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仰角英语知识点总结Elevation angle, also known as the zenith angle or the angle of inclination, is an important concept in the field of mathematics, physics, and engineering. It represents the angle between the line of sight and the zenith, which is the point directly overhead. In this article, we will discuss the various applications of elevation angle, the trigonometric functions related to it, and its significance in different fields.Trigonometric FunctionsElevation angle is commonly used in trigonometry to solve problems related to heights, distances, and angles. The three main trigonometric functions related to elevation angle are sine, cosine, and tangent. These functions are used to calculate the elevation angle in various scenarios such as in surveying, astronomy, and navigation.In surveying, the elevation angle is crucial in determining the height of a building, mountain, or any other object. The sine function is used to calculate the elevation angle when the height and distance to the object are known. The cosine function is used to calculate the distance to the object when the elevation angle and height are known. The tangent function is used to calculate the height of the object when the distance and elevation angle are known.In astronomy, the elevation angle is used to determine the position of celestial objects in the sky. The sine function is used to calculate the elevation angle of a star or planet when the observer's height and the object's distance are known. The cosine function is used to calculate the distance to the object when the elevation angle and observer's height are known. The tangent function is used to calculate the observer's height when the distance and elevation angle are known.In navigation, the elevation angle is used to determine the height of landmarks or other objects. The sine function is used to calculate the elevation angle of a landmark when the distance and observer's height are known. The cosine function is used to calculate the distance to the object when the elevation angle and observer's height are known. The tangent function is used to calculate the observer's height when the distance and elevation angle are known.ApplicationsElevation angle has various applications in different fields. In telecommunications, the elevation angle is used to determine the optimal positioning of satellite dishes and antennas for maximum signal reception. In aviation, the elevation angle is used to calculate the altitude of an aircraft and its distance from the ground. In architecture and construction, the elevation angle is used to design and build structures with the correct dimensions and angles.In sports, the elevation angle is used in activities such as rock climbing, skiing, and mountaineering to assess the steepness of a slope and the difficulty of the terrain. In photography, the elevation angle is used to determine the best angle for capturing a scene or a subject. In renewable energy, the elevation angle is used to optimize the positioning of solar panels and wind turbines for maximum energy production.SignificanceElevation angle is significant in many aspects of our daily lives. It affects how we perceive and interact with the world around us. In architecture, the elevation angle is crucial in creating aesthetically pleasing and functional buildings. In astronomy, the elevation angle is essential for observing celestial events and tracking the motion of celestial objects.In telecommunications, the elevation angle determines the quality of signal reception and the effectiveness of communication networks. In aviation, the elevation angle is critical for safe takeoff, landing, and navigation. In sports, the elevation angle affects the difficulty and challenge of various activities.ConclusionIn conclusion, elevation angle is a fundamental concept in mathematics, physics, and engineering. It is used in various trigonometric functions to solve problems related to heights, distances, and angles. Its applications are diverse, ranging from surveying and astronomy to telecommunications and sports. The significance of elevation angle in different fields underscores its importance in our daily lives. Its impact on architecture, navigation, communication, sports, and other areas highlights the need for a thorough understanding of this concept. Therefore, elevation angle is a valuable tool for solving practical problems and improving the quality of our built environment and our understanding of the natural world.。
钼靶乳腺投照标准When it comes to the standard for molybdenum target mammography, it is essential to understand the importance of this technique in breast imaging. 针对钼靶乳腺X线摄影的标准，了解这项技术在乳腺成像中的重要性是至关重要的。
Molybdenum target mammography is a widely used technique for breast imaging due to its superior image quality and ability to detect subtle abnormalities in breast tissue. 钼靶乳腺摄影是一种广泛应用于乳房成像的技术，因为它具有出色的图像质量，并能够检测乳腺组织中微小的异常。
The standard for molybdenum target mammography includes factors such as optimal positioning of the breast, appropriate compression of breast tissue, and proper exposure settings. 针对钼靶乳腺摄影的标准包括乳房的最佳定位、适当的乳房组织压迫以及正确的曝光设置。
It is crucial for healthcare providers to adhere to these standards to ensure accurate and reliable results in mammography screenings. 对于医疗保健提供者来说，遵守这些标准是至关重要的，以确保在乳腺X线摄影筛查中获得准确可靠的结果。
VSVPE +R –Q !更少消费表示集中和有限的需求更少消费更多消费表示需求最大化更多消费产品和服务必须有感受的诉求，如乐趣和道德感性需求理想需求产品和服务必须满足衡量标准，如质量、价格PeopleValues寻求永恒和谐的事物，淡泊的消费欲望寻求生活乐趣，更多的生活体验节省花费，经济上的节省导向寻求绩效和效率，理性的物质选择–+ER'R n e v er 'n e v e b e u r a b l e 'b e r a b l e ' m o r e o d q u a l i t y 'm o r e d q u a l i t y ''A p r i f i t f u l f i l 'A p i f i t f u l 'W h e n b u t o t h e d i 'W h e n b t o t h e d 'I t i s r e p a i ri n g'I t i r e p a i r i n g 16个国家中70000个消费群德国–英国–巴西–墨西哥–中国–日本定性和定量分析因子分析典型消费陈述85 标准陈述多纬分析•团对精神•彼此关爱在电信行业的体现行业领先、业务全面实力雄厚、历史悠久有口皆碑、有信誉的在电信行业的体现技术突破与整合应用创新在电信行业的体现•定制化服务（我的互联星空•一对一、大客户专区在电信行业的体现•网络游戏（动作类）在电信行业的体现•生活品质的提升宽带、无线产品所带来的现代在电信行业的体现•无线空间•移动办公在电信行业的体现•网上社区•移动QQ在电信行业的体现最便宜的话机，二手机The basic orientations简约型价值区传统感性价值区现代感性价值区高尚Fair Fair激情Passion Passion Nature Nature刺激/乐趣Thrill&Fun Thrill&Fun自然• 团对精神 • 彼此关爱 • 志趣相投古典Classic Classic进取AspirationTranquil Tranquil安逸自由自在Carefree Carefree简约Purism Purism归属感Clanning Clanning活力Vitality Vitality新潮/酷New&Cool New&Cool• 活力 • 动感多变 • 积极乐观 • 身心健康 • 亲切热情 • 中肯周到 • 诚挚的 • 想客户所想 • 精准严谨 • 井井有条 • 质量稳定 • 一丝不苟CN服务• 精明 • 货比三家 • 热衷于讨 价还价Service Service创新/科技24/7 Protech 24/7 Protech明智购物Smart Shopping Smart Shopping质量Quality QualityPersonal Efficiency Personal Efficiency个人效率可靠 全面成本Total Cost Total Cost Proven Proven定制化Customized Customized价格敏感区Source: Roland Berger - Strategic Brand Development Group传统理性价值区现代理性价值区21Paul是一个现代理性价值取向较为明显的人，他追求新事物、希望获得尊重 和认可，消费意识较强，但并不太追求时尚和享乐E-E激情 自然 古典 自由自在 归属感 活力 服务E+刺激/乐趣 蓝色代表消费者在这些元 蓝色代表消费者在这些元 素上需求较高 素上需求较高Legend保罗 Paul(高尚)ICP – Individual Consumer Profile (ID 0335)Level 1Level 2 不同意 安逸进取红色表示消费者在这些元 红色表示消费者在这些元 素上需求较低 素上需求较低简约新潮/酷创新/科技Level 1 同意Fair ERE0 R0 E+ R+Consumer value 简约型价值区 价格敏感区 传统感性价值区 传统理性价值区 现代感性价值区 现代理性价值区 Midfield area, high degree of consensus Pro-Value Anti-Value, Demarcation• 25 岁 • 男性 • 单身 • 中等收入 • 中等教育 • 在职 • 4口之家明智购物质量 个人效率 可靠全面成本定制化R-RR+CN!Warning, too weak, should be more intense Warning, too much, should be less intense Conflict with other valueSource: Roland Berger - Strategic Brand Development Group, TNS Data (Germany, March 2002, n=1.500, Population 14-65 yrs., CATI)22如何利用工具来帮助我们进行市场细分 Advanced consumer segmentation24从消费者的价值取向出发我们采用多维聚类的方法将中国消费者划分为 8类消费群都市青年 都市青年Self-centered Self-centered奢华的成功人士 奢华的成功人士ETraditional Maximalists Traditional Maximalists E工薪阶层 工薪阶层节俭主义者 节俭主义者EConformists ConformistsMinimalists MinimalistsE–+–+–+–+29%R14%R13%R12%R及时行乐型 及时行乐型Emotionalists EmotionalistsE专业人士 专业人士Modern Performers Modern Performers E小资型 小资型Progressive Maximalists Progressive Maximalists E知识分子 知识分子Traditionalists TraditionalistsE–+–+–+–+9%R8%R7%R6%R 25Source: Roland Berger - Strategic Brand Development Group (China, Dec.2003, n=3.500, Population Tier 1-2 Citys 14-70 yrs., CATI)Chinese Archetypes - preliminarySEL Chinese Archetype 2003 Study Tier 1-2 Cities TMA CONF MIN MPE PMA TRA EMO1)Share in Population of Tier 1-2 Cities-1--2--3--4--6--7--8--5-29%Self-centered14%13%12%8%7%6%9%Share in Population of Tier 1-5 Cities-6--5--4--7--3--8--1--2-9%10%11%8%13%8%21%Traditionalists14%Chinese Archetype 2001 Study Tier 1-5 Cities SEL TMA CONF MIN MPE PMA TRA DIS2)26Source: Roland Berger - Strategic Brand Development Group, Gallup/ Data (China, Nov2001/Dec2003, n=5.600/3.800, Population yrs., CATI)对于特定市场，我们可以分析该市场的不同类型消费群的结构比例就具体人群的消费群结构Tsd. Persons1.889467女性 14-19E100%276–..+1,889Mio. Persons176Share in sample13824.7%R76 14.6% 9.3% 7.3% 4.0%453634 1.8%28 1.5%Advent2.4%1.9%6.5%OtherWomen 14-19自我型 SELRationalNon- Maximal Emotional Minimal Traditional Altruist conformSource: Roland Berger - Strategic Brand Development Group, Ipsos Data (UK, Aug.2001, n=1.500, Population 12-65 yrs., CATI)27并针对不同细分市场的市场规模和消费能力来判别适合的目标市场Decreasing Economic Relevance市场细分名称 规模 消费能力 对于家电的消 费倾向 排序Rationalists RATMaximalists Self-centered Non-conform MAX SEL NONEmotional EMOAltruists ALTTraditionalists Minimalists TRA MIN1.18,5% 18,5%3.13,9% 13,9%5.9,3% 9,3%8.7,9% 7,9%4.12,5% 12,5%2.16,5% 16,5%7.8,4% 8,4%6.8,8% 8,8%2. 2.1. 3.6. 1.4. 4.3. 5.7. 7.5. 8.8. 6.1.2.3.4.5.6.7.8.1.) in Consumer ElectronicsSource: Roland Berger - Strategic Brand Development Group, TNS Data (Germany, March 2002, n=1.500, Population 14-65 yrs., CATI)28The 'Perception' of brands from the consumer's perspective29The difference between the aggregated value systems of brand users and non-users reveals the perceived value system of a brandE-EPassion Vitality Classic ClanningE+Thrill&Fun Consumer values that the users of Consumer values that the users of the brand most often agree with – the brand most often agree with – i.e. the most recognized value i.e. the most recognized value proposition of the brand proposition of the brandLegendProgressive hedonism patternNikeAVP - Actual Value Perception (415 vs. 1.085; zmax=12.7) maxUser Non-UserFair NatureCarefree New&CoolEPurismTranquilValue pole Value pole E = Emotional R = Rational + = More - = Less Value clusterService Smart ShoppingIntensity Precision Level 1Level 3Level 224/7 ProtechFair Consumer value, value proposition Midfield area, high degree of consensus Pro-Value Anti-Value, demarcation Warning, too much, should be less intense Warning, too weak, should be more intensePersonal Efficiency ProvenTotal Cost CustomizedR-RR+!Conflict with other valueSource: Roland Berger - Strategic Brand Development Group, Emnid Data (Germany, March 2002, n=1.500, Population 14-65 yrs., CATI)30E+E-R+ R-E R SmartShopping Total Cost Nature Fair Purism Tranquil Thrill&Fun New&Cool Carefree Vitality Clanning Passion Classic Customized PersonalEfficiency 24/7Protech Service Precision Proven Anti-minimalism pattern Anti-traditional pattern Consumer values that the users of disagree with i.e. 'aversions' that the brand might Consumer values that the users of disagree withi.e. 'aversions' that the brand might Consumer values that the users ofthe brand most often Consumer values that the users of the brand most often Progressivehedonism patternE +–R E +–R E+–RE +–R E +–R E+–RE +–R E +–RE+–RE+–RE+–RE+–R52467Carline 'S'Carline 'C'Carline 'E' 'Minimalist''Traditionalist''Luxury/ Status''Hedonist'E+–RE +–R E +–R E +–R E +–RE+ E-R+ R-E R Purism Purism Smart Shopping Smart Shopping Total Cost Total Cost Nature Nature Fair Fair Tranquil Tranquil Thrill&Fun Thrill&Fun New&Cool New&Cool Carefree Carefree Vitality Vitality Clanning Clanning Passion Passion Classic Classic Customized Customized Personal Efficiency Personal Efficiency 24/7Protech 24/7Protech Service Service Quality Quality Proven Proven E+ E-R+ R-E R Purism Purism Smart Shopping Smart Shopping Total Cost Total Cost Nature Nature Fair Fair Tranquil Tranquil Thrill&FunThrill&FunNew&Cool New&Cool Carefree Carefree Vitality Vitality ClanningClanning PassionPassion Classic Classic Customized Customized Personal Efficiency Personal Efficiency 24/7Protech 24/7Protech Service Service Quality Quality Proven Proven E+E-R+ R-E R Purism Purism SmartShopping Smart Shopping Total Cost Total Cost Nature Nature Fair Fair Tranquil Tranquil Thrill&FunThrill&Fun New&CoolNew&Cool Carefree Carefree VitalityVitality Clanning Clanning Passion PassionClassic Classic Customized Customized PersonalEfficiency Personal Efficiency 24/7Protech 24/7Protech ServiceService Quality Quality ProvenProvenNature SmartShopping Proven Customized Thrill&FunTotal Cost Fair Purism New&Cool Carefree Vitality Tranquil Quality Service Clanning Passion Classic Personal Efficiency 24/7Protech E +–RNature SmartShopping Proven Customized Thrill&Fun Total Cost Fair Purism New&Cool Carefree Vitality Tranquil Quality Service Clanning Passion Classic Personal Efficiency 24/7Protech E +–R借助Profiler 品牌战略分析工具可以明显地揭示各品牌的强势与弱势所在， 以及品牌所面对的竞争环境品牌 'A' – PVP ProjectionE品牌 'B' – PVP ProjectionE 2000<Carefree> <Carefree> <Clanning> <Clanning> <Protech> <Protech>Brand 'C' 品牌 'C' – PVP ProjectionE<New&Cool> <New&Cool> <Classic> <Classic>PVP 广告分析<Classic> <Classic> <Tranquil> <Tranquil>品牌投射–+<Protech> <Protech>–+<Quality> <Quality> <SmartShop> <SmartShop>–+<Protech> <Protech>1996-98 R<SmartShop> <SmartShop>R<Proven> <Proven>R品牌 'A' – AVP PerceptionEPassion Fair Thrill&Fun Vitality Classic Carefree New&Cool品牌 'B' – AVP PerceptionEPassion Fair Nature Purism Vitality Thrill&Fun品牌 'C' – AVP PerceptionEPassion Fair Nature Purism Classic Vitality Carefree New&Cool Thrill&Fun实际认知效果分析品牌认知Nature PurismClassic social hierarchy Carefree Clanning New&CoolLower 'ranks' in消费倡导者 的性格特征TranquilClanningTranquilTranquilClanning–Service Smart Shopping Quality 24/7 Protech+Personal Efficiency Proven Total Cost–Service Smart Shopping Quality 24/7 Protech+Personal Efficiency Proven–Service Smart Shopping Quality 24/7 Protech+Personal Efficiency Proven创新者的 性格特征RCustomizedTotal CostRCustomizedTotal Cost 最低要求者 的特征'RCustomizedSource: Roland Berger - Strategic Brand Development Group, Data from Metris (Portugal, Oct.2000, n=1.500, Population 15-65 yrs., CATI)41“节俭主义者”是品牌B 吸引的主导消费者类型，用户群结构对未来发展不利消费者基础与消费者类型分析主导的消费者类型品牌 B – AVP (年轻人)EPassion Fair Nature Purism Classic Vitality Carefree New&Cool Thrill&FunTranquilClanning–Service Smart Shopping Quality 24/7 Protech+Personal Efficiency Proven Total Cost100% 80% 60% 40% 20% 0% -20% -40% -60% -80% -100% Dev74,3% 46,0% 40,7% 37,3% 61,1%超过平均值 超过平均值社会阶级层次 较低!!!-31,7%-58,3%低于平均值 低于平均值- 60,8% 创新者 -60,8%-52,6% 胜利者 -52,6% 传统主义者 无关主义者 人道主义者 利他主义者 节俭主义者 自我抑制型 46,0% 40,7% 61,1% 37,3% 74,3% -31,7%RCustomized消费倡导者 -53,3%经济相关性不断下降!与主导的消费者类型冲突 与主导的消费者类型冲突42Source: Roland Berger - Strategic Brand Development Group, Data from Metris (Portugal, Oct.2000, n=1.500, Population 15-65 yrs., CATI)品牌C 吸引的消费者类型中，消费人群较为复杂消费者基础与消费者类型分析主导的消费者类型品牌 C – AVP (年轻人)EPassion Fair Nature Purism Classic Vitality Carefree New&Cool Thrill&FunTranquilClanning–Service Smart Shopping Quality 24/7 Protech+Personal Efficiency Proven Total Cost100% 80% 60% 40% 20% 0% -20% -40% -60% -80% -100% Dev68,4% 42,8%78,6%超过平均值 超过平均值48,7% 14,3%!8,3% -33,8%低于平均值 低于平均值!-64,7% 创新者 42,8% 胜利者 24,6%-58,0%RCustomized消费倡导者 68,4%传统主义者 无关主义者 人道主义者 利他主义者 节俭主义者 自我抑制型 -64,7% -58,0% -33,8% 48,7% 8,3% 14,3%经济相关性不断下降1.) 节俭主义者和消费倡导者/胜利者无法很好地匹配 C品牌的消费群中的节俭主义者的份额增长将有可能导致消费倡导者消费类型放弃此品牌!与主导的消费者类型冲突 与主导的消费者类型冲突43Source: Roland Berger - Strategic Brand Development Group, Data from Metris (Portugal, Oct.2000, n=1.500, Population 15-65 yrs., CATI)战略品牌分析解释了市场背景情况，及品牌B 在年轻消费者市场逐渐丧失 份额的背后原因品牌 'A' 品牌投射目前的品牌组成 (PVP)品牌 'B'品牌 'C'协调性品牌投射的长期效果 (PVP over time)品牌认知市场地位概况，驱动力 (AVP)消费者基础消费群类型的组成 (CBA)排名 目前增长趋势2.3.1.优好，适中差44Source: Roland Berger - Strategic Brand Development Group品牌B 无法在年轻消费者市场取得成功 – 必须引入一个全新的品牌D，以避 免过渡地对品牌B 进行无效品牌延伸市场特征语言， 图像，文字，音效 • 可预见 • 严肃认真 • 传统 • 精准 • 可信赖 • 前/ 后 • 追求完美 • 大方端庄 • 注重产品内部细节 • 新奇有趣 • 随时自发 • 主动积极 • 缤纷多变 • 注重产品外观 • 令人惊喜 • 与众不同 • 生动活泼 • 休闲市场划分 VIP’s品牌架构 • 更注重理性价值品牌执行要求的技能'B'强势大多数为30岁以上 的成功人士， 阅历 丰富，成熟稳重• 可靠 • 不注重感性价值 • 值得信赖 • 更注重感性价值 • 协调一致 • 不注重理性价值年轻人'B'弱势大多数为25岁以下的 青年人，反叛， 自我，蔑视权威品牌 ‘B’ 无法同时满足两种对立的目标消费群的不同要求因此必须引入全新的品牌D – 并且确保品牌B坚守其原有的品牌定位Source: Roland Berger - Strategic Brand Development Group45对于品牌D 的市场进入策略，有三种可选方案备选方案价格导向E Brand C主流价值导向E Brand C Brand A Brand A时尚型E Brand C目标品牌定位Brand A–+–+–+RRR主导品牌 定位元素<全面成本t> <明智购物> <科技/创新><归属感> <科技> <可靠/经典> <明智购物> <质量> <服务> <简约><科技/创新> <新潮/酷> <归属感> <激情> 反对-<经典> 反对-<可靠> 反对-<简约>辅助品牌 定位元素<归属感> <质量> <服务> <简约>Source: Roland Berger - Strategic Brand Development Group46采取“时尚型”的市场进入方案将为品牌D 带来更大的竞争优势，同时给品 牌C 和品牌A 带来威胁品牌 ‘D’ – 时尚型定位E <新潮/酷> 要素<Classic> <Classic>品牌 'C'E 品牌C无法很好地集中 在<新潮/酷>上…品牌 'A'E<Classic> <Classic>!–… 将会迫使品牌C直接对 品牌A进行竞争– 规避传统主义者 规避节俭主义者 R+关键驱动 要素+–+… 从而迫使品牌C往回退到<经典>， 并有可能最终退到<明智购物>上 R R• “时尚型”品牌定位凸显 <新潮/酷 >元素，相比较与<经典>结合， 这更易令人 信服 • 凸显<新潮/酷> 并弱化<经典> 能很好地吸引创新者消费群， 并影响消费倡导者• 品牌C很难成功地集中在 <新潮/ 酷>上，从而降低了其可信度， 无法很好地吸引“胜利者” • 品牌 ‘C’ 将被迫只集中在<经典 >上，并且最终在 <明智购物> 上• 品牌C 若集中在<经典>上，将 无可避免地产生与品牌A的直接 竞争 • 这将对品牌B产生好处Source: Roland Berger - Strategic Brand Development Group47通过以上策略性分析过程，导出了品牌D 的目标品牌价值定位，这将作为 其整个品牌营销组合的指导原则品牌 B – AVP (年轻人)EPassion Fair Nature Purism Classic Vitality Carefree New&Cool Thrill&FunFair Nature Purism Classic品牌 D – TVP (年轻人)EPassion Vitality Carefree New&Cool Thrill&FunTranquilClanningTranquilClanningPro-Innovator Attractor–Service Smart Shopping Quality 24/7 Protech+Personal Efficiency Proven Total Cost–Smart ShoppingService Quality+24/7 ProtechAnti-Minimalist SeparatorPersonal Efficiency ProvenMobile phone EnablerTotal CostR 分析100% 80% 60% 40% 20% 0% -20% -40% -60% -80% -100% DevCustomizedPro-Innovator Customized R Attractor策略性分析过程74,3% 46,0% 61,1%above average above average目标increase increase++ +-31,7%40,7%37,3%!!!-58,3% Maximalist -53,3%below average below average- 60,8%-52,6%-Sharedecrease decreaseInnovator Succeeder Traditional Indifferent Humanist -60,8% -52,6% 40,7% 37,3% 46,0%Altruist 61,1%G.Minimal Minimalist 74,3% -31,7%Maximalist14,7%Innovator Succeeder Traditional Indifferent Humanist11,7% 8,7% 19,7% 5,7% 7,7%Altruist8,7%G.Minimal Minimalist12,5% 8,7%Distance from Market Protagonists Decreasing Economic RelevanceDecreasing Economic Relevance Distance from Market ProtagonistsSource: Roland Berger - Strategic Brand Development Group48品牌D 的营销组合必须同时满足支持其品牌拥护者并打击其品牌竞争对手的 目的品牌 'D'Target Value Proposition Target Value PropositionEPassion Fair Nature Purism Classic Vitality Carefree New&Cool Thrill&FunTranquilClanning–Smart ShoppingService Quality+24/7 ProtechPersonal Efficiency Proven‘创新者'Target ProtagonistTotal Cost Customized‘节俭主义者'Target AntagonistsROKNOScale for approval产品• 开发显示 <科技> 特征的产品 ，如手机“个人游戏” 或“个人网 络” 等价格• 制定中高档定价策略 • 5-10% 略高于竞争对手渠道• 提出反对<科技>感觉的包装和 宣传品的创意 • 对代理商进行培训，吸引更多 的“创新者”并将“节俭主义者”驱 赶给品牌C推广• 基于TVP设计品牌标识，并进 行相关的品牌宣传推广Source: Roland Berger - Strategic Brand Development Group49。
机械毕业设计英⽂外⽂翻译493五轴数控铣床翻译【附】英⽂原⽂翻译⽂献：Five-axis milling machine tool kinematic chain design and analysis作者：E.L.J. Bohez⽂献出处：International Journal of Machine Tools & Manufacture 42 (2002) 505–520 翻译页数：Five-axis milling machine tool kinematic chain design and analysis 1. IntroductionThe main design specifications of a machine tool can be deduced from the following principles:● The kinematics should provide sufficient flexibility inorientation and position of tool and part.● Orientation and positioning with the highest poss iblespeed.● Orientation and positioning with the highest possibleaccuracy.● Fast change of tool and workpiece.● Save for the environment.● Highest possible material removal rate.The number of axes of a machine tool normally refers to the number of degrees of freedom or the number of independent controllable motions on the machine slides.The ISO axes nomenclature recommends the use of a right-handed coordinate system, with the tool axis corresponding to the Z-axis.A three-axis milling machine has three linear slides X, Y and Z which can be positioned everywhere within the travel limit of each slide. The tool axis direction stays fixed during machining. This limits the flexibility of the tool orientation relative to the workpiece and results in a number of different set ups. To increase the flexibility in possible tool workpiece orientations, without need of re-setup, more degrees of freedom must be added. For a conventional three linear axes machine this can be achieved by providing rotational slides. Fig. 1 gives an example of a five-axis milling machine.2. Kinematic chain diagramTo analyze the machine it is very useful to make a kinematic diagram of the machine. From this kinematic (chain) diagram two groups of axes can immediately be distinguished: the workpiece carrying axes and the tool carrying axes. Fig. 2 gives the kinematic diagram of the five-axis machine in Fig. 1. As can be seen the workpiece is carried by four axes and the toolonly by one axis.The five-axis machine is similar to two cooperating robots, one robot carrying the workpiece and one robot carrying the tool.Five degrees of freedom are the minimum required to obtain maximum flexibility in tool workpiece orientation,this means that the tool and workpiece can be oriented relative to each other under any angle. The minimum required number of axes can also be understood from a rigid body kinematics point of view. To orient two rigid bodies in space relative to each other 6 degrees of freedom are needed for each body (tool and workpiece) or 12 degrees. However any common translation and rotation which does not change the relative orientation is permitted reducing the number of degrees by 6. The distance between the bodies is prescribed by the toolpath and allows elimination of an additional degree of freedom, resulting in a minimum requirement of 5 degrees.3.Literature reviewOne of the earliest (1970) and still very useful introductions to five-axis milling was given by Baughman [1]clearly stating the applications. The APT language was then the only tool to program five-axis contouring applications.The problems in postprocessing were also clearly stated by Sim [2] in those earlier days of numerical control and most issues are still valid. Boyd in Ref.[3] was also one of the early introductions. Bez iers’ book[4] is also still a very useful introduction. Held [5] gives a very brief but enlightening definition of multi-axis machining in his book on pocket milling. A recent paper applicable to the problem of five-axis machine workspace computation is the multiple sweeping using the Denawit-Hartenberg representation method developed by Abdel-Malek and Othman [6].Many types and design concepts of machine tools which can be applied to five-axis machines are discussed in Ref. [7] but not specifically for the five-axis machine.he number of setups and the optimal orientation of the part on the machine table is discussed in Ref.[8]. A review about the state of the art and new requirements for tool path generation is given by B.K. Choi et al. [9].Graphic simulation of the interaction of the tool and workpiece is also a very active area of research and a good introduction can be found in Ref. [10].4. Classification of five-axis machines’ kinematic structureStarting from Rotary (R) and Translatory (T) axes four main groups can be distinguished: (i) three T axes and two R axes; (ii) two T axes and three R axes; (iii) one T axis and four R axes and (iv) five R axes. Nearly all existing five-axis machine tools are in group (i). Also a number of welding robots, filament winding machines and laser machining centers fall in this group. Only limited instances of five-axis machine tools in group (ii)exist for the machining of ship propellers. Groups (iii)and (iv) are used in the design of robots usually with more degrees of freedom added.The five axes can be distributed between the workpiece or tool in several combinations. A first classification can be made based on the number of workpiece and tool carrying axes and the sequence of each axis in the kinematic chain.Another classification can be based on where the rotary axes are located, on the workpiece side or tool side. The five degrees of freedom in a Cartesian coordinates based machine are: three translatory movements X,Y,Z (in general represented as TTT) and two rotational movements AB, AC or BC (in general represented as RR).Combinations of three rotary axes (RRR)and two linear axes (TT) are rare. If an axis is bearing the workpiece it is the habit of noting it with an additional accent. The five-axis machine in Fig. 1 can be characterized by XYABZ. The XYAB axes carry the workpiece and the Z-axis carries the tool. Fig. 3 shows a machine of the type XYZAB , the three linear axes carry the tool and the two rotary axes carry the workpiece.5. Workspace of a five-axis machineBefore defining the workspace of the five-axis machine tool, it is appropriate to define the workspace of the tool and the workspace of the workpiece. The workspace of the tool is the space obtained by sweeping the tool reference point (e.g. tool tip) along the path of the tool carrying axes. The workspace of the workpiece carrying axes is defined in the same way (the center of the machine table can be chosen as reference point).These workspaces can be determined by computing the swept volume [6].Based on the above-definitions some quantitative parameters can be defined which are useful for comparison, selection and design of different types of machines.6.Selection criteria of a five-axis machineIt is not the objective to make a complete study on how to select or design a five-axis machine for a certain application. Only the main criteria which can be used to justify the selection of a five-axis machine are discussed.6.1. Applications of five-axis machine toolsThe applications can be classified in positioning and contouring. Figs. 12 and 13 explain the difference between five-axispositioning and five-axis contouring.6.1.1. Five-axis positioningFig. 12 shows a part with a lot of holes and flat planes under different angles, to make this part with a three axis milling machine it is not possible to process the part in one set up. If a five-axis machine is used the tool can process. More details on countouring can be found in Ref. [13]. Applications of five-axis contouring are: (i) production of blades, such as compressor and turbine blades; (ii) injectors of fuel pumps; (iii) profiles of tires; (iv) medical prosthesis such as artificial heart valves; (v) molds made of complex surfaces.6.1.2. Five-axis contouringFig. 13 shows an example of five-axis contouring, tomachine the complex shape of the surface we need to control the orientation of the tool relative to the part during cutting. The tool workpiece orientation changes in each step. The CNC controller needs to control all the five-axes simultaneously during the material removal process. More details on countouring can be found in Ref. [13]. Applications of five-axis contouring are: (i) production of blades, such as compressor and turbine blades; (ii) injectors of fuel pumps; (iii) profiles of tires; (iv) medical prosthesis such as artificial heart valves; (v)molds made of complex surfaces.6.2. Axes configuration selectionThe size and weight of the part is very important as a first criterion to design or select a configuration. Very heavy workpieces require short workpiece kinematic chains. Also there is a preference for horizontal machine tables which makes it more convenient to fix and handle the workpiece. Putting a heavy workpiece on a single rotary axis kinematic chain will increase the orientation flexibility very much. It can be observed from Fig. 4that providing a single horizontal rotary axis to carry the workpiece will make the machine more flexible. In most cases the tool carrying kinematic chains will be kept as short as possible because the toolspindle drive must also be carried.6.3.five-axes machining of jewelryA typical workpiece could be a flower shaped part as in Fig. 14. This application is clearly contouring. The part will be relatively small compared to the tool assembly. Also small diameter tools will require a high speed spindle. A horizontalrotary table would be a very good option as the operator will have a good view of the part (with range 360°). All axes as workpiece carrying axes would be a good choice because the toolspindlecould be fixed and made very rigid. There are 20 ways in which the axes can be combined in the workpiece kinematic chain (Section 4.2.1). Here only two kinematic chains will be considered. Case one will be a T T T R R kinematic chain shown in Fig. 15. Case two will be a R R T T T kinematic chain shown in Fig.16.For model I a machine with a range of X=300mmY=250 mm, Z=200 mm, C=n 360° and A=360°, and a machine tool table of 100 mm diameter will be considered. For this kinematic chain the tool workspace is a single point. The set of tool reference points which can be selected is also small. With the above machine travel ranges the workpiece workspace will be the space swept by the center of the machine table. If the centerline of the two rotary axes intersect in the reference point, a prismatic workpiece workspace will be obtained with as size XYZ or 300×250×200 mm3. If the centerlines of the two rotary axes do not intersect in the workpiece reference point then the workpiece workspace will be larger.It will be a prismatic shape with rounded edges. The radius of this rounded edge is the excentricity of the bworkpiece reference point relative to each centerline. Model II in Fig. 15 has the rotary axes at the beginning of the kinematic chain (R R T T T ). Here also two different values of the rotary axes excentricity will be considered. The same range of the axes as in model I is considered. The parameters defined in Section 5 are computed for each model and excentricity and summarized in Table 1. It can be seen that with the rotary axes at the end of the kinematic chain (model I), a much smaller machine tool workspace is obtained. There are two main reasons for this. The swept volume of the tool and workpiece WSTOOL WSWORK is much smaller for model I. The second reason is due to the fact that a large part of the machine tool workspace cannot be used in the case of model I, because of interference with the linear axes. The workspace utilization factor however is larger for the model I with no excentricity because the union of the tool workspace and workpiece workspace is relatively smaller compared with model I with excentricity e=50 mm. The orientation space index is the same for both cases if the table diameter is kept the same. Model II can handle much larger workpieces for the same range of linear axes as in model I. The rotary axes are here in the beginning of the kinematic chain, resulting in a much larger machine tool workspace then for model I. Also there is much less interference of the machine tool workspace with the slides. The other 18 possible kinematicchain selections will give index values somewhat in between the above cases.6.4. rotary table selectionTwo machines with the same kinematic diagram (T T R R T) and the same range of travel in the linear axes will be compared (Fig. 17). There are two options for the rotary axes: two-axis table with vertical table (model I), two-axis table with horizontal table (model II). Tables 2 and 3 give the comparison of the important features. It can be observed that reducing the range of the rotary axes increases the machine tool workspace. So model I will be more suited for smaller workpieces with operations which require a large orientation range, typically contouring applications. Model II will be suited for larger workpieces with less variation in tool orientation or will require two setups. This extra setup requirement could be of less importance then the larger size. The horizontal table can use pallets which transform the internal setup to external setup. The larger angle range in the B-axes 105 to +105, Fig. 17. Model I and model II T T R R T machines. compared to 45 to +20, makes model I more suited for complex sculptured surfaces, also because the much higher angular speed range of the vertical angular table. The option with the highest spindle speed should be selected and it will permit the use of smaller cutter diameters resulting in less undercut and smaller cutting forces. The high spindle speed will make the cutting of copper electrodes for die sinking EDM machines easier. The vertical table is also better for the chip removal. The large range of angular orientation, however, reduces the maximum size of the workpiece to about 300 mm and 100 kg. Model II with the same linear axes range as model I, but much smaller range in the rotation, can easily handle a workpiece of double size and weight. Model II will be good for positioning applications. Model I cannot be provided with automaticworkpiece exchange, making it less suitable for mass production. Model II has automatic workpiece exchange and is suitable for mass production of position applications. Model I could, however, be selected for positioning applications for parts such as hydraulic valve housings which are small and would require a large angular range.7.New machine concepts based on the Stewart platformConventional machine tool structures are based on Carthesian coordinates. Many surface contouring applications can be machined in optimal conditions only with five-axis machines. This five-axis machine structure requires two additional rotary axes. To make accurate machines, with the required stiffness, able to carry large workpieces, very heavy and large machines are required. As can be seen from the kinematic chain diagram of the classical five-axis machine design the first axis in the chain carries all the subsequent axes. So the dynamic responce will be limited by the combined inertia. A mechanism which can move the workpiece without having to carry the other axes would be the ideal. A new design concept is the use of a‘HEXAPOD’. Stewart [16] described the hexapod principle in 1965. It was first constructed by Gough and Whitehall [20] in 1954 and served as tire tester. Many possible uses were proposed but it was only applied to flight simulator platforms. Thereason was the complexity of the control of the six actuators. Recently with the amazing increase of speed and reduction in cost of computing, the Stewart platform is used by two American Companies in the design of new machine tools. The first machine is the VARIAX machine from the company Giddings and Lewis, USA. The second machine is the HEXAPOD from the Ingersoll company, USA. The systematic design of Hexapods and other similar systems is discussed in Ref. [17]. The problem of defining and determining the workspace of virtual axis machine tools is discussed in Ref. [18]. It can be observed from the design of the machine that once the position of the tool carrying plane is determined uniquely by the CL date (point + vector), it is still possible to rotate the tool carrying platform around the tool axis. This results in a large number of possible length combinations of the telescopic actuators for the same CL data.8.ConclusionTheoretically there are large number of ways in which a five-axis machine can be built. Nearly all classical Cartesian five-axis machines belong to the group with three linear and two rotational axes or three rotational axes and two linear axes. This group can be subdivided in six subgroups each with 720 instances.If only the instances with three linear axes are considered there are still 360instances in each group. The instances are differentiated based on the order of the axes in both tool and workpiece carrying kinematic chain.If only the location of the rotary axes in the tool and workpiece kinematic chain is considered for grouping five-axis machines withthree linear axes and two rotational axes, three groups can be distinguished. In the first group the two rotary axes are implemented in the workpiece kinematic chain. In the second group the two rotary axes are implemented in the tool kinematic chain.In the third group there is one rotary axis in each kinematic chain. Each group still has twenty possible instances.To determine the best instance for a specific application area is a complex issue. To facilitate this some indexes for comparison have been defined such as the machine tool workspace, workspace utilization factor, orientation space index, orientation angle index and machine tool space efficiency. An algorithm to compute the machine tool workspace and the diameter of the largest spherical dome which can be machined on the machine was outlined.The use of these indexes for two examples was discussed in detail. The first example considers the design of a five-axis machine for jewelry machining. The second example illustrates the selection of the rotary axes options in the case of a machine with the same range in linear axes.翻译题名：Five-axis milling machine tool kinematic chain design and analysis期刊与作者：E.L.J. Bohez出版社：International Journal of Machine Tools & Manufacture 42 (2002) 505–520●英⽂译⽂摘要：现如今五轴数控加⼯中⼼已经⾮常普及。
GJournal of Mechanical Science and Technology 21 (2007) 789~798Micro Genetic Algorithm Based Optimal Gate Positioningin Injection Molding DesignJongsoo Lee*, Jonghun KimSchool of Mechanical EngineeringYonsei University, Seoul 120-749 Korea(Manuscript Received December 12, 2006; Revised March 26, 2007; Accepted March 26, 2007)--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------AbstractThe paper deals with the optimization of runner system in injection molding design. The design objective is to locate gate positions by minimizing both maximum injection pressure at the injection port and maximum pressure difference among all the gates on a product with constraints on shear stress and/or weld-line. The analysis of filling process is conducted by a finite element based program for polymer flow. Micro genetic algorithm (mGA) is used as a global optimization tool due to the nature of inherent nonlinearlity in flow analysis. Four different design applications in injection molds are explored to examine the proposed design strategies. The paper shows the effectiveness of mGA in the context of optimization of runner system in injection molding design.GKeywords: Micro genetic algorithm; Design optimization; Filling injection mold--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------1. IntroductionInjection molding process has been recognized as one of the most efficient manufacturing technologies since high performance polymer materials can be utilized to accurately manufacture a product with complicated shape (Chiang, et al., 1991; Chang and Yang, 2001; Himasekhar, et al., 1992; Kwon and Park, 2004). Also, the demand on injection molded products such as from conventional plastic goods to micro optical devices is being dramatically increased over the recent years (Piotter, et al., 2001; Kang, et al., 2000). In general, the injection mold process is initiated by the filling stage where the polymer materials fill into a cavity under the injection temperature. After the cavity is completely filled, the post-filling stage, that is, the packing stage is conducted to be additionally filled with the high pressure polymer, thereby resulting in the avoidance of material shrinkage. Subsequently, the cooling stage is required for a molded product to be ejected without any deformation. It is important to accommodate the molding conditions in the filling stage since it is the first stage in the overall injection molding design (Zhou and D. Li, 2001). After that, one can success-fully expect more improved molding conditions during post-filling stages such as packing, cooling stages. The paper deals with optimal conditions of the filling injection molding design in which the flow pattern and pressure for the polymer materials to be filled through gates of a runner are of significant. That is, one of design requirements are such that when the polymer comes into a cavity through a number of gates located at different positions, pressure levels on the surface of a product should be as uniform as possible. Such design can be performed through the intelligent gate positioning to generate the moreCorresponding author. Tel.: +82 2 2123 4474; Fax.: +82 2 362 2736 E-mail address: jleej@yonsei.ac.kr790 Jongsoo Lee and Jonghun Kim / Journal of Mechanical Science and Technology 21(2007) 740~749uniform distribution of injection pressure over the product surface.There have been a number of studies of optimal gate location in the context of CAE filling injection molding design problems where various kinds of optimizer have been employed to conduct design optimization (Kim et al., 1996; Young, 1994; Pan-delidis and Zou, 2004; Lin, 2001; Li and Shen, 1995). The paper explores the design of injection mold system using micro genetic algorithm (mGA). Ge-netic algorithm (conventional GA) is based on the Darwin’s theory of the survival of the fittest, and adopts the concept of natural evolution; the competitive designs with more fit are survived by selection, and the new designs are created by crossover and mutation (Lee, 1996; Lee and Hajela, 1996). A conventional GA works with a multiple number of designs in a population. Handling with such designs results in increasing a higher probability of locating a global optimum as well as multiple local optima. GA is also advantageous when the design problem is represented by a mixture of integer/dis-crete and continuous design variables. Nevertheless, it requires expensive computational costs especially when combining with finite element based CAE analysis tools. A conventional GA determines the population size depending upon the stringlength of a chromosome that is a coded value of a set of design variables. The main difference between a conven-tional GA and mGA resides on the population size. The population size in mGA is based on Goldberg’s concept such that ‘Evolution process is possible with small populations to reduce the cost of fitness function evaluation’ (Goldberg, 1988). This implies that mGA employs a few number of populations for GA evolution regardless of the number of design variables and the complexity of design parameters (Krishnakumar, 1989; Dennis and Dulikravich, 2001). The paper discusses the design requirements of filling injection mold optimization to construct the proper objective functions and design constraints. Four different design applications in injection molds are explored to examine the proposed design strategies. The paper shows the effectiveness of mGA in the context of optimization of runner system in injection molding design.2.Mold flow analysisThe flow of a polymer in injection molding process obeys the following governing equations:22()()0p pS Sx x y yw w w ww w w w(1)222()p x yT T T TC kt x y zU Q Q KJw w w ww w w w(2)where,2'2'h zS dzK³.In the above equations, p is a flow pressure, T is atemperature of polymer, and t is denoted as time.Parameters K,J, and k are viscosity, shear rate andthermal conductivity, respectively (Lee, 2003). It isassumed that polymer is a non-compaction substancein the filling analysis. The flow analysis in the presentstudy is conducted by Computer Aided PlasticsApplication (CAPA) (Koo, 2003), a finite elementbased commercial code for polymer flow of injectionmolding.The runner system in injection mold covers thepassage of molten polymer from injection port togates. The present study develops two different runnersystems where a cold system requires the change inpolymer temperature, and a hot system keep itunchanged while the flow passes through the runner.For the hot runner system has a geometricallyconsistent thickness due to the constant temperatureas shown in Fig. 1a. However, the CAE result of acold runner system depends on the thickness and shapeTable 1. Ten-bar truss design results.micro GA conventional GACase 1Case 2Case 3Case 1 Case 2 Case 3Reference[20]X17.868.157.858.15 7.30 7.81 7.90X20.410.180.190.10 0.83 0.45 0.10X38.387.998.158.20 8.77 8.37 8.10X4 5.05 3.83 3.89 3.97 3.27 4.16 3.90X50.120.960.15 1.10 0.75 0.55 0.10X60.410.250.250.10 0.82 0.30 0.10X7 6.41 5.67 5.87 5.84 6.74 6.30 5.80X8 5.23 6.29 5.52 5.68 5.06 5.26 5.51X9 3.83 3.85 5.05 5.07 2.89 3.86 3.68OptimalareaX100.500.250.250.40 1.16 0.42 0.14Optimalweight1599158715881593 1590 1585 1499# of functionevaluations57540542302533578894 69497 73533Jongsoo Lee and Jonghun Kim / Journal of Mechanical Science and Technology 21(2007) 789~798 791(a) Hot runner system(b) Cold runner systemFig. 1. Modeling of runner system.shape of a runner. The typical illustration of the geometric model in a cold runner system is shown in Fig.1b where the runner thickness is changed according to the temperature gradient.3. Molding design requirements3.1 Objective functionsOne of the most significant factors considered in the injection molding design is a flow pattern, which implies that a balanced flow should be maintained while a polymer arrives at each part of a design product. Once the improvement on flow balance is obtained, the flow of molten polymer smoothes and the maximum injection pressure is decreased with the same or at least evenly distributed injection pressure level at each gate. In a case where the certain part of a product within the mold is filled up earlier than other parts, each part would fall into over-packing and under-packing situations during the filling process of a polymer into mold. Such problem further evokes a malformation like twisting and bending, resulting from the difference in contraction rate during the course of cooling-off.The difference in pressure triggers the flow ofpolymer during the filling process, in which themaximum injection pressure is detected at theinjection port of polymer. The polymer always flowsfrom high-pressure region to low-pressure one. Whena flow pattern improves, the flow of polymer getssmoother with the maximum injection pressure decreased. However, the flow instability sometimeshappens, thereby requiring a higher pressure to fill up.That is, the maximum injection pressure needs to bereduced in order to improve the flow instability. Thepressure gap (i.e., the highest and lowest pressurevalues) among all of gates is also taken as anotherobjective function to determine whether the wholemold is being filled at once.Most commonly accepted design strategy toimprove the flow pattern is the adjustment of gatelocation. The present study controls the flow patternby developing the optimal gate positioning problemswith proper objective function(s) and design cons-traints. Objective functions for injection moldingdesign are considered as both ‘maximum injection pressure’ (MIP) and ‘maximum pressure difference’ (MPD). It should be noted that the maximuminjection pressure is calculated at the injection portand the maximum pressure difference is a numericaldifference between the highest and lowest values ofpressure among all of gates. The aforementioned statements could be interpreted as a multiobjectivedesign problem, hence the present study simplyemploys a weighting method as follows:**()()()MIP x MPD xF xMIP MPDD E(3)where, D and E are weighting factors as D+E=1, and xis a set of design variables which are Cartesian coordinates of gates on a product. Each component inthe above equation is normalized by optimal single-objective function value, (i.e., MIP*, MPD*). It ismentioned that the number of gates is considered as aproblem parameter in the study.3.1 ConstraintsWeld-lines are easily detected when more than twoflow fronts having different temperature values meetduring the filling process. The weld-line is one of theweakest points in molded product; it is very792 Jongsoo Lee and Jonghun Kim / Journal of Mechanical Science and Technology 21(2007) 740~749vulnerable to a shock and subsequently causes external defects of a very glossy polymer. The weld-line should be moved into a less weak region by adjusting the width of a product, the size and/or shape of gates and runners, and the position of gates, etc. The present study considers the position of a weld-line as a constraint in optimal gate positioning of mold design. Once a designer specifies areas where weld-lines should not be generated, all of the finite element nodes in such areas are constrained not to form the weld-lines.Shear stress is defined as a shear force imposed on the wall of a mold by the shear flow of a polymer. The magnitude of shear stress is proportional to the pressure gradient of each position. In general, the shear stress is zero at the center of a molded product, and reaches a maximum value on the wall. High shear stress triggers the molecule cultivation on the surface of a molded product. Flow instability such as melt fracture has a close relationship with the shear stress. The clear surface of a molded product can be obtained by reducing the magnitude of shear stress. That is, shear stress should be minimized during the mold filling process in order to improve the quality of a molded product, particularly on its surface. Maximum allowable shear stress depends on the kinds of polymer, and is generally taken as 1% of tensile strength of a polymer. Shear stress affecting the quality of end product is considered as another constraint.3.3 Formulation of optimization problemThe statement of a mold design optimization problem can be written as follows: Find12(,,){(,,),(,,),...,(,,)}N x i j k x i j k x i j k x i j k (4)to minimize**()()()MIP x MPD x F x MIP MPD D E (5) subject to shear stress(i, j, k) < shear stress allowable (6) weld-line(i, j, k) = designated area(s) only (7) where, lower upper x x x d d A set of design variables, x are Cartesian coordi-nates (i, j, k) of gates on the surface of a molded product, where N is the number of gates. A traditionalweighted-sum method in the context of multiob-jective optimization is employed by using two wei-Fig. 2. Micro GA process.ghting factors of D and E , where D +E =1. Multi-objective functions considered in the present study are ‘maximum injection pressure (MIP)’ measured at the injection port and ‘maximum pressure difference (PD)’ among all of gates. The constants, MIP* and MPD* are optimal objective function values obtained via single-objective optimization. The permission of weld-lines to designated areas only and the upper limits on shear stress are imposed as design cons-traints. The flow pattern analysis is performed by CAPA as mentioned in the earlier section, and the optimization is conducted through mGA. It should be noted that Cartesian coordinates (i, j, k) is recognized as nodal points when a molded product is discretized by finite elements in CAPA.4. Micro GAThe overall process of mGA in the present study is depicted in Fig. 2, and a stepwise procedure can be explained as follows:Step-1) Generate an initial population at random. The recommended population size is 3, 5, or 7.Step-2) Perform a conventional GA evolution untilthe nominal convergence is satisfied. In the presentstudy, the population size is selected as 5, and atournament selection operator is used. The crossoverprobability in mGA is 1.0 due to the small size in population, while a conventional GA is preferred to use it less than 1.0. The nominal convergence means that the difference of 1’s and/or 0’s among stringpositions is within 5% out of the stringlength, thereby resulting in the convergence to a local solution.Step-3) During the user-specified number of ge-nerations, a new population is updated; one individual is selected by elitism; the remaining individuals in aJongsoo Lee and Jonghun Kim / Journal of Mechanical Science and Technology 21(2007) 789~798 793new population are generated at random. It should benoted that the selection operation adopts ‘tournament’ for activating the diversity and ‘elitism’ for keeping the best solution. Since the updated populations except for the elitism are generated at random, mGA seldom considers the mutation.Fig. 3. Convergence histories of ten-bar truss problem.GFig. 4. Seven discrete design spaces for vehicle dashboard problem.Fig. 5. Initial gate location of vehicle dashboard.In summary, mGA enables to locate an optimal solution thanks to the small size of populations, tournament and elitism operations in selection, and the full participation in crossover. However, mGA has a drawback upon finding one of multiple local optima only due to the small size of populations and the nominal convergence strategy. A conventional GA is superior to maintaining the diversity while mGA is advantageous of savings in computational resource requirements.4.1 Truss designThe proposed mGA is verified by a typical ten-bar planar truss optimization problem. The objective is to find optimal cross-sectional areas by minimizing the structural weight subjected to stress constraints (Haftka and Gurdal, 1993). Optimal solutions are obtained via mGA and a conventional GA to compare with each other. The population size in mGA is 5, while a conventional GA requires 250 individuals in a population since the stringlength in this problem is 100. Crossover and mutation probabilities in a con-ventional GA used are 0.8 and 0.01, respectively. After two genetic search methods are conducted ten times by changing randomly generated initial popul-ations, the most fit design results are demonstrated in Table 1. The convergence history for each optimizer demonstrates that mGA produces the better design and locates the near-optimal solution at the earlier stage of evolution in Fig. 3.5. Results of design applications5.1 V ehicle dashboardA passenger car in-panel has been first examined. This model is supposed to have 7 gates, and design spaces for use in genetic evolution are shown in Fig. 4. Objective functions of MIP and MPD are taken into account, but no constraints are imposed in this model. The initial design is shown in Fig. 5; this design has been obtained through experience and trial-and-errors in an automotive part molding company. Optimized results by mGA are shown in Figs. 6 to 8, whose objective functions were considered as ‘MIP only’, ‘MPD only’ and ‘both MIP and MPD’, respectively. Design results for each case are summarized in Table 2 as well. It is noted that ‘both MIP and MPD’ is calculated with D changing from 0.0 to 1.0 with an increment of 0.1 while keeping D E .0.794 Jongsoo Lee and Jonghun Kim / Journal of Mechanical Science and Technology 21(2007) 740~749Fig. 6. Optimized design of vehicle dashboard (MIP only).Fig. 7. Optimized design of vehicle dashboard (MPD only).Fig. 8. Optimized design of vehicle dashboard (both MIP and MPD).In case of ‘MIP only’ in Fig. 6, the maximum injection pressure value has an improvement of 23.9% compared with an initial model, but the pressure distribution on the product becomes worse, resulting in over-packing on the left region. When a case of ‘MPD only’ is considered, the design performance in Fig. 7 is achieved in terms of not only maximum pressure difference but also maximum injection pressure as shown. It is expected that the flow gets smoother during the improvement of pressure distribution, and the maximum injection pressure is decreased as well. In case of ‘both MIP and MPD’ in Fig. 8, its result is quite similar to a case Table 2. Optimization results of vehicle dashboard.maximum pressure[MPa]maximumdifference [MPa] Initial design 242.69 20.26MIP only184.73 35.08MPD only231.22 12.44objectiveboth MIPand MPD229.92 12.58Table 3. Optimization results of TV monitor.maximumpressure[MPa]maximumdifference[MPa]shear stress <0.5 [MPa]Initial design 80.55 13.71 0.45MIP only68.46 4.06 0.43MPD only72.27 3.04 0.45 objectiveboth MIPand MPD68.46 4.06 0.43of ‘MPD only’ in terms of gate locations from Figs. 7 and 8 and the percentile improvement in Table 2. A weighted-sum method is used to obtain the mul-tiobjective optimal solutions by changing D andE simultaneously, but yields the same results out of a total of 11 weighting factor based trials. The reason why a few number of Pareto solutions are detected is such that the maximum pressure is not counter to pressure distribution in the filling injection molding.In other words, when the overall pressure distributionis improved thanks to the enhancement of flow balance and the smoothness of polymer flow, the maximum pressure is consequently decreased. As faras the pressure distribution of a modeled product is concerned, the change in gate position is noticeable; Gate_5 of optimized models moves from right to left region compared with an initial model.5.2 TV monitorThe model of a TV monitor equipped with 4 gatesis now optimized using objective functions and the upper limit on shear stress constraint, where the shear stress allowable is 0.5MPa. The initial design with 4 discrete design spaces is displayed in Fig. 9, and optimized pressure distributions are shown in Figs. 10 and 11. Design results for single-objective and mul-tiobjective optimization are tabulated in Table 3. In case of ‘MIP only’ generates the same result as weighting method based multiobjective solutions of‘both MIP and MPD’. In case of ‘MPD only, the maxi-Jongsoo Lee and Jonghun Kim / Journal of Mechanical Science and Technology 21(2007) 789~798 795Fig. 9. Initial gate location of TV monitor.Fig. 10. Optimized design of TV monitor (MPD only).Fig. 11. Optimized design of TV monitor (MIP only & both MIP and MPD).mum injection pressure and maximum pressure di-fference have been improved by 10.3% and 77.8%, respectively. It is expected that the enhancement on flow balance and smoothness may be made possible by optimizing the gate positions.5.3 CD trayThe CD tray use in a laptop computer has 4 gates for injection molding. The optimization on this modelFig. 12. CD tray (left) and its initial gate location (right).Fig. 13. Optimized design of CD tray (MIP only).Fig. 14. Optimized design of CD tray (MPD only).is conducted with a shear stress constraint, where the upper limit on shear stress allowable is 1.5MPa. Initial and optimized results for pressure distribution are shown in Figs. 12 to 15. From the summary of Table 4, the design solutions of optimal objective fun-796 Jongsoo Lee and Jonghun Kim / Journal of Mechanical Science and Technology 21(2007) 740~749Fig. 15. Optimized design of CD tray (both MIP and MPD).Table 4. Optimization results of CD tray.maximum pressure [MPa] maximumdifference[MPa]shear stress <1.5 [MPa]Initial design 82.66 1.192 1.22MIP only 73.91 7.085 1.26MPD only 80.44 0.332 1.12 objectiveboth MIPand MPD 78.79 0.376 1.14 ction values in this problem are quite similar to that in the vehicle dashboard. In case of ‘MIP only’, the maximum pressure difference value gets worse than the initial design, even though the maximum injection pressure value has been improved. The cases of ‘MPD only’ and ‘both MIP and MPD’ have turned out that both objective function values are improved. Also, the duplicated multiobjective design solutions are much close to the result obtained by ‘MPD only’, as in the vehicle dashboard design.5. 4 Plug receptacleThis problem employs the weld-line condition as a constraint instead of shear stress. In Fig. 16, the design space for optimally locating 2 gates is re-presented by a dotted region, and the restricted areas against weld-lines are designated by 5 solid regions. Actual mold designers do not locate the weld-line restriction just like this problem. Side or rear parts of a product might be preferred. However, this problem places the disjointed 5 weld-line restriction areas in the front to see how much the proposed design strategy of mGA works in the present study. Opti-mized results of weld-line distribution are shown in Figs. 17 and 18. It is clear to see that all the results areGFig. 17. Weld-line in optimized design of plug receptacle (MPD only).Fig. 18. Weld-line in optimized design of plug receptacle (MIP only & both MIP and MPD).Jongsoo Lee and Jonghun Kim / Journal of Mechanical Science and Technology 21(2007) 789~798 797Table 5. Optimization results of plug receptacle.max pressure [MPa] max difference[MPa] MIP only 160.30 0.51 MPD only 166.47 0.05objective both MIP andMPD160.30 0.51 satisfied with weld-line constraint. The design solu-tions for optimal objective function values are also similar to those of TV monitor. The solutions of ‘MIPonly’ and weighting method based ‘both MIP and MPD’ are the same (see Table 5).6. Concluding remarks The paper examines micro genetic algorithm in the context of engineering design optimization. Micro genetic algorithm is efficient in handling with smallpopulations over a conventional genetic algorithm. The proposed optimization algorithm is applied to filling injection mold design problem. The central of the paper is to locate gate positions by minimizingboth maximum injection pressure at the injection port and maximum pressure difference among all the gateson a product with constraints on shear stress and/or weld-line. Multiobjective design solutions show thatthe enhancement on flow balance and smoothness may be made possible by optimizing the gatepositions. The use of optimized runner systems wouldsubsequently expect to reduce defects such as deformation and twisting that are to be generatedduring the cooling process.Acknowledgments Authors greatly appreciate for the partial support from iDOT, Center of Innovative Design Optimi-zation Technology.References Chang R. Y . and Yang, W. H., 2001, “Numerical Simulation of Mold Filling in Injection Molding Usinga Three-Dimensional Finite V olume Approach,” Inter-national Journal for Numerical Methods in Fluids , V ol.37, Issue 2, pp. 125~148.Chiang, H. H., Hieber C. A., and Wang, K. K., 1991,“A Unified Simulation of the Filling and PostfillingStages in Injection Molding, I: Formulation,” PolymerEngi-neering and Science , V ol. 31, No. 2, pp. 116~124.Dennis, B. H. and Dulikravich, G . 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I., 1996, “Optimization of Injection-Molding Conditions UsingGenetic Algorithm,” proceedings of SPIE , V ol. 2644, pp. 173~180, March.Koo, B., 2003, CAPA User’s Manual V ersion 5.4, Suwon, Korea. (http://www.vmtech.co.kr)Krishnakumar, K.,1989, “Micro Genetic Algorithms for Stationary and Non-Stationary Function Optimi-zation,”Intelligent Control and Adaptive Systems , V ol.1196, pp. 289~296.Kwon T. H. and Park, J. B., 2004, “Finite ElementAnalysis Modeling of Powder Injection Molding Filling Process Including Yield Stress and Slip Phenomena,”Polymer Engineering and Science , V ol. 35, Issue 9, pp. 741~753.Lee J., and Hajela, P ., 1996, “Parallel Genetic Algorithm Implementation in Multidisciplinary Rotor Blade Design,” Journal of Aircraft , V ol. 33, No. 5, pp. 962~969.Lee, J., 1996, “Genetic Algorithms in Multidis-ciplinary Design of Low Vibration Rotors,” Ph. D.Dissertation in Mechanical Engineering, Rensselaer Polytechnic Institute , Troy, NY , May 1996. Lee, J., Kim J. and Jeong, H., 2003, “Optimal Design of Runner Systems in Injection Molding,” proceedings of CAPA User’s Conference, Seoul, Korea. Li C. S., and Shen, Y . K., 1995, “Optimum Design of Runner System Balancing in Injection Molding,”。
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Bio-manufacturing仿生机械和生物制造5)Virtual Manufacturing and Network Manufacturing虚拟制造与网络制造6)High-speed Automation and Intelligent Control, Intelligent Manufacturing,Knowledge-based Engineering高速自动化与智能控制，智能制造与知识工程7)High-precision Manufacturing Automation Technology 高精度制造与自动化技术8)CAD/CAE/CAPP/CAM计算机辅助设计、计算机辅助工程、计算机辅助工艺过程设计、计算机辅助制造9)PLM, PDM, ERP/ERM产品数据管理系统、产品生命周期管理、企业资源管理、企业权限管理10)Manufacturing E-commerce System制造业电子商务系统11)Quality Monitoring and Control of the Manufacturing Process 加工过程中质量监控与管理B.Material Science and its Application1)Iron and Steel and composites 钢铁和复合材料2)Micro / Nano Materials 微/纳米材料3)Optical/Electronic/Magnetic Materials光学/电子/磁性材料4)New Functional Materials and Structure Materials新型功能和结构材料5)Hydrogen and Fuel Cell Science, Biofuels and biological materials ,Other New EnergyMaterials氢能/燃料电池/生物燃料/生物材料及新能源材料6)Non-ferrous Metal material 有色金属材料7)Materials Forming and machining 材料成型与加工8)Surface Engineering/Coatings 表面工程/涂料9)Modeling, Analysis and Simulation of Manufacturing Processes制造过程建模、分析与模拟10)Special material and Welding & Joining特种材料与焊接11)Smart/Intelligent Materials/Intelligent Systems智能材料/智能系统12)Machinery industrial materials机械工业原料C.Mechatronics and intelligent Robot Technology1)Mechatronics modeling, optimization and simulation techniques and methodologies机电一体化模型、优化、仿真技术与方法2)Intelligent mechatronics, biomimetics, automation and control systems 智能机电一体化，仿生机械，自治系统3)Opto-electronic elements and Materials, laser technology and laser processing 光电元件和材料，激光技术和激光处理4)Elements, structures, mechanisms, and applications of micro and nano systems 微系统、纳诺系统元件、结构、机理和应用5)Teleoperation,telerobotics, haptics, and teleoperated semi-autonomous systems 遥操作、遥控机器人、触觉和遥操作自治系统6)AI, intelligent control, neuro-control, fuzzy control and their applications 人工智能、智能控制、神经控制、模糊控制和应用7)Architecture of intelligent robots智能机器人体系8)Perception, navigation and control of intelligent robots智能机器人的认知，导航和控制9)Intelligent teleportation智能遥操作10)Image processing and robot vision图像处理和机器视觉11)Simultaneous localization and mapping of mobile robots移动机器人同步控制和定位12)Uncertain environment modeling非特定环境建模13)Novel interfaces and interaction modalities新型界面和交互方式14)Motion planning and navigation路径规划和导航15)Haptic interaction 触觉交互16)Robot software architecture and development tools（机器人软件结构开发工具）17)Context awareness（关联感知）18)Social robots（社会机器人）D.Deep sea Mining Equipment, Complex Equipment Design and Extreme Manufacturing深海采矿装备、巨型锻压装备、复杂装备设计及极限制造1)Deep-sea robot 深海机器人2)Optimal Location and Communication of Deep-Sea光学定位与深海通讯3)Ocean Data Acquisition, Visualization, Modeling and Information Management深海数据采集、可视化、建模和信息管理4)Ocean V ehicles and Floating Structures大洋车辆及浮体结构5)Deep-sea Mining Machine 深海采矿机器6)Huge-scale water press and forging press巨型水压机和巨型模锻压机7)Large tonnage press大吨位压机8)Manufacture and Equipment of High Performance Materials and Components in StrongField强场下的高性能材料与原器件制造与装备9)Micro-Nano Manufacture and Equipment of Microelectronic Devices微电子元器件的微纳制造与装备10)Digital Manufacture Technology and Equipment of Complex Parts复杂部件的数字制造技术和装备11)Equipment of Special Operation in Extremely Harsh Environment极端环境下特种操作装备12)Integrated Intelligent Control of Complex Electromechanical System复杂机电系统智能控制E.Agricultural Equipment and its Automation1)Modern production equipment design and manufacture of main crops主要农作物的现代生产装备设计和制造2)Animal husbandry and Aquatic equipment design and manufacture畜牧业和水产设备的制造3)Facility agriculture equipment design and manufacture农业设施与装备的设计与制造4)Mechanized production equipment design and manufacture of fruits and vegetables果蔬的机械化生产与装备的设计与制造5)Comprehensive utilization technology and equipment development of agricultural biomass农业生物质的综合利用技术和装备6)CAD/CAM/CIMS application in agricultural equipment 农业装备的计算机辅助设计,制造与柔性制造系统7)Agricultural mechanization planning and management农业机械化与设计及管理8)Advanced Control and sensor technology in Agricultural equipment农业装备的先进控制技术9)Navigation and positioning technology in Agricultural equipment 农业装备导航与定位10)Agriculture robot technology 农业机器人技术11)Remote Diagnosis and Maintenance of Agricultural equipment农业装备的远程诊断与保养12)Energy saving technology of agricultural equipment 农业装备节能技术13)The Optimization and Utilization of Irrigation Equipment in agriculture 灌溉设备的优化和应用F.Intelligent Control and Detection Technology1)Autonomous Control and Fuzzy Logic自治控制与模糊逻辑2)Complex System modeling and intelligent controller design复杂系统建模与智能控制设计3)Genetic algorithms ,Machine learning / adaptive systems, Knowledge-based and expertsystems遗传算法、机器学习、自适应系统、专家系统4)Intelligent control application 智能控制应用5)Failure detection and identification故障检测和分类6)Chemical Sensor, Gas Sensors, Biosensors, Optical Sensors, Mechanical Sensors, PhysicalSensors化学传感器，气体传感器，生物传感器，光学传感器，机械传感器，物理传感器7)Intelligent Sensor, Soft Sensor, Wireless Sensors and Wireless Sensor Networks,Multi-sensor fusion / integration智能传感器，软件传感器，无线传感器及网络，多传感器融合与结合技术8)Data Acquisition and Measurement Engineering数据采集与测量工程9)Adaptive Signal Processing, Multimedia Signal Processing自适应信号处理，多媒体信号处理。
