal coordinates of the structure with the FEM model. Firstly, the theory of the optimization method is explained. Secondly, we apply this method to the optimization of an rectangular plate. The optimization of a natural mode and a impulse response are achieved. Finally, we combine this method with the component mode synthesis method in order to enable us to optimize the large structural systems.

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A Study on a multi-objective optimum design method applying qualitative reasoning to a part of the optimization process is proposed. A single-objective optimum design problem is solved by a monotonicity analysis, and then with the information of active constraints sets, we add these constraints to the objective function and turn the problem into a multi-objective optimum design problem. Qualitative reasoning is modified to be able to make use of the qualitative information which gives an approximate direction of the optimum search and saves the number of the iteration for optimization. It appears from the structural optimum design of an antenna that the proposed method is applicable for the optimization of complex systems, since an optimization can be easily carried out even with inadequate quantitative information.

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In this study, a hydraulic servo system is considered to be theoretically expressed in the fifth-order, and the gain margin of the fifth-order hydraulic servo system was calculated in terms of the natural frequency ratio of load to servo drive with various values of load-damping ratios and inertia ratios of load to servo drive. The experiments were conducted with various values of load stiffness and inertia of the hydraulic servo system to compare with the fifth-order theoretical model. It was found that the theoretical results showed good agreement with those of the experiments. It was also found from the theoretical model that the natural frequency ratio of load to servo drive must be greater than unity for a servo system to be stable. The relationship between the natural frequency ratio and the inertia ratio for a servo system to have optimal response was qualitatively clarified.

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This paper proposes a new method for rotor dynamics calculations, called the transfer coefficient method, which is more convenient than the conventional transfer matrix method. By treating only the displacement as the independent variable, where both the displacement and the force are considered as independent variables in the transfer matrix method, this method promises a substantial saving of computational time without loss of the accuracy of calculation. There are two types of transfer coefficient methods. In the first, the coefficients are treated as independent of the vibration frequencies, while in the other, the coefficients are considered dependent on the frequencies. Formulation of a fundamental rotor system and applications for either type are discussed in detail with a bearing box, a branched system, and a multi spool system as examples.

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This paper describes the tip displacement of a flexible miniature arm controlled by the piezoelectric bimorph cells cemented on the surface of the arm. The arm is driven by the torques generated by the cells, and the endpoint of the arm is controlled so that it moves in synchrony with the fluctuation of the target and maintains a constant distance to the surface of the target. The voltage applied to the cells is controlled by a feedback signal composed of the tip displacement and the velocity. A theoretical solution is obtained by considering the cell-arm system as a stepped beam and applying the time-discrete method to the governing equations of the system. Experimental results are obtained and compared with the theoretical ones. Both results are good agreement for a wide range of physical parameters involved.

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A manipulator with three joints and one flexible link is shtidied. The flexible link is modeled as a spring element capable of torsional deflection and bending deflection. The equation of motion is deduced using Lagrange's principle. The optimal regulator and kalman filter are designed for a specified configuration of the manipulator. It is verified through simulation and experiment that the designed controller is able to control both vibration and position when step input of reference angle is applied. It is, then shown that fixed feedback gain control leads to instability or insufficient damping of vibration. Symmetry of manipulator dynamics enables the use of one feedback gain matrix at four manipulator configurations, if the specified rows and columns are assigned the proper sign. With feedback gain matrices calculated at several manipulator configurations, fast control of position and vibration is obtained for the manipulator workspace.

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To a given double pendulum system whose parameters are unknown and whose output is limited, this paper relates two methods driving the second arm of the system from its natural pendant position to the right-up position. In this system, one-swing movement refers to when the second arm starts and ends with speed 0. The swing-up movement can be considered to be the combination of the one-swing movement. First, giving a required output over a finite time interval for one-swing movement, we can obtain a required input by using the learning control method proposed in this paper. Repeating this operation, the required inout to swing the arm to the inverted position may be constructed. However, the following control method may be effective if the required input can be obtained by system simulation even if the actual system parameters are different from those of simulation. In any case, the effectiveness of both is assured by experiment results.

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A new measuring method of displacement by means of variations of sound frequency and length of the air column in a closed resonant pipe has been investigated. This paper deals with the theoretical analysis of this device as a small and closed edge instrument (for example, a dog training whistle or a closed organ pipe). The electrical analogous circuit of a closed edge instrument was introduced for theoretical analysis. In the calculation, the velocity distribution of blown air on the mouth of the instrument was adopted. The results of the calculation of theoretical equations and experiments coincide significantly.

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The fundamental characteristics such as bearing stiffness and damping coefficient of an externally pressurized gas journal bearing with groove compensation are analyzed theoretically for the angular-mode displacement of the shaft. The equivalent clearance model is applied in the analysis to formulate the gas flow in the bearing clearance. The angular-mode characteristics of the bearing are discussed on the basis of the calculated results. It is especially noted that negative bearing stiffness or negative damping coefficient may be encountered at some cases with angular-mode displacement of the shaft.

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This paper describes the analysis of the air damper used for the variable reluctance magnetic thrust bearing. We previously investigated the variable reluctance magnetic bearing and noted that this magnetic bearing has many advantages compared with other types of bearings : neither the high-pressure gas nor the control circuit are needed. However, this bearing does not generate a damping force by itself and the motion of the rotor is unstable without a damping force. Therefore, some mechanism which generates the damping force is essential to the operation of this bearing. The air damper accompanies the bearing to supplement the damping force and consists of the neumatic capacitor and the neumatic resistors. The chamber arranged between the rotor and the fixed elements operates as the neumatic capacitor. The narrow radial gaps between the rotor and the fixed elements operate as the neumatic resistors. In this paper the theoretical analysis of the air damper is carried out. Also, an experimental analysis is performed and the results are compared with the theoretical predictions. In the suspension consisting of the magnetic bearing and the air damper, a damping factor as large as 0.2 is achieved.

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Recently, for the plastic gears being assembled in sound apparatuses, those having lower noise are desired. For this purpose, it has been attempted to use plastics filled with plasticizers for gears. When plasticizers are filled into plastics, the viscosity increases, while the strength and wear resistance decrease. However, these has been doubt expreassed as to their practicality. Therefore, in this study, gears were made of a material formed by nylon filled with moret than 10% plasticizers. The effect of silencing was confirmed, and the basic characteristics of the gears, such as the wear of teeth and the change of the tooth profile, were experimentally examined.

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A study of the mechanics of the South-Pointing Chariot with the bevel gear type differential gear train was conducted. Firstly the pattern of this South-Pointing Chariot is replaced with the combined planetary gear system in which two simple planetary gear trains are connected. Secondly, through theoretical analysis, it is confirmed that power circulation occurs in the system. Thus the principle that fulfills the fundamental function of the South-Pointing Chariot is explained. Thirdly, it is confirmed that this analyzing method could be applied to the mechanical variable-speed drive which uses the combined planetary gear system.

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Seizures occur when oil with solid lubricants such as graphite, molybdenum disulphide are used for sliding. The purpose of this paper is to solve the mechanism of seizures between carbon steels in oil with dispersed graphite. The main results obtained are as follows : Seizures depend on the surface roughness, that is, the smaller the roughness, the more the seizure. Friction coefficient during seizure is less than 0.25. Graphite powders dispersed in oil cause seizures due to the lack of oil at the contact between surfaces as a result of the running-in process. A minimum friction coefficient for a 5 vol.% graphite content exists.

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Recently, in attempts to improve the automobile fuel economy, various measures such as improvement of engine thermal efficiency and a decrease in vehicle weight have been undertaken. It is necessary to improve the efficiency by not only using lower viscosity gear oil, but also by making clear the power loss in automotive drive train. This paper proposes a method for measuring the power loss in automotive drive train which is based on the temperature rise of the lubricant due to the friction in the drive train. The applicable limit of this method is made clear. Namely, in the case that the lubricant temperature and difference in temperature between the lubricant and the wall increase as time increases, the power loss can be used to calculate the difference in the rate of lubricant temperature both with and without an element. Applying this method to an automotive axle, the effect of input torque, speed and lubricant temperature on gear loss was made clear.

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In designing bolted joints, it is important to know the contact stress and the force ratio (the ratio of an increment of the bolt axial force to an external load). Up to now, some investigations have been carried out on the characteristics of bolted joints with gaskets. However, the compressive spring constants K_cg of the bolted joint in which a clamped part is fastened to a base with a tap bolt including a gasket have not been studied. In the present paper, the characteristics of the bolted joint with a full-face metallic gasket are examined. Replacing a clamped part, a gasket and a base with finite hollow cylinders, respectively, the contact stress distribution, the force ratio and the compressive spring constants are analyzed using a three-dimensional theory of elasticity. In the experiments, the force ratio is measured and the contact stress is measured by an ultrasonic wave. Analytical results are in fairly good agreement with experimental results. In addition, a simple calculation method to obtain K_cg is proposed.

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It is well known that the life of TiN-coated hob becomes tremendously longer than that of non-coated hob. But even a TiN-coated hob, its rake surface must be must be resharpened when it was womn out. And then TiN-coating on rake surface is removed but only on flank surface. And TiN-coating on flank surface is still effective to decrease the flank wear. On the contrary, crater wear on rake surface of TiN-coated hob increases, same as that of non-coated hob. So, in high efficiency hobbing, the life of hob seriously depends on the crater wear. Here, the authors have clarified the effect of re-coated hob in case of high efficiency hobbing of the comparatively small module gears with TiN-coated and multi-start hobs that fre ofen used for motorcycles and automobiles. as a TiN-coated hob was used and then resharpened, only the rake surface can be re-coated with TiN layer and after that, it can attain the same cutting performance as a new TiN-hob. The most effective method to increase the life of TiN-coated hod and its cutting performance is to re-coat it after resharpened.

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This paper presents the modification of the 3D shape using the finite-element method. When designing a curved surface, we need to have modification processes. We have already developed schemes to modify a curved surface by means of reforming flattened shapes. We now use FEM for modification of 3D-curved surfaces as the next step and propose two methods to modify subregions of a curved shape using FEM. The first is based on the magnification ratio of coefficients of linear expansion and the second uses the normal vectors of elements. To illustrate the usefulness of the method, we apply them to a sphere and shoe model as typical applications.

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In the laser machining of ceramics, it is difficult to avoid the formation of a recast layers and cracks. These deffects significantly spoil some excellent properties of ceramics. This paper describes the feasibility of a crack-free processing method. for hot-pressed silicon nitride (Si₃N₄) ceramics with an yttrium aluminum garnet (YAG) laser. It is found that, in order to attain the defect-free machining, it is necessary to process the ceramics using a laser beam pulsed below 500 ns in duration and 10 kHz in repetition rate.

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This paper describes an experimental study carried out to investigate the relation between the development of stress in a molded polymer and the injection molding conditions. The mold used in the present study had a rectangular cavity constructed with a transparent window on each side : the birefringence patterns in the polymer during the filling and cooling processes were observed through an application of the photoelastic method. The results clearly show that the development process of birefringence in the polymer can be separated into three successive stages : the flowing stage, the relaxation stage, and the cooling stage. The amount of residual birefringence of the molded polymer is determined by both the unrelaxed shear stress in the near-wall region (skin region) and thermal stress due to cooling is the core region. It is concluded that the thickness of the skin region, where the shear stress due to flow of polymer melt is frozen, can be estimated on the basis of the relation between the relaxation time of shear stress and solidification time of injected polymer melt. This consequence enables us to draw a figure which shows the relation between the pattern of residual stress in the molded part and the injection molding conditions.

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An experimental method which enables one to measure directly the temperature distribution developed in a tool during orthogonal cutting is described. The technique depends on the physical phenomenon that any material melts at its inherent and definite melting point. The boundary between the melted and unmelted parts of a thin film deposited on the tool is considered to be an isotherm equal to the melting point of the film and gives the temperature distribution in the tool. The temperature at any position in the cutting tool can be estimated with satisfactory accuracy. Details are given of the method which has been recently developed by the author. Temperature distribution measured when high-carbon steel is cut was found to well illustrate the feasibility of the method under any practical cutting condition.

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For cogeneration systems, a planning method is proposed to determine optimal capacities of constituent equipment together with optimal maximum demands of utilities. The equipment capacities and the utility maximum demands are determined so as to minimize the annual total cost in consideration of the operational policy for the variations of both electricity and thermal energy demands. These design and operational problems are formulated as a nonlinear programming and mixed-integer linear programming problem, respectively. In consideration of their hierarchical relationship by a penalty method, they are solved by means of the generalized reduced gradient method, and the branch and bound method, respectively. Through a case study on a gas engine cogeneration system, the effect of optimization on the annual total cost is investigated to ascertain that more economical merits can be extracted by the proposed method than by the conventional trial and error method.

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