This thesis reviewed the mesh theory of plane double - enveloping worm gearing : the equations including the first enveloping equation , the second enveloping equation , contact line equations of the first enveloping and the second enveloping , boundary equations of the first enveloping and the second enveloping , the equations of relative velocity and absolute velocity 本文介绍了平面二次包络环面蜗杆传动的啮合原理基础：第一次包络啮合方程和第二次包络啮合方程，相对速度、相对角速度方程，第一次包络的接触线方程，第二次包络的接触线方程，以及第一次、第二次包络的一界线方程和二界线方程。
The paper researches a new type mechanical transmission mechanism - the rolling cone - type toroidal drive . the meshing efficiency has been studied completely and systematically and the parameters of drive are optimized on the base of analysis about meshing . by taking advantage of computer technology the main parts of the drive - stator , planet gear and worm are modeled and emulated 在对其进行啮合分析的基础上，对该传动的啮合效率进行了深入研究，并对该传动进行了参数优化，进而利用计算机技术，对该传动的主要零件? ?行星轮、环面定子和环面蜗杆进行了三维建模仿真，演示了该传动的运动情况。
The thesis developed the optimization design software of geometric parameter for the worm gear including strength check module , the drawing contact lines module , the change lines of tooth thickness of worm , and the parametric modelling software for the reducer which includes parametric modelling of parts and assembly . the cad prototype system is very convenient because of its accessible interfere , simple operation and written in chinese . by input design parameters ， the cad system can make optimization design and strength check for the worm gear ， draw contact lines of tooth flank of worm - gear and change line of tooth thickness of worm ， judge if the tooth flanks of worm undercut and if the sideward tooth of worm - gear hob come to a point ， make project design and structure design for the reducer and draw its 2d parts and assembly 研究和开发了平面二次包络环面蜗杆传动的参数优化设计和校核软件系统：包括几何参数设计计算模块，强度校核模块，绘制齿面接触线模块，蜗杆齿厚变化曲线模块和蜗杆根切判别模块；开发了平面二次包络环面蜗杆减速器外形与结构尺寸数据库以及传动效率数据库，建立了平面二次包络环面蜗杆传动公差及极限偏差数据库；开发了平面二次包络环面蜗杆减速器参数化建模软件：包括零部件的参数化建模模块和装配图的参数化建模模块，其中零部件的参数化建模包括蜗杆轴系的参数化建模、蜗轮轴系的参数化建模、箱体的参数化建模、端盖的参数化建模、轴承的参数化建模和其它零部件的参数化建模软件模块。
On the condition of “ many - head ” and “ small drive ratio ” ， the plane double enveloping hourglass worm can not settle the problem of undercutting and sharpening simultaneously . it has devoted to a new type hourglass worm _ sphere double enveloping hourglass worm . the coordinate system is established according to the frock . the meshing equation and the tooth equation of worm and gear have been developed and the distribution of contact line on gear tooth is analyzed . to evaluate the meshing quality ， four meshing quality indexes and five original parameters are put forward . through mass programming computing ， the relations between meshing quality and original parameters are derived and depicted by graphs 考虑到平面二次包络环面蜗杆传动在多头小传动比条件下根切与齿顶变尖的矛盾很难同时解决且啮合性能较差，介绍了一种新型环面蜗杆传动? ?球面二次包络环面蜗杆传动.在研究过程中，根据工装建立了坐标系，根据一二包过程的运动关系推得了啮合方程和蜗杆与蜗轮的齿面方程，分析了蜗轮齿面上的接触线分布.为了评价啮合性能，提出了4项性能指标和5项原始参数，通过大量编程计算得到了啮合性能指标与原始参数之间的关系，并以图表直观的表示
With the increasingly extensive application of the planar enveloping hourglass worm gearing , it becomes more important to rapid detection and high precision of the manufacture error . the surface of the planar enveloping worm gearing is complicate , and current domestic and international examination concerning its form generally is recur to the general three dimension measure apparatus or the special measure apparatus according to " the type of assemble " principle designed 由于平面包络环面蜗杆齿面比较复杂，其齿形、齿距、齿厚各不相等，因而关于它的制造误差检测也比较复杂。目前国内外关于其形面的检测一般是借助于通用三坐标测量机或按“装配式”检测原理（即测量状态与加工状态一致的原理）设计专用量仪进行的，一直没有十分成熟的专门产品问世。
Larger loading capacity under the same specification ; easily establishing lubricant oil film , smaller friction coefficient , higher transmission efficiency , saving energy ; highest accuracy up to grade 3 of din standard ; smoother functioning , lower noisiness and longer service life 平面包络环面蜗杆与普通圆柱蜗杆传动相比具有更大的承载能力，易于建立动压油膜摩擦系数小，传动效率高节省能源具有可磨削性，能达到din标准三级，面粗糙度优于ra0 . 4而且具有运行平稳噪音低寿命长等优点。
