Journal of Advanced Mechanical Design, Systems, and Manufacturing
Online ISSN : 1881-3054
ISSN-L : 1881-3054
Volume 14, Issue 6
Displaying 1-18 of 18 articles from this issue
Papers
  • Takashi HASHIMOTO, Hideyoshi YANAGISAWA
    2020 Volume 14 Issue 6 Pages JAMDSM0078
    Published: 2020
    Released on J-STAGE: July 02, 2020
    JOURNAL FREE ACCESS

    Studies on autonomous driving systems are being conducted to realize a safe and secure mobile society. According to these studies, the safety of the system and the driver’s feeling of safety often do not match. To enable automatic driving control according to the driver's comfort, previous researchers introduced a risk feeling index to quantify the driver’s feeling of safety. These studies, however, did not consider the effects of the drivers’ individual differences for the risk feeling index. We hypothesized that the risk perception was formed by the difference between the actual autonomous driving behavior and the driver's prediction for it. The driver's risk feeling is expected to vary depending on his/her prior prediction of autonomous driving behavior. We considered that this difference, which we term as the prediction error, explains an individual difference in the risk perception. The purpose of this study is to reveal the effect of the prediction error on the risk perception. We conducted an experiment to investigate the effect of these factors on the risk feeling in the overtaking scene using a driving simulator. We obtained two types of subjective evaluations to examine the effects of the prediction errors on risk perception. One is perceived risk based on the driver’s original prediction, and the other is perceived risk based on the predictions that we manipulated by conducting a learning session during the experiment. The results suggest that the risk is perceived based on both the experimentally manipulated prediction and the individual driving characteristic of anxiety while driving. These findings will enable the development of a secure automatic driving system that suits each driver by controlling the system appropriately based on the driving characteristic of the driver.

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  • Jie KOU, Jimin ZHANG, Hechao ZHOU, Chengping WANG
    2020 Volume 14 Issue 6 Pages JAMDSM0079
    Published: 2020
    Released on J-STAGE: July 09, 2020
    JOURNAL FREE ACCESS

    In this investigation, the planetary gear differential is intended to the independently rotating wheels as a passive control device of the left and right wheels. Based on dynamics and kinematics analysis of the railway vehicle system and differential system, the differential coupling wheels vehicle (DWV) model and the comparative models, including rigid-wheelset vehicle (RWV) model and the independently rotating wheels vehicle (IRWV) model, are built. Through numerical studies, it can be concluded that the longitudinal creep forces of independently rotating wheels disappear for the separation of the wheels. But in the coupling effect of differential on wheels, the differential coupling wheels vehicle regains longitudinal creep forces and the resetting capability on straight lines. Compared with the rigid-wheelset vehicle, the differential coupling wheels vehicle has superior dynamics, including safety, guiding performance and wear performance on sharp curves. However, due to lack of sufficient longitudinal creep forces, the dynamics of the differential coupling wheels vehicle is slightly worse than that of the rigid-wheelset vehicle on medium radius curves. In general, the differential coupling wheels vehicle solves the problem of guiding and safety of the independently rotating wheels vehicle, and has better dynamic performance than the rigid-wheelset vehicle on sharp curves, which indicates that the differential coupling wheels vehicle is applicable to the urban railway transit which contains many sharp curves.

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  • Kuanfang HE, Yin SI, Wei LU, Qinghua LU, Qi LI, Chenhua HUANG, Siwen X ...
    2020 Volume 14 Issue 6 Pages JAMDSM0080
    Published: 2020
    Released on J-STAGE: July 11, 2020
    JOURNAL FREE ACCESS

    In aluminum alloy double pulse metal inert-gas (DPMIG) welding, the outputting arc current waveform is distorted under the influence of various factors such as harmonics and impact loads. The arc distortion of aluminum alloy DPMIG welding affects the arc stability and welding quality. Based on the collected welding current signal, a feature extraction method is proposed for quality detection of the aluminum alloy DPMIG welding. The wavelet method is adopted to eliminate the noise of the welding current signal. The local mean decomposition (LMD) is performed to the welding current signal to obtain a series of Product Function (PF) components with real physical meaning. The Hilbert transformation is subsequently performed to the PF components to obtain the time frequency distribution of welding arc signal energy. The approximate entropy (ApEn) of the time frequency distribution of the welding current signal is calculated to evaluate the arc stability and the welding formation quality. Application of the proposed feature extraction method indicates that the combination of the wavelet and LMD can effectively extract the distortion components of the welding current signal. The time frequency distribution of the PF components of the welding current can clearly reflect the concentration and dispersion of the arc energy. The approximate entropy of the time frequency distribution of the welding current can be quantitively reflect the arc stability and the welding formation quality in the aluminum alloy double pulse MIG welding.

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  • Yuki KAWAMOTO, Shun TAKAHASHI, Masayuki OCHIAI, Akihiko AZETSU, Kenji ...
    2020 Volume 14 Issue 6 Pages JAMDSM0081
    Published: 2020
    Released on J-STAGE: July 15, 2020
    JOURNAL FREE ACCESS

    In recent years, many vehicles with internal combustion engines use low tension piston rings and low viscosity oils to reduce friction loss around the rings. However, the reduction of ring tension causes problems in oil consumption. We conducted the prediction of oil behavior around the oil control ring by two-phase flow simulation based on the level set method towards revealing the mechanism of several problems around the piston ring that included oil consumption. Firstly, the calculation results of the dam break, a benchmark problem for two-phase flow analysis, showed the validity of the analysis code. Then, we calculated the flow field around the ring and compared with experimental values at each grid resolution. The calculated values showed the same tendency as the experimental values in the case where the computational grid is enough for the oil film. Besides, the oil behavior is not only dominated by using the inertial force, but also by the vortex formed due to cylinder pressure. The calculation also suggested that the amount of oil in the groove affected transportation leading to oil consumption. From the investigation of the effect of oil viscosity, the thick part of the oil film was affected by the inertial force of the piston, and the thin part was affected by the viscosity. Moreover, the effect of the surface tension also affected the behavior of the oil under certain conditions. The result that assumed low viscosity oil showed the behavior that leads to oil transport.

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  • Hiroki KATO, Masaharu KOMORI, Tatsuro TERAKAWA
    2020 Volume 14 Issue 6 Pages JAMDSM0082
    Published: 2020
    Released on J-STAGE: July 16, 2020
    JOURNAL FREE ACCESS

    Human-powered vehicles, especially conventional wheelchairs, are essential tools for people with lower body disability. But their movement in a lateral direction is limited or impossible, which burdens users who want to change directions, especially in a narrow space. Thus, a human-powered vehicle that can move in a lateral direction is required. To move in any direction, many motor-driven omnidirectional vehicles have been proposed, but humans cannot manually power their mechanisms. To solve this problem, we are developing a human-powered vehicle, that is, driven by hands of the rider, that can move in both the longitudinal and lateral directions. This paper proposes such a vehicle, which has a mechanism to move in the lateral direction like people can do while walking. We designed it so that riders can operate its mechanism by analyzing the space reachable by the rider’s palms where they can effectively exert power. We constructed a prototype and conducted experiments to confirm that the vehicle moves as expected with relatively low effort. In the experiments, we confirmed the validity of vehicle operation by comparing the moving time of the vehicle with and without the lateral translation function for different travel distances and passage widths. Our results showed that the proposed vehicle moves more quickly or requires shorter moving distance in comparison with a conventional wheelchair because of the lateral movement function. In addition, we found that the threshold for utility of the function is whether the passage width is larger than the vehicle diagonal length.

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  • Shigeru NAGASAWA, Tetsuya YAMAMOTO, Kazuki UMEMOTO, Shigekazu SUZUKI, ...
    2020 Volume 14 Issue 6 Pages JAMDSM0083
    Published: 2020
    Released on J-STAGE: July 21, 2020
    JOURNAL FREE ACCESS

    In a creased line processing of paperboard, deviation error between a groove of counter plate and a creasing knife is important for assuring the quality of creasing profile. It seems that a tapered (biased) groove of counter plate makes an unbalanced punching position of creasing knife well-adjusted in a certain range. In this work, the effect of a 45° tapered groove of a 1.5mm counter face plate on the eccentricity of crease bulging of a 0.43mm white-coated paperboard was compared with that of a rectangular groove counter plate (0° tapered). After scoring the paperboard across the fiber grain direction, using the rule deviation of e= 0.0~0.4mm and the indentation depth of creasing knife d= 0.3~0.6mm, the surface profile of scored zone was observed and folding tests and in-plane tensile test were carried out. Through the experiments, it was found that (i) a certain extent of asymmetric profile of scored surface was improved when observing the surface profile before folding, (ii) the changing range of bending moment resistance at the 90° bending test was reduced, (iii) the crease deviation at 180° folding test was reduced, and (iv) the in-plane tensile strength of 180° folded specimen was relatively large, compared to that of the rectangular groove.

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  • Nihal D. SALMAN, György PILLINGER, Muammel. M. HANON, Péter KISS
    2020 Volume 14 Issue 6 Pages JAMDSM0084
    Published: 2020
    Released on J-STAGE: July 21, 2020
    JOURNAL FREE ACCESS

    The depth of tilting in agricultural soil is 30–40 cm, which approximates the equivalent contact diameter of tires for the off-road vehicle. The soil thus tends to have an upper loose layer and a hard layer underneath, which leads to changes in the soil behavior. The effect of the hard layer can be defined by determining a specific point (breaking point) in the pressure (p)-sinkage (z) curve. The present study aims to design and construct a bevameter instrument can be used to simulate the hard layer in soil. Besides, specifying the breaking point and the effect of the hard layer on the soil behavior. In addition to the feature of a high applied load can be measured, the significance of this device comes from the easiness of changing the thickness of the soil which is in demand to be investigated. The device includes a mechanical structure, a hydraulic system, measuring sensors, and a data collection unit. Two sinkage plates with different diameter were employed for characterizing the relationship between the applied load (applied pressure) and the vertical deformation (sinkage). Indoor tests were also conducted to evaluate the device’s performance and study soil penetration resistance. The test was developed using sandy loam soil sieved through a 0.5 mm mesh. The soil bin was filled with soil up to 0.3 m thickness as a layer of 0.1 m. The soil density and moisture content for the soil was calculated as 1.245 g/cm3 and 12.3%, respectively. The device’s results showed that the hard layer changes the soil’s behavior as the soil becomes more compact. This layer also increased the values of sinkage exponent (n) and sinkage modulus (k) and implicitly modified the soil properties. Many experiments were carried out and discussed to validate the results.

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  • Yu GUO, Yu HOU, Qi ZHAO, Xionghao REN, Tianwei LAI
    2020 Volume 14 Issue 6 Pages JAMDSM0085
    Published: 2020
    Released on J-STAGE: July 21, 2020
    JOURNAL FREE ACCESS

    Foil bearings, featuring various advantages (such as high-speed, good operation stability, low friction, long life, strong adaptability, wide temperature range, and oil-free), are promised to have good development prospects and application in high-speed centrifugal machinery. In order to evaluate the actual performance of the multi-leaf foil bearings and promote their further application in the high-speed turbo-machinery, the experimental research of multi-leaf foil bearings with rotor diameter of 25 mm are conducted in this paper. The static and transient tests of the multi-leaf journal bearings with different foil thickness are initiated on the journal bearing test rig to analyze their characteristics, such as the load-deflection, bearing Coulomb friction, start-up and operating friction torque, which could provide guidance for the structural parameter design and exploitation of the bearing. Afterwards, two different bearing combinations are adopted as the supporting components, namely A-type: multi-leaf foil journal bearing with aerostatic thrust bearing and B-type: multi-leaf foil journal bearing with multi-leaf foil thrust bearing. They are applied in the high-speed turbo machinery with the rotor diameter of 25 mm to assess the direct application of the multi-leaf foil bearings in high-speed turbo-machinery. The transient speed-up, high speed, and speed-down experiments of the rotor-bearing system are conducted and their transient characteristics and stability are compared. The experimental results indicate that the start-up (0.6x10-2~1.8x10-2N·m) and steady operation frictional torque (0.25x10-2~0.5x10-2N·m) of the multi-leaf foil journal bearing is relative small; the impeller-rotor system operates steadily and smoothly with good repeatability, supported by A-type and B-type, the maximum rotor speed at about 94krpm achieved in the tests is close under the support of A-type and B-type. However, there are smaller main frequency amplitude, nonsynchronous amplitude and better rotor orbit in the transient processes with the support of B-type, which indicates better stability.

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  • Shuai LI, Chaosheng SONG, Caichao ZHU, Hailan SONG, Xuesong DU
    2020 Volume 14 Issue 6 Pages JAMDSM0086
    Published: 2020
    Released on J-STAGE: July 28, 2020
    JOURNAL FREE ACCESS

    The mathematical model of teeth distribution optimization for the promote gearbox is presented considering the objective functions such as the volume, efficiency, strength difference for the adjacent stages, and the design variables such as module, sun gear teeth, face width and transmission ratio of all stages. The improved genetic algorithm is used to solve the model and an analysis model of the promote gearbox is established using Masta to verify the proposed model. Results show that, after optimization, the attribute value of the synthesized objective function increases by 82.73%, the volume decreases by 17.61%, and the efficiency increases by 0.02%. The objective function value of equal contact and bending strength decreases by 55.93% and 51.10%, respectively. The difference for the safety coefficients for the adjacent stages decreases obviously. The constraint conditions of single-stage and adjacent stages satisfy the requirements. Through the strength verification calculation by the analysis model, the variation trend of the strength before and after optimization is consistent with the proposed optimization model, which indicates that the multi-objective optimization model established in this paper and the improved genetic algorithm selected are correct and effective.

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  • Claire-Amelie JANOT, Hirokazu HIGUCHI, Kotaro YAMADA, Akihito ASAKURA, ...
    2020 Volume 14 Issue 6 Pages JAMDSM0087
    Published: 2020
    Released on J-STAGE: July 30, 2020
    JOURNAL FREE ACCESS

    To support the engineer in the selection of drills and their machining parameters, we propose a novel catalog mining system based on data mining techniques applied on drill catalogs by using twice the Fuzzy c-means method along with the Maximum Information Coefficient (MIC). We first perform the clustering algorithm Fuzzy c-means that returns the membership degree of every point to each cluster on the parameters defining a series of tools. We then use the maximum information coefficient (or MIC, index measuring the correlation between two parameters) to find the drill or material properties that have the most influence on the drilling conditions in each of the clusters in order to realize a second clustering that includes the drilling conditions. The Davies-Bouldin index (DBI), which evaluates the dispersion inside the clusters, is used to assess the result of the second clustering and find its optimal parameters. Finally, a multi linear regression is used to find the equations predicting the drilling conditions in each sub-cluster. The mean squared error indicator is used to validate the result of the prediction. A new flexible index based on the membership degree value computed by the Fuzzy c-Means algorithm is proposed to filter the points and clarify the borders of the clusters in order to optimize the data used in the regression.

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  • Hiraku KOMURA, Toshiki NAKAMURA, Masahiro OHKA
    2020 Volume 14 Issue 6 Pages JAMDSM0088
    Published: 2020
    Released on J-STAGE: July 30, 2020
    JOURNAL FREE ACCESS

    To develop a tactile display, we focused on the Velvet Hand Illusion (VHI), which is a tactile illusion phenomenon. The most important feature of VHI is that VHI is not generated in one wire but is generated in two or more wires. This means that we recognize the area surrounded by wires as a Gestalt and a smooth surface sensation is generated in the Gestalt. We assume that the VHI mechanism is related to the law of closure and the law of common fate in Gestalt theory. In this paper, we investigate the relationship between VHI and the law of closure by means of variation in a phase difference of two wires’ cyclic movement, and formulate VHI variation, taking into account the law of closure. We try to divide the law of closure into two factors: one of them is a factor of translation and the other is a factor of elasticity. We formulate the tactile Gestalt and verify the validity of this formulation by comparing the result of the psychophysical experiment to the estimation via the formulation. This work shows that the law of closure in the tactile Gestalt consists of the translation factor and the elasticity factor, and the VHI mechanism is described by the formulation of the tactile Gestalt.

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  • Mitsuru JINDAI, Shunsuke OTA, Toshiyuki YASUDA, Tohru SASAKI
    2020 Volume 14 Issue 6 Pages JAMDSM0089
    Published: 2020
    Released on J-STAGE: August 06, 2020
    JOURNAL FREE ACCESS

    Humans establish embodied interactions, such as bows and handshakes, when they first meet. Through these embodied interactions, it is believed that humans construct a relationship that is emotionally acceptable to each other. In interactions between humans and robots, the same efficiency is expected. There are two types of embodied interactions. The first type is interactions without physical contact, such as those in raising hand greetings and bows. The other type is interactions with physical contact, such as those in handshakes and hugs. Thus, differences are believed to exist between the motion characteristics of robots that are preferred by humans depending on the presence or absence of physical contact. Therefore, in this paper, the differences in motion characteristics of robots that are preferred by humans in their embodied interactions with robots depending on the presence or absence of physical contact are analyzed. First, in a raising hand greeting, which is an embodied interaction without physical contact, the motion characteristics are analyzed. Next, the motion characteristics preferred by humans are identified through sensory evaluations using a raising hand greeting robot system that is developed based on these analyses. Finally, the differences in the preferred motion characteristics with the presence or absence of physical contact are analyzed by comparing the preferred motion characteristics of a raising hand greeting with those of a handshake, which were clarified in a previous study.

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  • Jianhua GUO, Lai WEI, ZhenZhen HU, Rui FAN, QingMing HU
    2020 Volume 14 Issue 6 Pages JAMDSM0090
    Published: 2020
    Released on J-STAGE: August 20, 2020
    JOURNAL FREE ACCESS

    Some studies have shown that offset toothed double helical synchronous belts (OTDHSB) have lower transmission noise and higher fatigue life than straight toothed synchronous belts (STSB). However, the transmission errors of these belts have not been reported. The present study aims to elucidate the mechanisms of the transmission error due to the belt climbing at the beginning of the meshing and at the end of meshing. In theoretical analysis, a model was established under quasi-static conditions. The results of the model used to calculate the transmission error of the helical synchronous belt (HSB) agreed closely with the published paper results. And then, the influence of the belt width, the helical angle and the offset coefficient on the transmission error was studied using the model. Computational results revealed that the amplitude of the transmission error decreases as the increasing of the offset coefficient, belt width, and helical angle when the offset coefficient and helical ratio are less than 0.5 and 1 respectively. In addition, the amplitude of the transmission error is equal to zero when the offset coefficient and helical ratio are equal to 0.5 and an integer respectively.

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Technical Note
  • Yoshihiro SEJIMA, Ryosuke MAEDA, Yoichiro SATO, Tomio WATANABE
    2020 Volume 14 Issue 6 Pages JAMDSM0091
    Published: 2020
    Released on J-STAGE: August 26, 2020
    JOURNAL FREE ACCESS

    Pupil response plays an important role in expression of talker’s affect in an embodied interaction and communication. Focusing on the pupil response in human voice communication, we analyzed the pupil response during utterance, and demonstrated that the pupil enlarges and contracts in synchronization with the burst-pause (ON-OFF) of the utterance. In addition, it was confirmed that the pupil response is effective for enhancing affective conveyance by using the developed system in which an interactive CG character generates the pupil response based on the synchronization with the burst-pause of utterance. In this study, we developed a video communication system with a virtual pupil CG superimposed on the partner’s pupil for enhancing affective conveyance. This system generates a virtual pupil response in synchronization with the talker’s burst-pause of utterance. We performed a communication experiment under the condition that the virtual pupil CG is generated by being synchronized with the talker’s burst-pause of utterance. The effectiveness of the system was demonstrated by means of sensory evaluations of 12 pairs of participants in the video communication.

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Papers
  • Keigo TAKASUGI, Tetsuya FUKUDA, Ryota KITO, Naoki ASAKAWA, Yoshitaka M ...
    2020 Volume 14 Issue 6 Pages JAMDSM0092
    Published: 2020
    Released on J-STAGE: August 27, 2020
    JOURNAL FREE ACCESS

    To mitigate chatter vibration in high-speed high-precision machining, the structure of machine tools and the cutting conditions must be optimized. Therefore, it is necessary to analyze the dynamic characteristics of machine tools. Such analysis is frequently conducted with an excitation test using an impact hammer because of its convenience. However, the dynamic behavior in the cutting process is often different from that in the resting state. It is difficult to analyze machine tools during cutting because of the rotating spindle and discharged chips. Therefore, this study proposes a method called fast swept sine cutting (FSSC) for measuring dynamic behavior during the cutting process. In the method, the cutting force is the excitation force applied to the machine tool system. The sinusoidal excitation of a CNC lathe during the turning process is realized by using a workpiece that creates a sinusoidal cutting force. The proposed method allows the frequency response, including that at the resonance point, to be observed. The dynamic behavior observed using the proposed method is different from that observed using conventional impact testing. The frequency response function during the turning process is affected by the nonlinearity of the cutting system.

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  • Thepwachara RUCHIRABHA, Shigeru NAGASAWA
    2020 Volume 14 Issue 6 Pages JAMDSM0093
    Published: 2020
    Released on J-STAGE: September 05, 2020
    JOURNAL FREE ACCESS

    This research was aiming to investigate cutting characteristics of Polystyrene (PS) 3 mm square bars subjected to indentation of a center bevel (blade angle of 42°) steel blade and stacked on an AL anvil (underlay). To reveal the effect of contact width of workpiece against the anvil on the sheared edge profile of workpiece, the contact width was varied from 1 mm to 40 mm during the cutting test. In this process, the cutting load response was investigated and the sheared edge profile of workpiece was observed by a microscope. To discuss the effect of the anvil width on the deformation behavior of workpiece, a finite element method (FEM) analysis with elasto-plastic plain strain model was developed using a crack generation rule. Through the experiment and FEM analysis, a proportion of wedge penetration flow and crack propagation of sheared workpiece was revealed with the contact width. The peak maximum cutting force, pre-crack position and the breaking position were characterized with the contact width. When the contact width was two times or much larger than the thickness of workpiece, the wedge penetration flow form was remarkably appeared, while the crack propagation based smooth flat form was appeared when the contact width was narrower than the thickness of workpiece. A bent-down or bent-up deformation of workpiece varied with the contact width and its sign change occurred when the contact width was about two times of the thickness of workpiece. When choosing the narrower contact width than the thickness of workpiece, an asymmetric crack propagation occurred due to the misalignment of blade position against the left and right side edges of anvil.

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  • Binbin XU, Ziyue WANG, Wei LUO, Tianqi MA
    2020 Volume 14 Issue 6 Pages JAMDSM0094
    Published: 2020
    Released on J-STAGE: September 11, 2020
    JOURNAL FREE ACCESS

    In order to better implement maintenance strategies according to equipment levels, this paper proposes a method based on the grey correlation interval Analytic hierarchy process(AHP)-Entropy method to divide the importance of production system equipment. First, a three-level importance evaluation index system for the production system equipment is established considering the characteristics of the production system in five aspects of operating rate, reliability, maintainability, economy and detectability. Next, the interval number is combined with the AHP and the Entropy method to obtain the interval AHP and the interval Entropy method, and the two methods are combined into an interval AHP-Entropy method to determine the combined weight of each evaluation index. Combined with the evaluated equipment, the grey correlation comprehensive evaluation analysis is performed, the grey correlation degree is calculated and ranked, and the equipment is finally divided by the ABC classification method. Finally, the method is applied to the equipment division of the actual production system. Compared with the interval AHP and interval Entropy method, the evaluation difference rates are reduced by 20% and 15%, respectively, which verifies the effectiveness of the method and provides an accurate and scientific method for equipment division.

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  • Wentong LU, Libo ZHOU, Jun SHIMIZU, Teppei ONUKI, Hirotaka OJIMA, Take ...
    2020 Volume 14 Issue 6 Pages JAMDSM0095
    Published: 2020
    Released on J-STAGE: September 30, 2020
    JOURNAL FREE ACCESS

    The rotary in-feed grinding is the most promising process to ensure the controllability of wafer geometry including the thickness and flatness. This makes it be widely applied into manufacturing of mono-crystal wafers, such as silicon, silicon carbide, sapphire, lithium tantalate, and etc. Unlike the conventional surface grinding, however, the rotary in-feed grinding is a complex material removal operation in which the extent of interaction between the abrasives and wafer keeps varying during the wheel/wafer contact zone. Such characteristic property significantly influences the chip formation, the homogeneousness of surface topography, the variations in grinding forces and the power consumption in the radial direction of the wafer. In this paper, the grinding mechanisms including the geometry, statics and surface topography were theoretically analyzed on a proposed grinding model and organized as follows. Described in Section 2 is the geometric analysis which mathematically expresses the wafer profile and a variety of information regarding to the dimensions of chip formed. The results suggest that the chip cross section increases proportionally as increasing in the wafer radial distance. Based on the results of chip formation, the grinding forces respectively exerted on an individual abrasive, a single wheel segment and whole wafer are calculated in the Section 3. Also, the necessary grinding power and generated grinding heat are estimated by statics analysis. In the Section 4, the surface roughness and its variation in a radial direction of the wafer are then derived by taking into consideration of the distribution of abrasive protrusion in height-wise.

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