Undercutting and interference for thread form grinding with a tilt angle
Undercutting and interference for thread form grinding with a tilt angle
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DOI：
10.1016/j.mechmachtheory.2009.05.011
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发表时间：
2009-11
影响因子：
5.2
通讯作者：
Chi-Jung Chiang;Z. Fong
中科院分区：
文献类型：
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作者：
Chi-Jung Chiang;Z. Fong
在广泛用于生产精密螺纹、螺钉和齿轮的成形磨削中，通常根据给定的齿廓和所谓的啮合方程来计算砂轮廓形。然而，在存在根切或二次包络的情况下，计算出的砂轮不能保证产生所需的螺纹轮廓。为此，本文提出了一种确定砂轮廓形的几何方法，并给出了砂轮轴线倾斜时避免根切的条件。具体来说，我们计算的基础上，其关系的每个横向平面的砂轮成形磨削过程中的螺纹的轮廓。然后使用从所有螺纹轮廓点到砂轮回转轴线的最短距离来确定每个横向平面上的砂轮轮廓。获得这些距离允许导出公式以计算避免根切的最小倾斜角。这种几何方法比传统的啮合方程在数值上更稳定，根切方程的推导简单易懂。
In the form grinding that is widely used to produce precision threads, screws, and gears, the grinding wheel profile is usually calculated from a given tooth profile and the so-called equation of meshing. However, in the presence of undercutting or secondary enveloping, the grinding wheel calculated cannot be guaranteed to produce the desired thread profile. Therefore, this paper proposes a geometric approach to determining the grinding wheel profile and the conditions to avoid undercutting by means of the tilt grinding wheel axis. Specifically, we calculate the thread’s profile based on its relationship to each transverse plane of the grinding wheel in the form grinding process. The grinding wheel profile on each transverse plane is then determined using the shortest distance from all the thread profile points to the grinding wheel revolution axis. Obtaining these distances allows derivation of a formula to calculate the minimum tilt angle that avoids undercutting. This proposed geometric approach is numerically more stable than the conventional equations of meshing, and the derivation of the undercutting equation is straightforward and easy to understand.