多因素影响的电子螺旋导轨误差的理论分析

Theoretical Analyses on Errors of Electronic Helical Guides Influenced by Multi-factors

为了进一步提高电子螺旋导轨对内斜齿的加工精度,从插齿机传动链机构运动学的角度,研究了内斜齿螺旋线偏差的产生机理。首先,根据插削时各轴的运动关系,建立了插齿刀附加转动的数学模型,定义了附加转动系数;然后,分别建立了附加转动偏差以及主运动曲线偏差与螺旋线偏差之间的数学关系,定义了Zebra系数;最后,分析了螺旋线偏差的产生机理,总结了杆件长度、曲柄初始位置以及运动副间隙对螺旋线偏差的影响规律。

For improving the internal helical gear machining precision of electronic helical guides, this paper analysed the principles about how to cause the errors of spiral line of internal helical gears according to kinematics of the driving chains in a gear shaping machine. Firstly, a mathematical model of additional rotation of the tool was established according to the kinematic relationship of several axles, and an additional rotation coefficient was defined. Then, the mathematical relationships among the errors of spiral line and the errors of additional rotation and main motion were established respectively, and a coefficient Zebra was defined. At last, the mechanism causing the errors of spiral line was analyzed, and the influences of the length of rods and the position of crank and the gap of motion joints on the error of spiral line were concluded.