In the previous paper, exact solutions of the autonomous Duffing equation were obtained in terms of the Fourier series making use of the so-called q-expansion of the elliptic functions. A characteristic parameter which plays a central role in calculating the Fourier coefficients, must be determined as a root of the modulus equation essentially by a trial method. As for some algorithms as well as approximation formulae proposed in the previous Saper, a few extensions of the discussions are presented here to improve the accuracy. A new trial algorithm and a revised approximation formula are proposed for a case of ultra low frequency (strongly nonlinear square wave and pulse train), and a new expression of the Fourier coefficient is also discussed, which is suitable in particular for the case of quasi-linear oscillation. Some salient features of the solution are illustrated for the case of a snap-through spring system in a full swing as well as in half swing modes.

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This paper deals theoretically with a subharmonic oscillation of order 1/2 and some sort of summed-and-differential harmonic oscillations in a rectilinear vibratory system with nonlinear spring characteristics, which are expressed by the terms of the second, third and fourth powers of coordinates. Especially, the effects of quartic terms on these oscillations caused by the nonlinear terms up to the third power of coordinates are investigated. It is clarified that quartic terms have qualitatively different effects from those of quadratic terms, and that unstable vibrations occur due to quartic terms. These kinds of unstable vibrations have been observed experimentally in a rotating shaft system by the authors of this paper.

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The ball screw type damper discussed here is composed of a ball screw, a flywheel and a flyball governor. When the damper is attached to a single-degree-of-freedom system, the vibration system varies with the cases in which the ball which the ball nut is attached to the main mass or the foundation. The 1 st report was concerned with the former case. In this report, the forced nonlinear vibration, its stability and the effects of the vibration isolation of the damper for the latter case are discussed analytically and numerically. The results may be summarized as follows : (1) The damper is most effective for suppressing the resonance of the primary system when the natural frequency ratio of the governor to the primary system is turned to about 2. (2) Close agreement between the analytical and simulated results is obtained in the region of forcing frequency less than the natural frequency of the governor, and the vibration system is stable in this region. (3) There is little difference of the effect of vibration isolation between the two methods of attachment of the damper.

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The problem of the nonlinear forced oscillations of a square membrane is considered. For theoretical analysis, modal equations are first derived from the governing nonlinear partial differential equaions. Then, based on these modal equations, the characteristics of oscillations induced by harmonic excitation near a primary resonance point are discussed. Numerical calculation is conducted for a typical case in which the excitation frequency comes near the resonance point of the mode with one nodal line. It is shown that near this resonance point, two modes which exist with the same natural frequency and with the same modal form are excited simultaneously due to nonlinear coupling, and thus two-mode oscillations can occur. It is also shown that two kinds of two-mode oscillations are possible, one in which two modes are excited with a time lag of nearly π/2 and the other without a time lag. The former implies the occurrence of oscillations of the rolary type, and the latter the occurrence of oscillations with its nodal line shifted from that of the linear harmonic oscillation. Experimental analysis is also conducted, which confirms the validity of the theoretical analysis.

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The high frequency response of a beam carrying a rigid body at its middle under a point random force has been studied. Theoretical investigation has been carried out for both the spatial averaged response of the beam and the local response of the rigid body. The approximate expressions have been derived by studying the asymptotic behavior of the result of classical modal analysis. It is shown that the effect of the rigid body on the spatial averaged response of the beam is negligible and that the dependence on frequencies of the rigid body response is different from that of the beam spatial averaged response.

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This paper presents an analytical method of flexural vibration of a beam with partial coverage of a constrained viscoelastic layer. The problem of discontinuity of the neutral axis at the connecting point between the multi-layer and homogeneous parts which arises in the method used so far, is solved by treating the axial displacement of a base layer and that of a constraining layer as being independent, and by taking the axial force and displacement of a homogeneous part into consideration. Frequencies and loss factors of beams whose base layers are clamped at both ends are calculated numerically by use of the present method and the usual method. Experimental values are also presented and compared with calculated results. An a results, damping properties of partially covered beams are clarified, and it is found that the usual method can be used practically in many cases.

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In a parametrically excited system whose natural frequencies are p_i, p_j, p_k, and the parametric excitation frequency is Ω, an oscillation of a subharmonic type occurs when the relation p_i∼_- Ω/2 holds and that of a combination type occurs when the relation p_i + p_j ∼_- Ω/2 holds. When the restoring forces are linear, these oscillations are unstable oscillations. But it is known that, in a nonlinear system, the nonlinearity modifies the growth of the unstable vibration and results in the steady oscillation with finite amplitude. In this paper, the internal resonance phenomena in such a system with nonlinear spring characteristics are investigated. Especially, we treat the case where the relation lp_i + mp_j = np_k holds but each natural frequency is not an integer multiple of another natural frequency. By theoretical analysis, we clarified the followings : the kinds of parametric excitation terms and nonlinear terms which have an influence on oscillations ; induction of oscillation due to internal resonance ; occurrence of the almost periodic oscillations ; and so on.

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An approximate method assuming partially Gaussian probability density functions is applied for the analysis of symmetric and non-symmetric non-linear systems subjected to non-stationary white noise. And the first passage probabilities are obtained by use of the assumed probability density functions, based upon the assumption of Poisson process of threshold crossings. In the numerical calculations and simulations, the usefulness of the method is demonstrated in comparison with the Gaussian method used often so far, and it is indicated that the estimation accuracy of the probability density is very important in the first passage problem.

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This paper deals with coupled torsional-longitudinal vibrations of rotating pretwisted cantilever beams with tapered rectangular cross-sections. The Rayleigh-Ritz method is used to obtained pseudo-static torsional deformations stresses due to rotation and characteristic parameters of vibration. The influences of pretwisted angles, width or depth tapers of cross-section, speeds of rotation and pseudo-static torsional deformations on the characteristic parameters are investigated. The results show that these parameters have a considerable influence on the coupled torsional-longitudinal vibration of the beams.

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Experimental study on dynamic behavior of multiply supported piping systems in industrial plants is described. Nonlinear characteristics such as gap and friction appearing between the piping itself and supports is specifically investigated. The response reduction effect due to these nonlinearities is evaluated by the shaking test with a piping-support structural model. From the study, it is shown that the amount of response reduction can be represented by a "response reduction factor" and that the reduction characteristics are examined with the aid of equivalent linearization.

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This research is a fundamental study intending to develop industrial piping supporting restrainers which utilizes excellent energy absorbing behaviour of super plastic alloy materials. In order to achieve this purpose, energy absorbing effect of the super plastic alloy itself is examined, in the beginning, taking a Super Plastic Zinc (Zn 22% Al) as a representative material. In the next place, damping effect for piping system is investigated by shaking test whereby two types of simplified piping model having SPZ restrainer are introduced. From the shaking test it has become clear that dynamic energy absorption of SPZ restrainer for piping is conpicuous particularly in fairly high temperature circumstance (T > 120°C) comared with steel or brass restainers.

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This paper clarifies vibration response characteristics of a vertical mechanical structure subjected to horizontal and vertical nonstationary random excitation. The structure is modeled as a cantilever beam with a lump mass at its free end ; taking into account the first vibration mode for numerical computation of vibration response, response multiplication factor maps with respect to dominant frequencies, w_H and w_v, of both horizontal and vertical extitations are obtained for the structure's damping, , magnitude and randomness of vertical excitation. A very high response appears at w_v=2 and w_H=1 and its magnitude varies with a slight change in the power spectral density contained in nonstationary vertical excitation waves at w_v=2. For w_H=1, the conditions of unstable parametric random vibration are obtained for structure damping and magnitude of vertical excitations.

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In this paper, the vibration phenomena of circular cylinders both for the uniform cross flow and the gap cross flow are compared, making clear the similarities and the difference between both experimentally. The flow-induced vibration experiments were performed by utilizing the same fundamental test apparatus as in the 1st report, and by artificially expanding the flow band width of the cross flow which is exerted on the circular cylinders from the extremely narrow width to the uniform flow width. As a result, it is found that the critical velocity of the vortex shedding vibration and that of fluid elastic vibration become almost constant regardless of the flow band width, when the equivalent velocity is calculated using the continuity condition, and by applying the momentum flux theory on the cross flow jetted from a narrow gap, respectively.

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Based on the shallow water wave theory, basic equations which describe the nonlinear responses of sloshing are derived, and a numerical method is presented to simulate sloshing phenomena in a rectangular tank which is oscillated horizontally. As the vertical variable isn't contained in the basic equations, the discretization equations are easily obtained. They are the ordinary differential equations of time, which are solved with the Runge-Kutta-Gill Method. The feature in this process is that the dispersion relation included in the basic equations is replaced by that produced by the discretization. In experiments and numerical simulations with small water depths, stable progressive waves are observed, and the surface displacement shows nonlinear responses. Numerical results are in good agreement with experiments, so the applicability of this method is shown.

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This paper deals with the self-excited vibrations of a rotating Mindlin circular plate subjected to a concentrated frictional force exerted on its outer circumference. However, the internal resonance is considered here. It turns out, from the averaging method and a direct numerical integral method that (1) the generating vibration modes related to the internal resonance are fixed in space as the same manner in the single modes generated in a circular plated, and (2) in the internal resonance, the spatial vibration mode of the one with lower natural frequency deviates from that of a stationary circular plate in the rotating direction due to rotation, but the one of the other mode is almost same as that of the stationary circular plate. The internal resonance becomes also unstable, like a single mode, as the rotating speed is increased. The analytical results are confirmed by the experiment.

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There are many papers which dealt with the vibrations of a geared-rotor system and the gear noise, but there few papers which considered the effect of coupled lateral and torsional vibration. However, the analysis of the coupled vibration is important for reducing the vibrations and the noise. This paper presents the experimental results of the vibrations and the noise of the geared-rotor system constructed by a pair of the spur gears. In the response of angular acceleration in the gears, there are some resonant peaks caused by the excitation relating to the mesh frequency. And some other resonances appear in the response of the lateral vibration and the torsional vibration caused by the mesh frequency excitation. The gear noise is concerned mainly with the angular acceleration. Moreover, the tooth profile modification acts effectively on the noise of the geared-rotor system.

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There are many studies which deal with the vibration of a single-stage spur gear system, and its dynamic behavior has been investigated. In general, a multi-stage spur gear which has many sources of exciting force is used more often than a single-stage spur gear system. This study deals with the coupled lateral-torsional vibration of a two-stage spur gear system which has the same meshing period. First the equations of motion are derived which have periodically varing parameters. The form of tooth stiffness variation is assumed to vary as rectangular form and the solution of free vibration are obtained analytically. Then the stability of the system is analyzed. In this system, there are some instability regions which are not only principal parametric resonances but also combination resonances. Further, the influence of the phase difference between two meshing stiffnesses is discussed. In some cases, the phase difference between two meshing stiffnesses influences the instability regions considerablly.

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In this paper, a general purpose computer code based on the boundary element method (BEM) is developed for two-and three-dimensional acoustic problems. The main analysis system employs the direct boundary element formulation expressed in terms of the pressure and the particle velocity on the boundary. The computer code can be characterized by the following features : (1) Constant, linear and quadratic boundary elements are incorporated. (2) The method of sub-regions can be applied. (3) The mixed boundary conditions can be treated. (4) The symmetrical properties of the problem can be taken into account. (5) The infinite-domain problems can be treated without any difficulty. (6) The so called fictious resonance frequency in infinite-domain problems can be totally excluded.

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As a basic study for the establishment of the methodology for computer aided or automated design of machine structures, this report deals with an algorithm and a computer program for the automated generation of the skeletal structures of the motion transmitting systems of power transmitting or motion transmitting machines, such as machine tools and measuring apparatuses. The motion transmitting systems of the machines are considered as an aggregation of motion transmitting elements, such as gear mechanism, screw driving mechanism and cam mechanism, and their skeletal structures are generated automatically using their functional structures, the algorithm and the application results were explained in the second report of this study. Some results for machine tools are presented, which were generated by the implementation of this computer program.

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A newly designed diagnostic robot, Mark II, basically consisting of three modules with a joint between modules has capabilities of straight and spiral movement along the outside of pipelines, and of freely passing over obstacles, such as flanges, T-joints and other plant equipment by sensing and recognizing obstacles in front of it, and controlling its attitude automatically. By calculating the position and orientation of the robot using a transformation matrix, a control method of maneuverability in the passing of T-joints is shown. A method of compensating for the torque with occurs by, gravitation -al force is applied for each module independently to keep the holding torque constant, which leads to less vibrations in movement and hence yields better diagnostic results. The Mark II equiped with diagnosis sensors can identify the location and depth of flaws on the surface by inspecting pipelines in the spiral moving mode along the pipelines. The Mark II also has intelligent abilities, such as routing the most efficient path for inspection in plants, provided a plant map is given.

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This paper describes the control of multi-articulated vehicles in a backward maneuver, which have been almost ignored to date. First, the equations of multi-articulated vehicle motion in a backward maneuver were obtained by the geometrical method. By experiment, it was found that their behavior at a low speed could be treated geometrically. Next, the controllability of articulated vehicles in this maneuver were studied theoretically with modern control methods. With the optimal control theory, the steering of these maneuvers was studied. These analyses provided the feed-back coefficients of each state value of multi-articulated vehicles and also the effects of design parameters for these coefficients. Finally, the control limit was studied with the limit value of steering angle.

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This paper treats with the stability of a rigid rotor supported by double-row admission bearings with circular slot restrictors. In the theoretical analysis, the pressure reduction at the outlet of the slot is considered because gas flow is repidly bended, and the coefficient of the pressure reduction is determined experimentally. The theoretical results obtained are in good agreement with the experimental data. Furthermore, in this paper, it is experimentally shown that an aerostatic jouranl beaing with circular slot restrictors has higher stiffness and higher stability than those of conventional point source bearings with inherently compensated feeding holes.

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It is well known that inclusions in the workpiece have great influence on machinability. At the first stage, the lubricating ability of various non-metal materials was tested at an elevated temperature (700∼800°C). At the second state, a mixture of ferrous metal powders and non-metal additives was sintered, and a cutting test of these sintered materials was done. The coefficient of frictions at the tool-chip interface in cutting were examined, and the most effective additives were found. The conclusions obtained in this experiment are as follows : (1) The coefficients of friction at the tool-chip interface are able to reduce effectively by adding non-metal materials as an inclusion. (2) It is estimated that the most effective additives are lithium oxide, boron nitride, glass and tellurium oxide. Glass and boron nitride are the most prospective materials for improving machinability.

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Many investigations on the problems of ball motion in ball bearings have been reported. However, studies of the influence of race failure on ball motions are few. Recently, utilizing the Hall effect, a new method to measure three-dimensional ball motion was developed. It is now possible to analyze the angular velocity components of ball rotation from experimental data by this method. The authors carried out a series of experiments on ball motion using damaged bearings. In this paper the experimental results obtained under shaft speeds on N_i=12 rpm, 1000 rpm and a radial load P_r=490 N are reported. The effect of shaft speed and the influence of damaged race on ball motion are discussed based on the analysis of the experimental data.

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The design methodology in terms of plastic gears is essentially based on those developed for steel gears, in spite of the fact that various kinds of design methodology have been proposed for plastic gears in recent years. Recently, several problems have been pointed out in relation to this design methodology since there are several experimental evidence, none of which can be clearly explained by the existing methodology. Therefore Tsukamoto, one of our co-workers, has performed many experiments and has proposed an entirely new strength formula, adopting the quantity referred to as the product of the contact period of teeth and loading torque, based on experimental results. The present study is aimed at establishing a practical gear strength design formula by developing Tsukamoto's thory, which is not sufficiently clear in its physical definitions. In this report, a calculation method of the fatigue strength of a gear due to strain energy is proposed.

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A crossed axes is capable of roll-finishing under lower loading than a conventional parallel axes system, and a fairly good tooth form can be obtained. However, it is difficult to keep a smooth engagement between die-wheel and work-gear so that an interference between the tooth tip of the die-wheel and the tooth root of the work-gear can easily occur, so a roll-finished tooth flank has a small pit near the tooth bottom. In this report, in order to make this pit smaller, a relieving was given to the tooth tip of the die-wheel. According to experimental results of roll-finishing by such a die-wheel, the amount of a tip relieving must vary properly in the longitudinal direction. Then a fairly good roll-finished tooth form without any pit can be obtained by a crossed axes system.

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The influence of tip interference on scoring load capacity was studied using gears having tooth profile wear due to scoring on the approach side. The results were compared with those obtained with gears having no profile wear from viewpoints of scoring load and scoring temperature, taking the lubrication state on the working flank into consideration. The tip interference on the approach side should be reduced because, unlike on the recess side, it diminishes the scoring load capacity. In the mixed lubrication state, the bulk temperature on the working flank is suitable for an index in calculating the scoring load capacity of a spur gear pair. The scoring temperature on the recess side can be estimated well by the bulk temperature on the outer surface of the cylinder just before seizure in two-cylinder tests, provided that the specific sliding and the sliding velocity at the end of gear meshing are taken into account.

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The three grinding methods of a conical involute gear are described and it is proved that a conical involute gear can be ground practically. Niles-Type Taper Grinding, in which a Niles-Type gear grinding machine is used, is based on the principle of generating the gear by the generating rack and is the best method to grind a gear with a small cone angle. Table Sliding Taper Grinding, which is based on the principle of Table Sliding Taper Hobbing, is useful for grinding a gear with an arbitrary cone angle. Inclining Work-Arbor Taper Grinding, which is based on the principle of Inclining Work-Arbor Taper Hobbing, is the most useful method for grinding a gear with a constant cone angle.

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In order to reduce the measuring time of an automatic internal gear pitch tester which had been developed in the preceding study, improvement of the measuring device and review of the measuring method were carried out. By changing the allowance of positioning accuracy from 1μm to 10μm, the relationship between the adjusting time of the indicator and the allowance of positioning accuracy of the reference indicator were studied. Measuring accuracy is hardly dependent on the allowance of positioning accuracy. This leads to a considerable reduction in the measuring time. It is experimentally proven that this device enables one to measure the pitch error of internal gears with high repeatability and reliability in a short time.

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Few investigations have been carried out on the characteristic of a bolted joint with tap bolts subjected to external bending moments. In this paper, the characteristics of a T-flange connection with tap bolts, including a full face metallic gasket or a filler plate, are examined. For analysis, a T-flange, gasket (filler plate) and base were replaced with finite strips. Contact stress distribution, the force ratio for the external bending moment (the relationship between an increment (decrement) of the bolt axial force and the external bending moment) and the maximum stress produced in the bolts are analyzed using a two-dimensional theory of elasticity. Furthermore, the characteristics of a circular flange connection are estimated by using the two-dimensional model. For verification, experiments were performed with respect to the force ratio for the external bending moment, contact stress distribution and the maximum stress in the bolt. Analytical results are in fairly good agreement with experimental ones.

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In the previous report, the vibration screw tightening method using a D. C. motor was discussed. In the results it was clear that the vibration tightening torque coefficient decreased more than the ordinary tightening torque coefficient, and the amount of scatter of the vibration tightening torque coefficient also decreased and then the screw thread tightened by the vibrational method was hard to loosen. In this report the pneumatic method using an air motor is studied. It is a more compact and controllable device in comparison with the vibration tightening which uses the D. C. motor. Also, the low frequency torsional vibration from 0 to 4 Hz is added to the tightening tool. The basic characteristics of the screw tightening method by means of the pneumatic control vibration is compared with the results of the ordinary screw tightening method (i.e. a constant velocity tightening method using the air motor).

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The influence of tool geometry on hole deviation is investigated using four types of deep hole drilling tools, i.e., the normal type of gun drill, the standard type of BTA tool, the two-edged gun drill and a multi-edged BTA tool. Two types of workpiece are used, to make their influence clear : One of them has an asymmetric wall hardness of bonded plate is lower than that of the other. As a result, it is found experimentally and theoretically that the balancing of the cutting forces on the tool head contributed to a decrease of hole deviation. However, the existence of some unbalanced force is more effective for giving an accurate hole size than the complete balancing condition of the forces, because the latter condition gives oversized hole.

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An attempt was made to break chips produced by NC turning by intermittently decelerating the finish cutting speed. A personal computer was sued to control intermittent deceleration. The programming software is also developed to automatically create NC instructions by given data related to the interval of fee, decelerated feeding, tool and cutting condition with a personal computer. As a result, it was found that by optimizing the interval between decelerated feeding and rate of deceleration, chips will be broken into easily disposable smaller pieces.

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A new concept of "tribo-forming" for producing a thin-wall cup is proposed in the present work. The process proposed is similar to a backward extrusion. The solid workpiece is compressed between the punch and the anvil punch in the container cavity, but the anvil punch is retarded by pushing the punch under constant pressure. The cup wall is formed by stick friction between the internal face of the container cavity and the side face of the workpiece. The process combines extrusion with effective stick friction : hence the name "tribo-extrusion". A relative punch pressure p_m/Y in the tribo-extrusion was predicted at a relatively low value of 2∼2.5 within the 60∼97.5% in reduction of area by the upper bound approach when the stick friction drag was employed effectively. On the other hand, the value of p_m/Y predicted in the backward extrusion was higher than about 4 and increased as the reduction of area increased.

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Using three kinds of round bar work metals 5 mm in diameter, cylindrical cup-forming was examined in the tribo-extrusion proposed in the first report and the backward extrusion. The punch pressure p_m in the tribo-extrusion of the aluminium and the copper was about 30% lower than that in the backward extrusion. The p_m in the tribo-extrusion of low carbon steel was about 2.1∼2.35 GPa within the range of reduction of area of 70∼97%, while it was impossible to finish the cup owing to the danger of punch failure by the backward extrusion. The relative punch pressure p_m/Y in the tribo-extrusion of copper and low carbon steel ranged from 2.5 to 4, and these values were approximately consistent with those predicted theoretically. The cup surface was finished without galling, and the surface roughness R_max was about 0.5∼1.8 μm, regardless of the dry frictional condition. The cup wall thickness also was produced with a relatively high accuracy.

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At the present time, the machines with high accuracy and performance tend to be designed by CAE methods. But suitable and useful CAE methods are not established for all machine parts and elements. Thus, we must derive easy and useful methods for each machine part. This report deals with a new method using linear graph theory as one CAE method and analyzes the results of dynamic behaviour concerning power transmission mechanism. By this method, addition and deletion of machine elements are made flexibly, and performances of the system are analyzed rapidly. So this method is effective for extensive machine design.

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A method for the analysis of displacement, velocity and acceleration of an arbitrary mechanism is presented by using kinematic loops proposed in the preceding paper (1st Report). Furthermore, the forces and torques acting on joints are analyzed numerically. The equations of motion are derived from the Newton-Euler method. The recurrence relations are introduced to reduce the computing time. The proposed method is applied to an industrial robot including the closed loop, and proves to be an analysis with a high accuracy.

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The new architecture of knowledge and database management systems for process planning systems is presented. Recent progress in knowledge engineering technology gradually makes it possible to realize an automatic design system. Several researches aim at realization of an expert system for process planning, which needs an efficient management of a large amount of knowledge and data, and an inference mechanism pertinent to geometric and machining processing. To solve the first problem of them, we observed the knowledge and data used in process planning, then concluded the necessity of integration between them in a unified way. We introduced an extended Entity-Relationship model for this point. This model is composed of both entity and relationship types. The point of using this model to represent both knowledge and data is that most of the knowledge is associated with relationships. We are currently implementing a process planning system based on the above model for knowledge and data representation.

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An expert CAD system is developed for the design of a marine power plant using the "Artificial Intelligence" concept. Firstly, a discussion is given to understand the general design process and to apply the methodology using computers based on knowledge engineering. It was found that the knowledge base can support most effectively the conceptual design process in which the design solutions are searched using the "design knowledge". Then, an expert CAD system was built for a marine plant design. The CAD system architecture consists of the knowledge base for the design rules of the plant design and the frame type database in which various types of ship's main engines and machineries are stored. The system runs interactively to assist a designer in the synthesis phase of the design. The optimal candidate of an engine and machineries can be determined, selecting tradeoffs, selecting candidate solutions and performing design tasks. The expert CAD system developed might also advise an inexperienced designer on the appropriate procedures to solve a design problem.

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An ITV camera has an important role in teleoperation. This paper describes a method of controlling an ITV camera head according to the eye motion of the operator. The camera head has 3 degrees of freedom. Controllers of the camera head are destributed and built into the mechanical parts of each joint, so that they can be free from heavy wires. The eye motion of the operator is measured by image processing of the operator's face. An image of the face is obtained by a video camera mounted on the monitor display. The camera head rotates in the same direction as the visual line of the operator, so that the target is displayd at the center of the monitor display.

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In the FMS of next generation, its system configuration is to be of modular type, in which the basic module is that of FMC. This FMC enables the FMS technology to be available for town and medium-size industries. To cope with such trends surrounding the FMC, it is now required of establishing a design theory of special-purpose FMC and also a standardization method of FMC. In this paper, thus, the similarity evaluation method of the FMC for metal cutting has been investigated to propose a classification method of FMC. The similarity evaluation proposed here puts its main stress on the system configuration, especially on the characteristics of the system compnent and work flow pattern, and to enable the evaluation procedure to be simplified, the FMC is represented with the directed graph. Through some trial applications, it can be verified that the proposed method is reliable and effective from the practical point of view.

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