This paper presents a method for analyzing three-dimensional curved rods of general shape without symmetric axes. In the analysis, the exact solutions of the equlibrium equations for three dimensional curved rods have been obtained first, then the transfer matrix has been derived based on the exact solution with consideration of inertia forces. The analytical equations for finding the eigenfrequencies and mode shapes have been given. Numerical calculations have been carried out for three dimensional circular, elliptical, and parabolic spiral rods of circular and square cross sections without symmetric axes.

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A mathematical model of an isolated blade of a horizontal axis wind turbine generator is presented to describe coupled motions of flap, lag and torsion of the blade. An energy approach is employed to derive Lagrange's equation of motion. The blade is considered as a pretwisted beam of variable cross section to calculate kinetic, dissipation and strain energy. Quasi-steady blade-element strip theory is applied to compute the aerodynamic force which accounts for boundary layer shear winds and wind speed reduction due to tower shadow. The resulting equations, which have time-dependent coefficients, are numerically solved to show steady-state response and stability of the blade. Wind tunnel tests were conducted using a l/25 scale model to ascertain theoretical predictions. Comparisons indicate a fairly good agreement between them.

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This paper deals with the experiment of the flow induced force of interlocking type labyrinth seals. The test apparatus was made so that the shaft could rotate and whirl at the same time in the seal for obtaining the dynamic properties. The test was performed on a multi-stage labyrinth seal such as is used in a balance piston or a center seal in a centrifugal compressor. After ascertaining the data accuracy, the leakage flow was measured, and the dynamic properties were also measured by changing whirl speed, whirl amplitude, rotating speed, entrance swirl velocity and pressure difference. The measured force was separated into the tangential force (stability force) and radial force (restoring force), and their characteristics are discussed and compared with straight-type seals.

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The intended aim of the paper is to provide the scope of the effect of an attached damper upon the stability of a cantilevered viscoelastic tubular pipe conveying fluid. The effect of the damping coefficient of a damper is investigated in detail in connection with the position of the damper as well. It is found that a damper attached to a thin pipe may have a little stabilizing effect on the pipe. Any damper attached to the pipe at the discharge end may be most destabilizing. A lumped mass accompanied by a damper may be destabilizing. The theoretical predictions were checked by some experiments.

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Theoretical studies on the dynamic stability and active control of cantilevered pipes conveying fluid are conducted. In order to control the response of the cantilevered pipe, an active control force is derived by the torque produced by a pair of tendons attached to the pipe. The problem is solved by means of the Galerkin method, in conjunction with the optimal regulator theory. The effect of a tendon on the stability of a cantilevered pipe conveying fluid in the uncontrolled system is clarified. Furthermore, the effect of the internal damping is taken into consideration in the present study. The numerical simulation of the response of a cantilevered pipe conveying fluid is also carried out for various conditions. It is found that the active tendon control method is effective to stabilize the cantilevered pipe conveying fluid, even if the control input is limited.

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A theoretical and experimental study is presented for the displacement control of a one-link flexible arm with an end-point payload. The tip displacement of the arm is sensed by the gap-sensor fixed in space and controlled by a D. C. motor located at the other end of the arm. where the motor is driven by a feedback signal composed of the tip displacement and velocity. As an example. the problem of shifting the end-point of the arm from its initial position to the desired position by the amount of ω_t is considered. Theoretical results are obtained by applying the method of the Laplace transform to the governing equation. and the solution is obtained by the method of numerical Laplace inversion. Experimental results are obtained and compared with the theoretical ones, from which it is shown that both results are in good agreement for a wide range of parameters.

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This paper discusses a direct method for possible nilpotent Jordan matrices of state deadbeat controllers. The relation between the indices which are defined to obtain a nilpotent Jordan matrix and the degrees of the blocks of a nilpotent Jordan matrix is explained through a figure. By using this figure, a simple equation which shows the relation between the controllability indices of the system and the degrees of the blocks is derived. Then, all possible nilpotent Jordan matrices which are similar to the system matrix of the feedback system controlled by a state deadbeat controller can be directly obtained only from the controllability indices of the system.

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This paper shows that the average and variance of the accumulated damage caused by earth-quakes on the piping system attached to a building are related to the seismic response factor λ. The earthquakes refered to in this paper are of a non-stationary random process kind. The average is proportional to λ² and the variance to λ⁴. The analytical values of the average and variance for a single-degree-of-freedom system are compared with those obtained from computer simulations. Here the model of the building is a single-degree-of-freedom system. Both average of accumulated damage are approximately equal. The variance obtained from the analysis does not coincide with that from simulations. The reason is considered to be the forced vibration by sinusoidal waves, and the sinusoidal waves included random waves. Taking account of amplitude magnification factor, the values of the variance approach those obtained from simulations.

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This paper describes theoretical results and experimental investigation on the stabilizing effect of a flexible cylindrical journal bearing which is composed of a thin sleeve simply supported at three angular points. Numerical analysis method was developed in the previous paper to compute the instability threshold of a rigid rotor and flexible bearing system by solving simultaneously the equation of motion of the rotor, sleeve deflection equation and modified Reynolds equation which includes film rupture effect in the negative pressure region. It is found from the calculated results that a thin sleeve journal bearing has a stabilizing effect in a large eccentricity ratio, as the flexibility of the sleeve increases. From the experimental study on instability of a flexible rotor supported by the flexible thin sleeve bearing a remarkable increase in threshold speed can be found in the large eccentricity ratioregion as predicted by the theory.

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The dynamic behavior of a geared system may mainly depend on the torsional vibration, however, sometimes a coupled influence with its support system may not be neglectable. In spite of many recent theoretical papers in this field of interest, a typical behavioral system rule of this coupled system is not yet well discussed compared to the torsional behavioral system rule. This paper deals with this translation coupled dynamic system rule of a geared stage concerning the DOLF (K_A) frequency region and a rather high DLF (K_v) frequency area employing the normal mode method and the receptance operator technique.

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A theoretical and experimental study is presented for the damping of curved beams with an unconstrained viscoelastic layer. Natural frequencies and loss factors of flexural vibration are calculated for various boundary conditions, when a beam of the constant finite length is bent cylindrically. Boundary conditions considered in this paper are simple support-simple support, free-free, clamped-clamped, hinged-hinged and clamped-free. It is found that the loss factor of a curved beam changes complicatedly as the subtended angle increases. This behaviour may be divided into two groups according to the type of the boundary conditions and the modes of vibration; as the subtended angle increases, the loss factor for symmetric modes of clamped-clamped and hinged-hinged beams changes remarkably and behaves complicatedly, while that for all modes of free-free, simply supported-simply supported and clamped-free beams and antisymmetric modes of clamped-clamped and hinged-hinged beams changes slightly. This difference could be verified experimentally for curved beams with clamped-clamped and clamped-free ends.

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This technique uses a new type of intensity probe which consists of two microphones arranged side by side and which are slid back and forth by a small distance in the direction of the microphone axes. This probe is turned twice on its holder axis by steps of a fixed angle for measuring the three components of an acoustic intensity vector. It is the purpose of this paper to investigate, theoretically and experimentally, the error of the sound propagation direction measured by this automatic measurement technique. This error can be calculated from the measurement theory of the probe and the theory of fundamental errors in the acoustic intensity method. The calculated results agree fairly well with the measured ones. These results show that the error in measurement of sound propagation direction is influenced by the incident angle and frequency of the sound incident to the probe. The limit of the error due to these effects was clarified.

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Particle velocity is sampled at discrete points on a plane surface located close to the sound source. The farfield radiation is obtained by regarding the plane as the virtual vibrating surface. By using this method, farfield radiation patterns were evaluated for a point source on a rigid spherical baffle in air, and were compared with the real patterns obtained by solving the helmholtz equation. Moreover, radiation patterns for a point source on a rigid cubic baffle were evaluated from the measured particle velocity, and were compared with the patterns obtained by measured patterns in a free field. Through a theoretical model and an experiment, the accurate range of this estimation is discussed.

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In view of the troublesome nature of impact sound, a series of studies have been undertaken in order to find out a way to reduce this effect. This fourth report concerns the generation of impact sound at the impact side when a ball collides with a plate. Simply, a ball including a small accelerometer was collided with a freely suspended square steel plate. The pulse-like ball acceleration during the impact, the vibration of the plate, and the impact sounds at the impact and the anti-impact sides were measured simultaneously. These signals were stored in a wave memory instrument and analyzed by an FFT analyzer. From the results of analysis and considerations, it was found that the sound of the pulse at the impact side was composed of the direct sound and the reflected sound from the ball, and the sound due to the deformation velocity of the plate, etc. As a result, the generation of impact sound at the impact side has been clarified.

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An experimental expression of the restoring force of a tire compressed by a flat plate and a dull edge is derived. Using this expression, equations of motion of a light truck that runs over a low bar-like projection placed normal to the direction of the motion of the truck are set up. These equations are solved by a numerical method in the situation that the left-hand wheels of the truck run over the projection. Based on the solution, the force applied to the road by the truck in this situation is calculated. Experiments are made to measure the force applied. A force-measuring device equipped with a force-receiving flat top plate is settled in the road with the top plate flush with the road surface, and a bar-like projection is attached to the top plate. The force is measured when the left-hand wheels of the truck run over the device. It is concluded that the results of calculation show good agreement with those of experiment.

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As a working medium of the externally pressurized porous bearing, air is generally used. The reason why liquid is not adopted is due to the high flow resistance of usual porous materials for the bearing. Lately, a new porous metal made by pressure casting has been developed. This material has the advantage that flow resistance can be controlled by varying pore size and porosity. Furthermore, pores are not crushed by machining. Hence, it is intended to utilize this material for the externally pressurized oil bearing. The bearing performance is analyzed against a thrust bearing with land surface assuming one-dimensional Darcy's flow in the porous structure. The experimental results of pressure distribution on the bearing surface and load capacity coincide well with calculated values. This porous bearing can replace equivalent capillary resistor bearings.

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An experimental investigation is carried out to study the unbalanced whirl of herring-bone grooved gas journal bearings. The unbalanced whirls of both the cylindrical mode and the conical mode are measured individually by arranging the gap sensors at the appropriate positions along the rotor, and the relation of rotating frequency and whirl frequency is shown by measuring the acceleration of the bearing. These experimental results are compared with the theoretical predictions. This paper also describes the influence of the rotor centrifugal expansion on the whirl characteristics.

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This paper deals with how one can estimate the vibrational behavior of gears enclosed in a gear case by measuring the exterior vibration, i.e., the acceleration of the pedestal, through experimental investigation. In order to compare the vibration of gears with the vibration of a pedestal, accelerations of all principal directions on both gears and pedestals were measured simultaneously. It has been found that the accelerations of pedestals are well correlated to the ones of gears, especially to the rotational one. That is, the transfer function between the acceleration of the gear and the acceleration of the pedestal is necessary for the estimation. It proved that the transfer function obtained through the impact excitation while the gear unit endures a static torque without rotation is applicable to the dynamic estimation of gear vibration.

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For the purpose of clarifying the influence of tooth errors on the vibration behavior of power transmission helical gear pair with comparatively narrow face width, the nondimensional equation of the rotational motion has been numerically solved taking several kinds of errors into account. And the performance diagrams on vibration have been introduced, in which the acceleration level is shown by contour lines on the contact ratio plane which is formed by the transverse contact ratio (abscissa) and the overlap ratio (ordinate) . It has been made clear that the influence of the errors on the vibration depends upon the kind of error as well as the contact ratio and the rotational speed.

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The dynamic behavior of bevel gear type · differential gears was investigated under various gear operating conditions, using a power circulating type differential gear testing machine, by measuring the torque variations of the drive and driven shafts, and the tooth root stresses of a hypoid gear. In this experinent, two driven shafts of differential gears were equal in revolution. In comparison with these measured date, the dynamic characteristics of differential gears became clear.

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Successive indentations of ring-shaped lead specimens by a rack-shaped punch are investigated experimentally by various methods to form the teeth of ring gears. Most of the indented materials are found to flow in the circumferential direction to cause an increase in the ring diameter. In order to produce ring gears with moderate accuracy, it is most important to conform the acting surface of the work holder to the current inner surface of the ring during working. Metal flow is examined by the visioplasticity method during indentation. The roundness error and pitch error of the produced ring gears are also examined by using the approximated correction method.

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Carbide hobbing is suitable for high efficiency production with excellent hobbing precision, and moreover, it can make it possible to cut hard material gears. Recently it was been adopted by factories of automobile, electric and gear production. To decrease the cost of the tools, the authors want to lengthen the life of the carbide hob. In this paper, we report on the carbide hobs made by the PVD methods. For determining the life of carbide hob, the authors examined the effect of coating on carbide hobs. The results are as follows: (1) Coating a carbide hob of PVD methods can delay the occurrence of flank wear on a carbide hob. (2) It can delay the microchipping on a cutting edge with a small entrance. (3) It can delay the large chipping on a cutting edge with a large cutting volume. (4) It can delay the thermal crack on a cutting flank edge.

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In grinding operations, the accuracy of the shape of works depend on many elements, and hence, it is very difficult to compensate for them to improve the accuracy of these shapes. This paper is concerned with the periodical chage of work-revolution and the work-deviation from circularity to be sucessfully applied to active shape control in grinding operations. A summary of the results is shown below. 1. The work-deviation from circularity is in proportion to the maximum deformation of the grinding process and the change ratio of the periodical chage of work-revolution. 2. The speed of work-revolution is determined by three parameters, which are average work-revolution, maximum deformation and measuring output of a work shape. 3 . As the experimental results, it is found that the control of the speed of work-revolution is very effective for improving the accuracy of the work-deviation from circularity.

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This paper considers a shape determination problem of beams which are subjected to given random, loads. taking into consideration its dynamic responses. The optimum, shape is considered as one which minimizes the expected value of the strain energy that will be induced in the structure for a constant volume. A beam is discretized into finite elements and the method of modal analysis is applied to obtain its stationary response against Gaussian excitation. In the numerical treatment, an approximate method for sensitivity analysis is proposed and it works effectively with the use of a convenient optimization procedure by the "Energy-Ratio-Method". A considerable reduction of the expected value of strain energy is accomplished by several iterations of shape reformation. When the beam is supported symmetrically at both ends and is subjected to a concentrated load, the obtained beam has a symmetric shape with respect to Its central cross section, independently of the location of the load.

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This paper describes a computer orientated method to transform any arbitary region of a curved surface from 3-D to a flattened form. The strategy is based upon a modification of the plane stress problem of the finite element method. Several applications are presented. One is a pattern shell which has traditionally been used by footwear pattern engineers and another is a flattened form for the corresponding airplane model.

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This paper considers a man-machine system consisting of some numerically -controlled (NC) machines and a single worker. This system processed many kinds of items. The role of worker is loading the workpieces on and unloading the workpieces from machines. In such a system design, it is an important problem to determine the number of machine5 to be operated by the worker. First. we formulate the system as a stochastic model to analyze the above optimal problem. The desicion variable is the number of machines and the optimal criteria are 'the maximum production rate', 'the minimum total cost', 'the maximum profit rate' and 'the maximum return's rate of operating cost'. It is shown that the optimal numbers under these criteria depend on only the utilization of the worker. and hence the minimum total cost, and the maximum return's rate criteria are the same. It is proved that there exist the optimal numbers under these criteria if the worker's utilization is a concave function of the number of machines used. Furthermore, an ordering between the optimal numbers under the minimum total cost and the maximum profit rate criteria is suggested theoretically. The validity of the concavity and the ordering is established by many numerical experiments. The applicability of the results to practical problem is discussed via a case study.

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