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基于Pro/E的格利森制弧齿锥齿轮副的三维建模方法研究

2009-06-17
作者:王春香, 刘志军

    摘 要: 介绍了在Pro/E环境下,实现格利森制弧齿锥齿轮副的造型方法和步骤,从原理出发,利用方程建立渐开线,从而保证齿形的准确性。通过建立齿轮中各变量与模数、齿数等基本参数的关系,实现了不同模数、齿数齿轮的快速造型,提高了设计效率。
    关键词:渐开线;弧齿锥齿轮;Pro/E

 

    弧齿锥齿轮根据齿形的不同分为奥利康制和格利森制[1]。作为基础传动件,用于传递相交轴之间的运动和动力,并广泛应用于航空、航海、汽车、拖拉机、机床等行业中。传统的格利森弧齿锥齿轮的造型是已知齿轮的参数,利用啮合原理的方法建立齿面方程,由齿面方程获得大量齿面数据点,再由数据点啮合出齿面模型[2-3]。由于此种方法需要较多的啮合原理知识和大量的数据处理工作,不易被工程技术人员掌握。因此,寻找一种快捷有效的弧齿锥齿轮造型方法和性能分析有着重要的现实意义。
1造型方法
1.1设计参数

    设计参数包括:分度圆直径D;基圆直径DB;齿顶圆直径DA;齿根圆直径DF;齿宽B;齿基高HB;锥距PX;齿顶高HA;齿根高HF;全齿高H;分锥角DELTAD等;大端尺寸:分度圆直径DZ,齿顶圆直径DZa,齿根圆直径DZf,基圆直径FZb。小端尺寸:分度圆直径dZ,齿顶圆直径dza,齿根圆直径dZf,基圆直径dZb
    输入表1中各参数,定义基本参数M、Z、B、CX等值,通过关系式定义其余各参数的数值[4-5]

 


1.2创建基本曲线
    (1)首先将基准平面TOP向右平移一段距离D/2×tan(DELTA),创建基准轴A1基准点PNT 0。在FRONT平面内,以PNT 0为顶点绘制4条斜线,分别为分锥、根锥、基锥和顶锥母线。定义分锥母线终点尺寸为d2=D /2,与水平中心线夹角为d1=DELTA,与大背锥母线的夹角d3=90°;顶锥母线终点尺寸为d6=DA/2;根锥母线终点尺d5=DF/ 2;基锥母线中点尺寸d4=DB/2。绘制大、小端背锥母线,其间距离为d7=B,且均垂直于分锥母线。同时创建基准点PNT 1和PNT 2。如图1 所示(其中d…为Pro/E中自动生成的尺寸代码)。

    (2)过背锥母线分别做两个垂直于中心平面FRONT面的辅助平面DTM 2和DTM 3。在这两个平面内分别绘制各基础圆曲线,同时分别绘制2条过中心的竖直线,为以后创建坐标系做准备。如图2所示。

 


    (3)创建辅助坐标系,绘制大、小端齿廓渐开线。首先创建大端的渐开线的参考坐标系CS1,小端渐开线参考坐标系CS3。两坐标系分别位于齿轮中心轴与两辅助平面的交点处,Z轴垂直于所建辅助平面DTM 2和DTM 3。然后绘制渐开线,以FRONT面作为齿廓中心角的角分面。绘制渐开线时必须保证两渐开线FRONT面对称,才能保证背锥面上齿廓完全符合理论要求。设参数t=0~1,因此,在Pro/E草图环境中,笛卡儿坐标系下的渐开线参数方程为[6]

   

    最终生成的辅助坐标系和大、小端齿廓渐开线如图 3 所示。

 


    (4)创建扫描轨迹和齿廓线。根据齿廓中心角以及齿宽等参数的关系创建辅助平面DTM 4和DTM 5, 以DTM 5为对称面分别镜像两条渐开线,经过旋转生成如图4 所示的齿廓线;以分锥母线为参考,分别生成辅助平面DTM 6和投影曲面。在辅助平面DTM 6中根据刀具半径、螺旋角和齿轮的旋转方向绘制圆弧。将圆弧向投降平面投影,生成如图4所示的扫描轨迹[7]

 


    (5)生成完整模型。通过扫描混合命令沿投影曲线,生成第一个齿廓,之后通过复制、阵列得到其他齿形。定义旋转角度d111=360/Z,阵列个数p112=Z-1,得到完整非等顶隙弧齿锥齿轮的模型,同样的方法可得到小齿轮的模型,如图 5 所示为大小弧齿锥齿轮模型图。图 6 所示为弧齿锥齿轮副装配图。

 

 


    由于齿轮的各个参数与齿轮的模数M、齿数Z和分锥角THETA等建立了关系,  因此只要按设计要求修改模数、齿数等参数以及扫描曲线,就可得到不同弧齿锥齿轮副[8-10]。为以后的分析计算提供了方便。
    本文介绍了格利森制非等顶隙的渐开线弧齿锥齿轮副的造型方法,按照此种方法将参数稍做改动就可以创建等顶隙的渐开线弧齿锥齿轮副。
参考文献
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title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" 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title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" title="Pro/ENGINEER">Pro/ENGINEER" 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