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直廓环面蜗杆传动的高次方修形原理
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High-order Modification Principle of Globoidal Worm Drive
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    摘要:

    系统地建立了高次方修形直廓环面蜗杆传动的数学模型,用微分几何和啮合理论 等理论推导了蜗杆副的曲率参数,啮合函数以及曲率干涉界线函数 . 证明了直廓环面蜗杆的 齿面为不可展的直纹面,这与其蜗杆的齿面形成原理相吻合 . 利用最小二乘法拟合无量纲化 的修形数据得到普适型高次方修形曲线,基于此曲线推导出工艺传动比的计算公式,得到高 次方修形蜗杆传动 . 根据不同次修形曲线修形的数值算例分析表明,高次方修形可消除原始 型直廓环面蜗杆齿面的常接触线,有效的增大了蜗杆副齿面的共轭区面积,修形后蜗杆全长 可被利用,承载能力强. 但高次方修形后的蜗杆副齿面存在曲率干涉界线,有可能导致蜗杆副 发生根切.

    Abstract:

    The mathematical model of globoidal worm drive with high-order modification is established system? atically. The curvature parameters,meshing function and curvature interference boundary function of worm pair are derived by differential geometry and meshing theory. It is proved that the tooth surface of globoidal worm is an unde? velopable ruled surface,which is consistent with the principle of tooth surface formation. The least squares method is used to fit the dimensionless modification data to obtain a universal high-order modification curve. Based on the curve,the calculation formula of the process transmission ratio is derived,and the high-order modification worm transmission is obtained. According to the numerical examples of different modification curves,the analysis shows that the high-order modification can eliminate the constant contact line of the tooth surface of the original globoidal worm,and effectively increase the conjugate area of the tooth surface of the worm pair. After the modification,the full length of the worm can be used and the bearing capacity is strong. However,there is a curvature interference line on the tooth surface of the worm pair after high-order modification,which may lead to undercutting of the worm pair.

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赵亚平 ?,李帅 ,陈新元 ,李公法 .直廓环面蜗杆传动的高次方修形原理[J].湖南大学学报:自然科学版,2022,(2):20~30

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  • 在线发布日期: 2022-03-04
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