The purpose of this paper is to investigate the applicability of the constrained layer damping theory, which has been widely used for the vibration analysis of sandwich structures with viscoelastic damping layers. This theory proposed by Kerwin contains the following major assumptions : longitudinal direct stresses in the viscoelastic layer are negligible : transverse direct strains in each layer are also neglected ; and all layers displace laterally the same amount. In this paper, excluding these assumptions, the equations of motion of a three-layer sandwich beam are derived applying the two-dimensional theory of elasticity to the deformation of the viscoelastic layer. For simply supported beams, frequencies and loss factors are calculated from the accurate method presented here, and from the approximate method based on the constrained layer damping theory. The analytical results indicate that the approximate method can be used practically in many cases.

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The level crossing problem is discussed for a multi-dimentional nonlinear system subjected to an amplitude modulated nonwhite random excitation. The first passage probability and the probability distribution of the level crossings are approximately represented by a few low order factorial moments of crossings, which are calculated by using the equivalent linearization technique and assuming the Gaussian probability distribution of the response process. The dependence of occurrence of the level crossing upon the number of events is taken into consideration. Numerical results are compared with the corresponding digital simulation results for a single degree of freedom system with bilinear hysteresis excited by noise with an exponentially decaying harmonic correlation function.

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A new technique of identifying a nonlinear multi-degree-of-freedom system has been presented. The basic procedures of this technique are: (1) obtaining the data of a periodic force applied to the system and of the periodic steady-state oscillation induced by it; (2) expressing the nonlinearity of the system in the form of polynomials with unknown coefficients; and (3) determining the unknown coefficients by expressing the necessary quantities in Fourier series and applying the principle of harmonic balance. Some examples are given to demonstrate the validity of the presented technique.

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A power series expansion of the characteristic parameter is obtained in terms of the natural frequency, which is defined as an implicit function in a transcendental equation. It plays a central role in calculating the Fourier coefficient of exact solutions. A general algorithm is proposed to obtain the solution in the power series x=Σ b_nyⁿ to the equation Σ c_nxⁿ=y. The method is particularly effective when m (the modulus parameter of elliptic functions) approaches zero, which corresponds with the quasi-linear small oscillations in those systems with a hard, a soft or snap-through (half-swing mode) spring. The accuracy of existing (simple) approximate solutions to the autonomous Duffing equation, i.e., the perturbation, the averaging and the (two-term) harmonic balance methods, is examined by comparison with the present exact solutions.

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In order to make vibration analysis an easy and automated task for designers, it is desirable to develop interactive vibration analysis systems using personal computers or engineering work stations which have a user-friendly interface for easy input of the vibration model, and which can perform automatic generation of equations of motion, and automatic numerical analysis of them. As the first step towards such systems, an automatic generation system of equations of motion was developed for two-dimensional vibrations of multi-body systems. The system developed is written in Smalltalk-80 which is a typical object-oriented language, and can perform the following : (1) The system has user-friendly interface for graphic input of vibration model which enables users to make figures of a vibration model on the display by choosing the vibration model elements listed in the menu by a pointing device (mouse). (2) The system is applicable to extensive models of two-dimensional vibrations of multi-body systems which contain various constraints and nonlinear elements.

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An exact method using power series expansions is presented for solving out-of-plane free vibrations of inhomogeneous curved bars with varying curvatures and cross-sections. Equations of motion and boundary conditions are derived from the stationary conditions of the Lagrangian of curved bars. Natural frequencies and mode shapes are presented for elliptical and circular arc bars having both ends clamped and clamped-free ends.

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An exact method using power series expansions is presented for solving axisymmetric free vibration problems for thick shells of revolution having meridionally varying curvature. Based on the improved thick shell theory, the Lagrangian of the shells of revolution are obtained, and the equations of motion and the boundary conditions are derived from the stationary condition of the Lagrangian. The method is applied to thick shells of revolution having their generating curves of ellipse, cycloid, parabola, catenary and hyperbola. The results by the present method are compared with those by the thin shell theory and the effects of rotatory inertia and shear deformation upon the natural frequencies and the mode shapes are clarified.

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This paper proposes an oil damper with a variable damping mechanism. The piston of the damper has a fan-shaped orifice as a flow channel of oil. The magnitude of damping can be regulated continuously by varying the area of the orifice. Another merit of this damper is that its damping can be regarded as viscous, enabling a theoretical approach to be used in its study. We have analyzed the oil damper by assuming the flow of oil to be laminar and oscillatory However, it is too difficult to obtain an analytical solution from the basic equation, so the analysis was accomplished numerically using the finite difference method. It was confirmed that the theoretical results agree well with the experimental ones.

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This paper deals with an optimum design method of the squeeze film damper used to suppress rotor vibration. At first, the dynamic characteristics of the squeeze film damper with end seals are introduced by the modified conventional short bearing theory. Then, an improved method to determine the optimum damping coefficients of the damper is shown, based on the complex eigen value analysis. To confirm above methods. an analysis of and experiment on the test rotor are carried out with respect to parameters such as radial clearance, end-seal clearance and oil temperature. Both are in good agreement and this method makes the design of the optimum damper possible.

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This investigation deals with the seismic response analysis of a pipe-support system with friction characteristics. The friction characteristics are assumed to be as the Coulomb friction model. This paper highlights, particularly, the effect of friction forces upon the maximum response of the piping system subjected to random excitations including seismic motions as follows. (1) The maximum response of the piping is generally suppressed by the growth of friction force. (2) The response reduction factor based on the maximum response of the linear piping is proposed. This factor can be obtained only through the ratio of the natural period of piping to that of the supporting structure. (3) The other response reduction factor is proposed. This factor is based on the maximum linear piping response for the least feasible condition where the natural period of piping coincides with that of the supporting system. The maximum response for other than the least feasible condition can be obtained by using this factor.

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Most of the previous research work on engine speed hunting has been devoted to discriminating the divergence of a small disturbance given at an equilibrium state, resulting in a hunting frequency estimation different from that of the actual system. In addition, it is impossible to predict whether limit cycle would occur or not. In the author's previous report, a numerical simulation was given, which showed a transient process of a small oscillation developing into a sustained oscillation with a large amplitude. For a better understanding, however, it is desirable to be able to get the amplitude and frequency of hunting analytically. In the present report is given a linear approximation considering a phase lag of the subventuri pressure responding to the engine speed fluctuation. The results show that this linear theory surely predicts the instability of an equilibrium state at higher idling speeds, but riot the stability at lower speeds, and gives the hunting frequency almost correctly ; but the calculated value of the logarithmic increment of amplitude at the largest hunting state is twice that of the nonlinear simulation.

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A driven shaft system consists of a shaft with circular section and a rotor. The flexible shaft is supported by a universal joint at one end and a bearing at the other end. When a drive shaft rotates with a constant angular velocity, the driven shaft is subjected to the angular velocity fluctuation governed by a joint angle between the drive shaft and the driven one. However, when the driven shaft vibrates laterally and causes bending in itself, the joint angle is slightly changed and the rotating speed deviates. That is why the lateral-torsional coupled vibrations become unstable at the same time. These unstable vibrations occur when the drive shaft rotates at a speed of nearly half as great as the sum of the natural angular frequency regarding the lateral vibration and that regarding the torsional vibration.

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The effects of pressure difference between both ends of journal bearings, mean radial clearance and bearing length on the stability threshold speed are investigated experimentally. A testing apparatus to measure the stability threshold speed is constructed. A symmetric horizontal flexible rotor is supported by a rolling bearing at one end and by a test bearing block at the other. The test bearing block is composed of two identical cylindrical journal bearings with a full circumferential groove between them, and oil is supplied into the groove at high pressures. It is found that experimental results are in good agreement with the theoretical results described in the preceeding reports. It is also found that the theoretical analysis taking into account the pressure drops mainly due to the axial acceleration of the oil at the inlet end of the journal bearing is confirmed to be applicable to the stability analysis of a flexible rotor supported by journal bearings with pressure differences.

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The malfunction of induction disk type relays under earthquake conditions is caused by rotation of the disks induced by seismic excitation. The rotation of the disk results from torques generated by friction forces between the thrust bearing supporting the pivot at its bottom and the lower end of the pivot whirling in the bearing due to seismic excitation. This mechanism of malfunction was revealed by the authors and analysed in the former paper. In this paper, modification of the shapes of the bearing and the lower end of the pivot is proposed, to reduce the torques. The effectiveness of the modification was verified by both excitation tests and theoretical analysis. Furthermore the maximum accelerations of seismic excitation inputs having various dominant frequencies which did not cause the malfunction were investigated by analysis, and it was shown that an improvement of 1.3∼2.0 times in the maximum accelerations was obtained by the modification.

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This study concerns the seismic design of a cylindrical liquid storage tank with rigid foundation resting on elastic soil subjected to earthquake ground motions. The study is composed of the following two main parts: (a) the derivation of a vibration model for a cylindrical tank as a super-structure, and (b) the derivation of a whole vibration model for a tank-foundation-soil system, and the seismic response computation of the system. The previous paper dealt with the former part(a). This paper deals with the latter part(b), and describes, (1) the derivation procedure of a whole vibration model of a cylindrical tank-foundation-soil system, (2) the application of modal analysis to the derived model, and (3) the proposal of a conventional seismic design procedure for a cylindrical liquid storage tank with rigid foundation resting on elastic soil to earthquake ground motions.

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This paper presents a method for solving the dynamic response problems of a driven valve system of internal combustion engines. In this system there is a hysteresis behavior between the restoring force and the deflection for the locker arm. To treat this nonlinearity, the rigidity of each section is assumed to be the one of a partly linear spring. For the valve trains, the cam profile is complex in general. For treating a general cam profile, this paper applies a combination method of the Fourier expansion and the Laplace transform methods given by the author. Numerical calculations have been carried out for a sample problem of high speed driven valve trains, and the jump and the bounce phenomena are discussed in detail.

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This paper clarifies the mechanism of the impact phenomena of elastic bars by both wave propagation theory and the concept of mechanical impedance in the frequency domain, and investigates the optimum combination of elastic bars to obtain the maximum restitution. The method of the Laplace transformation is used for these analyses. The relation between the contact time of the col llsion and the mechanical impedance is clarified to obtain the maximum restitution coefficient.

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This study presents the characteristics of the mechanical efficiency and the crankshaft speed fluctuation ratio of various large capacity scroll compressors. To introduce the different suction volumes of the scroll compresor, the scroll height and the involute base circle radius are individually increased proportionally based on a small capacity scroll compressor, and their effects on the mechanical efficiency and the speed fluctuation ratio are discussed. It was discovered that it is better to increase the involute base circle radius rather than the scroll height to obtain higher mechanical efficiency. Also it was discovered that the speed fluctuation ratio is nearly the same, independent of the scroll height and the involute base circle radius.

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This paper discusses a canonical form of a state deadbeat controller for a discrete-time, linear, time-invariant system. A general form of the state deadbeat controller which shows the freedom of design has been obtained ; however, the design parameters have redundancy. To avoid the redundancy, a canonical form which is expressed by the linear combination of independent design parameters is derived for some subsets of the general form. Finally, illustrative examples are given to show the effectiveness of the proposed procedure.

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For the vibration control of a main structure subjected to a random input with a dominant frequency, an active dynamic vibration absorber is manufactured, which is equipped with a linear motor as an actuator and is digitally controlled by means of optimal feedback and feedforward links. First, by performing impulse excitation, the usefulness of the optimal feedback control is verified. Second, in the frequency responses obtained from a stationary random excitation, the effectiveness of the optimal feedforward link is demonstrated in comparison with a feedback link only. Further, in a nonstationary random excitation in which the same nonstationary random wave can be realized every time, it is confirmed that the active dynamic vibration absorber is useful also for nonstationary random input.

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For many assembly operations, a robot hand is required to have dexterity, achieved by position, force and compliance control of high degrees of freedom, as well as tactile sensing. The pneumatic servo control, which was used by the authors to control the force and compliance of artificial fingers and an elbow, did not result in a sophisticated movement with a high response. This problem comes from the lack of airflow control in the conventional pneumatic servo valve. A new type of pneumatic servo system, developed in this study, comprises two analog airflow valves with an electromagnetically driven plunger. Analysis and evaluation of the system are conducted, and examples are given to show how to design an electro-pressure transformer using the system, and to show the force and compliance control of the manipulator-joints.

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The pipeline maintenace robot Mark III with the inch worm mechanism, presented in the 3rd report, can pass over obstacles on pipelines, such as flanges and T-joints and others. For this motion control, the joint control methods for Mark III, especially the optimal trajectory generation are shown in this report. First, this robot system has the modified dual control mode, A and B with the transfer matrices different from the previous method. The control mode is changed mutually when the basic arm grasping the pipe is changed. Second, the static joint torques are calculated to determine the desired transfer matrix, and a configuration which has the minimum joint torques is selected. Third, an optimal trajectory is generated by dynamic programming in order to control joints from the present angles to the desired angles. It has two criteria : joint torques and position errors.

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When a plastic gear is used, there may be a problem as to which is better : intermeshing with plastic gears, or intermeshing with a plastic gear and a steel gear. In the former case, the wear is small since the coefficient of friction of the former is generally smaller than that of the latter. On the other hand, in the latter case, the temperature at the plastic gear becomes lower than in the former case, because the generated heat in the plastic gear conducts to the steel gear with good thermal conductivity, and it dissipates from the steel gear. This is advantageous for the plastic gear since it has a great defect in resistance to heat. In these ways, each intermeshing has its respective merits. In order to further study it in detail, we operated the plastic gear in both intermeshings and investigated the wear of the tooth, the change in tooth form, the temperature at the tooth, and the like.

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The influence of tooth profile modification on the surface durability of spur gears has been studied by using mirror-like finished gears with a high accuracy(=0.1μm R_max, JIS M 00 class). In order to explain the effectiveness of tooth profile modification, the durations of the elastohydrodynamic lubrication condition (EHL) at the point of contact were measured by utilizing an electric resistance method. The results clearly showed that the duration of the EHL condition on gear pairs with tooth profile modification were improved, especially at the first and the last points of contact. Even though low hardness gears are used, it is necessary to modify the tooth profile in order to form the lubricating oil film between the meshing teeth, and to reduce the surface distress.

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The new globoidal worm gear which consists of a wheel having pins and a worm having an arc-shaped groove has been proposed in the previous papers. The efficiency of the worm gear depends upon the oil film formed between the pin and the groove. The oil film formation and scoring resistance between a hardened steel pin of 12 mm dia and an arc-grooved roller of phosphor bronze are investigated. The formation of the film is measured by the electric discharge method and is analysed using FFT. Seven different profiles of the groove are examined and the optimal profile for high efficiency and high scoring resistance is chosen.

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A method for estimating the unbalanced whirl characteristics of herring-bone grooved gas journal bearings by solving the appropriate dynamics equations is outlined. This method covers both cylindrical mode and conical mode whirl, and the interference of the two modes is considered. Here, also, the theoritical analysis for the bearing angular stiffness is presented.

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In this report, two analytical models for a circular thrust bearing with a central supply hole are presented when the gas flow is choked at the inlet to the clearance space. These models are modifiable for an unchoked condition and enable one to analyze the dynamic performance of the bearing over a wide range of design conditions. From the experiment, it is concluded that the effects of the inertia forces are considerable when the feeding parameter is small, and that the presented analyses yield good predictions of both the bearing stiffness and the damping coefficient.

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The running accuracy characteristics of an externally pressurized gas thrust bearing will be theoretically studied in this research in relation to the machining deviations of forms of the bearing and the rotor. For the first step of the research, the load-carrying capacity fluctuation of the bearing, which may result in axial run-out of the rotor, is analyzed in this report. As the factors causing the load capacity fluctuation, two aspects of machining error of the bearing are taken into consideration ; one is perpendicularity of the rotor end surface, and the other is size deviation of the gas supply holes. The point source solution of Reynolds equation yields the load capacity characteristics under these form errors of the bearing.

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In this paper, the dynamic behaviour of oil film journal bearings in turbulent regime is theoretically investigated based on the nonlinearized treatment. The dynamic oil film forces considering the combined effects of turbulence and fluid inertia forces are analytically obtained under the short bearing assumption. The nonlinear equations of motion for a rigid rotor supported horizontally in two identical aligned oil film bearings are solved by the improved Euler's method forward in time. The relations between journal center trajectory and transient pressure distribution are examined for Reynolds numbers of Re=2 750, 4 580 and 5 500 and for the length-to-diameter ratio of L/D= 0.5. It is found that the fluid inertia forces have an advantage of improving the dynamic behaviour of turbulent journal bearings under certain operating conditions.

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For tightening bolted joints, the calibrated wrench method is widely used in practice. In this method the axial tension of a bolt is controled by measuring the wrench torque. However the method is not so accurate since the measurement of axial tension is indirect. In this paper, the statistical distribution of the magnitude of the axial tension in bolts, which were tightened by the calibrated wrench method, was formulated. As an example, the distribution of axial tension was shown for a metric fine screw.

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This paper presents a new method for solving the Reynolds equation with a matrix form, in which the Reynolds equation is reduced analytically without approximation to infinite dimensional linear equations with unknowns related to eigen values of operator R=▽·[(h³/6η)▽]. The paper also presents applications of the method to journal bearing problems under two boundary conditions : one is the half Sommerfeld condition and the other is the quasi Reynolds condition which assures 'continuity of the bulk flow' across the boundary. It will be shown that the present method requires much less computational time than FDM for obtaining accurate predictions.

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Plastics are used widely as sliding parts. In order to investigate the effect of the varied lubricants mixed in the nylon rollers, experimental equipment was designed and manufactured. In the experiment on the friction of the nylon roller, a nylon roller was rotated contacting with a steel roller in the same direction. From the results of the experiments, it was clarified that the lubrication properties, the friction characteristic and the wear resistance differ with each lubricant mixed in the roller, and the limit for use as the sliding parts could be obtained.

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A stress sensor for detecting pressure and frictional stress acting on the roll surface in rolling has been developed. Using this sensor, not only pressure but also frictional stress in the rolling direction and frictional stress in the width direction can be detected at the same time. The measuring performance of this sensor is investigated and an example of the measurement in rolling is shown. The accuracy of the measured data is confirmed.

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This paper describes especially the effect of the static stiffness of a surface grinding machine on the grinding accuracy of fine ceramics (Aluminum Oxide, Silicon Carbide and Silicon Nitride) which are ground by a conventional surface grinding operation. Fine ceramics are ground by two types of surface grinding machines which have different static stiffnesses. As a result, the amount of the residual depth of the cut of fine ceramics is showen to be proportional to the value of the static stiffness of the grinding machine, The static stiffness of a surface grinding machine can be estimated by the residual depth of cut of the fine ceramics being ground.

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Profile shifted (long addendum and short addendum) gears are being used as the latest small sized reduction gears for automobiles. Therefore, the authors have made experiments on hobbing to find out how to lesson the damage of the cutting edge in the case of profile shifted gears. In the case of the hobbing of profile shifted gears, addendum modinfication has greatly influenced hob damage in same-handed climb hobbing. In the case of reverse-handed conventional hobbing, addendum modification has little influence on hob damage : therefore, the reverse-handed conventional hobbing method is suitable for profile shifted gears.

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The tooth surface roughness of hardened and tempered gears has a considerable effect on their surface durability, because the effect of "running-in " is hardly expected. It is very advantageous in terms of economy and productivity that the tooth surfaces of hardened and tempered gears are finished smoothly by hobbing. In this report, a finishing hob with cemented carbide tips is developed, and the roughness and scratch of the tooth surface of the hardened and tempered gears finished with the carbide tipped hob are investigated in detail. Moreover, cemented carbide tips (including cermet, tips) for the finishing hob are selected by the intermittent cutting test of turning and by the fly-tool test on the milling machine. Finally, an improvement of the surface roughness with the finishing carbide hob is discussed.

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This paper deals with the thermal deformation and distortion of a column caused by the temperature variation in a machine shop. In general, the wall thicknesses of the column of machine tools, for example the machining center, are different between the front and rear sides, so the distortion is caused by the variation, that is by the difference of temperature rises between both sides. The behavior of thermal deformation is calculated numerically and analytically. The following results are obtained: (1) The maximum value of the distortion appears in the case of a heat transfer coefficient on the wall. (2) The coefficient is determined not only by natural convection but also by thermal radiation.

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When a ray is projected on an object with nonuniform reflection, the intensity distribution of the reflected ray is distorted, compared with that of the incident one. This paper proposes a new correction method applicable to this case. In the method, the distorted intensity distribution is corrected on the basis of a reflection distribution. The reflection distribution is measured by using a reference light having a uniform intensity distribution. First, a required spectrum distribution is clarified for the reference light, and a permeable band of filter mounted on an TV camera lens is determined. Then, the quantity of blurring at a boundary is found to be in proportion to the intensity difference between areas adjacent to the boundary, and the correction effect in relation to the blurring is determined quantitatively. By applying this correction method to a slit-ray position measurement, it is clarified that distortion is corrected and that the slit-ray position is measured several times more accurately than without correction.

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