A logarithmic profile is an essentially optimal geometry for rolling machine elements such as bearing rollers and raceways. Although some design methods of the profile have been proposed, they don't refer to the tolerance of geometry required in engineering applications and production. This paper shows how to define the tolerance range associated with the optimum profile suggested for bearing rollers by the authors. The overall tolerance is reasonably defined by giving the reduced amount of roller radius at three points so that the von Mises equivalent stress will not exceed a specified limit, where the point locations are measured from the intersection of the crowing curve and the chamfer curve not from the roller end. For the purpose of design usefulness, the tolerance expression is offered in dimensionless form.

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This paper investigates the vibration of one-degree-of-freedom magnetically levitated body. Especially, the influences of the nonlinearity of the system and the dynamical characteristics of electric circuit and magnetic circuit are focused. This paper considers the case that electric current supplied from a power-operational amplifier is limited in a positive range. Thus, the system has piecewise nonlinearity when the vibration amplitude is large. The nonlinear analysis for this system is discussed. The dynamical characteristics of the system is clarified by numerical simulation and theoretical analysis. These obtained results are confirmed by experiment.

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This paper deals with the analysis of collision vibration in continuous system excited by periodic displacement with arbitrary function. The analytical model is steady collision vibration of cantilever which collides with arbitrary location between fixed and free ends. Then, the cantilever collides elastically with the coil springs clamped on symmetrical faces when the amplitude of cantilever vibration exceeds the clearance at the springs location. In order to clarify the main resonance of the system, the resulting vibration is analyzed applying the Fourier series method for this system and an exact solution is proposed. Following the theoretical analysis, numerical calculation is performed and the resonance curves are constructed from resulting vibration. The numerical results show effects on the amplitude of forced vibration, the collision position and the stiffness of clamped springs for resonance curves. Experiments are also carried out to verify the theoretical results.

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In this paper, the authors propose a vertical seismic isolation system consisting of four V-shaped links, torsion springs, hinges, a table board and a base board, which has bilinear spring force characteristic. This characteristic is effective in reducing the static deflection of the vertical isolation system. The resisting force characteristic and seismic responses of this isolation system were analyzed numerically. The trial isolation system was made, and the static and dynamic resisting force characteristics were measured. The seismic responses of a mass installed on the table board were measured using a vibration machine. The experimental results were compared with the calculated results and the effects of vibration isolation in vertical direction and the validity of the calculations were substantiated.

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In order to calculate correctly high-speed nonlinear transient phenomena of a large order rotor system such as rotor collision and rubbing with stator repeatedly due to blade loss, a very small incremental time step is required in numerical integration. But a small time step is known to become a cause of divergence or flutter type numerical instability when a direct integration such as Newmark-β method is applied in terms of physical coordinate. Normal mode method, which uses eigen modes instead of physical freedoms, is effective on this numerical stability, but the modes in the calculation are usually complex modes and also need recalculation in accordance with varying rotational speed. Therefore, this method is inconvenient for an analysis of a rotor especially speed varying system. This paper presents a new method using constraint real mode synthesis in which rotor modes are derived by neglecting gyroscopic moment as at 0rpm and by fixing bearing connection interface freedoms to zero. This method is proved to be highly stable and also to have good accuracy and efficiency in the calculation.

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A system identification technique for a vibration isolation table is studied in this paper. The vibration isolation table is supported by four pneumatic actuators at corners of the square rigid table. A 3 DOF mathematical model of the vibration isolation table is constructed. The regulator for the pneumatic actuator is driven by a stepping motor. Proposed procedure to obtain the minimum-order-model is described as follows: First, the state space model is identified from input-output data by subspace method. Next, the low order curve fitting model is calculated by Frequency-Domain Least-Squares Approximation (FDLSA). And then, the characteristic eigenvalues near the eigenvalues of FDLSA model is picked out from the N4SID model, and the minimum order system that has the characteristic eigenvalues of N4SID model is reconstructed. And the procedure can be fully automated. Effectiveness of this approach is examined by experiments.

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The cure against sloshing is a very important subject on disaster prevention. However, only a few tanks were made in consideration of sloshing. Low-cost methods of sloshing suppression are desired. The authors predicted that horizontal plates installed near surface in the liquid beside the tank wall are effective to suppress sloshing. Analytical simulation and experiments were performed about parallelepiped tanks. The collocation method is used for analytical simulations. The simulations and the experiments confirmed the prediction that horizontal baffles suppress sloshing. The horizontal baffle plates obstruct up and down motion of liquid near the tank walls. As a result, sloshing becomes small. In this case, damping is not main factor of sloshing suppression. It is guessed that horizontal baffle plates are effective to suppress sloshing also in other shaped tank than the parallelepiped.

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A railway is organized by a variety of individual technologies, and functions safely and properly as a system, therefore it is necessary for the system safety to study each potential unsafe case caused by earthquakes. Recent reports imply that railway vehicles could be derailed by earthquake ground motions without fatal damages of vehicles or tracks. Thus, we should further study the derailment mechanism to pursue to minimize the risk of railway system safety against large earthquakes. Particularly, for more comprehensive understanding on the derailment mechanism of high speed railway vehicle, the derailment process should be experimentally studied. Therefore, in this study, we arrange an experimental setup with 1/10 scale vehicle and roller rig providing both conditions of high speed wheel/rail rolling contact and large amplitude excitations. Through the experiment, we obtained the outcomes. (1) Two types of vehicle derailment motions are observed; one is rocking derailment and the other is sliding derailment. Derailment motions are similar regardless of vehicle speed. (2) By contrast, the excitation amplitudes for derailment decrease according to the increase of vehicle speed particularly by low frequency excitations. (3) The excitation amplitudes for wheel lift of flange height are relatively independent of vehicle speed. (4) Based on the similarly of fundamental vehicle dynamics between the 1/10 scale vehicle and full scale vehicle, those observed mechanisms should be applicable to full scale vehicle.

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This paper presents a theoretical study on the controllability of tractor and semitrailer combinations in lane changes. The analysis is conducted by using a three DOF model incorporating the lateral deviation and yawing of vehicles. The steering sensitivity, settling time, and maximum deviation are defined as controllability features and are calculated together with the stability factor and critical speed, taking into consideration over-loading conditions. The following conclusions are drawn. (1) The steering sensitivity in lane changes is a function of the stability factor of the tractor combined with a semitrailer, the steering duration in lane changing and the width between centerlines of the lanes. (2) For uniform over-loading conditions, the steering sensitivity in lane changes to forward velocities increases with increased loading. For the front over-loading conditions, the steering sensitivity is greater than that of uniform over-loading conditions. For the rear over-loading conditions, the steering sensitivity is less than that of uniform over-loading conditions. (3) The settling time is similar to the steering sensitivity because of non-oscillatory behavior of vehicles in over-loading conditions. (4) The maximum deviation becomes small as the vehicle forward velocity approaches the critical speed in over-loading conditions.

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In this research, the dynamic characteristics of a small wheel bicycle are investigated. The bicycle model is formulated by using multibody dynamics. Then, the stability of bicycles is analyzed by parametric study using the bicycle model. The effects of the parameters of tire diameter and head angle are examined by focusing on a small wheel bicycle. The straight-ahead stability and upstanding stability are evaluated at each parameter. The results show the tendency of stability at each parameter and the influential parameter to the small wheel bicycle is found. The driving experiment using the small wheel bicycle is performed. In the experiment, the stability of the small wheel bicycles with variable head angle is evaluated by the subjects. It is confirmed that varying head angle increases the stability of the small wheel bicycle. The results are corresponding with the simulation results and it is shown that the simulation captures the tendency of the stability and expresses the characteristics of the small wheel bicycle.

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The characteristics of multi-surface liquid motion in a rectangular tank are investigated. The rectangular tank is divided into two parts by a baffle, which is vertical to the bottom of the tank and does not reach the bottom. The cases that two liquid surfaces have different areas from each other are mainly interested. Boundary element method is applied to the Laplace equation with linearized boundary conditions. A good agreement was found between the theoretical and experimental results. Effects caused by the position of the baffle, and the distance between the baffle and the bottom, upon the natural frequencies and corresponding mode shapes are discussed.

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This paper describes a modeling and a nonlinear control design method based on multibody dynamics (MBD). Each arm of the robot has seven degrees of freedom, similar to a human arm. The arm is a redundant manipulator, so it is difficult to control the arm generally. It is necessary to derive an accurate model of the arm. It is straightforward to set up three-dimensional equations of motion using MBD. A model for the robot is derived by MBD. We propose two controllers using the MBD model. One is consists of an LQI controller and inverse dynamics. The other one is a nonlinear controller using the structure of the MBD model positively. We tested the effectiveness of our proposed method by experiment. As a result, the tracking performance of the nonlinear controller based on the MBD model was about 18% better than the controller of the LQI controller with inverse dynamics.

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This paper proposes a four-wheel type trailer system of which steering mechanism is combined with SSM (Sensor Steering Mechanism). SSM is able to apply a front wheel steering type and a four-wheel steering one. In this paper the trailer system is constructed with a trailer and a tractor. Both vehicles have a selfstanding control system and are able to move on the track with a guideway. Previous paper discussed the high-speed moving characteristics of single body vehicle which is guided by the modified SSM. Simulated and experimented data were well coincided with the drifting maneuver at the corner. This paper derives dynamical equations of the trailer system and simulates the movement its on the test track at high-speed. Experimental data demonstrates the advantages of the proposed system.

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We describe a new robotic assist device: a passive assist arm (PAS-Arm). PAS-Arms are intended for direct physical interaction with a human operator, handling a shared payload. PAS-Arms are physically passive. Their purpose is not to enhance human strength, but to provide virtual guiding surfaces, which constrain and guide the motion of the payload within a shared workspace. PAS-Arms have three joints and a three dimensional workspace, but possesses only a two degrees of freedom, due to the reduction of degrees of freedom created by a combination of continuously variable transmissions (CVTs) and differential gears. We have developed an experimental system of the PAS-Arm. In this paper, we describe kinematic specification of the experimental system. We discuss the differential relation of transmission ratios created by the CVTs. We conducted the relationship between transmission ratio resolutions of the CVTs and resolutions of normal vector of the guiding surface, and the relationship between angular velocities of PAS-Arm's joints and time derivative of the transmission ratios. Assuming that the Euclidean norm of the angular velocities is constant, maximum time derivative of transmission ratios are in proportion to link lengths of the PAS-Arm. We also describe the design of the CVT for use in the experimental system.

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In face-to-face communication, we use not only verbal medium but also non-verbal medium for communication. In particular facial expressions are very imortant for emotional communication because they show emotions and feelings effectively. Therefore it is thought that facial expressions are necessary in order to make human-robot communication more naturally. In this paper, "Face Robot" that has human-like appearance and can display facial expressions similar to human being is developed. In order to improve the humanity, the skin of the face robot is taken from the cast of female's face (i.e. life-mask). We then add and improve control points of the face robot according to features of her face. Moreover we analyze her facial expressions in order to mimic her real-time facial expressions with the face robot. We then confirm that mimicking of her real-time facial expressions and face features with the face robot are reproduced successfully. Finally, we compare their facial expressions by comparison of facial characteristics points and sensory evaluations.

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For motion leanings field, how to get a motion form defined by a repeated motion patterns is an exciting research issue. Although there have been so many studies reported in relation to evolutionary learning of robotic motion, there are few studies concerning with motion form. We reported that reinforcement learning method has ability to emerge the motion form of robots using a one-dimensional caterpillar-type mobile robot. This paper clarifies transit motion forms under learning process of a starfish-type robot with two-dimensional mobile function. Moreover, the learning results show both unexpected motion results that are essential function for the reinforcement learning and two-dimensional learning knowledge manipulation in the viewpoint of learning knowledge generality.

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A hybrid tactile displaying method of realistic texture is realized by use of ultrasonic vibrator and force display. Various realistic tactile senses are displayed by controlling multiple factors including roughness, softness and friction sense. First, a tactile displaying system was constructed for displaying roughness, softness and friction sense, simultaneously, by compensating the interference among multiple parameters of ultrasonic vibration and force feedback on multiple tactile senses. Second, the proposed method for displaying softness and friction sense were verified by several sensory evaluation experiments. The relationship between each control parameter and the tactile senses were quantified as well. Then, material discrimination experiment was conducted. As a result, percentage of questions answered correctly was more than 87.5 in all materials. Finally, the tactile senses of real materials and hybrid artificial tactile senses were evaluated using adjectives. As a result, it was verified that the correlation coefficients between real materials and hybrid artificial tactile senses were quite large in the evaluation items on roughness, softness and friction sense.

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A two-dimensional microphone array is used to acquire spatial sound field distributions. The spacing between the microphones in the array should be shortened when the sound field would be acquired at the high frequency. The narrower spacing of the microphones would be also employed to acquire evanescent wave components of the sound field near the source. These components are utilized in the applications of the NAH (Near-field Acoustic Holography). This condition might causes some deviations included measured values because of the cylindrical bodies of the neighbor microphones closely located each other. Authors have already presented in the former experimental study that there are some deviations because of the existence of the structure of the microphone array in the measured sound field. In this study, analytical method based on the boundary element method has been developed, and verified with the experimental results mentioned above. Then characteristics of the deviations are investigated, that are caused respectively by the set of the bodies of all the microphones or the outer frame that holds the microphones. Finally, the maximum frequencies are defined to measure the sound field that is compromised as the true values with the various types of the microphone holders. It is also shown that the deviation caused by the small frame designed as a practical size is larger than the deviation by the set of all the microphones.

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This paper presents Frequency Response Function (FRF) estimation with the two-microphone method and its application for noise source separation. The cogeneration system radiates noise caused by its gas engine, which is power plant installed in the enclosure. Noise radiated from the enclosure consists of structure- and air-borne noise. Therefore, to reduce the noise radiated from the cogeneration system, it is significant to investigate the contribution of each noise source. In this paper, by using FRF which reference was volume velocity, contributions of noise sources in the cogeneration system were identified. Volume velocity source consists of a speaker, a tube and two probe microphones. FRF was estimated from the outputs of two microphones inside tube and that of a microphone at a response point. At first, the accuracy of the proposed method was investigated by the comparison between the test and the simulation by boundary element method. Next, the effectiveness of this method was confirmed by the noise source separation of the enclosure that includes an electro-magnetic shaker and the volume velocity source. Finally, noise source separation of cogeneration system was performed. As a result, a good agreement was observed between the measured results and the identified ones.

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In this paper, we consider an optimization problem of lens adjustment in semiconductor lithography equipment. The problem to obtain optimal adjustment of lens can be naturally formulated as a convex minimization problem. However, in such a formulation the objective function is convex but contains many nondifferentiable points, and thus methods based on derivatives cannot be applied. Other approaches using derivative-free optimization or meta-heuristic methods cannot guarantee that obtained solutions are truly optimal. From such a background, we formulate the problem as quadratically constrained and second-order cone programming problems, which can be handled by solvers using an interior point method. With the proposed formulations, computational simulations show that optimal adjustment of lens is obtained in a practical computational time.

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A novel mechanism CVT (Shaft Drive CVT) was developed by the authors. In the mechanism, the input and output shafts with conical disks are parallel and an idler shaft with conical rollers at both ends is placed perpendicular to the input/output shafts. This idler shaft transmits torque from the input shaft to the output shaft and its linear motion causes the speed to vary by changing the contact point between the input/output disk and the idler roller. The backup conical roller, which is mounted to the opposite side of the idler roller, is useful to enlarge the amount of transmitted torque. But it has a problem that the speed efficiency decreases largely when the loaded torque becomes to an allowable torque. To solve this problem, a counter shaft mechanism that connects the two backup rollers is proposed. It adds a new torque path and prevents the increase of slip. The effect of counter shaft is examined theoritically and confirmed by the experiment using the prototype CVT. The efficiency of 2 percentage points was improved by using the counter shaft.

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DLC (Diamond-Like Carbon) films are used in various fields because of their low coefficient of friction and their high wear resistance. Although there are many evaluation techniques for the surface strength of DLC films, those are not sufficiently established now. Regarding this background, we have proposed a new type of solid particle impact (micro slurry-jet erosion: MSE) test to swiftly evaluate the wear properties of thin hard coatings. In the present study, we evaluated the wear rate of DLC films deposited by the unbalanced magnetron sputtering method under different bias voltages (0V, -50V, -100V, -150V). The wear rate (μm/min) decreased with increasing bias voltage. Atomic force microscope (AFM) images of the worn surfaces showed that the surface roughness became smaller with higher bias voltage. From these results, we conclude that the wear debris become smaller in size and the number of detached particles decreases with increasing bias voltage. Thus, the high wear resistance of DLC films is related with their high hardness. Furthermore, our method can be recommended as a screening test when evaluating DLC films.

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Monolayer films of functional perfluoropolyethers (PFPEs) that are partially bonded to disk surfaces are widely used to lubricate magnetic disks. The bonding ratio (i.e., ratio of bonded thickness to total film thickness) possibly impacts the tribological behavior of the lubricant films. In this work, under lightly loaded (0-1mN) and slowly rotated (1 or 2rpm) conditions that prevent disturbance of the lubricant bonding state, we measured the frictional properties of 2-nm-thick PFPE Zdol2000 and Zdol4000 films as a function of bonding ratio adjusted up to 100% by anneal treatment. The friction forces of both Zdol2000 and Zdol4000 increased with increasing bonding ratio, but the increase was less noticeable for Zdol4000. Additionally, the friction of the non-annealed (5%-bonded) Zdol2000 films exhibited a linear increase with external load as described by Amontons' law, and it increased with sliding speed. In contrast, the friction of the 100%-bonded Zdol2000 films increased nonlinearly with external load as predicted by the Johnson-Kendall-Roberts model, and it showed no obvious speed dependency. These results suggest that mobile molecules show liquid-like frictional properties dominated by viscosity resistance, but bonded molecules exhibit elastomer-like frictional properties determined by energy dissipation during molecule deformation.

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It is well known that the plastic gears have some advantages, that is lightweight, low noise and operation of oil-less conditions. But plastic gears have been used only low torque conditions. As FRP gears have acquired higher strength and stiffness than the plastic gears, FRP gears are now attracting attention and they have replaced metallic gear in order to reduce weight and noise. Although there have been many researches on metallic gears, we have seen few reports about FRP gears. At present, FRP gears are designed mainly based on few test data of plastic gears and experiences that engineers have. In this research, we investigated the bending fracture characteristic of FRP gears to develop design criterion for FRP gears. According to the experimental results, it is clear that tensile, compressive and shear strength of FRP materials were needed to estimate the tooth bending strength.

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The cell migratory characterization in micro machined surface of compact bovine bone was evaluated on basic research for surgery healing control. The property of orthopedic surgery processing was investigated prior to evaluate the cell migration, and the property was classified in the four processing mechanisms of cutting, grinding, polishing and cracking in terms of engineering processing. The cell migratory characterization was evaluated in the machined surface with above four mechanisms. The result showed that the cell migration in straight direction along the groove tended to spread the indefinite direction, according to change in the mixture groove track from straight one. From these results, the cell migratory characterization was affected by the groove track in the machined surface as previous study reported by titanium surface. The effect on the cell migration was also controlled by the roughness in machined surface with the larger groove track.

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The orthogonal cutting test of compact bovine bone was conducted, and the fracture behavior in micro cutting with chip formation was investigated by considering the effect on the anisotropic tissue. The result showed that the effect of anisotropic tissue was observed in formation of the continuous chip and the interrupted chip with the uncontinuous cutting surface. The chip formation was also similar to mechanics of that in cutting of the other anisotoropic material such as wood. Therefore, the shape of chip formation in the compact bone was categorized by types of flow, crack, shear and tear as classified in cutting wood. The effect of anisotropic tissue in shape of the chip formation was observed from some fracture types with crack propagation. Form these results, the fracture behavior in micro cutting of compact bone was suggested that the crack of type I might be progressed straightly along the osteon tissue in compact bone, another crack of type II might be curved on the outskirts of the osteon tissue, and the other crack of type III might be progressed severely in lamella of osteon tissue.

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Recently developments with short-term and lower cost are strongly required for shorten life cycle of products. For these problems, FEM simulation is used to predict the result of processing instead of real test. The other side, TAGUCHI methods for robust design are also used to decide optimum processing conditions with narrow dispersion. In our former study, we had developed and evaluated regarding a simulation system of CAE without trial working for the products. In this study, the system was first manufactured for calculating regarding the optimum conditions on the design. This system consists of TAGUCHI methods, commercially produced CAE and management of productivity. The TAGUCHI methods were used for calculating SN ratio, sensitivity, average and standard deviation for all combination of all parameters. The CAE was used for shortening the total time of evaluation instead of real test. The management of productivity was used for selecting the optimum value regarding all parameters. The system was remade for high precision system using dispersion of error factors. Accuracy of the system was finally checked by using a few mathematical models. It is concluded from the result that; (1) The simulation system on CAE without trial working for products could use for deciding the optimum conditions on the design, (2) The system could consider regarding effect of using dispersion of error factors, (3) Accuracy of the system was excellent, and the system would use effectively in the industrial world.

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Recently the dies with cemented carbide are used for many products using its high stiffness and high wear resistance. The hand lapping is even now used as finishing process of them because of difficulty of its mechanization. The new lapping system was developed in our previous study from these reasons. And the lapping system could machine to flat surface of cemented carbide (V10) with mirror-like surface. In that case, mixture of diluted starch syrup and diamond grain was used as lapping slurry. However, this slurry can machine only flat bottom surface because of dropping the grain for lapping. So, it has to improve for the lapping to three dimensional work pieces including vertical surface, concave-convex surface. In this study, the mixture of polymer material and diamond grain was used as new lapping slurry for suspending the diamond grain using special properties of polymer. The distribution density of grain in the slurry medium was researched by experiment. Relationship between the lapping condition and the grain retention propaties on tool head was researched. Finally improving the surface roughness of large work piece was confirmed. It is concluded from the results that; (1) New lapping slurry with polymer can keep the diamond grain while enough time for machining. (2) The best lapping condition was confirmed from TAGUCHI methods and experiment. (3) New lapping slurry can be used for lapping the mirror-like surface of large or complex dies.

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NURBS (Non-Uniform Rational B-Spline) is well known to express free-form curves and surfaces in current CAD systems. Some NC controllers can accept NC data written in the NURBS interpolated format by using G 06.2 code, and NURBS interpolated machining enables us to decrease the amount of NC data, to eliminate the error due to the linear interpolation and so on. Although there are a few post-processors to generate NURBS interpolated NC data for simultaneous 5-axis controlled machining, most of them transform linear interpolated NC data into NURBS interpolated ones by the least square method and so on. Therefore, if the linear. interpolated NC data is huge, the conventional post-processor may require a long calculation time to generate NURBS interpolated ones. In addition, the post-processor lacks general versatility because it copes with a specific machining center. To solve these problems, the study deals with developing a generalized post-processor which can generate NC data without the linear approximation, while considering the axis composition of various machining centers. As the result, it is found that the developed post-processor efficiently generates practical 5-axis NURBS interpolated NC data.

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The static characteristics of a pneumatic bending actuator, which is made of fiber reinforced rubber, have been examined theoretically and experimentally. Fiber reinforced rubber used for the pneumatic bending actuators is a rubber construction that uses silicone rubber for the base material and nylon for the fibers. The theoretical expression for estimating the bending force of an actuator has been derived for an arc-shaped deformation model with one degree of freedom. Experimental measurements were carried out to examine the relationship between the bending angle and the bending force of actuators. Experimental results show that the derived expression is valid and useful for design of bending actuators of this type. The bending force increases as the thickness of the bottom side of a bending actuator becomes large.

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A "self-maintenance" (SM) machine has been developed and validated. It is so promising, since it reduces the probability of serious damages from malfunction and automates maintenance processes. It has been even commercialized in real market of photo copiers, but the implementation was specifically designed for a photo copier. Thus, a generic functionality of SM that can be additionally put on various kinds of machines would be highly demanded. This paper proposes such generic module for SM. This is structured in a form of "cellular machine", which consists of homogeneous "cells", so that it can adapt to the target machine to be maintained and it is highly fault-tolerant itself. This can be designed independently of a target machine. The paper presents a fundamental way to structure and design those modules and the module's algorithm of fault diagnosis. Those are verified in a design support system and fault simulation system on computer program.

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This research focuses on quantitative analysis techniques for optimization of conceptual designs for products where life-cycle considerations are crucial. A product for which energy saving is practically mandatory, such as a major home appliance, was chosen, and the proposed procedure for minimizing the total cost through the product's lifecycle focuses especially on the use and maintenance stages. A multiobjective optimization problem is developed to minimize two evaluative characteristics, the manufacturing cost of the product (I), and the sum of the energy and maintenance costs of the product over an assumed period of time (II), treating the longevity of specified portions of the product and energy consumption rate as design variables. The optimization simulation was carried out for a numerical example based on this model, and a Pareto optimum solution for costs (I) and (II) was obtained. Using this Pareto optimum solution, we analyzed the optimum values of design variables and clarified quantitatively how the design parameters affect the optimum solution. The proposed model demonstrates potential for use in decision making during the conceptual product design stage, when determining design variable values that meet desired lifecycle cost requirements is a goal.

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