变齿厚内齿轮平面包络外转子鼓形蜗杆传动装置设计

将鼓形蜗杆传动装置设计为机器人减速器并应用于机器人的转动关节，有利于机器人减速器的国产化。以变齿厚内齿轮齿面为工具齿面，通过分析鼓形蜗杆副的内啮合运动规律，建立6个标架。通过内齿轮上的辅助标架和工作标架，确定蜗轮转动角度、蜗杆转动角度及工作角度之间的关系。根据啮合原理，建立鼓型蜗杆副的啮合方程、二类界限曲线方程及一类界限曲线方程，再通过MATLAB R2013b绘制图像。依据U10PLUS KV170型电机参数，确定鼓型蜗杆传动装置的设计参数，通过MATLAB绘制蜗杆齿面螺旋线并输出ibl文件，再通过Creo2.0绘制鼓形蜗杆传动装置的3维模型。研究发现：1） 变齿厚内齿轮具有对称的楔形轮齿，在安装过程中可调节内齿轮的相对轴向位置，实现内齿轮与蜗杆在Creo虚拟环境下无干涉装配。2） 鼓形蜗杆副中心距为100 mm，与中心距为220 mm的相同设计参数的环面蜗杆副相比，鼓形蜗杆副的中心距减小，结构更加紧凑。3） 内齿轮设计宽度为110 mm，依据鼓型蜗杆副的接触线在蜗轮甲、乙两齿面的分布范围，确定内齿轮的工作宽度为75 mm。4） 分析一类界限曲线及蜗杆齿根线的空间位置关系，一界曲线分布在蜗杆齿根内部，确定无根切发生。5） 结合传统设计方法，设计具有驱动、传动及支撑一体化结构的变齿厚内齿轮平面包络外转子鼓形蜗杆传动装置。在驱动方面，电机安装在蜗杆内部，实现蜗杆与电机一体化；在传动方面，通过调整内齿轮的相对轴向位置，实现蜗杆副的侧隙调整和磨损补偿；在支撑方面，采用支撑轴进行定位安装，无需安装箱体，实现装置结构的简化。结果表明：内齿轮轮齿的对称楔形结构有利于蜗杆副的安装与调整，可实现蜗杆副的侧隙调整和磨损补偿，提高蜗杆传动副利用率；依据工作宽度设计内齿轮，有利于降低内齿轮制造成本；通过对蜗杆副的接触线、二类界限曲线、一类界限曲线及蜗杆齿根线的空间位置的分析，验证啮合传动的合理性；提出应用于机器人转动关节的驱动、传动及支撑一体化结构设计方案，实现变齿厚内齿轮平面包络外转子鼓形蜗杆传动装置的设计。

Design of Beveloid Internal Gear Plane Enveloping External-rotor Drum-worm Transmission Device

The drum-worm transmission device was designed as a robot reducer applied to the robot joint, which benefits the domestic localization of robot reducer. Surfaces of the beveloid internal gear tooth were used as the tool surfaces. By analyzing the internal meshing motion of the drum-worm pair, 6 frames were established. Relationships between the worm-wheel''s rotation angle, the worm''s rotation angle and working angle were determined by the auxiliary frame and the working frame on the internal gear. According to meshing principles, equations of the drum-worm pair''s meshing, second limit curve and first limit curve were established and then drawn by MATLAB R2013b. According to parameters of the U10PLUS KV170 motor, design parameters of the drum-worm transmission device were determined. Spirals of the worm-tooth''s surfaces were drawn by MATLAB to output ibl files, and then 3D-models of the drum-worm transmission device were drawn by Creo 2.0. The assemble of the internal gear and the worm in the Creo simulation environment without interference-fit was realized by adjusting the relative axial position of the beveloid internal gear with symmetrical wedge teeth. Comparing with the 220 mm-center-distance toroidal worm pair with same design parameters, the center distance of the drum-worm pair was reduced to 100 mm, which indicated that the drum-worm pair was more compact. According to distributions of the drum-worm pair''s contact lines on both surfaces of a tooth, the internal gear''s width was reduced from the 110 mm design-width to the 75 mm working width. Analyzing relative positions between the worm pair''s first limit curve and tooth-root lines, the non-undercutting was determined by the first curve distributed inside the worm''s tooth-root. Combined with traditional design methods, the beveloid internal gear plane enveloping external-rotor drum-worm transmission device with an integrated structure of drive, transmission and support was designed. In terms of driving, the motor was installed inside the worm to realize the integration of the worm and the motor. In terms of transmission, the relative axial position of the internal gear was adjusted to realize the worm pair''s backlash adjustment and wear compensation. In terms of support, the support shaft was used for positioning and installation to simplify the device structure without cabinet installation. Symmetrical wedge teeth of the internal gear benefited installation and adjustment of the worm pair to realize the backlash adjustment and the wear compensation as well as the improvement of utilization ratio of the worm pair. Designing internal gear according to working width benefited the reduction of manufacture cost of the internal gear. Rationalities of the meshing transmission were verified by analyzing spacial positions of the worm pair''s contact lines, second limit curve and first limit curve as well as the worm''s tooth-root lines. The design scheme of an integrated structure of drive, transmission and support applied to the robot joint was proposed, and the design of the beveloid internal gear plane enveloping external-rotor drum-worm transmission device was realized.