Time-Varying Mesh Stiffness Calculation and Dynamic Modeling of Spiral Bevel Gear with Spalling Defects

Time-varying mesh stiffness(TVMS)is a vital internal excitation source for the spiral bevel gear(SBG)transmission system.Spalling defect often causes decrease in gear mesh stiffness and changes the dynamic characteristics of the gear system,which further increases noise and vibration.This paper aims to calculate the TVMS and establish dynamic model of SBG with spalling defect.In this study,a novel analytical model based on slice method is proposed to calculate the TVMS of SBG considering spalling defect.Subsequently,the influence of spalling defect on the TVMS is studied through a numerical simulation,and the proposed analytical model is verified by a finite element model.Besides,an 8-degrees-of-freedom dynamic model is established for SBG transmission system.Incorporating the spalling defect into TVMS,the dynamic responses of spalled SBG are analyzed.The numerical results indicate that spalling defect would cause periodic impact in time domain.Finally,an experiment is designed to verify the proposed dynamic model.The experimental results show that the spalling defect makes the response characterized by periodic impact with the rotating frequency of spalled pinion.

GEOMETRIC MODELING OF GENERATING-MANUFACTURED SPIRAL BEVEL GEARS BASED ON CUTTING SIMULATION

A geometric modeling method for generating-manufactured spiral bevel gears（SBGs） is proposed. It consists of two steps： （1） creating a reference model by simulating the process of cutting spiral bevel gear,（2） reconstructing the final solid model by collecting data points from the reference model and fitting these points into NURBS surfaces. In this method,cutting simulation avoids abstruse mathematical theories and complex methods,thus making it convenient to obtain data points on the complex tooth surface before the gear is manufactured and efficient to increase the accuracy of the solid model. Also,the representations of tooth surfaces of the final model is unified as a NURBS surface function. The NURBS surface is continuous and smooth,thus it is available for wide applications in CAD/CAE. The experiment proves that the method can be used to establish an accurate pair of SBG models,thus providing a feasible and effective way for CAD/CAE modeling.

Analysis and modeling of error of spiral bevel gear grinder based on multi-body system theory

Six-axis numerical control spiral bevel gear grinder was taken as the object, multi-body system theory and Denavit-Hartenberg homogeneous transformed matrix （HTM） were utilized to establish the grinder synthesis error model, and the validity of model was confirmed by the experiment. Additionally, in grinding wheel tool point coordinate system, the errors of six degrees of freedom were simulated when the grinding wheel revolving around C-axis, moving along X-axis and Y-axis. The influence of these six errors on teeth space, helix angle, pitch, teeth profile was discussed. The simulation results show that the angle error is in the range from -0.148 4 tad to -0.241 9 rad when grinding wheel moving along X, Y-axis; the translation error is in the range from 0.866 0 μm to 3.605 3μm when grinding wheel moving along X-axis. These angle and translation errors have a great influence on the helix angle, pitch, teeth thickness and tooth socket.

Accurate Modeling of the Spiral Bevel and Hypoid Gear with a New Tooth Profile

Distinguishing with traditional tooth profile of spiral bevel and hypoid gear, it proposed a new tooth profile namely the spherical involute. Firstly, a new theory of forming the spherical involute tooth profile was proposed. Then, this theory was applied to complete parametric derivation of each part of its tooth profile. For enhancing the precision, the SWEEP method used for formation of each part of tooth surface and G1 stitching schema for obtaining a unified tooth surface are put forward and made the application in the accurate modeling. Lastly, owing to the higher accuracy of tooth surface of outputted model, it gave some optimization approaches. Given numerical example about the model can show that this designed gear with spherical involute tooth profile can achieve fast and accurate parametric modeling and provide a foundation for tooth contact analysis （TCA） in digitized design and manufacture.

Mathematic model and tooth contact analysis of a new spiral non-circular bevel gear

A novel spiral non-circular bevel gear that could be applied to variable-speed driving in intersecting axes was proposed by combining the design principles of non-circular bevel gears and the manufacturing principles of face-milling spiral bevel gears.Unlike straight non-circular bevel gears,spiral non-circular bevel gears have numerous advantages,such as a high contact ratio,high intensity,good dynamic performance,and an adjustable contact region.In addition,while manufacturing straight non-circular bevel gears is difficult,spiral non-circular bevel gears can be efficiently and precisely fabricated with a 6-axis bevel gear cutting machine.First,the generating principles of spiral non-circular bevel gears were introduced.Next,a mathematical model,including a generating tooth profile,tooth spiral,pressure angle,and generated tooth profile for this gear type was established.Then the precision of the model was verified by a tooth contact analysis using FEA,and the contact patterns and stress distributions of the spiral non-circular bevel gears were investigated.

NC Machining of Spiral Bevel Gear and Hypoid Gear Based on Unity Transformation Model

A unity transformation model (UTM) was presented for flexible NC machining of spiral bevel gears and hypoid gears. The model can support various machining methods for Gleason spiral bevel gears and hypoid gears, including generation machining and formation machining for wheel or pinion on a universal five-axis machining center, and then directly produce NC codes for the selected machining method. Wheel machining and pinion machining under UTM were simulated in Vericut 6.0 and tested on a five-axis machining center TDNC-W2000 with NC unit TDNC-H8. The results from simulation and real-cut verify the feasibility of gear machining under UTM as well as the correctness of NC codes.

ALGORITHMS OF GENERATION MOTION AND DIRECT INTERPOLATION FOR SPIRAL BEVEL GEAR NC MACHINING

The generating motion of the generating gear and the work gear on spiral bevel gear NC machining is analyzed. The mathematical model of the tooth surface of spiral bevel gear is presented. A direct interpolation algorithm of spiral bevel gear NC machining is proposed, thus establishing the relationship between the motion of the cutter-head center and the rotation of the work gear. The interpolation algorithm is implemented to control the gear cutting on self-developed spiral bevel gear NC cutting machine. An example is given to verify the mathematical model and the interpolation algorithm.

弧齿锥齿轮齿面建模和参数化设计系统软件开发

基于弧齿锥齿轮的复杂齿面设计和实际啮合情况,提出一种利用齿廓成型刀具的齿廓建模方法,能有效实现弧齿锥齿轮齿廓的精确建模.以弧齿锥齿轮为主要建模对象,提出自动化建模及装配方法,开发一种参数化设计系统软件.该软件能够实现弧齿锥齿轮的自动化快速建模和装配,缩短建模时间,提高设计质量与效率,有助于推动产业数字化转型,发展高端装备制造业.

等距螺旋锥齿轮的精确建模与金属粉末注射成型工艺试制

等距螺旋锥齿轮作为一种新型锥齿轮,其螺旋齿面具有法向等距的特点,适用于金属粉末注射成型工艺批量化生产。根据坐标变换理论推导出球面渐开线和等距圆锥螺旋线的参数方程,再基于齿面形成原理建立齿面数学模型;在MATLAB中对齿面数学模型编程计算出齿面离散点坐标,并通过UG逆向工程完成等距螺旋锥齿轮的精确建模;利用ANSYS仿真分析等距螺旋锥齿轮的啮合接触,得出齿轮的传动性能;最后通过金属粉末注射成型工艺完成等距螺旋锥齿轮的试制。研究结果表明,齿面数学模型结合离散点逆向建模可确保模型的精度,金属粉末注射成型工艺可用于等距螺旋锥齿轮的批量化生产。

基于AFOSM的螺旋锥齿轮磨损可靠性分析

运用当量齿轮理论对螺旋锥齿轮啮合过程进行简化,基于Archard模型建立螺旋锥齿轮的磨损模型,将轮齿中点法截面上各点磨损量对比,挑选出轮齿中点法截面危险点,对危险点进行磨损可靠性分析,基于改进一次二阶矩法(AFOSM)建立极限状态函数,进行MATLAB编程求得螺旋锥齿轮在所选设计参数下的可靠度和设计点,计算工作扭矩与工作转速变化对其可靠度的影响,采用蒙特卡洛法进行可靠性仿真分析,两种方法计算结果接近,表明该方法具有较高的效率和准确性。以上工作可为螺旋锥齿轮的可靠性设计和维护提供一定的参考和借鉴。

基于CATIA的差速器直齿圆锥齿轮参数化建模与有限元分析

介绍了一种利用CATIA软件对汽车差速器直齿圆锥齿轮进行参数化建模和有限元分析(FEA)的设计方法。该方法最大的特点是建模与有限元分析使用同一软件平台,避免了接口传递可能产生的数据错误,是一种简便可行、运行效率高的齿轮设计与分析方法。最后结合实例,完成了某型差速器直齿圆锥齿轮的建模和有限元分析。

重型弧齿锥齿轮铣齿机数控加工模型建立与仿真

通过分析弧齿锥齿轮加工原理及传统机械摇台式弧齿锥齿轮铣齿机的结构和机床运动关系,建立了弧齿锥齿轮铣齿机加工坐标系。采用刀盘主轴进给方式代替传统的整体工件箱部件或摇台部件进给方式,建立了重型弧齿锥齿轮铣齿机三维结构模型。分析了由传统机械摇台式弧齿锥齿轮铣齿机调整参数转变为重型数控弧齿锥齿轮铣齿机调整参数的原理和计算方法,建立了重型弧齿锥齿轮铣齿机的数控加工模型。通过计算实例,得到了重型数控弧齿锥齿轮铣齿机铣齿加工时机床各运动轴的瞬时位置。建立了重型弧齿锥齿轮铣齿机仿真加工机床模型,并进行了仿真加工,仿真结果满足弧齿锥齿轮铣齿机功能性验证要求。

基于网络集成的弧齿锥齿轮数字化闭环制造技术

为突破弧齿锥齿轮数字化闭环制造过程信息继承性与集成性低的局限,实现弧齿锥齿轮齿面数字化闭环过程的集成运行和齿面制造信息的集成管理,该文提出了一种弧齿锥齿轮的网络化闭环制造模型,建立了网络化闭环制造的运行机制,采用基于TCP/IP(transmission control protocol/internet protocol,传输控制/网络通讯协定)的分布式集成控制模式构建网络化闭环制造模型的通信网络,利用Web服务应用集成方法建立闭环制造过程信息集成机制,并通过设计开发闭环制造集成系统实现网络化闭环制造信息的集成统一管理。应用结果表明:该模型及其实现技术可行实用,实现了齿面制造过程的数字化和集成化运行,使齿轮副的齿面精度和啮合性能都得到明显提高。以该文的准双曲面齿轮副滚动检测试验为例,辐射噪声降低约7%,振动加速度幅值降低约15%。该研究为弧齿锥齿轮的网络化和集成化制造提供参考。

整体结构式弧齿锥齿轮铣齿机虚拟加工

弧齿锥齿轮铣齿机结构和加工原理复杂,是复杂制造装备的典型代表,因此,提高中国弧齿锥齿轮铣齿机的制造水平具有重要意义。通过分析弧齿锥齿轮加工原理和凤凰Ⅱ型弧齿锥齿轮铣齿机结构及运动关系,推导了整体结构式弧齿锥齿轮铣齿机各轴运动参数的计算方法,利用VERICUT三维仿真加工软件平台,建立了整体结构式弧齿锥齿轮铣齿机虚拟加工模型,并对一对给定几何参数的弧齿锥齿轮进行了虚拟加工。仿真结果表明,机床各运动模块与切齿刀盘在虚拟加工过程中没有出现干涉等设计缺陷,虚拟加工结果满足弧齿锥齿轮铣齿机功能性验证要求。弧齿锥齿轮铣齿机仿真加工可以为弧齿锥齿轮铣齿机设计提供参考依据。

基于加工方法和啮合理论的螺旋锥齿轮精确实体造型

提出了基于加工方法和啮合理论的螺旋锥齿轮精确齿面的实体造型方法。通过分析锥齿轮的加工方法和齿轮啮合理论,建立了螺旋锥齿轮齿面数学模型。根据齿面均匀离散点的输出数据,对齿面进行重构,实现了螺旋锥齿轮的精确实体造型,采用了齿面偏差法对生成实体模型精度进行了评估。研究结果对于螺旋锥齿轮数字化设计和制造具有重要意义。

弧齿锥齿轮齿面接触应力分析

弧齿锥齿轮工作时齿面接触应力的大小直接影响其使用寿命和安全。本文运用自主开发的弧齿锥齿轮设计分析系统建立齿轮的轮齿网格模型,将模型数据变换后导入ANSYS软件中,经过装配和结构扩展进行轮齿的接触应力分析,得到了多齿对接触情况下,齿面等效接触应力的分布及其变化规律。

对数螺旋锥齿轮参数化建模方法研究

对数螺旋锥齿轮处处螺旋角相等,且加工简单。为了提高对数螺旋锥齿轮建模的正确性和效率,文章提出了一种基于CATIA的对数螺旋齿轮参数化建模方法。推导了球面渐开线方程和圆锥螺旋线方程。以CATIA为二次开发平台,运用VB宏命令编制软件自动完成球面渐开线以及圆锥螺旋线的绘制并形成齿宽中点处的齿槽齿廓,通过缩放,旋转,多截面曲面,拼接,封闭曲面以及填充等命令形成完整齿槽体,进而由布尔去除运算并阵列生成精确齿轮参数化模型。为后续锥齿轮的有限元仿真、动力学仿真以及修形设计奠定了技术基础。

含过渡曲面的弧齿锥齿轮齿面精确建模

针对用SGM法加工的弧齿锥齿轮,根据刀具、机床和被加工齿轮的相互运动及切齿过程,由齿轮啮合方程和弧齿锥齿轮切齿原理详细地推导出弧齿锥齿轮过渡曲面和齿廓曲面方程,得到弧齿锥齿轮精确数学模型,根据一对锥齿轮的加工参数在MATLAB中编程计算并采集了齿面数据点,然后导入Pro/E建立了含有过渡曲面的弧齿锥齿轮三维模型。建立的含过渡曲面的弧齿锥齿轮模型为弧齿锥齿轮的数字化制造与有限元分析提供基础条件。

弧齿锥齿轮成形三维虚拟仿真研究

通过分析弧齿锥齿轮加工原理及加工机床的结构和运动关系,并基于空间啮合理论,建立了刀刃锥面方程和啮合方程,应用图形变换原理,推导了弧齿锥齿轮NC机床运动参数的计算方法。基于VERICUT软件平台,建立了弧齿锥齿轮NC机床模型及弧齿锥齿轮三维虚拟仿真加工模型,对一对具体的弧齿锥齿轮进行了几何参数、刀具参数和NC机床运动参数的计算,并在VERICUT环境下进行了虚拟仿真加工,验证了弧齿锥齿轮NC机床模型及三维虚拟仿真加工模型的正确性。

克林贝格螺旋锥齿轮的建模与仿真

在分析克林贝格螺旋锥齿轮切齿原理和基本运动的基础上 ,以一对齿轮副参数为例进行建模 .利用AutoCAD 2 0 0 0中的二次开发工具VBA(VisualBasicApplication)参数化建模 ,开发出该类齿轮的建模软件 ,实现克林贝格螺旋锥齿轮三维仿真 .对建模软件的结果进行分析 ,说明利用克林贝格螺旋锥齿轮建模软件所仿真出来的图形与理论一致 .