PRINCIPLE AND TRANSMISSION TECHNOLOGY OF BERTRAND CONJUGATE SURFACES

Bertrand surface is presented by abstracting and subliming the common characteristic of the usual surfaces including rotational surfaces, developable surfaces, normal circular-arc surfaces, etc. Basic characteristic of Bertrand surface is that normals along generator are coplanar. Bertrand conjugate principle is studied and its basic characteristic is that the instantaneous contact line between a pair of Bertrand conjugate surfaces is generator. Bertrand conjugate can be divided into three kinds of typical conjugation forms in terms of the generators that are general plane curve, circular-arc and straight line. Basic conjugate condition is given respectively, and structure condition, which reflects transmission forms and directrix characteristic of this kind of conjugation, is researched. As typical engineering application of Bertrand conjugate surface principle, transmission technology of loxodromic-type normal circular-arc bevel gear is studied.     

法向圆弧锥齿轮加工干涉研究

法向圆弧锥齿轮是基于Bertrand共轭原理发展起来的一种新型传动形式,除具有优良的传动性能,还具有良好的工艺性,十分便于采用指状或盘状铣刀进行成型法加工。研究了一对共轭法向圆弧锥齿轮廓面的诱导曲率特征,给出了曲率轴在法向圆弧共轭曲面干涉判断中的应用,以曲率轴为手段研究了齿廓加工时不发生曲率干涉和过切干涉的条件,提供了一种铣刀盘直径的近似求法。     

Mathematical model and manufacture programming of loxodromic-type normal circular-arc spiral bevel gear

In this paper, loxodromic-type normal circular-arc spiral bevel gear is proposed as a novel application of the circular-arc tooth profile at the gear transmission with intersecting axes. Based on the principle of molding-surface conjugation, the study develops a mathematical model for the tooth alignment curve and the computational flow at the design stage to enable the generation of the tooth surface. Machining of the tooth surface is then carried out to determine the interference-free tool path of the numerical control (NC). Moreover, a pair of loxodromic-type normal circular-arc spiral bevel gears is manufactured on computer numerical control (CNC) machine tools. The proposed theory and method are experimentally investigated, and the obtained results primarily reflect the superior performance of the proposed novel gear.     

圆弧齿轮啮合原理的误区──简论用接触线法形成圆弧齿轮点接触共轭齿面的弊端

通过对几十年来广为采用的，以接触线法为基础形成圆弧齿轮点接触共轭齿面的啮合原理的分析，指出这一理论所存在的诸多弊端，以及在实际应用中可能引起的混乱。认为这一理论应当抛弃，并用以包络法为基础的新型圆弧齿轮点接触共轭齿面的形成原理取而代之。     

斜航式法向圆弧螺旋锥齿轮的参数化有限元建模

给出了斜航式法向圆弧螺旋锥齿轮的参数化建模方法。推导了在CAD/CAE软件中建立齿轮齿面的方程,解决了建模过程中由于齿面复杂而引起的技术难点。利用ANSYS软件的APDL语言生成齿轮轮廓的主要关键点,结合实体造型功能建立生成齿轮模型的宏文件,完成参数化程序建立。最后,给出了一对齿轮的实体模型以及基于实体模型建立的有限元模型。     

线面对构齿轮啮合原理

根据曲线和曲面两种几何元素的接触特点,提出了线面对构齿轮啮合原理。定义了线面接触与线面啮合的概念,给出了线面啮合运动三要素;建立了线面啮合基本理论,得到与已知曲面相啮合的共轭曲线方程的通用表达式;通过在曲线每一点处的法平面上建立截面齿廓,进而构建连续曲面。以平行轴内啮合渐开线齿轮为例,通过在渐开线内齿轮齿面上选取接触曲线,构建新的线面啮合齿轮副,分析了线面啮合齿轮啮合过程的一般规律。研究结果表明,根据线面啮合原理,通过选取合适的几何参数,可以构建出一对正确啮合的点接触齿轮。该原理为齿轮齿面构建提供了新方法。     

准端面双圆弧齿轮及其齿面方程

叙述了准端面双圆弧齿轮的形成原理,推导了了这种齿轮的通用齿面方程通过端面齿廓图谱的分析,经与目前广为采用的法面圆弧齿轮以及理想的端面圆齿轮的对比,指出了准确面圆弧齿轮在克服法面圆弧齿轮传动接触区位置对误差敏感性方面所具有的独特优点;     

Kinematic errors on helical gear of triple circular-arc teeth

Two imaginary skew rack cutter curves with stepped triple circular-arc teeth are presented in this paper. A helical gear pair that includes the gear and pinion surfaces was generated by using two matched imaginary skew rack cutter surfaces. The mathematical models of the helical gear pair with stepped triple circular-arc teeth were developed based on theory of gearing. With the use of these models, the analysis of kinematic errors can be illustrated and evaluated by computer programming and tooth contact analysis (TCA). The assembly errors used had several kinds: ideal assembly errors, vertical misalignment angles, horizontal misalignment angles, manufacturing errors of helical angles, and center distance deviation. TCA revealed that the sensitivity of horizontal misalignment angles was lower than that of manufacturing errors of helix angles but higher than that of vertical misalignment angles.     

分阶式双渐开线齿轮啮合特性分析

分阶式双渐开线齿轮是一种新型齿轮,故对其传动的重合度、接触线长度等进行了分析研究,给出双渐开线齿轮传动重合度、总接触线长度的精确计算公式,并提出端面重合度与纵向重合度的最佳组合及最差组合条件,其结果对设计、分析渐开线斜齿轮及双渐开线齿轮传动具有重要意义。     

微线段齿廓齿轮的弯曲强度分析

介绍了微线段齿轮的形成原理,建立了微线段齿轮有限元计算的力学模型,论证了计算中的奇点问题,并提出相应的解决方案,用正交试验法设计了一组算例并用有限元法进行计算,从而说明微线段齿轮的弯曲强度确实要优于渐开线齿轮。     

考虑中心距误差的圆弧齿轮泵流量脉动特性研究

新型圆弧齿轮泵有效地解决了传统齿轮泵存在的困油和流量脉动问题,然而,齿轮泵加工过程与装配安装相关的中心距误差对圆弧齿轮泵出口流量脉动特性有重要影响。推导了圆弧齿轮齿廓方程,并建立了圆弧齿轮泵内部齿腔压力模型,齿腔容积模型及流量脉动模型。在不同中心距误差下,分别在轻负荷工况(600 r/min,2 MPa)和中等负荷工况下(1480 r/min,8 MPa)进行流量脉动仿真。结果表明:当中心距误差在0.01 mm以内时,圆弧齿轮泵的出口流量逐渐增大,具有良好的动态特性;随着中心距误差增大到0.02 mm,圆弧齿轮泵的出口流量大幅度减小,该泵的动态特性变差。因此,需将中心距误差控制在一定范围内。中心距误差为0 mm及0.01 mm时,主从动齿轮的齿腔容积未发生较大变化;当中心距误差为0.02 mm 时,主、从动齿轮齿腔提前进入啮合,预示啮合位置发生变化。     

微线段齿轮齿根应力的对比试验研究

采用应变电测法设计微线段齿轮与渐开线齿轮齿根弯曲应力比较试验的装置,对试件的设计与加工进行严格的控制,并确定比较试验方案,给出处理现场数据的公式及计算结果的T－σ折线图,对结果的显著性检验证明,微线段齿轮的抗弯曲性能要大大优于相应的渐开线齿轮。     

Improved operation of transmissions

The geometric stability of the active surfaces is investigated in a cylindrical involute gear transmission with external engagement and in worm transmissions. The factors responsible for instability of the initial geometry in various types of transmissions are identified. Elimination of such instability significantly improves their performance.     

任意转角位置的双渐开线齿轮的齿面数学模型

运用渐开线展开和曲线包络原理,建立了双渐开线齿轮端面齿廓数学模型,用数据验证了模型的准确性。在端面齿廓数学模型基础上建立了任意转角位置的双渐开线齿轮齿面数学模型,使用该模型获得了三种典型刀具齿顶圆弧半径的双渐开线齿轮三维仿真图形,并进行了啮合仿真,从而验证了齿面数学模型的正确性和可行性。该齿面数学模型表述简单,使用时无须坐标变换,能快速、真实地描述双渐开线齿轮任一轮齿在任意转角位置时齿面上的任一点。为双渐开线齿轮三维数字化设计、制造,啮合干涉、运动学和动力学分析提供了简捷的新理论依据。     

双圆弧齿轮滚刀齿形计算及优化设计

从理论上分析了由目前广泛采用的近似造形方法引起的滚刀齿形精度问题,总结出影响滚刀齿形精度的主要因素。利用从双圆弧齿轮基本齿廓方程出发推导出的双圆弧齿轮滚刀通用齿面方程,求出双圆弧齿轮滚刀前刀面齿形方程。通过比较双圆弧齿轮滚刀的理论齿形和设计齿形,求解出双圆弧齿轮滚刀的齿形误差计算公式,并以滚刀设计截面内的最大齿形误差最小化为目标进行双圆弧齿轮滚刀齿形优化设计,最后利用双圆弧滚刀齿形优化后的相关设计参数完成三维参数化造型。     

Geometric stability of the active surfaces in a spherical transmission

The geometric stability of spherical transmissions is studied by geometric monitoring. On that basis, the contact conditions of the active surfaces of worm turns and gear teeth in the transmissions may be determined before running-in, after running-in, and at any stage of wear. Geometric monitoring is preferable to theoretical investigation of the contact conditions with known theoretical surfaces of the transmission.     

Modifying the teeth of cylindrical helical transmissions to reduce vibration

Low noise and vibration are required of gear transmissions. Appropriate modification of the lateral tooth surfaces in helical (chevron) cylindrical transmissions significantly reduces the vibration excited by the variable coupling rigidity and discrete (abrupt) tooth loading.     

基于电子齿轮箱的数控插齿机内联传动结构

CNC技术及其软件的应用是改变目前插齿工艺落后最有效的手段。利用数字控制取代螺旋导轨,对于实现斜齿轮插削加工具有重要的现实意义。本文根据硬件电子齿轮箱的锁相控制原理,研究了软件电子齿轮箱的基本结构和信息处理过程,并根据数控插齿机的运动控制特点,探讨了基于电子齿轮箱原理的数控插齿机的内联传动结构,推导了各轴的运动关系式,提出了运用软件实现"电子分齿"传动和"电子差动"合成的插齿运动控制方法,并对形成附加转动的加减速定位控制进行了研究。     

球齿轮渐开线齿廓曲面磨削加工方法研究

球齿轮是在其球冠面上分布着一道道环形齿的新型齿轮。在分析球齿轮形状特征的基础上,将普通齿轮的范成法加工原理推广应用到球齿轮渐开线齿廓曲面的磨削加工上,形成了球齿轮渐开线齿廓曲面的范成法精密磨削加工方法。并设计了五自由度的加工机床方案。该方案的创新之处在于当球齿轮与盘形砂轮进行啮合运动时,球齿轮并不是绕过球心的竖直轴转动,而是绕平行于过球心的竖直轴的轴转动,盘形砂轮的运动是在二维平面内的平动。推导出了球齿轮渐开线齿廓曲线曲面的参数方程,仿真和实际的加工实验验证了该方案的正确性。     

双螺杆泵同步双圆弧齿轮传动热网络分析

综合传热学、摩擦学和齿轮啮合原理等,建立了双螺杆泵同步双圆弧齿轮箱热网络模型和热平衡方程组,确定了热源、热阻、对流换热系数等参数的计算模型,计算了该部件在润滑油润滑条件下的边界温度,为双圆弧齿轮传动热分析提供了理论基础.