Forming method of hourglass worm gear hob rake faces based on double-cone grinding wheel
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摘要:
多头环面蜗轮滚刀通常采用螺旋槽，以降低刀齿负前角的绝对值、并均衡每个刀齿左右两侧的前角，从而提高滚刀的切削性能。由于环面蜗轮滚刀螺旋线上各处的螺旋升角不同，所以各个刀齿左右两侧的前角均衡问题更为复杂，鲜有螺旋槽前刀面的精确成形方法的研究。基于环面蜗杆专用数控机床，提出采用双锥砂轮磨削螺旋槽环面蜗轮滚刀前刀面的方法，根据齿轮啮合理论，建立由双锥产形面展成平面二次包络环面蜗轮滚刀螺旋槽前刀面的数学模型，给出每个刀齿两侧在分度环面螺旋线上的前角计算公式。算例计算结果表明：如果采用直槽滚刀，对应的前角在-19.530 3°~19.530 4°；通过合理的参数选择，可使得螺旋槽滚刀对应的前角在-8.1°~7.3°，有效减小了刀齿负前角的绝对值。对环面蜗轮滚刀螺旋槽进行仿真加工，并且在仿真软件中对前角进行测量，测量结果与计算结果相吻合，证明本文方法的正确性。
Abstract:For multi-thread hourglass worm gear hobs, spiral flutes are typically used to reduce the absolute value of the negative rake angle and to equalize the rake angles on the left and right sides of each tooth, which will improve the cutting performance of the hob. Because of the different spiral angle on the basic worm helical surface, the rake angle on both sides of each tooth is more difficult to balance. However, there are few researches on the precise forming method of the spiral flute rake face. Based on the NC machine tool for hourglass worm, a method for grinding the rake face of spiral flute with double-cone grinding wheel is proposed. According to the gear meshing theory, a mathematical model was established for the rake face of the planar double enveloping hourglass worm gear hob spiral flute formed by the double-cone grinding surface. The formula for calculating the rake angle on both sides of the tooth is given. The calculation results show that if the hob with straight flute is used, the rake angles are between -19.530 3° and 19.530 4°. Through proper parameter selection, the rake angles can be between -8.1° and 7.3° when the hob with spiral flute is used, which effectively reduces the absolute value of the negative rake angle of the tooth. The spiral flute of hourglass worm gear hob was simulated and the rake angle was measured in the simulation software. The measured results coincide with the calculated results and this proves the correctness of the method.
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Key words:
- hourglass worm gear hob /
- chip flute /
- rake face /
- rake angles /
- double-cone grinding surface
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图 3 砂轮在刀座静坐标系中的位置
Figure 3. Position of grinding wheel in tool holder's static coordinate system
图 4 不同容屑槽两侧前角变化规律
Figure 4. Change law of rake angles on both sides of different spiral flutes
图 6 测量分度环面上刀齿两侧的夹角
Figure 6. Measured angle between sides of the teeth on indexing tours
表 1 平面二次包络环面蜗轮滚刀及双锥砂轮的基本参数[6]
Table 1. Basic parameters of planar double enveloping hourglass worm gear hob and double-cone grinding wheel [6]
参数 数值 中心距a/mm 160 速比i12 10 滚刀头数z1 4 蜗轮分度圆压力角α/(°) 21.8667 蜗轮分度圆直径d2/mm 255 蜗杆分度圆直径d1/mm 65 滚刀齿顶圆弧半径Ra1/mm 122.24 滚刀齿根圆弧半径Rf1/mm 133.24 滚刀工作长度Lw/mm 90 滚刀喉部分度圆导程角γm/(°) 21.4205 产形平面轴线倾角β/(°) 22.5 主基圆直径db/mm 95 
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表 2 直槽前刀面对应分度环面上各刀齿左右两侧的前角
Table 2. Rake angles of both sides of each tooth on indexing torus corresponding to rake face of hob with straight flutes
齿号 左侧 右侧 前角/(°) 轴向位置/mm 前角/(°) 轴向位置/mm 1号 -15.7159 -43.5 16.9998 -35.8 2号 -18.1932 -24.5 19.0122 -15.4 3号 -19.5303 -4.71 19.5304 4.71 4号 -19.0126 15.4 18.1937 24.5 5号 -17.0004 35.8 15.7165 43.5
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表 3 螺旋槽前刀面对应分度环面上各刀齿左右两侧的前角
Table 3. Rake angles of both sides of each tooth on indexing torus corresponding to rake face of hob with spiral flutes
齿号 左侧 右侧 前角/(°) 轴向位置/mm 前角/(°) 轴向位置/mm 1号 5.5645 -37.6659 -5.4788 -30.6111 2号 6.6612 -21.2130 3.0636 -13.3234 3号 7.2522 -4.1854 6.2043 3.9941 4号 1.6208 13.3526 0.7470 21.4250 5号 -1.3445 31.1470 -8.1071 38.3567
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表 4 测量螺旋槽前刀面对应分度环面上各刀齿左右两侧的前角
Table 4. Measured rake angles of both sides of each tooth on indexing torus corresponding to rake face of hob with spiral flutes
齿号 左侧 右侧 前角/(°) 轴向位置/mm 前角/(°) 轴向位置/mm 1号 5.6286 -37.6659 -5.3759 -30.6111 2号 6.3011 -21.2130 2.5098 -13.3234 3号 7.1336 -4.1854 5.6398 3.9941 4号 1.6094 13.3526 0.1771 21.4250 5号 -1.0385 31.1470 -8.3156 38.3567
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