DIRECT DIGITAL DESIGN AND SIMULATION OF MESHING IN WORM-GEAR DRIVE

A direct digital design method (DDDM) of worm-gear drive is proposed. It is directly based on the simulation of manufacturing process and completely different from the conventional modeling method. The loaded tooth contact analysis (LTCA) method is analyzed, in which the advanced surface to surface searching technique is included. The influence of misalignment errors and contact deformations on contact zone and transmission error (TE) is discussed. Combined modification approach on worm tooth surface is presented. By means of DDDM and LTCA, it is very convenient to verify the effect of worm-gear drive's modification approach. The analysis results show that, the modification in profile direction reduces the sensitivity of worm-gear drive to misalignment errors and the modification in longitudinal direction decreases the TE. Thus the optimization design of worm-gear drive can be achieved prior to the actual manufacturing process.     

精磨双凸面蜗杆的一对螺旋蜗杆传动的计算机设计、啮合的形成和仿真(续)

作者们基于以下研究提出了精磨蜗杆的螺旋蜗杆传动的计算机设计和分析方法。1．滚刀的理论螺线表面是用一维面生成的。2．蜗杆表面与滚刀螺线表面相比齿廓和轴向为凸面。3．蜗杆的双凸面可局部承受接触和获得给定范围的传动误差的预先设计的抛物线函数。蜗杆传动的计算机设计可以显示和避免蜗杆齿面形成奇异点和齿棱。模拟双凸面蜗杆和蜗轮齿面的啮合和接触来确定支承接触轴线不对中和传动误差的影响。开发和应用数值解的计算机程序。数值计算实例说明所提供的开发原理。     

精磨双凸面蜗杆的一对螺旋蜗杆传动的计算机设计、啮合的形成和仿真

作者们基于以下研究提出了精磨杆的螺旋蜗杆传动的计算机设计和分析方法。1．滚刀的理论螺线表面是用一维面生成的。2．蜗杆表面与滚刀螺线表面相比齿廓和轴向为凸面。3．蜗杆的双凸面可局部承受接触和获得给定范围的传动误差的预先设计的抛物线函数。蜗杆传动的计算机设计可以显示和避免蜗杆齿面形成奇异点和齿棱。模拟双凸面蜗杆和蜗轮齿面的啮合和接触来确定支接触轴线不对和传动误差的影响,开发和应用了数值的计算机程序。数值计算实例说明所提供的开发原理。     

Mathematical model and bearing contacts of the ZN-type worm gear set cut by oversize hob cutters

The ZN-type oversize hob cutter for cutting of worm gears is investigated. The mathematical model of the ZN-type worm gear set is developed based on the cutting mechanism and hob cutter parameters. Influences of oversize hob cutter regrinding, worm-thread number and assembly errors on the bearing contacts and kinematical errors of the ZN-type worm gear set are investigated. A numerical example is given to demonstrate the bearing contacts and kinematical errors of the worm gear set.     

Parametric analysis of the end face engagement worm gear

A novel specific type of worm drive, so-called end face engagement worm gear(EFEWD), is originally presented to minimize or overcome the gear backlash. Different factors, including the three different types, contact curves, tooth profile, lubrication angle and the induced normal curvature are taken into account to investigate the meshing characteristics and create the profile of a novel specific type of worm drive through mathematical models and theoretical analysis. The tooth of the worm wheel is very specific with the sine-shaped tooth which is located at the alveolus of the worm and the tooth profile of a worm is generated by the meshing movement of the worm wheel with the sine-shaped tooth, but just the end face of the worm(with three different typical meshing types) is adapted to meshing, and therefore an extraordinary manufacturing methods is used to generate the profile of the end face engagement worm. The research results indicates that the bearing contacts of the generated conjugate hourglass worm gear set are in line contacts, with certain advantages of no-backlash, high precision and high operating efficiency over other gears and gear systems besides the end face engagement worm gear drive may improve bearing contact, reduce the level of transmission errors and lessen the sensitivity to errors of alignment. Also, the end face engagement worm can be easily made with superior meshing and lubrication performance compared with the conventional techniques. In particular, the meshing and lubrication performance of the end face engagement worm gear by using the end face to meshing can be increased over 10% and 7%, respectively. This investigate is expect to provide a new insight on the design of the future no-backlash worm drive for industry.     

Computerized design of low-noise face-milled spiral bevel gears

An advanced design methodology is proposed for the face-milled spiral level gears with modified tooth surface geometry that provides a reduced level of noise and has a stabilized bearing contact. The approach is based on the local synthesis of the gear drive that provides the “best” machine-tool settings. The theoretical aspects of the local synthesis approach are based on the application of a predesigned parabolic function for absorption of undesirable transmission errors caused by misalignment and the direct relations between principal curvatures and directions for mating surfaces. The meshing and contact of the gear drive is synthesized and analyzed by a computer program. The generation of gears with the proposed geometry design can be accomplished with existing equipment. A numerical example that ilustrates the proposed theory is presented.     

以蜗杆为母面的二次包络环面蜗杆传动

本文提出以蜗杆为母面，直接利用现有普通滚刀，在第一次包络时加工出蜗轮和蜗轮同开关的工具齿轮，实际只需加工出一个齿，做成沿螺旋线布刀的装配式刀具，这是一个更为经济而现有刀具不能加工的先进新方法。这种也能实现瞬时双线接触。     

基于实例推理的蜗轮滚刀设计

开发基于实例推理的蜗轮滚刀设计系统。针对蜗轮滚刀的特点 ,提出蜗轮滚刀的实例检索、实例评价及实例修改方法。为蜗轮滚刀的设计提供了一条快捷的途径     

变位非正交面齿轮副小轮齿向修形轮齿接触分析

建立了变位非正交面齿轮的加工坐标系和啮合坐标系,推导了变位小轮及变位非正交面齿轮的齿面方程,计算得到了面齿轮数值齿面,分析了变位对非正交面齿轮齿宽的影响。在变位的基础上研究了对小轮进行齿向鼓形修形,而面齿轮不修形的修形方式。分别对未变位、变位、变位加小轮齿向修形的三种非正交面齿轮传动形式进行考虑安装误差的轮齿接触分析。研究表明：随着变位系数增大,非正交面齿轮最小内半径、最大外半径及极限齿宽均减小;变位不影响非正交面齿轮副的接触规律;小轮齿向修形能降低接触轨迹对安装误差的敏感性,会引起幅值较小的直线型传动误差。     

锥面二次包络圆柱蜗杆传动的啮合性能分析

以微分几何与空间啮合理论为基础,推导了锥面二次包络圆柱蜗杆传动两次包络过程中的啮合方程和主要啮合性能指标方程,以图直观的表示出其形状、位置和分布状况。研究发现蜗杆副在砂轮半径一定的变化范围之内,其接触性能和传动啮合性能变化不大,为这类蜗杆传动中蜗轮滚刀的设计制造提供了理论基础。     

Modification design method for an enveloping hourglass worm gear with consideration of machining and misalignment errors

The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for eliminating or reducing these errors on the tooth profile of the ADEHWG is seldom reported.The gear engagement equation and tooth profile equation for considering six different errors that could arise from the machining and gear misalignment are derived from the theories of differential geometry and gear meshing.Also,the tooth contact analysis(TCA) is used to systematically investigate the influence of the machining and misalignment errors on the contact curves and the tooth profile by means of numerical analysis and three-dimensional solid modeling.The research results show that vertical angular misalignment of the worm wheel(Δβ) has the strongest influences while the tooth angle error(Δα) has the weakest influences on the contact curves and the tooth profile.A novel efficient approach is proposed and used to minimize the effect of the errors in manufacturing by changing the radius of the grinding wheel and the approaching point of contact.The results from the TCA and the experiment demonstrate that this tooth profile design modification method can indeed reduce the machining and misalignment errors.This modification design method is helpful in understanding the manufacturing technology of the ADEHWG.     

平面包络内啮合蜗杆传动关键参数对接触区域的影响分析

为了研究关键设计参数对平面包络内啮合蜗杆传动接触性能及承载能力的影响。基于齿轮啮合原理,构建平面包络内啮合蜗杆传动的空间齿面接触线方程,利用数值计算方法求得空间齿面接触线,并将其映射到蜗轮齿面,通过分析中心距、传动比、母平面倾角、蜗轮回转轴倾角、蜗轮转角、蜗杆分度圆系数、主基圆系数等不同参数对蜗杆齿面接触区域的分布情况,找出合理的设计参数范围,此外,根据初步分析结果,选取一组较为合理参数生成了平面包络内啮合蜗杆传动的三维模型。研究表明,传动比、母平面倾角、蜗轮转角对平面包络内啮合蜗杆传动的接触区域有较大影响,母平面倾角在18°~36°、蜗轮回转中心轴倾角在30°~54°、蜗轮转角在90°~138°之间取值时,平面包络内啮合蜗杆传动的具有较好的接触区域。研究结果为平面包络内啮合蜗杆传动的后续研究奠定了理论基础。     

失配点啮合环面蜗杆传动的研究

提出了用锥面和直线分别展成蜗杆和蜗轮滚刀，获得失配点啮合环面蜗杆传动的方法。分析了该失配啮合传动的基本原理。求解了蜗杆副的占面接触状态和加工工艺参数。结果表明该失配啮合传动可实现良好的点接触。     

用齿轮滚刀切制蜗轮的可行性分析

通过对蜗轮加工原理的分析,认为通过采取一定的措施,用齿轮滚刀加工蜗轮是可行的,可以满足使用要求。     

Geometrical aspects of double enveloping worm gear drive

Double enveloping worm gearing is expected to have contact over larger number of teeth and higher load carrying capacity compared to single enveloping worm gearing. In this paper, contact in this gearing is analysed by geometrical simulation of worm gear tooth generation using intersection profiles of different axial sections of worm representing the hob tooth profile with transverse plane of worm gear. The analysis reveals that in the engaging zone a straight line contact always exists in the median plane and intermittent contact exists at the extreme end sections of worm. This has lead to the idea of using two fly cutters positioned at the location identical to the extreme end sections of worm to generate full worm gear tooth thereby eliminating the need for hobs of complex geometry. For a given worm, a mating worm gear is machined in a gear hobbing machine using fly tool in two settings and nature of contact with the worm is checked by a blue test.     

砂轮磨损对准平面二次包络环面蜗杆传动性能的影响

分析了砂轮磨损对准平面二次包络环面蜗杆传动的蜗杆几何尺寸以及接触和运动精度的影响。分析结果表明 :准平面包络环面蜗杆传动由于在蜗杆和蜗轮滚刀磨削过程中不可避免出现砂轮磨损 ,这种蜗杆传动实际上是瞬时呈双点接触的点接触环面蜗杆传动 ,因而该传动能在一定程度上降低蜗轮副对制造及安装误差的敏感性。     

Mathematical model and tooth surfaces of recess action worm gears with double-depth teeth

In this study, the surface equations of recess action (RA) worm gears with double-depth teeth, generated by a ZN worm-type hob cutter, are proposed. Based on the generation mechanism and the theory of gearing, a mathematical model of a series of worm gears, semi RA, full RA and standard proportional tooth types, with double-depth teeth is developed as the function of design parameters of the ZN worm-type hob cutter. According to the derived tooth surface equations, computer graphs of a series of worm gears with double-depth teeth are plotted. Tooth surface variations of the generated RA worm gears due to the varying pitch line, pressure angle and tooth height of the hob cutter are also investigated.     

采用标准齿轮滚刀加工蜗轮的方法研究

在没有涡轮滚刀的情况下，通过研究涡轮蜗杆与圆柱齿轮的啮合条件，以及涡轮蜗杆与圆柱齿轮间模数、压力角的关系，推导出一种使用标准齿轮滚刀近似加工蜗轮的方法。然后确定用标准齿轮滚刀加工的蜗轮与蜗杆能正确啮合的调整方法，该方法在实际中有很大的利用价值。     

齿廓方向修形的斜齿面齿轮啮合特性研究

主要研究了修形面齿轮副传动的啮合特性.提出了一种沿齿廓方向抛物线修形的面齿轮齿面结构,对传统斜齿面齿轮和修形的斜齿面齿轮副的啮合进行了比较.计算机仿真表明,修形的斜齿面齿轮传动啮合性能明显改善,接触路径沿两齿面齿长方向分布,有效避免了边缘接触;啮合区域对安装误差较为敏感,特别是轴夹角误差的大小,对啮合印痕在齿面上分布的影响尤其明显,容易导致接触区域向面齿轮的大端和小端偏移.