How to express the uncertainty of measurement methods or measurement results is a keen requirement in measurement science. Some practical examples of the evaluation on measurement uncertainty are shown. The present situation among international organizations to establish general rules for evaluating and expressing the uncertainty in measurement is also reviewed.

View full abstract

The free vibration of a disk-beam coupled system having cyclically symmetric structure is investigated by the Ritz method in this study. The orthogonal polynomials generated using the Gram-Schmidt process and the eigenfunction of a uniform disk are employed as admissible functions. The continuity conditions between the disk and beams are satisfied by means of artificial springs at their joints. By this approach, the mass matrices derived from kinetic energies of the system become diagonal, and this will make the numerical manipulation of the matrices easy and stable. It is also described in this paper that the mode shapes of the disk-beam coupled vibration consist of specific circumferential wave components and thus the modes can be classified. Numerical calculations are carried out, and the frequency parameters and mode shapes are obtained to investigate the vibration of the disk-beam coupled system.

View full abstract

This paper presents an application of the simulation system of the vehicle-occupant dynamic interaction which was developed by the author. During the application of this system, the effects of bridge expansion joint and vehicle speed on human dynamic behavior were investigated using this computer simulation system. The expansion joint of highway bridge is modeled by Fourier series function. The randam roughness of an actual highway surface has been taken into account in the simulation system. It was found that projection of expansion joint and the shape of obstacle exert a serious influence upon human ride comfort. Some results are presented in the form of parametric plots. Allowable height of expansion joint in the vehicle speed range of 40 to 160 km/h, and a standard of maintenance are presented.

View full abstract

This paper describes an active isolation system which is different from conventional active isolation devices. Based on the idea that separates the roles of levitation and active isolation, a new type of actuator using both an air spring and magnetic bearings is designed. The isolation table with loading is levitated by the air springs, and the active isolation of microvibration is realized by magnetic bearings. The control system of the isolation device includes two control loops, one being the levitating control loop of PID controller, and the other the isolating control loop with absolute velocity feedback. The experiment is a success, with the results showing that the acceleration transmissibilities of the table versus the floor with active control are reduced to below one-tenth of those in the case with only passive control in both horizontal and vertical directions.

View full abstract

This paper describes the new theoretical modal analysis of a thick cylinder. The five element-simultaneous second differential equations of elastic vibration of a thick cylinder, which are derived considering rotatory inertia and out-of-plane shear deformation, are rewritten into the ten element-simultaneous first differential equations by introducing new variables. The first differential equations can be solved under various boundary conditions by applying Euler's method. In this paper the equations were solved for a thick cylinder with both ends free. The calculated natural frequencies and mode shapes coincided with those obtained by the experimental and FEM modal analyses with practically sufficient accuracy for all modes.

View full abstract

In this paper, a new hierarchical optimization method for structures is presented. The special features of this method are that the sensitivities of the design object are obtained using the eigenvalues of substructures as design variables, and the sensitive substructures are only modified to satisfy the design object. In this study, the present method is applied to the natural frequency assignment problem. The procedures of design are as follows. First, the sensitivities of eigenvalues of the overall structure to the eigenvalues of substructures are calculated. Second, the most sensitive substructures are selected. Third, the dynamic characteristics of sensitive substructures are modified to satisfy the design object. Finally, the eigenvalues of the overall structure are calculated. The present method is applied to a natural frequency assignment problem of a gate structure. The results of the present method and the conventional method are compared in terms of the accuracy and calculating time, and show that the present method is effective in practical examples.

View full abstract

We have aimed to develop on intelligent jig for automatic deburring and assembly by robots. It can manipulate and fix a heavy target object, and makes the relocation of the jig unnecessary. In this paper, we have proposed the new mechanism (RBSF mechanism) which consists of the rotational base and several one-DOF fingers. It makes the manipulation (mainly rotation) of a heavy target object possible. Because of the specialization of this mechanism, sliding occurs between the target object and fingertips. In this study, we analyze the kinematics and dynamics of the RBSF mechanism. We also discuss the feasibility of the generation of object acceleration and angular acceleration by the RBSF mechanism.

View full abstract

Recently, industrial robots have been introduced at plants, and have contributed to automation. However, their tasks are limited to welding and painting. The tasks of fixing a target object have not been automated. Hence, in order to automate such fixation tasks, we have worked to develop an intelligent jig which has the functions of fixation and manipulation of a heavy target object, and have proposed a new mechanism (RBSF mechanism) which consists of a rotational base and several one-DOF fingers. Because of the specialization of the RBSF mechanism, we cannot assign arbitrary acceleration or angular acceleration to the target object. In this paper, we discuss motion planning based on the analysis of kinematics and dynamics described in the first paper. The results of the simulation and experiment to verify the feasibility of the manipulation by the RBSF mechanism are shown.

View full abstract

A spring function of the magnetic force can be approximated by a simple function, F(x)=A[D/(B+x)]^P + C, where x is the pole-gap distance. It has been established experimentally in our previous study that the constants B and C greatly increase the approximation accuracy of the formula, although they have never been used conventionally. However, the procedure to obtain B and C together with A, D and P is rather complicated. The present study is devoted to the revision of the algorithm and the program. The performance of the method is examined by numerical examples to verify the accuracy of the function approximation as well as the constant identification. The influence of the random noise superimposed on the data and the ability to identify some special test data are examined. A numerical discussion of the strongly nonlinear spring property which was found previously is also presented. A listing of the program is accompanied by its instruction manual.

View full abstract

Through phase plane analysis, a nonlinear system is defined on the phase plane, and the solution is obtained as a trajectory. Based on the idea that the relationship between the nonlinear system and its solution could be compared with the relationship between class and instance of object-oriented systems, a simulation program for the phase plane analysis was written in the programming language TAO. Simple oscillation, damped oscillation, and self-sustained oscillation of Van der Pol equation, Rayleigh equation, and the stick-slip oscillation were implemented in that program. Compared with the existing functional programming approach, the effectiveness of object-oriented phase plane analysis for nonlinear vibration was discussed and proven through the program.

View full abstract

A highly reliable paper-feeding mechanism is necessary for printers. To achieve this, it is important to estimate the friction force and deformation of the paper. This is not easy, however, because the guide is usually bent in a "C" or "U" shape. The paper is bent by friction with the paper guide, and paper deformation is large. A simple beam model considering the friction force of the paper guide is therefore introduced to simulate paper behavior. The results of numerical simulations and experiments are shown in this paper. These results indicate that this calculation model is quite useful in predicting paper behavior and improving paper-handling machines.

View full abstract

Elastic yarns in the winder system of a textile machine are deformed into a certain convex polygon in the process of winding at an operating speed of the bobbin holder rotating viscoelastically in contact with the drive roll. The polygonal deformation increases and develops into a serious vibration of the machine. This paper presents a model and a theoretical analysis to investigate the mechanism of this vibration phenomenon which is regarded as instability due to the time lag. The bobbin holder and the drive roll are both modelled by the one-mass one-shaft system. From the numerical computations using parameters obtained experimentally, the analytical results showed a good agreement with the phenomenon generated in the actual machines.

View full abstract

The purpose of this research was to reduce the total acoustic power of noise sources located in a free field, which leads to lowering of the noise level in the entire area around the noise sources. The condition realizing total power reduction was considered in this paper. The original noise sources and additional sources were modeled as point monopoles to derive equations for the power reduction effects to achieve the above purpose. Next, the power reduction effects in some typical cases were calculated when the existing active control system with an error microphone was adopted. The error microphone was set to minimize the noise level. It was found that the error microphone location significantly affected the power reduction effects and unsuitable locations caused the power increase even if the noise level at the error microphone was sufficiently lowered. The actual power reduction effects were examined using loudspeakers and adaptive noise control system on the basis of the LMS algorithm. Good agreements were obtained when the experimental results were compared with theoretical estimations.

View full abstract

A new type of infrared radiation thermometer with optical fiber that has quick response time (3 μs) and microscopically measurable area (φ11O μm) was developed for thermal analysis of the grinding phenomenon. The temperature obtained depended on the heat flow rate during grinding operation and heat of oxidation of removed chips. The measured signal also indicated two parts ; the base part and the impulse part. The former seemed to indicate the average temperature of grinding wheel surface, while the latter seemed to indicate the temperature of chips. The heat energy generated by oxidation was larger than the total amount of energy released by the grinding operation. When the grinding point came above the embedded optical fiber, the measured value indicated only the temperature of grinding wheel surface.

View full abstract

In this paper, we consider the robust stabilization control of an inverted pendulum with uncertain position of the center of gravity. For this purpose, using a nonlinear feedback compensator, a simplified model of the inverted pendulum system with structured uncertainty is derived. Then, the quadratic stabilization technique is applied to this model for the design of a robust stabilization controller. Experimental results are also shown to verify the usefulness of the proposed design method.

View full abstract

This paper describes two kinds of velocity-command-type trajectory control systems of a two-link flexible arm and experimental results using joint actuators and an active mass damper. One servo system has been developed which consists of a trajectory controller based on model-following servo control for the imaginary rigid body coordinate and an elastic deformation controller on LQI control. This system was shown to be effective from the experimental results and has the merit that controller gains can be easily calculated as constant values in spite of the flexible arm nonlinearity. Another servo system consists of a trajectory controller for the elastic deformation caused by gravitational force and a vibration controller using an active mass damper, which was also found to be effective.

View full abstract

For a small underwater robot floating in water, it is impossible to position the arm precisely only with the arm actuator, because the body is moved by the action of a fluid drag force and an inertial force acting on the arm. In this study, the positioning of the arm using a redundant counter arm and an internal reaction wheel is proposed for suppressing the flow disturbance around the robot. The counter arm, which is located in an axially symmetrical position, is used to cancel the forces acting on the operating arm. The reaction wheel is used to cancel the moment acting on the body. The arm positioning system using these actuators for the floating underwater robot is developed based on the optimal control theory. The performance of this system was confirmed by experimental models. It was shown that the counter arm and the reaction wheel are very effective for the precise positioning of the arm.

View full abstract

This paper presents a simple hybrid method for controlling both the motion and contact force of a manipulator without calculating inverse dynamics. The contact force is converted into a velocity vector according to the force/velocity conversion law. The velocity vector which is tangent to the constraint surface is calculated by the velocity servo. The desired velocity vecotor is obtained as a sum of the above two velocity vectors. The desired axial velocity vector is calculated from the desired velocity vector using inverse Jacobian matrix. Motion and force control is performed using DC motors whose desired values are the above desired axial velocity vector. The stability of the motion control system is also considered.

View full abstract

This paper describes an analytical method for the simulation of the vibrational behavior of spatial serial manipulators composed of multiple elastic links. The adjacent links joint method was proposed to calculate the internal forces and moments acting interactively between two adjacent elastic links connected with an offset and spatial twist angles. The anisotropic stiffnesses and damping coefficients of the elastic link were derived from the synthesis of the bending, compressive and torsional stiffness of a cantilever as a simple model of the elastic link. The position and the postures of the joint between the two adjacent links can be obtained by solving a system of linear equations. The free and transient vibrations of a spatial 2-link manipulator were analyzed and experimentally examined. The calculated natural frequencies and amplitudes of vibratory acceleration agreed well with the measured values.

View full abstract

This paper proposes a method to evaluate the kinematic structure of parallel link manipulators, based on the output force/torque of the mechanisms. As is well known, the relationship between the actuator force/torque and the output force/torque of manipulators is expressed by a manipulator Jacobian. In the conventional method based on the Jacobian matrix, both force and torque are analyzed simultaneously. However, it is not natural to deal with both force and torque simultaneously, since the force and torque have different dimensions. In this paper, we consider the output force and the output torque independently, and introduce the translatability and the rotatability of the manipulators. The kinematic structure is then analyzed based on the translatability and the rotatability of the manipulators. The translatability and the rotatability depend on the maximum output force and output torque of the manipulators, respectively, for given actuator forces. The proposed method is more natural than the conventional method and is useful for the design of the manipulator kinematic structure. An example illustrates the method.

View full abstract

This paper proposes a method for planning the collision-free trajectory for a manipulator. In this method, geometrical constraints to avoid obstacles are represented by constraint potential functions. The dynamical equation of the manipulator is expressed by a path parameter `s' which does not depend on time and is solved as a two-point boundary value problem. Input torques giving a desired trajectory are composed of two parts. One is for a shortening of the travelling time, and the other is for an avoidance of the collision by a potential function. Finally, the proposed method is applied to a manipulator with three links.

View full abstract

Recently, many research works of quadruped locomotion robots, which are considered to be operable on irregular terrain, have been carried out. In the case of realizing ideal motion control of the quadruped locomotion robot, it is assumed that hierarchical cooperative control consisting of decentralized control and centralized control is desirable. In the case that the locomotion robot moves at high speed, it is impossible to follow the desired trajectory because using only the feedback control method includes time delay. It is known that feedforward control input is valid for such motion control. In this paper, decentralized control is realized to apply optimal tracking control using feedforward control input to the quadruped locomotion robot, as the first step. As a result, it is determined that the angle variation of the foot and the stride applying optimal tracking control input are large compared with using only feedback control. It is verified that feedforward control input is useful to control the trajectory of the tip of the foot in high speed locomotion.

View full abstract

The Langevin-type ultrasonic motor is one of the promising actuators for robots since it has a simple construction, high response, and large torque at low speed. This paper proposes a robot hand having ultrasonic motors as the fingers without moving elements. This robot hand can grasp a cylindrical body and rotate it by three fingers at the same time. The driving characteristics of the robot hand were examined experimentally under various conditions. It was confirmed that large torgue was obtained when the suitable contact angle and pressing force of the ultrasonic motors were used. The reduction of the output torque is small even if the diameter of rotational body deviates from the designed value.

View full abstract

The robot finger force sensor should be as small as possible in order to install it in the tip of the robot finger. This paper proposes a new robot finger force sensor which is easily fabricated due to its simple structure and uses neural network to process interacting signals and solve nonlinearity of the sensor. For the above purpose, a trial fabrication of the new finger force sensor with capacitance-type clearance detectors was attempted and the experiments for the finger force sensor were carried out. Then it was shown that the sensor worked effectively as a robot finger force sensor. In addition, this new method is more accurate as compared with the conventional method pseud-inverse matrix.

View full abstract

Generally, real objective systems for controlling are nonlinear dynamic one. On the other hand, usual control theories are linear. Therefore, they are not so suitable for such nonlinear dynamic systems. Recently, neural network (NN) which has an ability to describe nonlinear dynamic characteristics are studied and applied in many technical fields. Proposed here is a control method which is suitable for nonlinear dynamic systems. This method uses real time identification of the transient system by NN and applying an usual linear control theory. These identification and applying are carried on at an interval of each control cycle time. Therefore, it can be applied for strong nonliner dynamic systems on the whole. There are 3 simulation examples applied the method, in the paper, and all show relatively good results.

View full abstract

Avoiding wasted time for learning and trapping at a local optimum are two important problems in learning of neural network. The tabu search method with random waves, to solve global optimization of continuous variables is introduced, and a new method which combines this and the steepest descent method is proposed. The reliability and effciency of the tabu search method and the new method are examined with the help of the one-dimension test function. They outperform the steepest descent method in the search of the global optimum. Using these methods as learning algorithm of a neural network, they are applied to examples of an exclusive OR problem, off-line identification of a dynamic system and on-line identification of a multi-degree system (cantilever) by simulation. In each case, it is shown that the neural network can learn quick and effectiveIy.

View full abstract

This paper proposes a framework for integrating independently learned knowledge by Boltzmann machines. Auto-associative neural networks based on distributed representation have some advantageous properties of dealing with knowledge. However, as to the supplement of knowledge under a dynamically changing environment, or the merging of independently acquired knowledge, they do not work well enough because of difficulty in supplementary learning. Therefore we propose a model for integrating knowledge by connecting independently learned network modules without additional learning. First, localized representation, which is indispensable for realizing interaction between knowledge in different modules, is introduced. Although it will spoil the flexibility of distributed representation, competitive learning adopted for translating representations preserves it to some extent. Secondly, the configuration of the connected network is explicated, and is behavior is illustrated. It is completely realized by activation, competition, and inhibition of Boltzmann machine. Finally, to demonstrate the effectiveness of the proposed model, results of computer simulation on a navigation problem of obstacle avoidance are shown.

View full abstract

The elastohydrodynamic oil film formed between a steel ball and a sapphire disk was observed by an optical interference method. In this study, the influence of a slip on the elastohydrodynamic oil film was investigated by creating a difference between the steel ball velocity and the sapphire disk velocity. The experiment shows that the film thickness formed under the condition of a constant mean velocity decreases with the increase of the slip. This finding is entirely different from the isothermal elastohydrodynamic theory. There is a possibility that this experimental result is due to the effect of oil temperature increase caused by the shearing heat and the effect of the non-Newtonian response of oils.

View full abstract

So far we have treated wheel/rail contact problems as a two-dimensional line contact and studied the behavior of traction force under various surface conditions. Here, in order to investigate the influence of lateral slip or traction on the longitudinal traction, we carried out some experiments of elliptic contact under water lubrication. The longitudinal traction force and slip were measured by applying a force perpendicular to the rolling direction with a special rolling contact testing machine. The relationship between traction coefficient and slip ratio obtained through experiments was compared with the results of our numerical analysis which used the boundary element method. It was recognized that under water lubrication, the experimental results approached the numerical ones as the rolling speed decreased, which gave the same tendency as our former line contact experiments and two-dimensional analytical results. When the force perpendicular to rolling direction increased, the maximum traction coefficient decreased. It could be explained through numerical analysis that the decrease of longitudinal traction due to lateral force was attributable to the increase of slipregion on the contact surface.

View full abstract

Tribological properties of structural materials of a superconducting magnet for a nuclear fusion reactor were investigated at temperatures of 293 K, 77 K and about 5 K in vacuum. Specimen materials were JN 1, JN 2 and SUS 316 L steels, copper and its alloys, and GFRP. The properties of the coefficient of friction against the number of cycles were classified into two groups : smooth friction and fluctuating friction. The latter was caused by the strong adhesion dependent on the material combination and temperature. The coefficient of friction of the smooth friction was low less than 0. 6. The upper coefficient of friction of fluctuating friction reaches more than 3. The temperature dependence of the coefficient of friction was also examined from 5 K to 130 K. Combinations of Cu-Cu and JN 2-cupronickel showed high friction over the temperature, but JN 1-Cu and JN 2-Cu showed clear temperature dependence where the friction was high at temperatures between 45 K and 90 K.

View full abstract

This work deals with the development of a manufacturing technique for high-aspect-ratio (height/width) micromechanical parts. The micromechanical parts or micromolds are made by writing with a UV laser beam on the surface of a liquid photopolymer layer. The author examine the shapes of the solidified polymer that can be obtained by writing using several shapes of beams along typical contours. The examination is done both theoretically and experimentally. The results show that a beam with a uniform intensity has a higher resolution than a gaussian beam in obtaining a determined solidified width and vertical sidewall along the thickness of the polymer layer. By using a beam with uniform intensity, high-aspect-ratio polymer microstructures are made.

View full abstract

Analytical results are presented for nonlinear vibrations of a timing belt with parametric excitation in tension and meshing impact forces, with application of the Galerkin method to the basic equation. The steady-state responses are calculated using the harmonic balance method. The numerical results yielcl the following conclusions. The resonant amplitude increases with the increase of pully speed for constant tension. In the case of variable tension, the resonant peak value varies with rate of variable tension, and inceases with increase of tension. Amplitude reduction by means of periodic variation of tension is effective for tension and rate of variable tension.

View full abstract

This paper presents a study on the friction and wear characteristics of gears in high vacuum. A gear testing machine of the power circulating type with a vacuum chamber was developed, in which the coefficient of friction between the contacting tooth surfaces, and the temperatures of the gear teeth and the shaft can be measured under various running conditions. The running tests for S 45 C, SUS 440 C and MoS₂-coated SUS 440 C gears were carried out in air and high vacuum environments by using the gear testing machine, and the coefficient of friction between the contacting tooth surfaces, the wear of the gear teeth, and temperature changes of the gear teeth, the shaft, etc., were measured. On the basis of these results, the friction and wear characteristics of gears in high vaccum were determined to a considerable extent.

View full abstract

A detailed description of elastic behavior due to contact is necessary for the analysis of vibrational behavior of a pair of helical gears having a tooth flank deviation which yields partial face contact under light load conditions. This paper shows how we can obtain the relationship between load distribution and the compressive deformation of meshing surfaces assigning the tooth contact pattern with geometry of two surfaces. Tooth surface contact is approximated by the contact between a finite-length cylinder surface whose radius varies along its center axis and a plane with the same width. Our results have been verified by experiment.

View full abstract

This paper introduces a simulator which can depict the rotational vibration of a helical pair with various kinds of deviations during transmission of a light load, causing incomplete contact between the gear pair. This situation occurs frequently in the case of an automobile moving at constant speed. Firstly, the relationship between deflection and load distribution of a single pair of meshing teeth is analyzed. Secondly, the method for the determination of multi-tooth pair load sharing is introduced. Afterwards, a numerical procedure which solves the equation of motion by means of the Runge-Kutta-Gill method is given. This procedure is verified by experiments for various kinds of tooth surface deviations.

View full abstract

This paper presents a study on the root and contact stresses of WN (Haseg SymMarC) gears. The validity of the method for calculating root and contact stresses of Haseg SymMarC gear teeth in mesh was confirmed by comparing the calculated root and contact stresses of Haseg SymMarC gear teeth with measured stresses. The root and contact stresses of Haseg SymMarC gears with various dimensions were calculated, and the effects of center distance, helix angle, face width, and number of teeth on the maximum root and contact stresses of Haseg SymMarC gear teeth in mesh were determined to a considerable extent. Furthermore, the root and contact stresses of Haseg SymMarC gear teeth were compared with those of SymMarC and involute gear teeth. The change of maximum root and contact stress of Haseg SymMarC gear with center distance is much smaller than that of SymMarC gear, and the maximum root and contact stresses of Haseg SymMarC gear were found to be much larger than that of SymMarC and involute gear teeth in the case of the normal center distance.

View full abstract

The pair of spiral bevel gears fabricated by Klingelnberg's cyclo-palloid method can be expected to have a good contact pattern because the gear tooth surfaces are fundamentally conjugate. In practice, however, the first gear pair having a good contact pattern is difficult to obtain because of the machine setting errors such as tool setting errors and workpiece setting errors in gear cutting. In this paper, an inspection method for detecting the machine setting errors in spiral bevel gear cutting in a Klingelnberg cyclo-palloid system is proposed. In this method, the coordinates of many points on the gear tooth surface are measured using a coordinate measuring machine and a geometrical gear tooth surface expressed as the functions of the machine settings is estimated by the method of least squares so that the surface can fit the measured data. The deviations of the estimated machine settings from the design values are considered to be the machine setting errors. The machine setting errors in gear cutting were detected using this method and corrective cutting which compensated for the errors was carried out. Consequently, more accurate gear could be obtained.

View full abstract

The acoustic emission (AE) technique is applied to the analysis of fatigue crack growth in a carburized gear tooth. Marked AEs are detected in the early stage of crack growth and the final stage just before the tooth failure. Through-hardened bend specimens are also tested to determine the AE from carbon steels with different hardnesses, and the AE energy rate is found to be proportional to the stress intensity factor range (ΔK) and crack growth rate. The AE for carburized gears is then simulated from the AE of the bend specimens whose hardness and ΔK are approximately equal to the hardness at the crack tip and ΔK of the gear tooth concerned. The simulation demonstrates higher AE at the early stage and at the final stage of crack growth, and it is characteristic of the measured AE.

View full abstract

The present paper describes hot finish rolling of injection-molded helical gears with a process of reversing the gear rotation. The finished work gear has a pressure angle error on its tooth profile. This is due to a sliding between die and work tooth flanks, so that the reversed process added to the ordinary one should be useful for reducing the pressure angle error. Thus, some experiments are performed under several operating conditions to reveal the effect of the combinations of rolling time and applied load for rolling in the ordinary and the reversed processes on finished tooth profiles. As a result, given lower applied load and shorter rolling time in the reversed process than in the ordinary one, the pressure angle error can be reduced and a more accurate tooth profile of the finished work gear can be obtained.

View full abstract

This paper deals with a software system for the displacement analysis of arbitrary mechanisms, which has been discussed by many researchers. However, concerning the topological analysis of the mechanism and the automated generation of joint information, the previous works still leave several problems unsolved. We propose more general methods than those previously proposed to handle the spatial constraints involving the higher pair by means of solid models and to analyze the structure of the mechanism by considering directions of multiple closed loops. Furthermore, the technique of mathematical programming is applied to the displacement analysis. The practical applicability of the developed system with the methods described in this paper is demonstrated through several examples.

View full abstract

This paper deals with the theoretical identification of alignment errors for five-axis machining centers. The form-shaping function which takes geometrical errors into account is theoretically derived for the error analysis of precision machine tools. The relationship between error sources and machined error is expressed by using the transformation matrices. In the five-axis machining center, errors in the relative position between the workpiece and the cutting tool directly affect the accuracy of the operation being performed. This positional error originates from numerous factors including geometrical errors of the structure elements, kinematic errors related to the motion of these elements, or thermally induced errors, static and dynamic deflection, etc. Alignment errors have basic effects on the machining error. In this paper, therefore, the effect of alignment errors is clarified by using the form-shaping function. Assuming the use of a double-ball-bar device, the measurement method for alignment errors in a five-axis machining center is proposed. Additionally, eleven (11) alignment errors in a five-axis machining center can be identified from measured values obtained by double-ball-bar.

View full abstract

A method is proposed to solve the large-scale production planning problem with setup times and limited overtime. A Lagrangean relaxation method is adopted to decompose the problem into two subproblems, and the Lagrangean dual problem is solved by the subgradient method. In our approach, however, the subgradient method is applied iteratively, and the initial value of the Lagrangean value is derived from the last value of the previous iteration. The heuristic method is also proposed to improve the solution of the uncapacitated lot-sizing problem that is one of two subproblems. This heuristic method uses only the cost of the lot-sizing problem to utilize unused regular time. In our computational study 250 feasible solutions out of 288 test problems are obtained. The test problems range from 12 periods and 100 products to 24 periods and 1000 products. The average difference between the best feasible solution and the lower bound is 3. 5%, and the performance of the method is enhanced to 1. 7% under the condition of a low-cost premium for overtime.

View full abstract