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自定中心振动筛
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自定中心振动筛设计,自定中心振动筛,设计
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一、 选题的依据：筛分作业是煤炭加工的重要环节，它广泛地应用于筛选厂和选煤厂，对煤炭进行粒度分级、脱水、脱泥、脱介。就煤炭加工而言，筛分技术和分选技术处于同等重要的地位。我国生产的原煤一半以上是动力用煤，不同用户对动力用煤的粒度要求是不一样的，尤其是化工，发电等部门，对煤炭粒度要求很严格，如果超过规定限度，不但影响这些部门的正常生产，还会造成不小的浪费。例如在煤炭气化的过程中，若使用粉煤含量过高的块煤，不仅影响炉内气流畅通，降低造气量，严重时还导致气化炉填塞；机车和船舶由于锅炉通风强，烟简短，如燃用含有较多粉煤的块煤时，粉煤不仅燃烧不完全而且还随着烟气飞走，造成浪费和环境污染；大型火力发电厂，绝大部分使用粉煤锅炉，若供应原煤和块煤，显然是不经济的。总之，将原煤筛选成多种粒度的产品，对路供应给各类用户，对合理利用煤炭资源是十分重要的。筛分可以为其他选煤方案创造条件。目前的各种选煤方法和分选设备往往都受到粒度的限制，不同的选煤方法都有一定的入料限制，过粗的大块不能分选，而粒度过细也很难回收。在选煤厂主要是将原煤分成块煤和末煤两种粒级，分别进行跳汰选煤和重介选煤。重介选煤对入料中的煤泥含量很敏感，它直接影响到介质系统的正常工作和重介分选的效果。通过分选去除细泥，减少煤泥对介质系统的污染，以及高晖泥对精煤产品的污染；也可使跳汰机洗水粘度降低，有利于细粒煤的分选，从而提高分选效果。 在动力煤选煤厂中，通常将小于6mm的干粒粉煤给发电厂或者其它用户，而大于6mm的没选入跳汰机分选，这也是依靠筛分作用来完成的。总之，在选煤加工过程中，筛分作业不仅关系着动力煤产品对路供应，关系着动力煤，炼焦煤洗选产品质量的提高，也关系到煤炭资源的合理利用，环境保护和生产部门的经济效益。二、 国内外研究概括及发展趋势（含文献综述）：改革开放以后，我国各行业都得到长足的进步。振动筛的应用也越来越广泛，但同时对振动筛的各项性能都有了新的要求。在此大背景下，我国振动筛技术通过自主研发和吸收消化国外先进技术，也得到了长足的进步。相继研制出DYS大型圆振动筛、YA型圆振动筛、ZKX系列直线筛和SZZ型自定心振动筛等。近几年来，国内外对振动筛的研制越发重视。目前，振动筛的发展已经朝着大型化、智能化、高效集中、使用寿命长方向发展。世界上振动机械产品处于领先地位的公司主要有德国的SCHENCK公司、美国的ALIS-CHALMERS公司、日本的HITACHI公司等，他们生产的产品代表了世界范围内振动筛发展的主流趋势。而在国内，只有太行公司、鞍山矿山机械股份有限公司、上海冶金矿山机械厂等少数几家企业开始大型振动机械的研制、开发与生产。但基于振动机械的工业环境复杂、条件恶劣、生产企业小，再加上我国振动机械工业起步较晚，我国产品与国外产品还存在较大差距。但是，随着改革开放的不断发展，我国的振动筛技术要会不断进步，逐步缩短与国外先进的差距。目前，河南新乡众多厂家生产的SZZ系列自定心振动筛，产品标准为QJ/AKJ02.08-89自定中心振动筛和QJ/AKJ02.09-89自定中心振动筛，已具有相当先进水平。三、 研究内容及实验方案：本次设计的主要部件是单轴性振动的激振器。激振器的轴参与振动，结构简单、容易制造。设计为自定中心，皮带轮偏心，在工作过程中不参与振动，大大的延长皮带的使用寿命，工作也较稳定。设计内容还包括筛箱的设计，轴以及轴承的选择和强度的校核。振动筛及零部件材料的选用和加工方法等。研究的方法主要以理论计算为主，部分部件采用筛分设备的实践经验，用比较法进行设计和简单的计算。四、 目标、主要特色及工作进度目标： 主要参数 清筛进程 200m/h 中等粒度石碴占总量 50% 污土占总量 25% 每米道床石碴体积 1.5m3 石碴的紧方容量 2.0 t/m3按以上要求完成振动筛设计。主要特色： 具有结构可靠、激振力强、筛分效率高、振动噪音小、坚固耐用、维修方便、使用安全等特点。工作进度：1. 收集资料、外文资料翻译、开题报告 （第1周第2周）2. 总体方案设计 （第3周第4周）3. 参数确定及设计计算 （第5周第7周）4. 振动筛装配图设计及零部件图设计 （第8周第15周）5. 毕业设计论文 （第16周第17周）五、 参考文献：1 璞良贵，纪名刚主编.机械设计.第七版.北京：高等教育出版社，2001 2 孙桓，陈作模主编.机械原理.第六版.北京：高等教育出版社，2002 3 成大先主编.机械设计手册.北京：化学工业出版社，2004 4 闻邦椿，刘树英编著. 机械振动学.北京：冶金工业出版社，20005 Ye Zhonghe, Lan Zhaohui. Mechanisms and Machine Theory. Higher Education Press, 2001.7自定中心振动筛设计 学生姓名：刘城建 班级：0781052 指导老师：吴晖摘要：目前我国各种选煤厂使用的设备中,振动筛是问题较多、维修量较大的设备之一。这些问题突出表现在筛箱断梁、裂帮,稀油润滑的箱式振动器漏油、齿轮打齿、轴承温升过高、噪声大等问题,同时伴有传动带跳带断带等故障。这类问题直接影响了振动筛的使用寿命,严重影响了生产。自定中心振动筛可以很好的解决此类问题，因此本次设计的振动筛为自定中心振动筛，该系列振动筛主要用于煤炭行业中物料分级、脱水、脱泥、脱介等作业。其工作可靠，筛分效率高，但设备自身较重。设计分析论述了设计方案，包括振动筛的分类与特点和设计方案的确定；对物料的运动分析，对振动筛的动力学分析及动力学参数的计算，合理设计振动筛的结构尺寸；进行了激振器的偏心块等设计与计算，包括原始的设计参数，电动机的设计与校核；进行了主要零部件的设计与计算，皮带的设计计算与校核，弹簧的设计计算，轴的强度计算，轴承的选择与计算，然后进行了设备维修、安装、润滑及密封的设计，最后进行了振动筛的环保以及经济分析。关键词：振动筛；激振器；自定中心 指导老师签名：Custom Design Center ShakerStudent name: Liu Chengjian Class:0781052 Supervisor: Wu HuiAbstract: At present, Chinas coal preparation plant all the equipment used in the shaker is more problems, maintenance of one of the larger equipment. These issues in sieve outstanding performance me off beam, crack help, lubrication oil dilute the box-type vibrator oil spills, fighting tooth gear, bearing temperature rise too high, major issues such as noise, accompanied by dancing with broken belts, such as fault zone. Such issues directly affecting the life of the shaker, which has seriously affected the production. 2YAH1548-round good shaker can solve such problems, so this shaker designed for round 2 YAH1548-shaker, the series of major shaker in the materials used in the coal industry classification, dehydration, desliming, such as referrals from Operations. Its reliable, efficient screening, but their heavy equipment. Design analysis on the design options, including the classification and shaker features and design programmes to be confirmed; materials on the movement of the shaker and the dynamics of the parameters, to design the structure of vibrating screen size; conduct The eccentric block of the exciter, such as design and calculation, including the original design parameters, motor design and verification; were the main components of the design and calculation, belts and check the design and calculation, the design of spring, the axis of Strength, the choice of bearings and calculation and then proceed to the maintenance of equipment, installation, lubrication and seal the design, a shaker final environmental and economic analysis. Key words: shaker; Vibrator; Self-centering Signature of Supervisor:南昌航空大学科技学院学士学位论文低能耗机器人悬浮机构的应用摘要 （文档摘要）本文给出一种采用悬浮装置直接驱动机器人手臂来操纵重型物体的低能量操纵方法。考虑到在水平面内悬吊工具的操作，利用悬吊在水平面内的工具的动态行为给出了混合位置/力跟踪计划的运算法则，为了垂直操纵悬浮机器人手臂,由考虑到弹簧秤的重力补偿，这种混合位置/力的动力学模型已经发展。为了显示应用于工业的可能性，这种模型在倒角作业领域已经展开。模拟和实验证明了此拟议系统的可行性。文本全文(5295个字)著作权MCB UP Limited (MCB) 2000截至2000小型断路器有限公司(简称MCB)Mohammad Jashim Uddin: 博士, 山形大学系统和信息工程系, 日立 4-3-16, 日本Yonezawa 992-8510,电话: +81 238 26 3237; 传真: +81 238 26 3205.Yasuo Nasu:山形大学机械系统工程部教授,日立 4-3-16, 日本Yonezawa 992-8510,Kazuhisa Mitobe: 副教授, 山形大学机械系统工程部教授,日立 4-3-16, 日本Yonezawa 992-8510,Kou Yamada: 副研究员, 山形大学电子及信息工程系, 日立 4-3-16, 日本Yonezawa 992-8510,鸣谢: 在此作者真诚的感谢Yoshihiro Ishihara先生, Yoshiyasu Hariu先生, Hidekazu Satou先生, 及 Kazuo Abe先生在机器人的制作和控制软件的执行中所做出的努力Mohammad Jashim Uddin还将感谢教育部，科学会，运动商及(MONBUSHO)给出的奖学金, Japan. Received: 5 January 2000 Accepted: 7 February 20001. 简介：在水平的运动中，工具重量在连接摩擦上有相当大的影响，它直接地影响推进时的转动力矩。在垂直的运动中，地心引力效果在操作体的动力学上有相当大的影响。机器人的操纵应该在推进转力矩的可允许极限和力量感应器的能力里面。悬浮工具系统(STS)是一种新提议的横向操纵重型工具的处理策略，悬吊机器人手臂系统(SRAS)是一种新提议的机器人手臂用在垂直面实现低功率驱动和小容量感应器的操作方法。由于和传统的系统比起来具有很多优点，悬浮工具系统和悬吊机器人手臂系统已经成为工业应用领域越来越感兴趣的话题。当需要结构的坚硬性和高性能动态的时候，并联操作结构与现有的机器人系列相比，提供了许多明显的优点。因此, 这种机制在过去二十年受到了一定的关注(自1983). 一般说来，直接驱动式机械手, ,容易出现过快的操作幅度, 然而其输出动力却很小。为了使其能拿起物体，在多个机械手的协调性控制方面做了很多研究(Schneider and Cannon, 1992; Walker et al., 1988). 当两个或更多机器人手臂用来完成一单一的任务时，其承载、处理、操纵能力会得到增强。 然而, 一个单一的机械手不能操纵重物，因为其驱动转矩滞留在一个固定的极限。当前，许多工业机器人被用于研磨作业。大部分的研磨机器人操作受限于环境. 许多研究人员开展了工业机器人的力量控制(Kashiwagi et al., 1990; Whitney and Brown, 1987). 然而, 在那些系统中,研墨工具以传统的方式直接装在机器人手臂上，而且需要一个很大的驱动力，虽然对有关在垂直面内机器人手臂的操作有所研究 (Nemec, 1994), 但没考虑到重力的补偿，一般，由一个或多个机械手完成一个任务的可能性取决于其运动学和动态的能力。自动化机器人的修边已经在(Her and Kazerooni, 1991)被描述。在惠特尼等地报道，美洲狮 560 机器人的机械手焊珠研磨系统已经具有视觉系统 (1990). 在所有先前的修边或研磨的研究中,大功率驱动器被应用于机器人系统。在垂直面内，由于机械手的巨大的重力的影响，研磨加工过程变得非常困难，尤其是当驱动器的转矩极限小于重力的影响范围。机器人系统通常应用于一个受约束的环境，所以，要控制最终受力器在自由方向的位置和在被约束方向的触点压力 。由Raibert 和Craig (1981)提出的混合位置/力控制方案在别的现存的控制方案上拥有相当大的声望。本文中, 将阐述具有一种悬吊工具系统的机械手混合位置/力控制方案。考虑到悬浮工具在水平面内的动态性能，我们将延伸说明到混合控制方案的基本原理。在垂直的运动中,讨论由弹簧秤引起的重力补偿的动态性能。2. 系统描述：Asada和Ro (1985) 设计了直接驱动五杆并联机器人,具有如下许多优点：没有后冲，微小的摩擦，高机械硬度以及精确的运动。这种实验装置系统包含一个两自由度机器人，具有一个五杆连接结构和悬架系统。图1和图2展示了机器人结构的计算机辅助设计，在水平面和竖直面内分别附带一个弹簧平衡器。表一显示了五杆连接机制的一些重要性能。2.1. 运动学和动力学方程：本节讨论的连接结构是一个五杆闭环连杆机构，如图3。有两个输出环节，分别由两个独立的直驱马达驱动，两个马达安装在底架上， 1，2，3，4杆的长度分别由sub1, lsub2, lsub3, & lsub4表示。输入杆的角度由qsub1 和 qsub2表示，从Y轴测量所得。终点坐标(见方程式1)(见方程式2)，从方程 (1)和 (2)得该机器人的反转运动学为：(见方程式3)( 见方程式4)，工作空间是一个Jacobian矩阵22矩阵,可以表示为：(见方程式5)，机器人手臂的惯量矩阵是一个2 x 2 矩阵，可以表示为 (见方程式6) A=Isub1+msub1lsup2subC1+Isub3+msub3lsup2subC3+msub4lsup2sub1 B m= (msub3lsub2lsubC3+msub4lsub1lsubC4)cos(qsub1-qsub2) C m= (msub3lsub2lsubC3+msub4lsub1lsubC4)cos (qsub1-qsub2) Dm=Isub2+msub2lsup2subC2+Isub4+msub4lsup2subC4+msub3lsup2sub2 科里奥利公式和向心力矩阵是一个 2 x 1 矩阵，可表达为:(见方程式 7)(见方程式 8)，重利矩阵是一个2 x 1矩阵，可以表示为：( (见方程式9)( (见方程式10)，g是由重力引起的重力加速度。2.2.硬件描述：控制系统的一个硬件示意图如图4，一部奔腾微型计算机, 133 兆赫, 被用来控制此系统。输入（A/D）和输出（D/A）转换具有八条通道和12字节的处理能力。伺服系统驱动器有三种控制模式：位置控制模式速度控制模式和转矩控制模式。此计算机主板具有三个端口和24字节脉冲处理。一个低容量的三轴力传感器 (逐渐校正到19.62 N) 装在机器人手臂顶端和气动夹子之间。运算放大器与一个低通滤过器设计在一起，以消除预想不到的噪音，表2显示了直驱马达的一些重要性能。2.3. 工作空间与异常：对于一个给定的末端受动器位置，反转运动学一般具有两个可行的解决方案。异常的结构会分开这两种解决方案，在异常的结构中，操纵器的最终受动器不能在一个特定的方向移动。异常分为两种：固定异常和不定异常。一个闭环操纵器可能既有固定异常又有不定异常，在一个静止的异常中, Jacobian 点阵具有零决定因素，然而在一个不定异常中，Jacobian点阵的决定因素为无穷大。Ting (1992) 、 Asada和 Ro (1985) 指出了五杆闭环连杆机构的异常问题。对于五连杆结构，Jacobian 矩阵的决定因素J被定义为(见方程式11)；对于五连杆机构，当( 见方程式12)的情况时，固定异常存在。由方程式 (10)知,固定异常发生在工作空间的边界，所以，籍由选择链环尺寸来获得一个自由空间的宽阔异常。机器人手臂的笛卡尔工作空间是最终受力器的总电子扫频量，同时机器人手臂执行所有的可行的动作，最终受力器伴有一种特殊的力，即法向力和切向力。迪卡尔工作空间受限于机器人手臂的几何学分析和铰链的机械约束以及驱动器的旋转极限。力量工作空间受限于最终受力器的发向力和切向力。实际上，力量工作空间是机械人手臂的一个笛卡尔工作空间的子集。当驱动器的旋转力矩在如下范围内时：0sup- = qsub1 =180sup- & 0sup- = qsub2 =180sup-.图5展示了五连杆机构在水平面内的模拟卡迪尔工作空间。笛卡尔总工作空间应付 5.0 N 的力量工作空间，在10.0 N的力量工作空间情况下是卡迪尔工作空间的一个子集。当弹簧秤的提升力设为9.81 N 和驱动器的旋转力在以下范围时：0sup- = qsub1 =180sup- and 180sup- = qsub2 =360sup-.图6展示展示了五连杆机构在竖直面内的模拟卡迪尔工作空间。笛卡尔总工作空间应付 5.0 N 的力量工作空间，在10.0 N的力量工作空间情况下是卡迪尔工作空间的一个子集。3. 悬浮动态悬浮工具系统和悬浮机器人手臂系统的模型分别如图7图8 所示。 弹簧秤的性能参数见表III 。在悬浮系统中, phi是旋转角度, psi 是方位角。为了将悬浮系统形象化，我们考虑做如下假设：高架铁路的弹性变形，钢索的质量，滚动阻力，风力以及忽略噪音。最终受力器的卡迪尔坐标定义如下： (见方程式13)( 见方程式14)，有效的提升力Fsub取决于弹簧秤的设置，与悬浮的质量有关而不是钢丝绳的长度变化。在悬浮工具上的有效力被定义为： (见方程式15)( 见方程式16)。现在，水平面内的悬浮力为：(见方程式17)。在竖直面内的有效力Fsubvy和 Fsubvz 被定义为：(见方程式18)( 见方程式19)。此时，在竖直面内来自弹簧秤的补偿力可被定义为：(见方程式20)4. 系统动力学混合位置/力控制方案以一个工作空间的直角分解为基础。在平面运动中，考虑到悬浮工具的动态影响，我们讨论位置/力控制模型 。在这部分中，竖直面中的混合位置/力控制模型从弹簧秤的重力补偿方面来描述。5. 仿真结果为了探讨机器人手臂在横向和纵向面内的执行性能，利用前面章节的MATLAB仿真程序进行了动态模型模拟，仿真框图如图10。轨迹发生器,运动器,控制器,操作器动力, 以及约束条件都在MATLAB函数中被描述了。端口用来连接标量或矢量信号汇集成一个更大的矢量信号。转换器用来选择输出矢量的有用信号。5.1.水平面内为显示工具重力的影响，利用混合位置/力模拟以实现水平面运动。在模拟过程中，总操作时间为10秒，混合的时间为0.5秒，要求速度为0.02米/秒。最终受力器的轨迹在一个被约束的表面，从(0.0, 0.3) 到 (0.2, 0.3) 。模型工具的重量是2.0 kg 。 假设是特制钢，弹簧秤的提升力看作是19.62 N ，所需的力为5.0 N 。从图11可看出, 与传统的工具系统相比，由于特制钢工具系统具有更小的连接摩擦，故其位置误差更小。 此外，从图12可看出，由于小的悬浮力作用于此悬浮工具系统，故其引起力的误差更小。5.2. 竖直面内在竖直面内，当驱动器力矩极限在重力影响范围之内时，弹簧秤的提升力是必要的，用以补偿重力。一个特征曲线图用来说明提升力的必要性以使机械手在力矩的极限内保持在一个预设的速度。图13表示了在速度为0.01米/秒时弹簧秤的提升力和马达的驱动力矩之间的关系Fsubb。 在此特征曲线图里，提升力达到5.0 N ，由于假想摩擦力的影响（方向力河切向力），马达驱动力保持不变。此时，由于受到提升力的影响，马达的驱动力将增加。从此特征图可以看出，当提升力从5.2 N变到16.5 N时，在驱动力极限内机器人手臂能够被操作。我们进行了悬浮机器人手臂操作的混合位置/力控制模拟实验。在模拟实验中，总操作时间为10秒，混合的时间为0.5秒，最大速度为0.01米/秒，从特征曲线图可知，提升力设定为9.81 N ，要求的力是5.0 N。在垂直向上的运动中，机械手的轨迹在一个被约束的表面，从(0.3, 0.0) 到(0.3, 0.1) 。图14 展示了机械手的有效的提升力和重力 。在竖直面的运动，弹簧秤的提升力是补偿重力的主要部分，以及有效力非常小。图15和图16分别展示了位置轨迹和力的轨迹。输出的位置轨迹与要求的位置轨迹之间存在一个小的固定误差以及力的输出与要求的力输出有一个小的时间滞后。6. 实验结果为了证明以上系统地有效性和正确性，我们在水平面和竖直面都进行了实验，实验结果如下部分所示。6.1. 静力图17和图18分别展示了在静态时沿X轴和Y轴的有效力Fsubhx 和Fsubhy。很明显， 当机器人手臂抓住悬浮工具时，有效的静态力大小接近最佳，但是当机器人手臂抓住工具而没有悬浮时，由于工具自身重量的影响，有效力将非常高。由于工具自身重量，机械手顶端会偏离引起位置误差。有效的静态力造成连接摩擦影响驱动器的驱动力矩。6.2.水平运动在本实验中，机械手抓取一个2.0千克的悬浮工具的运动轨迹在一条从(0.1, 0.34) 到 (0.2, 0.34)的线上。速度指令为0.02米/秒，所需的力是10.0牛。从弹簧秤上悬吊起工具所需的力为19.62 N 。在实验开始之前，最终受力器与一个被约束的表面接触，图19展示了本实验的位置轨迹，图20展示了力的轨迹。实际的位置轨迹与所需的位置轨迹存在一个稳定的小误差，以及实际力与要求的力输出有一个小的时间滞后。6.3. 竖直运动在竖直平面内，当驱动器的驱动力矩极限在重力影响范围之内时，机器人手臂不能进行自动操作。在本实验中，弹簧秤的提升力设定为15.0 N，足够将在低速运行的机器人手臂悬吊起来。机械手的轨迹在一个从(0.28, 0.22) 到 (0.28, 0.26)的被约束表面上。指令速度为0.005米/秒，所需的力为2.0牛 。图21和图22分别展示了位置轨迹和力的轨迹。实际的位置轨迹与要求的位置轨迹之间存在一个小的固定误差以及实际的力的与所需的力轨迹有一个小的时间滞后。图23 说明了所需的驱动力矩，此力矩在驱动器的最大极限之内。7.工业应用为证实上述被应用于工业的机器人系统的低能耗，倒角作业已经实行。图24 展示了在竖直平面内的实验装备，在传统的系统中，用旋转的铁碳锉刀修毛刺的结果显示，在304不锈钢上用0.88牛的解点压力和0.01米/秒的速度可生成一个可令人接受的倒角。在上述被提议的机器人手臂系统中，已经应用于SS400倒角作业。悬吊此低能耗机器人手臂的提升力为15.0牛。用一个重0.13千克（直径为16 mm）的气动砂轮以最大旋转速度为每秒30000转的速度进行铣削 ，倒角表面的照片如图25所示，图26 显示了在匀速为0.01米/秒的法向摩擦力fsubn及切向磨削力fsubt。法向磨削力保持在所需的大小2.0牛，因为在毛坯尺寸中没有大的变化。切向力大约是法向力的一半，图27展示了通过一次单一的磨削倒角表面的剖切图。倒角结果显示了倒角面的宽度0.36 +- 0.07 mm ，此结果在公差范围内。8. 结论上述提议的悬浮系统的主要目标是用能耗操作器完成中午的作业。在水平面和竖直面内都已经讨论过。在水平运动中，悬浮系统具有一些优点，当重型工具超出驱动器的驱动力矩极限时，它可以利用弹簧秤的提升力进行操作。此系统的连接摩擦力小于传统的系统，在桡腕关节产生的阻力更小，这对小容量的力传感器来说更是一大益处。此外，在竖直运动中，悬浮力补偿了作用在操作器上的重力。悬浮工具的动态模型和悬浮机器人手臂系统已经发展和执行，利用当前的动力学公式，开展了模拟和实验以证明上述提议的系统的有效性。在竖直平面内，倒角作业已经开展了。在竖直平面内操作机器人手臂需要一个大力矩驱动的驱动器以克服重力。弹簧秤的提升力补偿了工具在竖直平面内的重力。倒角表面的结果证明了悬浮机器人手臂的自动磨削系统可以以低功率驱动力传感器和低能量驱动器在大尺寸的金属切削过程中具有广泛的可应用性。 Application of suspension mechanisms for low powered robot tasksAbstract: The manipulation methods of a low powered direct-drive robot-arm for heavy object manipulation using a suspension device are presented. Manipulation of a suspended tool in the horizontal plane is considered. The algorithm is presented of the hybrid position/force tracking scheme with respect to the dynamic behavior of suspended tools in the horizontal plane. To manipulate the suspended robot-arm vertically, the hybrid position/force dynamic model has been developed by considering the gravity compensation of the spring balancer. In order to show the possible industrial applications chamfering operations have been carried out. Simulations and experiments demonstrate the feasibility of the proposed systems.IntroductionCopyright MCB UP Limited (MCB) 2000 Mohammad Jashim Uddin: PhD student, Department of Systems and Information Engineering, Yamagata University, Jonan 4-3-16, Yonezawa 992-8510, Japan. Tel: +81 238 26 3237; Fax: +81 238 26 3205.Yasuo Nasu: Professor, Department of Mechanical Systems Engineering, Yamagata University, Jonan 4-3-16, Yonezawa 992-8510, Japan.Kazuhisa Mitobe: Associate Professor, Department of Mechanical Systems Engineering, Yamagata University, Jonan 4-3-16, Yonezawa 992-8510, Japan.Kou Yamada: Research Associate, Department of Electrical and Information Engineering, Yamagata University, Jonan 4-3-16, Yonezawa 992-8510, Japan.ACKNOWLEDGMENT: The authors gratefully acknowledge Mr Yoshihiro Ishihara, Mr Yoshiyasu Hariu, Mr Hidekazu Satou, and Mr Kazuo Abes efforts during fabrication of the robot and implementation of the control software. Mohammad Jashim Uddin would like to acknowledge his scholarship by the Ministry of Education, Science, Sports, and Culture (MONBUSHO), Japan. Received: 5 January 2000 Accepted: 7 February 20001. IntroductionIn horizontal motion, tool weight has a considerable effect on joint friction. It affects directly the driving torque. In vertical motion, the gravity effect has a considerable influence on the dynamics of the manipulator. Robotic manipulation should be within the allowable limits of the driving torque and capacity of the force sensors. Suspended tool system (STS) is a newly proposed object handling strategy to manipulate heavy tools horizontally and suspended robot-arm system (SRAS) is a newly proposed robot-arm manipulation method in the vertical plane using low power actuators and small capacity force sensors. Due to their many advantages compared to conventional systems, STS and SRAS have become topics of growing interest for applications in industry.Parallel manipulators offer significant advantages over current serial manipulators when structural stiffness and high-performance dynamic properties are required. Therefore, such mechanisms have received some attention over the last two decades (Hunt, 1983). Direct-drive arms, in general, tend to have excessively fast operating ranges, whereas the output forces are extremely small (Asada and Ro, 1985). For object handling, there are many researches on the coordinated control of multiple robot-arms (Schneider and Cannon, 1992; Walker et al., 1988). When two or more robot-arms are used to perform a single task, an increased load carrying, handling, and manipulating capability can be achieved. However, a single manipulator cannot manipulate a heavy object because the actuator torque stays within a fixed limit. Many industrial robots are currently used in automated grinding operations. Most of the grinding robots operate in a constrained environment. Force controlled grinding robots for industrial uses are developed by many researchers (Kashiwagi et al., 1990; Whitney and Brown, 1987). However, in those systems, the grinding tool is directly mounted on the robot-arm in a conventional way and requires a large actuator power. There are some researches on robot-arm manipulation in the vertical plane (Nemec, 1994), but compensation for gravity was not considered. In general, the feasibility of a task to be performed by one or more arms depends on both the kinematic and dynamic abilities of the manipulators.Automated robotic deburring has been described in (Her and Kazerooni, 1991). Robotic weld bead grinding system by PUMA 560 robot with vision system has been reported in Whitney et al. (1990). In all the previous deburring or grinding researches, big power actuators were used in the robot system. In the vertical plane, the grinding process is very difficult due to the enormous gravity effects of the manipulator, especially when the actuator torque limit is beyond the range of the gravity effects.Robotic systems usually operate in a constrained environment. So, it is necessary to control the position of the end-effector in the free direction and the contact force in the constrained direction. The hybrid position/force control scheme proposed by Raibert and Craig (1981) has gained considerable popularity over the other existing force control schemes.In this paper, hybrid position/force control scheme of robot-arm with a suspended tool system is described. We extend the basis of hybrid control scheme by considering the dynamics of the suspended tool system in horizontal motion. In vertical motion, the dynamics of gravity compensation by spring balancer is discussed.2. System descriptionAsada and Ro (1985) designed a direct-drive five-bar parallel drive manipulator, which has many advantages such as: no backlash, small friction, high mechanical stiffness, and accuracy of motion. The experimental system consists of a robot with two degrees of freedom (DOF) having a five-bar link configuration and a suspension system. Figures 1 and Figure 2 show the CAD design of the robot configuration with a spring balancer in the horizontal and vertical plane, respectively. Table I shows some important properties of the five-bar link mechanism.2.1. Kinematic and dynamic equationsThe link mechanism discussed in this section is a closed-loop five-bar link mechanism as shown in Figure 3. There are two input links that are driven by two independent direct-drive motors. Both motors are fixed to the base frame. The length of links 1, 2, 3, and 4 are denoted by lsub1, lsub2, lsub3, & lsub4, respectively. The angles of the input links are denoted by qsub1 and qsub2 measured from Y-axis. The end point coordinates are given by:(see equation 1)(see equation 2)From equations (1) and (2) the inverse kinematics of the manipulator is obtained as:(see equation 3)(see equation 4)The task space Jacobian matrix is a 2 x 2 matrix and can be expressed as:(see equation 5)The inertia matrix of the robot-arm is a 2 x 2 matrix and can be expressed as:(see equation 6)whereA = Isub1+msub1lsup2subC1+Isub3+msub3lsup2subC3+msub4lsup2sub1 B m= (msub3lsub2lsubC3+msub4lsub1lsubC4)cos(qsub1-qsub2) C m= (msub3lsub2lsubC3+msub4lsub1lsubC4)cos (qsub1-qsub2) D m= Isub2+msub2lsup2subC2+Isub4+msub4lsup2subC4+msub3lsup2sub2 The Coriolis and centripetal forces matrix is a 2 x 1 matrix and can be expressed as:(see equation 7)(see equation 8)The gravity matrix is a 2 x 1 matrix and can be expressed as:(see equation 9)(see equation 10)where g is the acceleration due to gravity.2.2. Hardware descriptionA hardware schematic diagram of the control system is shown in Figure 4. A Pentium based microcomputer, 133 MHz, is used to control the system. The A/D and D/A converter has eight channels and 12-bit resolution. The servo driver has three control modes: position control mode, velocity control mode, and torque control mode. The counter board has three ports and 24-bit pulse resolution. A low capacity three-axis force sensor (calibrated to work up to 19.62 N) is mounted between the robot-arm tip and the pneumatic gripper. The operational amplifier is designed with a low pass filter to eliminate unexpected noise. Table II shows some important properties of direct-drive motors.2.3. Work space and singularityFor a given end-effector position, there are in general two possible solutions to the inverse kinematics. The singular configuration separates these two solutions. At the singular configuration, the manipulator end-effector cannot move in certain directions. There are two types of singularities, stationary singularity and uncertainty singularity. A closed-loop manipulator may have both stationary and uncertainty singularities. At a stationary singularity, the Jacobian matrix has zero determinant, whereas at an uncertainty singularity, the determinant of Jacobian matrix is infinity. Ting (1992) and Asada and Ro (1985) pointed out the singularity problem for the five-bar closed link manipulator.For the five-bar link configuration, the determinant of Jacobian matrix, J, is defined as follows:(see equation 11)For five-bar link configuration the stationary singularity will exist when:(see equation 12)From equation (10), the stationary singularity occurs on the boundary of the workspace. Thus, by selecting link dimensions, a wide singularity free workspace can be obtained. The Cartesian workspace of a robot-arm is the total volume swept out by the end-effector as the robot-arm executes all possible motions. The force workspace of a robot-arm is the total volume swept out by the end-effector as the robot-arm executes all possible motions with a specific force at the end-effector, normal force and tangential force.The Cartesian workspace is constrained by the geometry of the robot-arm as well as mechanical constraints of the joints and the limit of the actuators rotation. The force workspace is constrained by the normal and tangential force applied at the end-effector. Actually, the force workspace is a subset of Cartesian workspace of a robot-arm.Figure 5 shows the simulated Cartesian workspace of the five-bar link mechanism in the horizontal plane when the actuator rotation is limited within the following ranges: 0sup- = qsub1 =180sup- & 0sup- = qsub2 =180sup-. The total Cartesian workspace copes with 5.0 N force workspace, where the 10.0 N force workspace is a subset of Cartesian workspace. Figure 6 shows the simulated Cartesian workspace of the five-bar link mechanism in the vertical plane when the lifting force of the spring balancer is set to a force of 9.81 N and the actuator rotation is limited within the following ranges: 0sup- = qsub1 =180sup- and 180sup- = qsub2 =360sup-. The total Cartesian workspace copes with 5.0 N force workspace, where the 10.0 N force workspace is a subset of Cartesian workspace.3. Suspension dynamicsThe models of the suspended tool system and the suspended robot-arm system are shown in Figure 7 and Figure 8, respectively. The properties of the spring balancer are shown in Table III. In the suspension system, phi is swing angle, and psi is orientation angle. In order to simplify the suspension system, the following assumptions are considered. The elastic deformation of the overhead rail, the mass of the wire rope, rolling resistance, wind forces, and noise are neglected. The Cartesian coordinates of the end-effector are defined as follows:(see equation 13)(see equation 14)The active lifting force, Fsubb, in the wire rope depends on the setting of the spring balancer, which is related to the suspended mass but independent of the variation of the rope length. The active forces on the suspended tool are defined as follows:(see equation 15)(see equation 16)Now, the suspension force in the horizontal plane is:(see equation 17)The effective forces Fsubvy, and Fsubvz in the vertical plane are defined as follows:(see equation 18)(see equation 19)Then, the compensation force from the spring balancer in the vertical plane can be defined as follows:(see equation 20)4. System dynamicsThe hybrid position/force control scheme is based on an orthogonal decomposition of task space. The hybrid position/force control model is discussed for planar motion by considering the dynamic effect of the suspended tool. In this section, hybrid position/force control model for vertical motion is described by gravity compensation of the spring balancer.5. Simulation resultsIn order to investigate the performance of robot-arm in the horizontal and vertical planes, simulations have been carried out using the dynamic models developed in the preceding sections by MATLAB Simulink program. The Simulink block diagram is shown in Figure 10. The trajectory generator, kinematics, controller, manipulator dynamics, and constraint conditions are described in MATLAB functions. The ports are used to combine scalar or vector signals into a larger vector. The switches are used to select the desired signals of the output vector.5.1. The horizontal planeHybrid position/force simulation is carried out for horizontal motion to show the effect of tool weight. In simulation, total manipulation time is 10.0 sec, where the blend time is 0.5 sec. The commanded velocity is 0.02 m/sec. The end-effector tracks on a constrained surface from (0.0, 0.3) to (0.2, 0.3). The model tool weight is 2.0 kg. In case of STS, the lifting force of the spring balancer is considered as 19.62 N. The desired force is 5.0 N. From Figure 11, the position error is smaller in the STS compared to the conventional tooling system due to smaller joint friction. Moreover, from Figure 12, the suspended tool system creates smaller force error due to the smaller suspending force affect of the tool.5.2. The vertical planeIn the vertical plane, to compensate for gravity forces the lifting force of the spring balancer is essential when the actuator torque limit is beyond the range of gravity effect. A characteristic graph is developed to know the required lifting force to move the manipulator within the torque limit at a desired velocity. Figure 13 shows the relationship between the lifting force of the spring balancer, Fsubb, and the motor torques at the velocity of 0.01m/sec. In this characteristic graph, up to 5.0 N lifting force, the motor torque remains constant due to the effect of assumed grinding forces (normal force and tangential force). Then the motor torque increases by the influence of the lifting force. From the characteristic graph, the robot-arm can be manipulated within the torque limits when the lifting force varies from 5.2 N to 16.5 N.Hybrid position/force control simulations have been carried out for suspended robot-arm manipulation. In simulation, total manipulation time is 10.0 sec, where the blend time is 0.5 sec. The maximum velocity is 0.01 m/sec. From the characteristic graph, the lifting force is considered as 9.81 N. The desired force is 5.0 N. In vertically upward motion, the manipulator tracks on a constrained surface from (0.3, 0.0) to (0.3, 0.1). Figure 14 shows the active lifting force and the gravity force on the manipulator. In vertical motion, the lifting force of the spring balancer compensates a big portion of the gravity force and the effective force is very small. Figure 15 and Figure 16 show the position trajectory and force trajectory, respectively. The position output tracks the desired position with a small steady state error and the force output goes to the desired force after a short time.6. Experimental resultsIn order to prove the effectiveness and validity of the proposed system, experiments have been carried out in both horizontal and vertical planes. The experimental results are shown in the following sections.6.1. Static forcesFigures 17 and Figure 18 show the effective forces Fsubhx and Fsubhy at static condition along X and Y-axis, respectively. It is obvious that when the robot-arm grasps the suspended tool, the effective static forces are near to the optimal forces, but when the robot-arm grasps the tool without any suspension, the effective forces are extremely high due to the weight effect of the tool. The arm tip is deflected by the weight of the tool, which causes the position error. These effective static forces create joint friction, which affects on the driving torque of the actuator.6.2. Horizontal motionIn this experiment, the manipulator tracks on a line from (0.1, 0.34) to (0.2, 0.34) by grasping a 2.0 kg suspended tool. The commanded velocity is 0.02 m/sec. The desired force is 10.0 N. To suspend the tool from the spring balancer 19.62 N lifting force is required. Before the experiment starts, the end-effector is in contact with a constraint surface. Figure 19 shows the experimental position trajectory and Figure 20 shows the experimental force trajectory. The actual position trajectory tracks the desired position trajectory with a small steady state error and the actual force goes to the desired force trajectory after a short time.6.3. Vertical motionIn the vertical plane, the robot-arm cannot manipulate itself, when the actuator torque limit is beyond the range of the gravity effect. In this experiment, the lifting force of the spring balancer is set to 15.0 N, which is sufficient enough to suspend the robot-arm at low speed. The manipulator tracks on a constrained surface from (0.28, 0.22) to (0.28, 0.26). The commanded velocity is 0.005 m/sec. The desired force is 2.0 N. Figures 21 and Figure 22 show the position trajectory and force trajectory, respectively. The actual position trajectory tracks the desired position trajectory with a small steady state error and the actual force goes to the desired force trajectory after a very short time. Figure 23 shows the required torque, which is within the maximum limit of the actuators.7. Industrial applicationTo verify the proposed low powered robot-arm system for industrial application, the chamfering operation has been done. Figure 24 shows the experimental setup in the vertical plane. In a traditional system, the deburring result (Kazerooni et al., 1986) shows that by using the carbide rotary files, an acceptable chamfer can be generated on 304 stainless steel at a contact force level of 0.88 N at a velocity of 0.01 m/sec.In the proposed suspended robot-arm system, the chamfering operation has been done on SS400 steel. A lifting force of 15.0 N suspends the low powered robot-arm. A pneumatic grinder of 0.13kg weight with mounted point grinding wheel (WA80, 16 mm diameter) has been employed in the down-cut grinding operation at the maximum rotational speed of 30,000 rpm. The chamfered surface photograph is shown in Figure 25. Figure 26 shows the normal grinding force, fsubn, and tangential grinding force, fsubt, at a constant velocity of 0.01 m/sec. The normal grinding force remains at desired force level of 2.0 N because there is no significant variation in burr size. The tangential force is about half of the normal force. Figure 27 shows the profile of the chamfered surface for a single pass grinding operation. The chamfering result shows a chamfer width of 0.36 +- 0.07 mm, which is within an acceptable geometric tolerance.8. ConclusionThe main objective of the proposed suspension systems is to perform heavy object manipulation with a low powered manipulator. Suspension systems are discussed both in the horizontal and vertical planes. In horizontal motion, the suspension system has some advantages. It can manipulate heavy tools beyond the range of actuator torque limit using the lifting force of the spring balancer. The joint friction is less than the conventional system. It creates a smaller force effect on the wrist joint, which is in favor of the small capacity force sensors. Moreover, in vertical motions, the suspension forces compensate the gravity effect of the manipulator.The dynamic models of suspended tool and suspended robot-arm system have been developed and implemented. By using the presented dynamic formulation, simulations and experiments have been carried out to verify the effectiveness of the proposed systems. Chamfering operations have been carried out by the suspended robot-arm in the vertical plane. To manipulate the robot-arm in the vertical plane a large actuator torque is desired to overcome the gravity forces. The lifting force of the spring balancer compensates the gravity forces and the tool weight in the vertical plane. The result of the chamfered surface proves the wide possible application of the suspended robot-arm grinding system in automation industries where high metal removal processes are possible with small capacity force sensor and low powered actuators.References: 1. Asada, H. and Ro, I.H. (1985), A link design for direct-drive robot arms, ASME Journal of Mechanisms, Transmission, and Automation in Design, Vol. 107 No. 4, pp. 536-40.2. Her, M.G. and Kazerooni, H. (1991), Automated robotic deburring of parts using compliance control, Transaction on ASME Journal of Dynamics Systems, Measurement, and Control, Vol. 113 No. 1, pp. 60-6.3. Hunt, K.H. (1983), Structural kinematics of in-parallel-actuated robot arms, ASME Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 105 No. 4, pp. 705-12.4. Kashiwagi, K., Ono, K., Izumi, E., Kurenuma, T. and Yamada
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