Improved methods on the Component Mode Synthesis (CMS) are proposed, using both unconstrained flexible modes and physical boundary displacements as the generalized coordinates, to facilitate the effective application to the dynamic analysis in the structural design procedure. A component can be treated as one of the elements of FEM analysis, if their connection points are in the physical coordinates. But utilization of unconstrained modes makes the analysis sensitive to higher mode truncation effects. The static modes are introduced to compensate for the truncation errors. By using mode orthogonal transformations, it is found that the errors are substantially reduced. Two methods are derived depending on the method of transformation, regulated on either normal modes or static modes. These theories are applied to a simplified satellite model. From these examinations, it is proved that the proposed methods are as accurate as those established methods using constraint modes.

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Vibration analysis of infinite thick rotating cylindrical shells is described on the basis of the two-dimensional elasticity theory. Starting from the state of plane strain, the basic equation in the steady rotating state, which is used to obtain the initial stresses, is derived from Hamilton's principle, and the frequency equation, including the effect of the initial stresses due to the rotation, is formulated by Ritz's method. The numerical results for the frequencies in the non-rotating and rotating state are compared with those based on Timoshenko type shell theory and the available range in the latter theory is examined about the thickness and rotating speed of a shell.

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This paper presents an efficient FEM eigenvalue analysis technique for symmetrically laminated composite plates by using a personal computer. In order to realize the analysis on a personal computer, a 12 d. o. f. ACM element considering the anisotropic behavior of symmetrically laminated composite is formulated and a subspace iteration algorithm is used for the analysis. A shaking test using CFRP symmetrically laminated composite plates is performed to prove the effectiveness of the method. It has been shown from the study that the proposed technique could be of practical use for plates with a wide variety of fiber angle and dynamic coupling between bending and torsion.

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The excitation mechanism of a self-excited oscillation due to the fluid discharge over a flexible weir was investigated both theoretically and experimentally. A new type of hydroelastic instability was discovered during test operations of the Super-Phenix LMFBR reactor in France. According to the recent report by Aita, this phenomenon includes two types of instability modes : one is sloshing mode which means the oscillation of a weir associated with coupled sloshing modes of both feeding and restitution fluid collectors ; the other is a hydroelastic mode which means the oscillation of a weir associated with fluid-shell modes. In this report, the excitation mechanism of a sloshing mode is discussed by calculating the excitation energy brought by discharge to the fluid-structure system. The theoretical results for the range of sloshing mode instability almost agreed with the experimental data.

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This paper presents an analytical method for determining the steady-state response of laminated composite rectangular plates. The bending rigidities are obtained by use of the orthotropic thin plate theory. The Ritz approach is used to yield a governing equation of motion, and steady-state response solution is derived for a simply supported laminated plate. In numerical example, driving point impedance is calculated for three types of FRP (Fiber Reinforced Plastic) materials, and the effects of varying the orientation angle of lamina and configuration of a laminate are discussed.

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When a vertical cylindrical rotor is partially immersed in water and driven at supercritical speeds, the rotor-shaft system is suspected of undergoing an unstable vibration. This paper uses experiments to show the existence of an unstable whirling vibration for a vertical cylindrical rotor partially immersed in water, and its characteristics with respect to the depth of rotor immersion in water and the rotation speed. The unstable vibration was found to occur at supercritical speed for a limited range of water immersion, and its dominant frequency coincided with the natural one of the rotor-shaft system. The visualization of water surface wave around the rotating cylinder revealed that a very peculiar wave traveling backward to the cylinder rotation seems to be a major cause for the unstable vibration.

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An effective and practical Lanczos method is presented for large generalized eigenproblems. The number of Lanczos vectors is determined based on the current relation between the number of vectors generated and the number of converged eigenvalues. Based on the CPU time of generating vectors and the triangular factorization, it is judged whether shifting to accelerate the convergence should be applied or not. The shift value is chosen so that the convergence rate of unconverged eigenvalues is larger in the next stage. The error bounds of eigenvalues are formulated for a good choice of the shift in Sturm sequence check. The procedure is implemented in the ADINA program, and it is compared with the subspace method and the accelerated subspace method in computational efficiency. The results of some sample solutions show the presented Lanczos method is one time to ten times faster in calculation than the subspace method and the accelerated subspace method.

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An investigation is made into the dynamic instability of a high-speed rotor containing a partitioned cavity filled with two kinds of liquids of different density. The system considered simulates a centrifuge of two-liquid type, in which the cylindrical cavity is divided into fan-shaped compartments in order to suppress asynchronous whirling motions induced by waves in the liquids traveling around the cavity. Assuming rotor motion to be small, liquids inviscid, and external damping negligible, perturbed motions of the system are analyzed. The theory shows that the rotor containing a partitioned cavity is still possible to exhibit unstable behavior in the region where the rotor speed is nearly equal to the sum of the critical speed of the rotor and natural frequency of the liquids. To verify the theory, experiments have been carried out. The effects of some of the system parameters on the unstable region are also discussed.

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This investigation treats the damped free vibrations of a beam with viscoelastic support inserts like rubber along both ends. The beam material and support inserts have structural damping, which is replaced by equivalent viscous damping. In the analysis, the support inserts are considered to consist of massless line springs of the Winkler type. The frequency equation is derived and the effects of the length and the stiffness of a support insert on the natural frequency and logarithmic decrement of the system are discussed. A series of experiments were carried out on the beams with support inserts. Measured results are in good agreement with the theoretical results obtained by the method in this paper.

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The effects of axial force on the composite loss factor and natural frequency of a viscoelastic sandwich beam which is composed of a core layer of viscoelastic material and thin elastic outer layers are investigated. Assuming the vibratory energy dissipation to take place due to the shear deformation of the viscoelastic layer, the equation of motion and boundary conditions for a viscoelastic sandwich beam is derived from Hamilton's principle. The value of the composite loss factor of the sandwich beam increases as the compressive force increases and decreases as the axial tensile force increases. Experiments have been carried out with a cantilever sandwich beam subjected to no axial forces and the fixed ends one subjected to axial force. Good agreement has been found between the experiments and calculations.

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Rolling noise arises from the interaction of the vibration characteristics of rails and railway vehicle wheels through the points of contact. This paper deals with the coupled linear vibration between wheels and a rail on the basis of the previous reports taking also the coupling in both vertical and horizontal directions into account. The vertical irregularity on the head surface of the rail is regarded as a source of excitation. As a result, it became clear that (1) the vertical vibration of the rail, the horizontal ones of wheel and rail, and the vertical one of the wheel contribute to the rolling noise according to high vibration level, and (2) it is effective for the attenuation of vibration propagation through the points of contact along the rail to increase the distributed spring constants of the foundation and the dampings of the rail.

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In order to estimate critical speeds and self-excited vibration ranges of a flexible rotor partially filled with liquid, we propose a computational method of eigen values by using transfer matrices in which the elements are developed into power series of the vibration frequency. Experimental results agree well with the computed solutions.

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The effect of seismic waves on the stability of a rotor supported by oil film bearings is investigated by calculating the loci of centers of the rotor and the journal using the time-marching method. It will be shown that the rotor-bearing system, operated at a speed above twice the critical, becomes unstable when a sufficiently strong shock is given to the system, in spite of the fact that the rotational speed of the rotor is lower than the linear stability limit. At first, the effect of an artificial sinusoidal shock is considered, and then that of a real seismic wave (Taft in California, USA, 1952) is examined.

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An analytical study is presented on leakage-flow-induced vibrations in a one-dimensional, narrow, tapered passage. The fluid-dynamic forces and the moments acting on the walls of the passage when one of them is vibrating in coupled translational and rotational modes are obtained, and fluid-dynamic mass matrices, damping matrices and stiffness matrices are determined. The amount of work done on the wall by fluid forces is also calculated as a function of the components of fluid-dynamic matrices for the purpose of examining the mechanism of flutter generated from the flow through a narrow passage in the case of two degree-of-freedom system. It is found that not only single-degree-of-freedom translational or rotational flutter, but also coupled two-degree-of-freedom translational-ratational flutter may occur.

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The stabilities of a rigid, thin plate which can vibrate in coupled modes of translational and rotational motions in a one-dimensional, narrow, tapered passage are studied, and the critical flow rates, natural frequencies and modes at the stability boundaries are determined theoretically and experimentally. The theoretical results agree very well with those obtained from experiments. The types of flutter are also examined theoretically. The divergent-type and flutter-type instabilities can occur, and flutter type is classified into single degree-of-freedom flutter, which can also occur in the case of single degree-of-freedom system, and two degree-of-freedom flutter, which can occur only in the case of two degree-of-freedom system. Single degree-of-freedom flutter hardly occurs when the passage is convergent or when the pivot of rotation is near inlet of the passage, but two degree-of-freedom flutter is apt to occur in either condition.

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This paper deals with a nonstationary vibration of a flexible rotating shaft with nonlinear spring characteristics. Especially, we investigate a phenomenon during constant acceleration and deceleration passing through a critical speed of a 1/2-order subharmonic oscillation of forward precession. In numerical simulation, we examined the influence of the angular acceleration λ and the initial angular position ψ₀ of a rotor unbalance on the maximum amplitude of the subharmonic oscillation. As a result, the followings are clarified : (1) in order to always pass through this critical speed with a finite amplitude during acceleration, an angular acceleration greater than a certain value λ₀ is necessary, (2) the maximum amplitude depends on ψ₀ markedly, and (3) whether the shaft can pass through this critical speed or not depends on ψ₀ when 0 < λ < λ₀. We ascertained the validity of these theoretical results by experiments.

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This paper deals with the stability of the rotating body driven through flexible joint due to the transmitted torque. The flexible joint is assumed to have an torque-transmitting direction within the intersecting angle between driving shaft and driven shaft and the restoring moment proportional to the intersecting angle. The transmitted torque induces the instability same as the previous studies on the universal joint system. In the flexible joint system, the torque-transmitting direction has shown to be the important influence on the stability. The moment through joint that may cause instability is also observed experimentally.

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It is well known that the water contained in the pump impeller has the additional mass effect when the pump rotor vibrates in water, but no theoretical discussion has been presented about the analytical method used to evaluate it. In this paper, two additional water mass effects for the lateral vibration and the torsional vibration are discussed by the experiment and the approximate analytical method, and it is ascertained that almost all the water in the impeller is effective for the lateral mode. On the other hand almost no water is effective for the torsional mode.

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A gas and liquid reaction column exists in a petrochemical or a chemical plant, in which many perforated plates, or sieve trays are spaced at regular intervals. In such a column an unstable vibration by fluid force occurs at the sieve trays under a certain condition, and this vibration excites the column structure. For the purpose of investigating the cause and the mechanism of the instability and obtaining the useful data for the tray design, some experiments were carried out by using a visible experimental apparatus, that is, a two-dimensional model of an actual column. From the analysis of tray vibration and bubbling at submerged orifices, it was found that the excitation force which causes the tray vibration is pressure fluctuation of gas after the bubbling synchronizing the tray vibration and a self-excited vibration system is formed between the structural vibration of tray and the pressure fluctuation due to bubble formation.

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This paper presents a numerical method of simulating nonlinear sloshing phenomena in a rectangular tank and a cylindrical tank which are rocked horizontally. Based on the shallow water wave theory, basic equations which describe the nonlinear responses of sloshing, are derived. They are discretized on space, and the ordinary differential equations with respect to time are obtained. With the nearly equal ratios of the second order natural frequency to the fundamental one, a correspondence between the nondispersive-discrete system and the dispersive-continuous system is obtained. These ordinary differential equations are solved with the Runge-Kutta-Gill Method, and the time responses of sloshing are obtained. Numerical results are in good agreement with experiments, so the applicability of this method is shown. Especially in case of shallow water, various nonlinear phenomena which are observed in experiments are displayed in numerical simulations.

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An experimental investigation was carried out on the swirling flow-induced pressure pulsations in a pipe connected to a swirl generator with inlet guide vanes. As a result, the following was found : The pressure fluctuations with discrete frequencies are generated at the pipe inlet. Their frequencies are expressed by Strouhal numbers. When the fundamental frequency of the inlet pressure fluctuations coincides with the natural frequencies of the pipe, resonant pressure pulsations are generated. In the experiments, resonances of the first three modes are observed with the reduced velocities of 2. 0 -2.5 which correspond to Strouhal numbers of 0.4-0.5. So, it is concluded that the swirling flow-induced pressure pulsations in a pipe are considered as resonant phenomena caused by the Strouhal-type excitation.

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Much resarch on the dynamic response of driven valve systems of internal combustion engines has been reported. However, the analytical model proposed in the previous reports constructed under the assumption that the valve did not separate from the rocker arm during the cam rotation. This model is applicable to the system with small rigidities. Recently, to have stable motion in high speed engines, the rigidity of the valve system increases, so that the previous model cannot be applied to the engines. This paper proposes a method for obtaining the jump and bounce phenomena of the valve system with large rigidities by considering the set force of the valve spring which gives large effects on the valve response. Numerical calculations have been carried out for one of the recest engines, and the experimental tests also have been performed to verify the present analysis.

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This study presents a computer simulation to reveal the mechanism that the rolling piston of the rolling-piston type rotary compressors decreases effectively the power losses due to mechanical frictions. It is assumed from a previous experimental study that a fluid lubrication is formed between the rolling piston and the crankpin. The oil viscosity coefficient is given on the basis of experiments on oil pressure and temperature. The frictional state at the other pairs of machine elements is classified into two representative boundary frictions. Their frictional coefficients are determined numerically form the experimental data on the mechanical efficiency and the rolling-piston mean velocity, thus the power losses due to mechanical frictions can be calculated. To examine the calculated results, the computer simulations of other possible cases are presented. To confirm the validity of the calculated frictional coefficients, the rolling-piston mean velocity different operating conditions is calculated and the calculated results are compared with experimental ones.

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A practical and systematic design method for a robust controller is proposed. This method is in consideration of robust stability and pole assignment. The controller designer has propriety and is of a small order. The method is applied to the positioning servo with a voice coil motor, and the effectiveness of this method is investigated with computer simulations and experiments. As a result, the design guide about controller order and the modeling accuracy of plant are obtained. The effectiveness of this design method is also proved.

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This paper presents a new method to gain the structural reliability of a nonlinear single degree of freedom system with the material uncertainty and deteriorating characteristics due to a nonzero mean random excitation, by utilizing the Fokker-Planck equation approach (F-P method). Since the obtained moment equations of nonlinear systems by F-P method are not closed form, some approximations should be taken to get the closed form. In the presented paper, the response moments can be obtained to analyze the closed moment equations which are derived from the approximation of higher-order moments by lower-order moments with the aid of a truncation technique of higher-order cumulants. This paper shows the analysis of a Duffing oscillator subjected to a stationary Gaussian white noise as a typical example, and demonstrates that the resulting statistical values of the response agree well with the Monte Carlo simulation.

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The purpose of this study is to examine several methods and develop programs to predict the exterior sound environment of rockets and fairing's interior sound pressure level around spacecraft at lift-off. As a result, we found the following : 1) predicted results of the exterior sound environment are in good agreement with real flight environments using the acoustic efficiency of a rocket engine estimated from the improved Wyle Lab. Method. 2) The interior sound pressure level can be predicted with fairly good accuracy by finite element method for the low-frequency range and by acoustic statistical energy analysis which considers the energy flow between the many small acoustic space elements constituting the acoustic field for the high-frequency range. The developed prediction method will be effectively applied to predict the input acoustic level for the estimation of spacecraft's responce by acoustic excitation.

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In order to obtain as large a delivery as possible without changing the inner space V_c of a gear pump casing, the authors introduced a method to design and make gear pumps with teeth of Z₁ =Z₂ =2 to 5. They presented a new tooth profile of helical gears suitable for the pumps producing no fluctuations in delivery. Equations were derived for calculating the theoretical delivery V_th of the gear pumps and also the thrust which occurs on the gears. Experiments were conducted using four kinds of trial gear pumps with teeth of Z₁ =Z₂ =3 or 4. In the case of the gear pump with Z = 3 and a transverse module of 15.65, the volumetric efficiency was about 98% and the total efficiency was about 90% when the pump was operated at about 1.5 MPa using a machine oil as pumping fluid. The volume ratio V_th/V_c of the trial pump was about 0.5 while it was about 0.2 in the case of a conventional gear pump with almost the same delivery.

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In the present report, the possibility of the roll-finishing of a quenched gear was discussed. In order to reveal the effects of the quenching of a gear on a roll-finished tooth form, computer simulations were carried out. In the simulation, an increase of flank hardness by quenching was regarded as an increase of contact compliance of the tooth flank, i. e. an increase in resistance to contact deformation. The simulation result showed that an increase in contact compliance reduced the amount of rounding down at both tooth edges on a roll-finished tooth trace. Then, experiments of the roll-finishing of a quenched work-gear were carried out. In these experiments, the roll finishing of work-gears with flank hardness H_RC = 40 induced a fairly good tooth form, as in the simulation results. However, when the flank hardness of the work gear was H_RC = 55, a strong interference between the tooth tip of the die-wheel and the tooth root of the work-gear was induced and roll-finishing did not proceed.

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In the present report, we discuss whether roll finishing can achieve any profile modifications in work gears. As a target tooth form of a roll-finished gear, for example, a tooth form with tip and root relief was selected. Computer simulations were carried out to determine an optimum tooth form of a modified die wheel which gives such a target tooth form. Then, experiments of roll finishing were carried out using the die wheel with a modified tooth form determined by simulations. The results of these experiments showed a good agreement between a roll-finished tooth form and a target one. The computer simulation program, which has been developed in the present study is very effective for the determination of an optimum tooth form of a modified die wheel which gives any profile modification to a roll-finished tooth form. Also, it is possible to give any profile modification by roll finishing.

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A working load analysis was carried out on a bolted joint of an axle structure of construction equipment (wheel loader) under machine operation. The bolt was set in a final reduction system using a planetary gear mechanism. The working load was measured by a stud with strain gages. From the measurement of the bolt in actual products, the load and stress frequency diagrams were obtained. The estimation technique for the fatigue strength was shown. It was discussed that these techniques can be applied for the simultaneous multi-design.

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The dynamic response of a flying head slider due to a rectangular bump is simulated numerically by solving the modified Reynolds equation directly in the time domain. The response is also measured accurately using visible laser interferometry. The experimental results agree well with the numerical results, both indicating a wide range of movement. As a result, the modified Reynolds equation is confirmed to be quite suitable for an accurate prediction of the slider dynamic response even at a low flying height. Furthermore, the ordinal perturbation method is compared with the direct numerical simulation method and the differesces between both methods are clarified.

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In this study, basic characteristics of porous-ceramics air bearings, such as stiffness, load carrying capacity and stability, and analyzed by means of the finite element method. The validity of an FEM computer program developed in this study is examined through experimentation. The effects of anisotropic permeability, porosity and thickness of porous-ceramics materials on the stiffness and pneumatic instability are investigated. The effect of air supply area on the load carrying capacity and stiffness are also analyzed. The effect of the characteristics of porous materials on the occurrence of pneumatic instability is analyzed through the simulation of the dynamic response of bearing. Consequently, it is pointed out that the porosity and thickness of the porous-ceramic materials should be kept as small as possible in order to obtain higher stiffness and stability.

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porous materials are widely used as surface materials of hydrodynamic (self-acting) and hydrostatic (externally-pressurized) bearings. In this study, porous materials with such functions are applied to the annular plain seals employed in pumps by inserting ones into the inlet part of the seal. The Reynolds equation for the fluid film in the seal clearance is modified to include a so-called filter term and the effect of tangential velocity slip, and the pressure equation for the porous medium is obtained from Darcy's law and the continuity equation. These equations are applied to the system and are numerically solved with the pressure drop mainly due to the axial acceleration of liquid at the inlet end of the seal being taken into account. It is found that the annular plain seals with porous materials have larger f_k (f_k : fluid film force component along the line of centers) and smaller f_θ( f_θ : fluid film force component perpendicular to the line of centers) than that of ordinary solid annular plain seals owing to the functions of hydrostatic lubrication and inducing seepage of liquid into the porous medium.

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Oil film distribution over the piston skirt of a small reciprocating air compressor was numerically predicted. The research is closely associated with the secondary movement of the piston and also the oil consumption of the compressor. The computation was performed for four different kinds of pistons whose skirts have different profiles. The result was compared with the visualization result.

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This paper proposes a self-loading flying head slider mechanism, which operates under the non-contact start mode conditions with magnetic disk media in magnetic recording disk storage. Fundamental research was carried out. The flying head slider mechanism consists of a negative pressure air bearing slider, a slider suspension mechanism and a twin-structure piezoelectric actuator as the head-loading mechanism. The head-loading mechanism for the twin-structure piezoelectric actuator is confirmed to have good characteristics, simulating the mechanisms analysis. Furthe more, microdynamics and static characteristics for self-loading phenomenon of a negative pressure air bearing slider were computed and static and dynamic flying characteristics for self-loading flying head slider mechanism were analyzed, using the finite element method. As a result, it became clear that the self-loading negative pressure flying head slider mechanism proposed in this paper had good flying characteristics and high reliability. The feasibility for realizing a self-loading flying head slider mechanism, which operates under non-contact start stop mode conditions with magnetic disk media, was shown.

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A high-nickel alloy is well known as a difficult-to-machine material. Tool damage in the cutting of this material is not explained sufficiently although many researches have been done. In order to clarify the tool damage screw thread turning and reveal the mechanism of the tool wear, the high-nickel alloy was turned with the tool of four grades of carbide tools, and the cutting forces and the tool wear were investigated. Moreover, the cutting temperature was measured. The main results obtained are as follows : In screw thread turning of high-nickel alloy, the groove wear on the flank was formed. This qroove wear was also observed in outer turning. The flank groove wear almost grew larger than the boundary wear. This flank wear seems to be caused by the softening of the tool materials and the diffusion arising from the cutting temperature.

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Finishing end mills which can reduce dimensional inaccuracy and surface profile error in the finish process of end milling are presented. Computer simulation against chip geometry and variable distance from work surface to cutter axis are performed for the design of cutter shape with high rigidity. The performance of newly developed end mills are verified through the measurement of spiral chip diameter, cutting force variation and surface profile error in the face milling. it is shown that the magnitude of surface profile error can be reduced from 60% to 70% by the newly developed end mills, compared with the standard type. While the characteristic of surface profile error remains unchanged, for the cutter geometry with standard pitch was adopted. The cutter also possess a sufficient space to extrude chips which are produced in the finish process of end milling.

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A noncontact measurement method of the diameter of a rotating bar work is proposed. Surface velocity of the work is measured by detecting the movement of a laser speckle caused by the running surface. The speckle is observed by a camera which installs a line-charge-coupled device (CCD). The image moves a bit during the respective scannings. The velocity was evaluated by taking the ratio of the number of the pixel where the maximum correlation takes place to the time spent for every scanning. Since the correlation was taken by means of the ensemble, the number of the pixel could be averaged. The best agreement of the measured diameter with that by micrometer was 0.03%, which still requires improvement of the method.

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A method of detecting grinding cracks during the grinding process has not yet been developed in fine ceramics. The objective of this study is to example whether grinding cracks, which are generated during the grinding process, can be detected in-process by monitoring the acoustic emission AE. AE signals, which were detected during grinding, have been analyzed and compared with the signal before grinding cracks are generated. AE between 1.0 - 1.2 MHz are detected when grinding cracks are generated, while they are not detected when grinding cracks are not generated in fine ceramics. By utilizing this relationship. it becomes possible to detect grinding cracks in-process.

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Experimental equipment used to assess the tool-workpiece compatibility in deep drawing is designed and built. In this construction, a die is divided into two coaxial parts and the one with die profile radius can be rotated so that the meridian component of frictional force reduces with increasing its peripheral velocity. A sophisticated procedure, which clarifies contact ratio and frictional shearing stress in the tool-workpiece interface using experimental results and theoretical relationships, is introduced. By means of experimental drawing of copper and stainless steel sheets with three kinds of die materials (carbide, die steel, and aluminum bronze), the response of the contact ratio and frictional shearing stress to changes in blank holding force, drawing ratio and ironing ratio, is evaluated. Consequently, a deeper understanding of the phenomenon acquired, and it is confirmed that the contact ratio and the frictional shearing stress behave independently to determine the tool-workpiece compatibility.

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Recently, 3-dimensional graphic technologies are topics of rapidly growing importance in the industrial fields such as those dealing with curved surfaces. When designing for a curved surface, methods for transformation of arbitrary regions on the curved surface into flattened forms are very important in manufacturing processes. The purpose of this paper is to describe a scheme for transformation of various regions on a curved surface subject to the following conditions. First, materials which constitute regions on a curved surface have different types of elasticity. Second, an objective curved surface has some regions whose shapes are fixed. Third, lengths of border lines between two regions need to be made equal to each other. As typical and practical applications, examples of shoe models corresponding to each case are presented to illustrate the method that transforms the various regions into flattened forms.

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In order to easily determine the power required for cutting and cutting force from the cut amount in hobbing, the technique using the space between teeth of gears as the criterion was proposed. In this study, simple equations for calculating the area of the space between teeth and the cut amount were derived. The results may be summarised as follows. (1) The simple equations for calculating the cut amount in Hobbing were derived. (2) The term of the number of teeth was eliminated from the simple equation for cut amount in hobbing, therefore, theoretically, the number of teeth is irrelevant. (3) However, the effect of the number of teeth appears in the area of the space between teeth of gears.

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A method utilizing a unit cutting-power value determined from a series of hobbing tests, using the rate of metal removal in hobbing, to predict the cutting force in hobbing is discussed. Because this method uses simple calculation equations, calculation is easy, and the method can also be applied to the special tooth profile gears other than involute gears. The results may be summarized as follows. (1) As calculation equations for predicting the cutting force were made, there was no term related to the number of revolutions of a hob, and theoretically, its effect is nonexistent. (2) In hobbing experiments. the unit cutting-power values under various conditions were determined using S45C material. When these values are determined for various gear materials beforehand, it becomes possible to predict the cutting force for hobbing these gear materials.

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