Journal of Advanced Mechanical Design, Systems, and Manufacturing
Online ISSN : 1881-3054
ISSN-L : 1881-3054
Volume 6, Issue 7
Displaying 1-25 of 25 articles from this issue
Paper
  • Kuo-Wei LIAO, Buo-Chang LU, Si-Ping YU
    2012 Volume 6 Issue 7 Pages 1015-1030
    Published: 2012
    Released on J-STAGE: September 28, 2012
    JOURNAL FREE ACCESS
    A concurrent approach, which considers variability in design parameters, is proposed for a reliability-based design optimization (RBDO) problem. The RBDO is reformulated as a system with a bi-level structure, consisting of upper and lower levels. The upper level has one sub-system, while the lower level includes two sub-systems. Two major calculations in the RBDO, the reliability analysis (RA) and the deterministic optimization (DO), are decoupled via two sets of pseudo-linking variables, which are copies of the responses in both levels. The objective of the upper level is to minimize the difference in the pseudo-linking variables between the two levels. The main tasks in the lower level are to execute the DO and RA concurrently. The proposed procedure prevents the RBDO from performing the inherited double-loop calculation and improves the computational efficiency. Another benefit is that the RBDO can be solved by any individual RA and DO software. Convergence of the proposed bi-level approach is discussed through the concept of overlapping coordination methodology. Details of a RBDO problem that was solved by the bi-level algorithm are revealed through three numerical examples.
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  • Mongkolwongrojn MONGKOL, Panichakorn JESDA
    2012 Volume 6 Issue 7 Pages 1031-1045
    Published: 2012
    Released on J-STAGE: September 28, 2012
    JOURNAL FREE ACCESS
    The time-dependent modified Reynolds equation, elasticity equation, and energy equation with initial conditions were formulated and solved numerically using a multi-grid multilevel with full approximation technique for an involute spur gear. In this analysis, the normal load and sudden overload are applied on either two pairs or one pair of gear teeth. The transition from two pairs to one pair and vice versa are modeled as a step variation of load. The effects of overload, surface roughness, non-Newtonian lubricant properties of the meshing gear in the region along the line of action are examined. The results show that lubricant properties and surface roughness have significant effects on film thickness, film temperature and friction coefficient for spur gears with rough surfaces. The minimum film thickness is decreased rapidly with the decrease of lubricant power law index. For gears operated at a sudden overload condition, the film temperature and friction coefficient are severely increased.
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  • Ryuta NAKAMURA, Akira IWABUCHI
    2012 Volume 6 Issue 7 Pages 1046-1056
    Published: 2012
    Released on J-STAGE: September 28, 2012
    JOURNAL FREE ACCESS
    In previous study, the role of graphite on tribological behavior of cast iron was examined, and the model of cast iron in wear mechanism was proposed. However, this wear mechanism is the model for macro scale test, and has the possibility of showing behavior different from the model shown by the macro scale test in micro-nano scale test. Then, in this study, nano scratch test was carried out by using cast iron and S45C steel as a comparison, it aimed to examine role of graphite in cast iron for the micro-nano scale. As a result, it was understood that the model shown in the macro scale test was the same in micro-nano scale test. And in micro-nano scale, it thought that formation and maintenance of graphite film were dependent on the stick slip phenomenon by increase in indentation depth accompanying increase in load.
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  • Yoshiaki SHIMIZU, Toshiya WAKI, Tatsuhiko SAKAGUCHI
    2012 Volume 6 Issue 7 Pages 1057-1070
    Published: 2012
    Released on J-STAGE: September 28, 2012
    JOURNAL FREE ACCESS
    To meet higher customer satisfaction and shorter production lead time under rapidly changing demands and global competition, importance of just-in-time and agile manufacturing is raising much more attentions than before. To cope with such circumstances, assembly line is shifting to mixed-model assembly line. Under such situation, it is essential to extend system boundary wider and resolve the problem totally. Moreover, in this study, we pay our attention to the latest production manner applied in car industry and extend our conventional model associated with due dates of finished products. Finally, we have formulated a bi-objective optimization problem that aims at reducing total sum of tardiness and total volume of inventories at the same time. Besides the usual one-through approach to solve the resulting problem, we adopt a two stage approach associated with multi-objective analysis. To reveal some properties of the proposed approaches, we provide a case study and discuss effectiveness of the method and usefulness of the results.
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  • Suk-Jae JEONG, Hosang JUNG
    2012 Volume 6 Issue 7 Pages 1071-1080
    Published: 2012
    Released on J-STAGE: September 28, 2012
    JOURNAL FREE ACCESS
    Over the past few decades, buffer allocation problems have been investigated extensively. It is widely known that buffers play important roles in the manufacturing system, including preparing disruption and improving efficiency. However, due to a physical limit for buffer space and the related cost burden, optimal buffer allocation has become an important issue. In this paper, a solution for optimal buffer allocation in a flexible manufacturing system (FMS) with finite buffers is presented. Unlike most previous studies, which mainly focused on input buffers only and operation dispatching in simple production lines, this paper considers both input and output buffers together in complex production lines where multiple workstations, multiple automatic guided vehicles, and complicated paths exist. Also, we address a practical buffer allocation problem by increasing total number of buffers and changing a buffer profile (capacities of multiple input/output buffers). A simulation and a genetic algorithm are used to solve our problem. While the simulation models the process of the complex FMS, the genetic algorithm determines the optimal buffer allocation. The proposed solution performs better than the conventional heuristic used in practice.
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  • Jirasak SRIRAT, Satoshi KITAYAMA, Koetsu YAMAZAKI
    2012 Volume 6 Issue 7 Pages 1081-1092
    Published: 2012
    Released on J-STAGE: September 28, 2012
    JOURNAL FREE ACCESS
    In this paper, variable blank holder force (VBHF) trajectory and tools motion are optimized simultaneous by a sequential approximate optimization (SAO) with radial basis function (RBF) network. In deep drawing, wrinkling and tearing are major defects that are strongly avoided in sheet forming. These defects are then taken as the objectives directly. The Forming Limit Diagram (FLD) is employed to evaluate the risk of wrinkling and tearing quantitatively. The design variables are taken so as to optimize the VBHF trajectory and the tools motion simultaneously. In numerical examples, a square cup deep drawing is handled. The optimum result shows that simultaneous optimization of the VBHF trajectory and the tools motion result in the successful deep drawing. In particular, the forming energy can be drastically reduced, in comparison with only the optimization of VBHF trajectory. This result implies that the simultaneous optimization of both VBHF trajectory and tools motion will be effective approach to reduce the forming energy.
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  • Jirasak SRIRAT, Satoshi KITAYAMA, Koetsu YAMAZAKI
    2012 Volume 6 Issue 7 Pages 1093-1106
    Published: 2012
    Released on J-STAGE: September 28, 2012
    JOURNAL FREE ACCESS
    In this paper, the initial blank shape is optimized via sequential approximate optimization (SAO) with radial basis function (RBF) network. In deep drawing, the wrinkling and tearing are major defects. In addition, too small initial blank shape will results in the boundary of blank drawn into a trimming contour, which is the geometrical defect. Therefore, these three defects are taken as the design constraints. On the other hand, the flange area, which is often called the earing, is taken as the objective function. Also, variable blank holder force (VBHF) trajectory is determined. In this paper, new algorithm to evaluate the earing and the geometrical defect is also proposed for the SAO. Numerical result shows that the optimization of the initial blank shape with VBHF trajectory leads to defect-free product. In comparison with the use of square blank shape with a constant blank holder force, 60% reduction of the waste of material can be achieved.
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  • Hitoshi KIMURA, Mokutaro KATAOKA, Shotaro SUZUKI, Daisuke AKIMOTO, Nor ...
    2012 Volume 6 Issue 7 Pages 1107-1120
    Published: 2012
    Released on J-STAGE: September 28, 2012
    JOURNAL FREE ACCESS
    This study aims to build a totally flexible mechanical system with hydraulic skeleton driving mechanism. The main components of this system are two types of flexible bags. One is a structural bag with constant inner pressure. The other is an actuator bag with controlled inner pressure. Such flexible system will provide various advantages, for example, safety, portability, lightweight and dealing with fragile objects. Efficiency is also an advantage because only actuator parts consume driving fluid with the proposed system. This paper deals with a flexible robotic arm as an example of the proposed mechanism. With geometric relationship, effective parts arrangement and driving force at the joint are discussed in this paper. Quantitative estimations of structural deformation and driving force of flexible bags are important for design of the proposed system. However, numerical analysis of flexible bags is difficult because of their large nonlinear deformation. This study tries to analyze large nonlinear deformations of flexible bags with the nonlinear finite element analysis software ABAQUS. From the analytical results, this paper discusses unique effects of structural deformation depending on the driving force. The validity of the analysis is verified by experimental results. Both results show that the effect of concave deformation of a structural bag at the joint is 10 times larger than normal cantilever deformation. Pick and place motion of a raw egg is also performed with a proposed robotic arm avoiding large concave deformation without complex control such as force sensing and so on.
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  • Toshiyuki OBIKAWA, Bunji KANI
    2012 Volume 6 Issue 7 Pages 1121-1131
    Published: 2012
    Released on J-STAGE: October 05, 2012
    JOURNAL FREE ACCESS
    Many parts and structures for aerospace engineering, marine engineering, bioengineering, etc. are made of titanium alloy because of its excellent physical, chemical, biological and mechanical properties. These days, bio and medical technologies have developed, so more precise and smaller parts of this alloy are required to be machined. However, end milling of this alloy is not easy though many different types of coated end mills have been developed. In this paper, a micro ball end mill with a microstructured rake face was fabricated using focused iron beam irradiation. Then, the effects of different microstructured rake faces on cutting forces of titanium alloy Ti-6Al-4V were experimentally investigated for better machining conditions of this alloy. As a result, it was found that some particular types of microstructured rake faces reduced the cutting forces effectively.
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  • Nobuhiro SUGIMURA, Hitomi WATABIKI, Wiroj THASANA, Koji IWAMURA, Yoshi ...
    2012 Volume 6 Issue 7 Pages 1132-1142
    Published: 2012
    Released on J-STAGE: October 10, 2012
    JOURNAL FREE ACCESS
    Machine tools are recognized as key elements of manufacturing systems, and product quality and cost mainly depend on performances of the machine tools. Much progress has been made in the machine tool technologies, aimed at improving the performances of the machine tools from various viewpoints, such as accuracy, reliability, productivity, and flexibility. The machining accuracy is one of the most important characteristics of the machine tools. From the viewpoints of the design and the manufacturing of the machine tools and their components, one of the important issues is to clarify the relationships between the kinematic motion deviations of the machine tools and the geometric tolerances of the components, such as the guide ways and the bearings. The objectives of the present research are to establish mathematical models representing the kinematic motion deviations of the machine tools, on the basis of the geometric tolerances of the components, and to apply the models to theoretical analysis of the kinematic motion deviations of the machine tool components.
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  • Keiichiro TAKATO, Susumu SHIRAYAMA
    2012 Volume 6 Issue 7 Pages 1143-1153
    Published: 2012
    Released on J-STAGE: October 19, 2012
    JOURNAL FREE ACCESS
    In order to establish a sustainable society, a fundamental concept of industrial product design is to reduce as far as possible the use of starting resource materials. For education with respect to the design and manufacture of products, it is necessary to consider the environmental impact of materials selection. In the present study, we focus on bamboo as a design material because it has a wide habitat, grows rapidly, is carbon neutral, and can be consecutively deforested. In order to evaluate a practical educational approach, we examined the taketombo, which is a popular traditional Japanese flying toy made from bamboo, with respect to basic areas of mechanical engineering. In the present paper, practical design education is described based on the taketombo. By adopting this teaching material for design education, students who were not stimulated by traditional educational equipment, such as a Gettingen-type wind tunnel, became interested in our launch pad. Through this product design exercise, which incorporates responsible consideration for the environment in addition to ecological concepts, students were educated through design experience of the taketombo.
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  • Miaolei ZHOU, Wei GAO, Zhigang YANG, Yantao TIAN
    2012 Volume 6 Issue 7 Pages 1154-1167
    Published: 2012
    Released on J-STAGE: October 19, 2012
    JOURNAL FREE ACCESS
    As the core part of the electro-hydraulic servo system, the electro-hydraulic servo valve plays an important role in the system. Due to the piezoelectric actuator has characteristics of fast response, easy control and high control accuracy, it can be used as the electric-mechanical converter of the electro-hydraulic servo valve. However, this kind of the piezoelectric direct drive electro-hydraulic servo valve has hysteresis and creep nonlinearities. In order to improve the output accuracy of the system, a high-precise fuzzy control method with the dynamic Preisach model in feedforward loop is proposed. The control scheme is separated into two parts: a feedforward loop with the dynamic Preisach model and a feedback loop with high precise fuzzy control. The high precision fuzzy control adopts Lagrange interpolation method. The experimental results show that the proposed method can resolve the hysteresis and creep nonlinearities and reach a higher dynamic performance, the control effect is better than the conventional fuzzy control method.
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  • Pusit MITSOMWANG, Shigeru NAGASAWA, Seksan CHAIJIT, Masatoshi FUJIKURA ...
    2012 Volume 6 Issue 7 Pages 1168-1179
    Published: 2012
    Released on J-STAGE: October 23, 2012
    JOURNAL FREE ACCESS
    This paper reports on the cutting characteristics of a polycarbonate (PC) sheet stacked on a flexible underlay by a wedge indentation. In order to investigate the effect of underlay stiffness on sheared profile of PC sheet, the stiffness ratio kr in the thickness direction was varied. Indentation of a 42° center bevel blade into a 0.5mm thickness PC sheet that was stacked on the flexible underlay was carried out experimentally and numerically. Deformation profile of wedged PC sheet was observed by a CCD camera in order to reveal the effect of underlay on the cutting performance of the PC sheet. On the experimental works, it was found that the underlay mechanical properties affected the cutting load response and deformation features of the PC sheet. To discuss the effect of underlay stiffness on the deformation profile of the PC sheet, a finite element method (FEM) analysis with elasto-plastic model was conducted. Through the experiment and FEM simulation, it was revealed that the deformation profile of wedged PC sheet was remarkably related to the bent-up angle of the PC sheet, which was mainly caused by sinking and lateral elongation of the underlay. Moreover, in order to obtain a smart profile of the PC sheet, the stiffness ratio kr must be chosen in a suitable range.
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  • Chao ZHI, Tadahiko SHINSHI, Minoru UEHARA
    2012 Volume 6 Issue 7 Pages 1180-1189
    Published: 2012
    Released on J-STAGE: November 05, 2012
    JOURNAL FREE ACCESS
    A valveless micro pump, utilizing a multi-layer thin film NdFeB/Ta permanent magnet (TFPM), is presented. The micro pump consists of a diaphragm actuator, comprising a TFPM, 6µm in thickness and 3 mm in diameter, which is bonded to a membrane made of polydimethylsiloxane (PDMS) of about 80µm in thickness, together with a pump chamber and a pair of diffuser elements. TFPM is sputtered on a 50µm thick Nb sheet. The diffuser elements are used to generate a one-way fluid flow. The chamber is made of acryl plates. UV negative film resist is used to bond the different layers. Compared to sinusoidal driving signal with same amplitude, a square driving signal can generate a higher flow rate. Applying a square wave voltage, ±7.5V in amplitude, the pump flow rate attains 130µL/min at a frequency of 15Hz. The flow rate is highly dependent on frequency and driving signal type. Diaphragm displacement, pump frequency is measured and analyzed.
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  • Kai FENG
    2012 Volume 6 Issue 7 Pages 1190-1205
    Published: 2012
    Released on J-STAGE: November 12, 2012
    JOURNAL FREE ACCESS
    We propose a mathematical model for analyzing the effect of shaft and bearing flexibility on the dynamic behavior of helical gears. A primary feature of this study is that gear mesh stiffness is not just determined by the geometry of the gear pair but also by the center distance between the two gears. We present a six-degrees-of-freedom (DOF) model of helical gears to calculate the mesh forces from the deformations of teeth and the mesh stiffness of the corresponding spur gear pair. The pressure angle and contact ratio of the gear pair are treated as time-varying values and updated at each iteration during calculations. The predicted results show that if the deformations of the shafts and bearings are taken into consideration, the pressure angle and contact ratio will change significantly and the gear pair will exhibit larger vibration. We conducted experimental tests to validate the proposed model. The experimental data show good agreement with the predicted results.
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  • Nozomu KOGISO, Young-Soon YANG, Bong-Jae KIM, Jae-Ohk LEE
    2012 Volume 6 Issue 7 Pages 1206-1221
    Published: 2012
    Released on J-STAGE: November 20, 2012
    JOURNAL FREE ACCESS
    Single-Loop-Single-Vector (SLSV) method is to resolve the excessive computational cost problem in the reliability-based design optimization (RBDO) by decoupling the nested iteration loops. The key idea of the method is that the reliability constraint is transformed to the equivalent deterministic constraint by approximating the most probable point (MPP) using the point obtained from the previous iteration. However, the SLSV method sometimes suffers from numerical instability or inaccuracy problem. Thus, in this paper, a new modified SLSV method is proposed to improve its convergence capability effectively by utilizing Inactive Design and Active MPP Design together with modified-HMV (Hybrid Mean Value) method. The effectiveness of the proposed method is verified through some numerical examples.
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  • Xuda QIN, Linjing GUI, Hao LI, Bin RONG, Dongsheng WANG, Hongzhou ZHAN ...
    2012 Volume 6 Issue 7 Pages 1222-1233
    Published: 2012
    Released on J-STAGE: November 20, 2012
    JOURNAL FREE ACCESS
    The objective of the present work was to study the effect of the application of minimum quantity lubrication (MQL) in high-speed helical milling of Ti-6Al-4V compared with dry and flood coolant (wet) condition. The single factor experiment to study the relationship between cutting force, hole surface roughness and cutting parameters under various coolant-lubricant conditions were implemented. Tool life under various cooling conditions and fixed moderate cutting parameters have also been studied. Uniform flank wear, micro-chipping, thermal cracking and flaking were the dominant tool failure modes under all coolant-lubricant conditions. It was found that dry condition produced the poorest result in terms of cutting force, tool life and hole surface roughness as general expected. MQL presented comparable performance with flood condition in terms of cutting force and hole surface roughness, and even a better tool life performance than flood condition. This testified the flood condition can be replaced by the MQL condition, thus alleviating pollution and saving cost during helical milling of Ti-6Al-4V process.
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Review Paper
  • Qing Song AI, Yan WANG
    2012 Volume 6 Issue 7 Pages 1234-1249
    Published: 2012
    Released on J-STAGE: December 06, 2012
    JOURNAL FREE ACCESS
    The combination of natural process and engineering design & modeling activities has been proposed due to the demand of intelligent manufacturing and conceptual design. A product gene (PG) concept, as a combination of mechanical design and biological growth is proposed in recent years. PG is the application of genetic engineering to the mechanical-design field. In this paper, a comprehensive review is carried out on the research of PG theory and its application. The PG theory research, which focuses on the similarity and difference between biological gene and PG, is divided into three parts: concept and characteristics, data model, and operation technologies of PGs. Furthermore, to implement PG into the design and modeling area, PG research application is also discussed. Then a comparison between PG and other design & modeling methodology is conducted. Finally, the conclusion and discussion of future development of PG research are advanced.
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Paper
  • Chyi-Yeu LIN, Jinn-Feng JIANG, Yi-Jie CHEN, Hung-Yuan WEI, Cheng-Hsien ...
    2012 Volume 6 Issue 7 Pages 1250-1262
    Published: 2012
    Released on J-STAGE: December 06, 2012
    JOURNAL FREE ACCESS
    A windshield warning system for vehicles is presented. The system assists drivers in identifying potential hazardous object without the need to divert attention from the road. The target is identified by the camera and the software system and then used to construct the line-of-sight equation based on the coordinate system of the moving vehicle. The explicit equation of the intersection point of the line of sight and the windshield surface is derived using an algebraic method. A warning mark is then projected at the intersection point on the windshield by a two-degree-of-freedom laser projector, allowing the driver to easily identify the obstacle. The feasibility of the proposed system was verified using an actual vehicle (Luxgen® 7 MPV).
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  • Shigeru NAGASAWA, Yuki KOMIYAMA
    2012 Volume 6 Issue 7 Pages 1263-1272
    Published: 2012
    Released on J-STAGE: December 07, 2012
    JOURNAL FREE ACCESS
    A prototype-rotary creaser was experimentally applied to an AB double-wall corrugated fiberboard to reveal creasing characteristics of the corrugated fiberboard and mechanical factors on failures of its height wise crease. Through this work, the followings were obtained. (1) There are appropriate combinations of pre-creaser gap and main-creaser gap for restricting the failure occurrences in the inside liner; (2) The pre-stage creasing for crushing corrugated medium was severely necessary for reducing the failures of the inside liner and performing the high-precision positionment for bending; (3) Dependency of water content and feed velocity on the failures of the inside liner was revealed.
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Technical Note
Paper
  • Jungchul KANG, Masaharu KOMORI, Shuai ZHANG, Koki SUGIYAMA
    2012 Volume 6 Issue 7 Pages 1281-1297
    Published: 2012
    Released on J-STAGE: December 07, 2012
    JOURNAL FREE ACCESS
    Transmissions that can change their velocity ratio are used in various mechanical devices to achieve a wide range of torques or speeds. For machines with transmissions, such as transportation vehicles, it is required to keep the output speed or the output acceleration constant even during the velocity ratio changing process in order to transport the passengers or goods smoothly. Therefore, a method of velocity ratio change is required that can keep the output shaft at a constant speed or a constant acceleration. However, this is impossible in geared transmissions because they cause an interruption in the power transmission during the velocity ratio changing process. To solve this problem, a novel method of making the output shaft rotate at a desired speed even during the velocity changing process using an uninterrupted transmission system with noncircular gears is proposed in this study. Theoretical analysis is performed to clarify the appropriate input speed required to realize the desired output speed. A method of changing the velocity ratio under high rotational speed is proposed. An experimental device of the novel uninterrupted transmission system is constructed. An experiment to control the output speed during the velocity ratio change is performed under high rotational speed, and the effectiveness of the proposed method is verified.
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  • Hiroyuki KAWAMOTO, Satoshi IESAKA, So WATANABE
    2012 Volume 6 Issue 7 Pages 1298-1306
    Published: 2012
    Released on J-STAGE: December 07, 2012
    JOURNAL FREE ACCESS
    We studied the mechanism of and countermeasures against a pale image defect observed in the halftone area following a solid image in a two-component magnetic brush electrophotographic development system. We build a model machine that consisted of a pseudo-photoreceptor drum, development sleeve, and stationary magnetic roller to perform direct observations of the toner and carrier particles in the development area. The image was formed on an insulated film electrode pasted onto the drum. Instead of a digital halftone image, an analog halftone image was formed on the pseudo-photoreceptor. A parameter experiment showed that the image defect was enhanced when the voltage difference between the solid area and halftone area was large, the AC voltage superposed on the DC development voltage was low, the development gap was large, and the ratio of the sleeve speed to the drum speed was low. However, the defect was almost independent of the toner-to-carrier concentration ratio as well as the frequency and waveform of the superposed AC voltage. The dynamic behavior of the toner particles in the development area was directly observed using a high-speed microscope camera, and the cause of the print defect was investigated.
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  • Takabumi WATANABE, Yoshiyuki MIWA
    2012 Volume 6 Issue 7 Pages 1307-1318
    Published: 2012
    Released on J-STAGE: December 20, 2012
    JOURNAL FREE ACCESS
    The goal of this study is to capture the relationship between the bodies of two performers who improvise expressions while keeping their hands in contact (hand contact improvisation). Therefore, we developed a system that measures the motion of the hand and the center of pressure (COP) of ground reaction forces of the entire body's motion. Some of the participants of our experiments were skilled in improvised physical expression and some were beginners. The experiments showed that the period during which the motion of both subjects' entire bodies preceded the motion of their united right hand was long in the trial for which subjects reported that sympathetic embodied awareness was generated. This indicates that the implicit process of each subject operated prior to an explicit process that created their hand motions and both processes of each subject operated between the two subjects synchronously while sympathetic embodied awareness was generated. Next, we focused on fluctuation as a mean of enhancing the implicit process of embodiment. Therefore, a device was developed to present load fluctuation to the hands of test subjects during hand contact improvisation. The effects of load fluctuation were evaluated using measurement results of the entire body. The results indicated that by presenting fluctuation that has little effect on the subject's consciousness, the implicit embodiment of a performer can be activated, and the connection between both can be strengthened. We also obtained ideas for designing an interface to support the co-creation of expression.
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  • Kuo-Wei LIAO, Hu-Jhong LU
    2012 Volume 6 Issue 7 Pages 1319-1336
    Published: 2012
    Released on J-STAGE: December 27, 2012
    JOURNAL FREE ACCESS
    Topology optimization often incorporates a reliability analysis to take the randomness in the design parameters into account. This strategy is inherently a double-loop procedure due to the probabilistic constraints in optimization. To simplify the calculation procedure, an equivalent-deterministic constraint, which is constructed by adding a penalty on the right hand side (RHS) of a limit state function, is used to reformulate a reliability-based topology optimization (RBTO) problem into a deterministic topology optimization (DTO) problem. To obtain a converged solution, the DTO and the search of equivalent-deterministic constraints must be executed iteratively. The accuracy and efficiency of the proposed approach are investigated through several numerical examples. Results indicated that the proposed algorithm is able to deliver an optimal topology with predefined reliability. Furthermore, one can incorporate the proposed algorithm with existing software to facilitate the design process.
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