光刻机工件台：关于解耦矩阵校准测试的办法和科研
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/9658f50eb9fd443596254364e1bc7f50~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=L%2FCHB5TmsUGemztLzeeQs1%2F0orc%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;">文 | 祥说</strong></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;">编辑 | 祥说</strong></p>
<h1 style="color: black; text-align: left; margin-bottom: 10px;">介绍</h1>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">自1973年<span style="color: black;">第1</span>台光刻机在荷兰<span style="color: black;">面世</span><span style="color: black;">败兴</span>，光刻机的伺服精度与日<span style="color: black;">加强</span>，<strong style="color: blue;"><span style="color: black;">此刻</span>已取得了长足的发展。</strong></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">光刻机的<span style="color: black;">重点</span>系统<span style="color: black;">包含</span>：光学系统、机械减震系统、<span style="color: black;">测绘</span>反馈系统、工件台和掩模台系统等。</p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/876d525a8134459d9ddc16e55b8a7af7~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=oa%2Bera%2FCX59XzfKtJoPcrdbBOsc%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">超<span style="color: black;">精细</span>工件台<span style="color: black;">做为</span>光刻机的3大关键技术之一，其<span style="color: black;">需求</span><span style="color: black;">拥有</span>纳米级的定位精度和同步运动精度。</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">因为</span>工件台的制造工艺、非质心驱动和<span style="color: black;">测绘</span>反馈<span style="color: black;">安装</span>的<span style="color: black;">原由</span>，<strong style="color: blue;">工件台的<span style="color: black;">实质</span>位置和<span style="color: black;">目的</span>位置存在<span style="color: black;">必定</span>的误差。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/6e7c28ac63c74ba49fa58507ed22921b~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=wnAXCLlnLV5WfllhLWhuqCNSW5I%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">因而采用<span style="color: black;">恰当</span>的测校技术对工件台<span style="color: black;">有些</span>参数进行校准，<strong style="color: blue;"><span style="color: black;">作为</span>改善其定位精度和同步运动精度的<span style="color: black;">重点</span>手段。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/916c91b189434e318407e0a79f10e8d1~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=tYjpQqwTxTcG4fvrNSmNLWZ2KZo%3D" style="width: 50%; margin-bottom: 20px;"></div>
<h1 style="color: black; text-align: left; margin-bottom: 10px;">光刻机工件台解耦的基本原理分析</h1>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">工件台<span style="color: black;">重点</span>由3大部分<span style="color: black;">构成</span>：<span style="color: black;">基本</span>框架、平衡质量块、粗微动台体，<strong style="color: blue;">微动台是光刻机的核心部件，是微动台进行纳米级运动的关键。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/6fdc2f927740408f900cfcec78aedba1~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=xrqZfLZx0yPetPLye8GttboBpE4%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;">刻片时微动台<span style="color: black;">经过</span>调平、调焦等动作，并进行纳米级的<span style="color: black;">揭发</span>运动，使硅片晶圆完整。</strong></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">微动台按功能分为4个<span style="color: black;">公司</span>：Chuck部件、执行<span style="color: black;">公司</span>、<span style="color: black;">测绘</span><span style="color: black;">公司</span>、E-Pin部件<span style="color: black;">揭发</span>。Chuck部件<span style="color: black;">重点</span><span style="color: black;">包含</span>45°微晶镜块和真空吸盘。</p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p9-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/9331506dd47a44c397f4cf650fc0e501~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=2Siz9S3V%2B2yThUyA%2FClsIU%2FKcMw%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">45°微晶镜块<span style="color: black;">做为</span>反射镜，<span style="color: black;">协同</span>双频激光干涉仪进行高精度<span style="color: black;">测绘</span>；<strong style="color: blue;">真空吸盘用来固定硅片，防止在上下片过程中硅片滑落；</strong></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">另一</span>，Chuck部件装载<span style="color: black;">测绘</span>宏微相对位置传感器的磁极，执行<span style="color: black;">公司</span><span style="color: black;">重点</span><span style="color: black;">包含</span>微动平面音圈电机本体及垂向音圈电机。</p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/0c79026ba1914f49be7e31ce87564853~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=ZumOwS9ATkEL6Yrvoj2mThOlckA%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">执行<span style="color: black;">公司</span>采用3个平面音圈电机实现执行<span style="color: black;">公司</span>动子的水平X、Y向运动以及Rz偏转。</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">采用3个垂向音圈电机实现执行<span style="color: black;">公司</span>动子的垂向Z向运动和Rx、Ry偏转，<strong style="color: blue;"><span style="color: black;">这般</span>可实现微动台六自由度<span style="color: black;">精细</span>运动<span style="color: black;">掌控</span>；</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/a487349219884c79a2e549948211847b~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=xZMcycYGUYaW0Lgh4AuS4IbyWC4%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">另一</span>，台体垂直方向上还安装重力<span style="color: black;">赔偿</span>器，用来抵消微动台重力，<strong style="color: blue;">来减少音圈电机出力，6个音圈电机布局示意图如图1所示。</strong></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">因此呢</span>，<span style="color: black;">因为</span>微动电机六自由度的存在，并且其结构<span style="color: black;">精细</span>，系统<span style="color: black;">繁杂</span>，不可避免地存在耦合现象，且耦合会影响工件台的工作效率、套刻精度。</p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/71c4e0384eef4b0a8e8518ea270ce665~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=Z87jkOlwKQr6bBaYcZoX%2FjgTct4%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">倘若</span>不<span style="color: black;">思虑</span>耦合<span style="color: black;">功效</span>来设计<span style="color: black;">掌控</span>系统，<strong style="color: blue;">在<span style="color: black;">实质</span>中<span style="color: black;">常常</span>会带来很大的<span style="color: black;">掌控</span>偏差，<span style="color: black;">因此</span>需要对其进行解耦。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/d1b649df84a948a4b71a337b4b47687b~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=ADkAGriBJSoSKFh47I8Kzyv2NVQ%3D" style="width: 50%; margin-bottom: 20px;"></div>
<h1 style="color: black; text-align: left; margin-bottom: 10px;">工件台GB解耦矩阵校准的建模分析</h1>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">倘若</span>将微动台看做一个整体，在<span style="color: black;">掌控</span>微动台体沿着某个方向平移，<strong style="color: blue;">或沿着质心坐标系的某个轴做旋转时。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/10cd1607aef84777b11d8f961b064095~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=Pjuol5%2FO754FhzwQNbtA%2BvoScU8%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">需要由<span style="color: black;">掌控</span>系统计算出所需要的力或力矩的<span style="color: black;">体积</span>，<strong style="color: blue;">并能够恰当地<span style="color: black;">掌控</span>各个电机，使得它们的合力恰好是所需要的。</strong></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">这般</span><span style="color: black;">能够</span>对应<span style="color: black;">每一个</span>自由度的位移或转角设计各个自由度的闭环<span style="color: black;">掌控</span>系统，各自闭环系统的输出其<span style="color: black;">理学</span>含义是对应的力或力矩<span style="color: black;">体积</span>。</p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/8d6400131e51431191a09d07c46361a5~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=ooLh9qeb9q2Vq1EMiZlNQ35A3CY%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">磁浮平面电机可分为6个<span style="color: black;">理学</span>轴，分别为H1，H2，H3，Z1，Z2，Z3，它们的相互<span style="color: black;">功效</span>可使电机产生6个自由度的运动。</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">其中，<span style="color: black;">理学</span>轴H1，H2，H3产生水平X向和Y向运动，Z1，Z2，Z3产生垂直Z向运动，水平向和垂直向的相互<span style="color: black;">功效</span>产生旋转运动。</p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/2b3ae2e658d9433bb6503eb9c617f828~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=u9i9BpKiSzOretvgLUSlP6NuK9o%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">当电机在X向和Y向出力时，存在从<span style="color: black;">掌控</span>中心到质心点的增益规划和从质心点到执行器的增益平衡。</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;">工件台微动台在质心坐标系下和几何坐标系下的受力模型如图2所示。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/e9459992b10e453d93442de53fd4ab9e~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=k3f3Qs%2ByYz8bA6FdQI6AlWK%2Bahk%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">Fh2和Fh3与X轴的夹角为60°,3个水平向矢量电机内切圆半径为R，Fh2与内切圆切点、内切圆圆心和微动台质心3点共线。</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">从图2<span style="color: black;">能够</span>得出，磁浮平面电机动子在水平向由3组三相线圈驱动，实现X，Y，RZ三自由度运动。</p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/7b122007c6714baeb09b1d7ef33fd2d1~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=S9408SCFz41HyKCehMro9og7QvY%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">其中，力Fh1和Fh2，Fh3实现X和Y向驱动，Fh1和Fh2，Fh3差动实现RZ的运动。<strong style="color: blue;">垂向由<span style="color: black;">一样</span>3组三相线圈驱动，实现Z，Rx，Ry三自由度运动。</strong></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">其中，FZ1，FZ2，FZ3实现Z向驱动，Fh1和Fh2，Fh3，FZ1，FZ2，FZ3差动实现Rx向和Ry向驱动。</p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/746ddca28c4d412c9309ad9bf9165b88~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=Es5hwgE2knMxfYYQ8IlVA2mF5Ew%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;"><span style="color: black;">针对</span>平面电机动子质心处的<span style="color: black;">规律</span>力及力矩同<span style="color: black;">理学</span>轴各电机驱动力关系可如公式（1）所示：</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p6-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/ec7e8f71a5e24cb5a0dd04d0f85c4d62~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=vj%2F%2BfZvGfglfKwCivzxKlI0fdzk%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;">GB逆矩阵如公式（2）所示：</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/11bca14b288643ac93a0797d21a317d4~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=JQI8wOzW5TBV2f2ppBbcBY7HaGw%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">GB逆矩阵参数配置只能用于工件台的理想模型，<strong style="color: blue;"><span style="color: black;">实质</span>上<span style="color: black;">因为</span>制造误差，<span style="color: black;">倘若</span><span style="color: black;">需求</span>高<span style="color: black;">掌控</span>性能，这个矩阵不准确，只能用作默认设置。</strong>该矩阵的36个元素均需要进行校准。</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">GB解耦矩阵的<span style="color: black;">功效</span>是将<span style="color: black;">规律</span>轴<span style="color: black;">掌控</span>器的输出力转换到各个<span style="color: black;">理学</span>轴上。</p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/b2efd47bd5e94a348ac610cf4a59e23a~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=eUxvptTvHop84A2pca%2FWlzb8XcI%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">SI<span style="color: black;">暗示</span>输入<span style="color: black;">敏锐</span>度传函（输入为u，输出为in，见图3），SP<span style="color: black;">暗示</span>过程传函（输入为u，输出为out，P<span style="color: black;">暗示</span>in和out之间的传函），<strong style="color: blue;">则in和out处的输出分别为：</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/37a7febd36134b479ece3428ac523eef~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=ET0g1p%2BulGaUQ7SWCfHBkOhU4UI%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">工件台伺服<span style="color: black;">掌控</span>环路描述如图4所示。Raw Mechanics<span style="color: black;">暗示</span>B点到C点之间的过程传函，<strong style="color: blue;">Compensated Mechanics<span style="color: black;">暗示</span>A点到C点之间的过程传函。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/c0e560af00c64899bdd55ffc4bf6ba3f~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=A1bOFsA1y7w4lkrsFa7YkXG01Q4%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">A点到B点之间的过程传函即为GS矩阵与GB矩阵的乘积，<span style="color: black;">因此呢</span>，<strong style="color: blue;">GB矩阵可<span style="color: black;">经过</span>计算Hmraw（原始机械传函）、Hmc（<span style="color: black;">赔偿</span>机械传函）和GS矩阵来获取。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/15c87328a24a41f4ba69f115a72b0834~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=piT9p6cWi22Tdbo5DUDFfHz6%2FXU%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">计算机械传函，利用所描述的过程传函计算<span style="color: black;">办法</span>可分别计算Hmraw和Hm。<strong style="color: blue;">原始机械传函与<span style="color: black;">赔偿</span>机械传函的关系如下：</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/e272da602613433f947bcf01e510de83~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=%2FbgbrxWMoMtBhCsaW%2FiB%2F7bxioc%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">计算理想机械传函和GS0矩阵，校准后<span style="color: black;">赔偿</span>机械传函应该等于一固定的传函Hmd。</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">其中，GBcal为校准后的GB矩阵，<strong style="color: blue;">Hmd和Gs0（Gs0<span style="color: black;">暗示</span>工件台<span style="color: black;">处在</span>零位时微动台<span style="color: black;">功效</span>点与质心之间的转换关系）计算公式如下：</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/69039f21202b470082a57f06e9f9157f~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=p%2FQCp%2Bs8G7MzYi4Kryvc1xES%2Fiw%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">其中，xstep、ystep、zstep为工件台在原点时名义重心相对<span style="color: black;">测绘</span>点的位移，xcog、ycog、zcog为工件台在原点时名义重心相对<span style="color: black;">实质</span>重心的位移，其<span style="color: black;">详细</span>值由<span style="color: black;">设备</span>常数给定。</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">其中，Mass为Chuck质量；Jzz为Chuck绕Z轴旋转的转动惯量；<strong style="color: blue;">Jxx为Chuck绕X轴旋转的转动惯量；Jyy为Chuck绕Y轴旋转的转动惯量；Ts为采样周期。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/cfbb4c059dc848e28354b4cca2d6f038~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=%2F8nIfTj8hQdnkKGh00%2FsOHZWIJA%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">当原始机械传函确定后，校准后的GB矩阵，且GB校准矩阵需取某一频率段的均值，<strong style="color: blue;">该频率范围是。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p6-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/5afad4f3db2e4471b939ebb711bdd059~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=WtjqHUkah%2BLo2xHzE6BRYEDh60U%3D" style="width: 50%; margin-bottom: 20px;"></div>
<h1 style="color: black; text-align: left; margin-bottom: 10px;">实验数据分析</h1>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;">校准前，<span style="color: black;">经过</span><span style="color: black;">设备</span>常数获取的GB矩阵的值为：</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/29050c21a9dc45309c154da1175cd932~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=12H85X2ozTn2PjmM6Tr%2ByJGS7ZA%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">校准后的GB矩阵，<strong style="color: blue;">如式（14）所示：</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/d0559dbff53f404bb8b9dafcde517508~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=nnnGO9sceMM84pzR85j3EvK6Qvo%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;">在频域上进行分析测试。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/0c9a9b7e0e91419fbd395828ef4159c9~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=eaornXRYsPO151fHzQL3E49ql%2FY%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">如图5所示，当对X轴注入噪声，噪声水平为20Hz～50Hz时，<strong style="color: blue;">校准后的机械传涵幅值大幅度降低，即GB解耦矩阵校准后，X方向对RY方向的串扰<span style="color: black;">明显</span>降低。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/44b29c1e3c54480f813b7d97586ae152~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=FYNFJH7yVrH9uH2zSONxPvsMtgM%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">如图6所示，当对Y轴注入噪声，噪声水平为20Hz～50Hz时，校准后的机械传涵幅值大幅度降低，<strong style="color: blue;">即GB解耦矩阵校准后，X方向对RY方向的串扰<span style="color: black;">明显</span>降低。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/d862c65168134299b2064322606c83bc~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=A%2BHsksK4u6VwOu77enQ5pEN4MVQ%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">如图7所示，当对Y轴注入噪声，噪声水平为20Hz～50Hz时，在X方向上校准后的机械传涵幅值<span style="color: black;">显著</span>降低，<strong style="color: blue;">即GB解耦矩阵校准后，Y方向对X方向的串扰<span style="color: black;">明显</span>降低。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/67810d9763b24062872970da4d65d320~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=oCo2UG4a%2BmLtTdFzWcULx%2BcL%2F5E%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">如图8所示，当对RX轴注入噪声，噪声水平为20Hz~50Hz时，在Y方向上校准后的机械传涵幅值<span style="color: black;">显著</span>降低，<strong style="color: blue;">即GB解耦矩阵校准后，RX方向对Y方向的串扰<span style="color: black;">明显</span>降低。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/7cbe0dd61a984a86973a7e9c4aca52df~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=OkWVjqSE9ER9IDv68aZCh44VXWw%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">如图9所示，当对Z轴注入噪声，噪声水平为20Hz～50Hz时，校准后的机械传涵幅值大幅度降低，<strong style="color: blue;">即GB解耦矩阵校准后，Z方向对RX方向的串扰<span style="color: black;">明显</span>降低。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/040da12636954200bb5a77e821abd43b~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=dTc4zz6Aaw2vn6ShoXZyVe5agZo%3D" style="width: 50%; margin-bottom: 20px;"></div>
<h1 style="color: black; text-align: left; margin-bottom: 10px;">结论</h1>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;">本文<span style="color: black;">重点</span><span style="color: black;">科研</span>工件台微动台GB解耦矩阵的测校<span style="color: black;">办法</span>。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/ff2c10d471c1470a9f620f0fbef0c517~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=zjmBShRm1bE0CrIcoE1%2Bh8hV%2BMY%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">按照</span>工件台结构特点，分析得出六自由度之间的耦合会影响工件台的工作效率、套刻精度，在微动台与音圈电机的力学层面分析。</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">给出了<span style="color: black;">详细</span>的解耦关系式，<span style="color: black;">而后</span>对微动GB解耦矩阵校准<span style="color: black;">办法</span>进行了<span style="color: black;">科研</span>，<strong style="color: blue;">从工件台的伺服<span style="color: black;">掌控</span>环路上的机械传涵为出发点，设计了传递函数法对微动台GB解耦矩阵校准<span style="color: black;">方法</span>。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/9951c43e71cb4c608138645eb57bd2ee~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=oDJ8imiTw2zE0yHhyGxqT1qhfm8%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">按照</span><span style="color: black;">最后</span>测试数据，频域上分析得出工件台微动各轴之间的串扰有着<span style="color: black;">显著</span>降低，<strong style="color: blue;">很好地满足了课题的需要，验证了<span style="color: black;">办法</span>的有效性。</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/tos-cn-i-6w9my0ksvp/4056b3c94a6c409ab9ef784442fea576~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1728824805&x-signature=7qBC705Eh%2B3fViSuGautmrW%2Bblw%3D" style="width: 50%; margin-bottom: 20px;"></div>
<h1 style="color: black; text-align: left; margin-bottom: 10px;">参考文献</h1>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">1. Wei Kai, Wang Weifeng, Fan Wenchao, et al. Research on Motion Decoupling and Position Control of Photolithography Microstage . Industrial Control and Application, 2015</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">2. Ge Renhua, Geng Li, Yang Yongchang. Development Analysis of Integrated Circuit Design and Manufacturing Technology . Microelectronics, 2004,31 (6): 5-8</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">3. Lei Jiake. Hardware design of motion control system for magnetic levitation planar motors . Wuhan: Huazhong University of Science and Technology, 2013:1-11</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">4. Zhang Ming, Zhu Yu, Duan Guanghong. Micro vibration and its suppression of ultra precision air floating worktable . Manufacturing Technology and Machine Tool, 2005 (11): 47-49</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">5. Wang Chunhong, Duan Guanghong, Zhu Yu. Analysis of synchronous motion error of lithography machine simulation workpiece stage mask stage . Manufacturing Technology and Machine Tool, 2007 (9): 42-43</p>
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