Mathematical model of a helical gear with asymmetric involute teeth and its analysis

This paper describes a simple approach based on the gear theory for deriving a helical gear with asymmetric involute teeth. A helical gear with asymmetric involute teeth can be easily obtained through the envelope theory for the one-parameter family of surfaces. The mathematical models for asymmetric helical gears can be provided by the application of two imaginary rack cutters. The investigation on the undercutting analysis of the asymmetric helical gear is studied based on the developed mathematical model and the method of tooth-profile shifting. Here we provide geometric modeling of the designed asymmetric helical gear meshing when assembly errors are present. Stress analysis for the helical and the cylindrical forms are constructed. To illustrate the effectiveness of the approach, an analytical expression of helical gear with asymmetric involute teeth is given.     

基于Pro/E渐开线圆柱齿轮参数化设计及模态分析

根据渐开线圆柱齿轮生成原理,在Pro/E中建立了渐开线圆柱齿轮的参数化模型,该模型不仅可以自动精确生成直齿、斜齿及其变位齿轮,而且通过条件控制语句,实现了任意齿数的齿轮设计.根据模态分析理论,利用Pro/MECHANICA对斜齿轮的模态进行了分析计算,总结了在定分度圆下不同齿数模数组合及轴孔直径对齿轮固有频率的影响,为渐开线圆柱齿轮传动的合理、高效设计和动态响应分析提供了理论依据.     

基于Pro/E的非对称渐开线斜齿圆柱齿轮参数化设计及应力分析

非对称渐开线斜齿圆柱齿轮作为一种新型的齿轮,目前对其还没有展开详细的研究。从齿轮范成法加工角度出发,根据齿条型刀具上各曲线部分参数,推导求得非对称渐开线斜齿圆柱齿轮端面主动侧、从动侧的渐开线、齿根过渡曲线方程。以轮齿端面曲线方程为基础,结合三维造型软件Pro/E,建立出非对称渐开线斜齿圆柱齿轮的三维模型。由于建立后的齿轮模型已经参数化,通过更改基本参数,可以快速生成需求的齿轮。同时,以建立的模型为基础,结合有限元分析软件,对对称与非对称渐开线斜齿圆柱齿轮两个特殊啮合位置的轮齿齿根弯曲强度进行了分析、比较。     

渐开线斜齿圆柱齿轮弹流润滑模型的建立

渐开线直齿圆柱齿轮的弹流润滑问题已经基本成熟，而对同样是线接触的渐开线斜齿圆柱齿轮的弹流润滑求解却研究甚少并颇有争议。分析了斜齿轮齿廓曲面的形成及啮合特点，建立了研究渐开线斜齿圆柱齿轮弹流润滑的物理模型和数学模型．通过数学推导，得到了膜厚方程，通过多重网格法即可获得渐开线斜齿圆柱齿轮在某一瞬时的弹流润滑数值解。     

渐开线斜齿圆柱齿轮的三维造型

渐开线斜齿圆柱齿轮的三维造型存在两大难点:端面齿廓的绘制和轮齿的生成。利用渐开线的参数方程式并通过AutoLISP编程绘制出端面齿廓一侧的渐开线;在对轮齿端面齿廓进行几何分析与计算的基础上,确定并绘制出其对称线及齿顶圆弧,并利用该对称线获得轮齿端面齿廓另一侧的渐开线;绘制出齿轮轮齿两端的齿廓曲线及通过齿廓曲线两端点的齿根螺旋线后,用AutoCAD的“边界曲面”命令,构造斜齿圆柱齿轮的轮齿表面模型。     

Geometric design of involute spur gear drives with symmetric and asymmetric teeth using the Realized Potential Method

The index gear drive potential is defined for the estimation of the quality of spur gear drives as a maximum contact ratio obtained at the contact of teeth profiles along the full line of action. In this paper, a new method is proposed for the geometric design of symmetric and asymmetric involute meshing in which the contact ratio of the gear drive is equal to its potential. This method is appropriate for the geometric design of spur gears with a small teeth number and is based on the generalized model of involute meshing. The gear drive potential is assigned as an input value, from which, after appropriate calculations, the geometry of rack-cutters, gears and involute meshing can be determined. Using the proposed method, the areas of the realized potential and the areas of the existence of involute gear drives are defined. In addition, many numerical examples are solved. In the cases of symmetric and asymmetric meshing, the minimum teeth number is obtained when the gear drive potential is larger than one.     

基于Pro/E关系式的渐开线斜齿圆柱齿轮参数化设计

针对渐开线斜齿圆柱齿轮齿廓形状复杂,设计精度低的特点,根据渐开线方程生成精确的渐开线齿廓截面。应用Pro/E参数化的设计原理,建立各尺寸参数间的关系式,将设计意图用参数的方式融入到产品模型里,实现渐开线斜齿圆柱齿轮建模的参数化。关系式确保零件在参数化建模过程中拓扑结构不发生改变。     

变位斜齿轮的热弹流润滑数值分析

运用斜齿轮有限长线接触数学模型,对渐开线变位斜齿轮进行热弹流润滑数值分析;分析正变位、负变位、等变位3种变位系数下斜齿轮的热弹流润滑状态,计算不同变位系数下斜齿轮的油膜压力、膜厚及温升,并与标准斜齿轮传动计算结果进行比较。结果表明:热弹流润滑条件下,斜齿轮的变位对油膜压力影响不大,对膜厚有较大的影响;变位斜齿轮正传动时,随变位系数的增大,压力减小,膜厚增大;沿最长接触线时,与标准斜齿轮的传动相比,变位斜齿轮正变位系数下压力最小、膜厚最大、温度最低,因此,选择正变位系数更有利于斜齿轮的润滑。     

采用碟形砂轮的斜齿面齿轮磨齿技术研究

为了制造出高精度硬齿面斜齿面齿轮和获得抛物线传动误差并改善啮合性能,对采用碟形砂轮加工双向修形的斜齿面齿轮的磨齿方法进行了研究。设计了渐开线失配的碟形砂轮齿面,分析了碟形砂轮磨削斜齿面齿轮的展成原理,根据展成原理和用渐开线失配的碟形砂轮并改变砂轮的运动,推导出双向修形斜齿面齿轮的齿面方程。给出了双向修形斜齿面齿轮的齿面计算和接触分析实例,结果表明:理论齿面的最大齿面误差为5.98×10-4μm,采用碟形砂轮加工双向修形斜齿面齿轮的磨齿方法是可行的,获得了斜齿面齿轮抛物线传动误差,避免了边缘接触并改善了斜齿面齿轮的啮合性能。     

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.     

基于Pro／Engineer标准渐开线斜齿圆柱齿轮参数化设计

介绍了一种基Pro/E渐开线斜齿圆柱齿轮的精确参数化建模的方法.利用软件中的程序和关系,实现了斜齿圆柱齿轮的参数化建模,仅改变齿轮的相关参数就能快速生成新齿轮,从而极大地提高设计效率.     

TI 环面蜗杆砂轮磨齿原理

根据空间交错轴齿轮啮合理论，对ＴＩ环面蜗杆砂轮磨齿原理进行了理论研究，推导出了基本方程，分析了磨削渐开线直、斜齿圆柱齿轮时的接触线分布规律，并得到了齿面上不存在啮合界限线的判定条件，经微机模拟接触过程，表明此方法是一种高效的齿面磨削方法。     

Pro/E Wildfire3.0中标准渐开线斜齿圆柱齿轮参数化设计

介绍在Pro/E Wildfire 3.0环境下,实现标准渐开线斜齿圆柱齿轮的参数化设计方法和步骤,从原理出发,利用方程建立渐开线,保证渐开线齿轮齿形的准确性.通过改变相关参数及关系式,能够快速地实现齿轮的参数化造型设计和修改定型,同时也解决了渐开线斜齿圆柱齿轮精确造型的难题.     

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。     

基于UG二次开发的齿轮参数化精确建模方法研究

以范成法原理为理论基础,用编程工具V C++6.0对三维软件UG NX5.0进行二次开发,实现了包括变位斜齿轮等各种圆柱渐开线齿轮的三维精确建模。针对目前三维环境下进行三维精确建模过程中存在的问题,选择利用两条引导线与两组齿廓曲线进行扫掠生成单齿,然后进行阵列生成全齿的方法对齿轮进行精确建模,有效简化了CAD模型。为了实现精确建模,通过计算临界齿数确定采用何种程序生成过渡曲线,生成的齿廓准确,为复杂曲面零件的CAX建模与分析提供了新途径。     

ANALYSIS OF TRANSMISSION CHARACTERISTICS OF COSINE GEAR DRIVE

Based on the mathematical model of a novel cosine gear drive, a few characteristics, such as the contact ratio, the sliding coefficient, and the contact and bending stresses, of this drive are analyzed. A comparison study of these characteristics with the involute gear drive is also carried out. The influences of design parameters including the number of teeth and the pressure angle on the contact and bending stresses are studied. The following conclusions are achieved： the contact ratio of the cosine gear drive is about 1.2 to 1.3, which is reduced by about 20% in comparison with that of the involute gear drive. The sliding coefficient of the cosine gear drive is smaller than that of the involute gear drive. The contact and bending stresses of the cosine gear drive are lower than those of the involute gear drive. The contact and bending stresses decrease with the growth of the number of teeth and the pressure angle.     

基于Pro/E的渐开线斜齿轮参数化造型方法研究

渐开线斜齿轮是机械设备中常用的传动零件,其齿形复杂,传统的齿轮建模过程比较繁琐。介绍了在Pro/E环境下,运用三维参数化设计功能,实现标准渐开线斜齿轮的造型方法和步骤。该方法从原理出发,利用方程建立渐开线,保证齿轮齿形的准确性。通过修改相应的设计参数及关系式,能够实现不同模数、齿数齿轮的快速造型,提高设计效率。     

旋转齿轮瞬时接触应力和温度的分析模拟

建立了高速齿轮传动轮齿瞬时接触温度的分析方法和模型;采用赫兹接触理论和有限元接触分析方法分析了标准渐开线齿廓和齿顶修形齿廓的齿面接触压力;研究了啮合过程中轮齿的相对滑动速度和齿面摩擦因数以及摩擦热流密度的计算方法;建立了轮齿本体温度的有限元温度分析模型;计算了轮齿接触面的瞬时温升;分析了标准和齿顶修形渐开线齿轮的轮齿本体温度和瞬时接触温度及相关因素对它们的影响。     

渐开线斜齿轮Pro/E参数化建模方法研究

介绍了在Pro/E环境下,如何运用三维参数化设计功能,实现标准渐开线斜齿轮的造型方法和步骤,该方法从原理出发,利用方程建立渐开线,保证齿轮齿形的准确性。通过修改相应的设计参数及关系式,能够实现不同模数、齿数齿轮的快速造型,提高了设计效率。     

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。