二次螺旋钢丝中心线曲线变化周期的简化证明  

A Simplified Proof of the Curve Period of the Center Line of Double Spiral Steel Wire

作　　者：沈志军 支宇堃 刘迪 SHEN Zhijun;ZHI Yukun;LIU Di(R&D Center,Xianyang BOMCO Steel Tube&Wire Rope Co.,Ltd.,Xianyang 712000,China;Material Product Quality Supervision&Inspection Research Center,Chongqing Institute of Metrology Quality Inspection,Chongqing 401121,China)

机构地区：[1]咸阳宝石钢管钢绳有限公司研发中心,陕西咸阳712000 [2]重庆市计量质量检测研究院材料产品质量监督检验研究中心,重庆401121

出　　处：《成组技术与生产现代化》2024年第4期49-56,共8页Group Technology & Production Modernization

摘　　要：在一个封闭图形周长为一个圆形物体周长的N倍时,若让该圆形物体分别在该封闭图形轮廓线的外侧、内侧围绕封闭图形滚动(不发生滑动)一周,则该圆形物体会相应转动(N+1)圈、(N-1)圈。基于这一运动学事实,根据钢丝绳生产实际,简化证明了二次螺旋钢丝中心线的曲线变化周期,并得出了二次螺旋钢丝中心线的投影属于摆线的结论。借助天体力学已有结论对简化证明过程进行了解读。依据证明过程,解释了对称关联因子的物理意义。When the perimeter of a closed curve is N times of the circumference of a circular object,if the circular object rolls around the closed curve without slipping,it is(N+1)times outside the closed curve and(N-1)times inside the closed curve.Based on this kinematic fact and the actual production of ropes,the curve period of the central line of the double spiral wire is simplified and proved,and the proof process is interpreted with the help of existing conclusions celestial mechanics.According to the proof process,the physical meaning of the symmetric correlation factor is explained,and it is concluded that the projection from the central line of double spiral wire belongs to the cycloid.

关 键 词：二次螺旋钢丝 钢丝绳 对称关联因子 简化证明 微分几何 

分 类 号：O168.11[理学—数学] TG356.45[理学—基础数学]