Design of Pinion Machine Tool-settings for Spiral Bevel Gears by Controlling Contact Path and Transmission Errors

This paper proposes a new approach to design pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. It is based on the satisfaction of contact condition of three given control points on the tooth surface. The three meshing points are controlled to be on a predesigned straight contact path that meets the pre-designed parabolic function of transmission errors. Designed separately, the magnitude of transmission errors and the orientation of the contact path are subjected to precise control. In addition, in order to meet the manufacturing requirements, we suggest to modify the values of blank offset, one of the pinion machine tool-settings, and redesign pinion ma- chine tool-settings to ensure that the magnitude and the geometry of transmission errors should not be influenced apart from minor effects on the predesigned straight contact path. The proposed approach together with its ideas has been proven by a numerical example and the manufacturing practice of a pair of spiral bevel gears.

Mathematical modeling and characteristics analysis for the nutation gear drive based on error parameters

We focused on the mathematical modeling and characteristics analysis for the nutation drive based on error parameters. The crown gear tooth profile equation was introduced according to the national standard double circular arc tooth profile and based on the equal tooth strength principle. The nutation drive meshing coordinate system was set up by introducing the cone vertex error, tilt error, nutation angle error and spiral angle error. The tooth profile equations of the double circular arc external and internal spiral bevel gears were further obtained based on the crown gear tooth profile equation concerning above mentioned error parameters. The influences of the nutation gear reducer tooth contact conditions were analyzed with the gear tilt error and axial misalignment error. Finally, the correctness of the theoretical analysis was verified by the contact spot test.

Influence of Setting Error of Tool on Tooth Profile and Contact Point of Face Gear Drive

In order to analyze the influence of setting error of tool on both tooth profile and contact characteristic of orthogonal face gear drive,the coordinate systems with and without setting error are established.Moreover,the equations of tooth profile and contact points of face gear drive are derived by envelope principle.According to the equations,the change of tooth profile and the contact points position on face gear are analyzed.The tooth surface and contact points are obtained by numerical simulation.Results show that the tooth profile and contact characteristic of face gear drive are not sensitive to the setting error of tool.

New method for calculating face gear tooth surface involving worm wheel installation errors

The machining principle and realization method for the continuous generative grinding face gear by a worm wheel are introduced. Based on a five-axis linked CNC grinding machine, a new method is presented to deprive the equation of face gear error tooth surface by assuming the tool surface as the error surface, where actual tool installation position error is introduced into the equation of virtual shaper cutter. Surface equations and 3-D models for the face gear and the worm wheel involving four kinds of tool installation errors are established. When compared, the face gear tooth surface machined in VERICUT software for simulation based on this new method and the one obtained based on real process(grinding face gear by using a theoretical worm wheel with actual position errors) are found to be coincident, which proves the validity and feasibility of this new method. By using mesh planning for the rotating projection plane of the face gear work tooth surface, the deviation values of the tooth surface and the difference surface are acquired, and the influence of four kinds of errors on the face gear tooth surface is analyzed. Accordingly, this work provides a theoretical reference for assembly craft of worm wheel, improvement of face gear machining accuracy and modification of error tooth surface.

Influence of Alignment Errors on Contact Pressure during Straight Bevel Gear Meshing Process

Straight bevel gears are widely applied in automotive, aerospace, chemical and many other fields as one of the most common type of gears. Currently, the researches on straight bevel gears have focused on the fields of fatigue, wear, noise and vibration, while little attention is paid to the effect of multiple alignment errors on the gear tooth wear. To study the influence of alignment errors on the gear tooth wear, a simulated model of a straight bevel gear pair is established. Then, the contact pressure on the tooth surface is analyzed under the various alignment errors according to the Archard wear relationship. The main combinations of alignment errors played vital roles on the tooth wear are investigated. The result shows that under the single alignment error, the contact pressure moves to the tooth heel and increases greatly at here when ？P=0.1 or ？G=0.1; when ？E=–0.03, the contact pressure greatly increases at the tooth heel, but it obviously increases at the tooth toe when ？E=0.03; the alignment error ？γ=1 has little effect on the contact pressure on the tooth surface. Moreover, the combination of ？P, ？G, ？E〈0 and ？γ is the most dangerous type among the multiple alignment errors. This research provides valuable guidelines for predicting the tooth wear under various alignment errors.

Excitation Prediction by Dynamic Transmission Error under Sliding Friction in Helical Gear System

Monte Carlo method was adopted to calculate the meshing error considering the manufacture error and assembly error of the meshing point along the time-varying contact line for helical gear pair. The flexural-torsion-axis dynamic model coupled was established under the tooth friction force and solved by the perturbation method to compute real dynamic tooth load. The change laws of the friction force and friction torque were obtained in a meshing period. The transmission error formulation was analyzed to introduce meshing excitations. The maximum dynamic transmission error, the maximum meshing force and the maximum dynamic factor were calculated under different speeds, external loads and damping factors. The conclusions can provide theoretical basis for the gear design especially in tooth profile correction.

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.

Smooth Operation with Manufacture Error and Modification of Cycloidal Pin Gearing

The paper considers the modification or the manufacture error of cycloidal gear, then analyzes the relationship of pin circle meshed with the modified cycloidal gear, discuases the amount of error that leads to destroying conjugate action and results in the changes of tbe instantaneous velocity ratio and so as to affect the smooth operation of cycloidal pin gearing. The idea of the relationship between amount of modification aud manufacture error and the smooth operation can be gotten from the curve diagrams of the instantaneous velocity ratio. Therefore, the directions for improving the reature of the cycloidal pin gear transmission are clear.

ERROR PROCESSING METHOD OF CYCLOIDAL GEAR MEASUREMENT USING 3D COORDINATES MEASURING MACHINE

An error processing method is presented based on optimization theory and microcomputer technique which can be successfully used in the cycloidal gear measurement on three dimensional coordinates measuring machine (CMM). In the procedure, the minimum quadratic sum of the normal deviation is used as the object function and the equidistant curve is dealed with instead of the teeth profile. CMM is a high accurate measuring machine which can provide a way to evaluate the accuracy of the cycloidal gear completely.

Analysis and correction of the machining errors of small plastic helical gears by ball-end milling

Many small-size precise plastic helical involutes gears are used in electrical appliances to transmit rotary movements con- tinuously and smoothly. Ball-end milling is an effective method for trial manufacture or small batch production of this type of gear, but the precision of the gear is usually low. In this research, the main sources of the errors of the gear, machining errors of the tooth profile and trace of the gear obtained were analyzed. The correction amounts for these errors are then determined by using a CNC gear tester. They are used to generate a new 3D-CAD model for gear machining with better nrecision.

A Method for Identification and Compensation of Machining Errors of Digital Gear Tooth Surfaces

In order to generate the digital gear tooth surfaces(DGTS)with high efficiency and high precision,a method for identification and compensation of machining errors is demonstrated in this paper.Machining errors are analyzed directly from the real tooth surfaces.The topography data of the part are off-line measured in the post-process.A comparison is made between two models:CAD model of DGTS and virtual model of the physical measured surface.And a matching rule is given to determine these two surfaces in an appropriate fashion.The developed error estimation model creates a point-to-point map of the real surface to the theoretical surface in the normal direction.A“pre-calibration error compensation”strategy is presented.Through processing the results of the first trail cutting,the total compensation error is predicted and an imaginary digital tooth surface is reconstructed. The machining errors in the final manufactured surfaces are minimized by generating this imaginary surface.An example of ma- chining 2-D DGTS verifies the developed method.The research is of important theoretical and practical value to manufacture the DGTS and other digital conjugate surfaces.

ANALYSIS OF TOOTH FORM ERROR OF EQUAL BASE CIRCLE BEVEL GEAR

The basic principle of equal base circle bevel gear (EBCBG) is illustrated simply Thetooth surface equation of EBCBG manufactured by end milling cutter with involute profile is de-rived. The tooth form error is analyzed on the basis of spherical involute

基于媒介齿轮的修正型渐开线包络环面蜗杆传动啮合性能分析

环面蜗杆传动因其多齿啮合特性而具有承载能力强等优势,但其约束数相应增加,对制造误差及装配误差更为敏感。为降低重载环面蜗杆传动的误差敏感性,提出了一种修正型渐开线齿轮包络环面蜗杆传动。构建渐开线齿轮与媒介齿轮及环面蜗杆三者之间的啮合几何学模型,建立了传动副空间点接触局部共轭接触分析方法;通过数值分析及有限元仿真分析,揭示了修正型渐开线齿轮包络环面蜗杆传动啮合特性的变化规律。结果表明,该新型环面蜗杆传动具有较低的误差敏感性,同时保持了高载荷下的承载能力。针对某人机交互7000 m自动化钻机重载机器人回转关节,研制了修正型渐开线包络环面蜗杆传动减速器样机,并进行了相关性能试验,验证了理论分析的准确性。

考虑制造误差和油膜作用力的齿轮敲击动力学分析

为准确评估变速器空套齿轮受角加速度激励的敲击表现,采用集中参数法建立了模拟变速器敲击台架试验的10自由度扭转动力学模型;在包含时变啮合刚度、间隙非线性和拖曳力矩的基础上,进一步考虑齿轮制造误差和润滑油膜作用力。敲击台架试验结果表明包含楔入和挤压效应的润滑油膜作用力模型能正确反映变速器的敲击响应;数值分析结果表明润滑油膜可以减少制造误差位移激励和时变啮合刚度参数激励产生的齿面敲击,敲击强度随制造误差幅值的增加呈凹函数变化,当制造误差的幅值增加到某一数值时,齿轮副在无角加速度激励时亦产生敲击现象。润滑油温度对敲击的影响与角加速度激励有关:无角加速度激励时,低温时较低幅值的齿轮低频圆周误差通过改变油膜作用力方向产生敲击;油膜作用力产生的敲击响应频率比齿面接触的敲击响应频率更低;当存在角加速度激励时,敲击强度随温度的升高呈凸函数增加。

非圆齿轮电火花线切割加工工艺参数对齿廓误差的影响

线切割加工非圆齿轮时电参数是影响齿廓误差的关键因素之一.设计正交试验,分别采用非圆齿轮齿根、齿廓中部和齿顶的最大齿廓误差对线切割加工非圆齿轮进行分析.通过方差分析方法和主效应分析法,研究线切割加工电参数峰值电流、脉冲宽度、脉冲间隔和跟踪对非圆齿轮齿根、齿廓中部和齿顶的齿廓误差影响规律.同时,对齿廓误差、加工时长和工艺参数进行回归分析,并建立回归模型,基于灰狼优化算法对回归模型进行多目标优化求解.通过研究结果可以得出线切割加工非圆齿轮齿廓不同部位的最优参数组合,可为实际加工提供参考.

基于Romax的新能源汽车减速器齿轮修形研究

以某增程式新能源汽车减速器系统为研究对象,Romax为研究平台。结合齿轮的微观修形理论,以传递误差、面载、齿根应力和接触应力作为优化目标,结合第二代遗传算法提出了一种以齿向鼓形量、齿向斜度、渐开线鼓形量、渐开线斜度综合修形的全新修形方法。通过对优化前后各目标参数的分析对比,得出修形后减小了传递误差、齿根应力等、改善了面载、应力偏载等问题,同时齿轮的传动性能得到了明显提升,其研究方法可更好地指导企业生产实践。

考虑齿形误差影响的摆线针轮承载特性分析

针对缺乏考虑齿形误差的承载分析软件,导致分析结果不符合实际工程状况的问题,提出了1种包含摆线轮齿形误差的摆线针轮副承载特性分析方法。利用三次非均匀B样条准确描述出包含齿形误差的摆线轮实际齿廓,构建并分析了摆线针轮误差齿廓接触分析模型(error tooth contact analysis,E-TCA),得到了初始啮合位置参数及啮合间隙。在此基础上,建立了齿形误差影响下的摆线针轮副负载接触分析模型,确定了零部件多体接触之间的力矩平衡和变形协调关系,利用能量最低原理获取了真实承载特性。通过有限元模型验证了RV-40E型号减速器的摆线针轮承载特性。结果表明:由于齿形误差的影响,啮合齿数减少了1对,啮合应力和传动误差增大了5.3%和5.7%。

双曲型法向圆弧齿轮传动的动力学分析

为探究啮合刚度、传动误差及侧隙对双曲型法向圆弧齿轮传动动态响应的影响,建立齿轮副的动力学方程,并在数值计算的基础上进行仿真分析。运用有限元方法,计算接触位置处的载荷及变形,并对时变啮合刚度、静态传动误差和侧隙进行量化分析。仿真结果表明:对振动位移响应影响最大的是侧隙,其次是时变啮合刚度;对动态啮合力影响最大的则是时变啮合刚度和侧隙。

摆线轮工作齿廓的二次分段修形方法

针对常规修形方法存在计算复杂、齿廓曲线形状控制不够灵活等问题,提出了一种摆线轮工作齿廓的二次分段修形方法。通过摆线轮齿廓压力角变化规律的分析,将工作齿廓最小压力角的位置作为二次分段修形的基准点,建立二次分段修形模型。利用直线法简单函数,推导出二次分段修形方法下各齿段修形量的计算公式及齿廓方程。采用轮齿接触分析的方法,研究了二次分段修形齿廓的传动误差和回差,并进行对比实验验证摆线轮工作齿廓二次分段修形方法的正确性和可行性。结果表明:二次分段修形的摆线轮工作齿廓与理论齿廓曲线更加吻合,传动误差和回程误差分别减少约14%和19%。

齿轮加工机床几何误差补偿研究综述

齿轮的加工精度是制约高端装备发展的关键瓶颈,高性能齿轮加工机床是实现齿轮高精度加工的选择。齿轮加工机床结构和运动的复杂性增加了其几何误差补偿的难度。通过分析近年来国内外多轴通用机床的几何误差补偿技术并结合齿轮加工机床几何误差补偿发展现状,对齿轮加工机床几何误差补偿技术展开综述,总结几何误差的来源,介绍多体系统理论、旋量理论、微分运动矩阵及变流理论4种可应用于几何误差建模的理论,分析采用激光干涉仪和球杆仪对直线轴及旋转轴进行几何误差测量与辨识的方法,概述通过NC数据修改对几何误差进行补偿的方法,为齿轮加工机床几何误差补偿设计提供参考。