A distributed dynamic mesh model of a helical gear pair with tooth profile errors

A dynamic model of a helical gear rotor system is proposed.Firstly,a generally distributed dynamic model of a helical gear pair with tooth profile errors is developed.The gear mesh is represented by a pair of cylinders connected by a series of springs and the stiffness of each spring is equal to the effective mesh stiffness.Combining the gear dynamic model with the rotor-bearing system model,the gear-rotor-bearing dynamic model is developed.Then three cases are presented to analyze the dynamic responses of gear systems.The results reveal that the gear dynamic model is effective and advanced for general gear systems,narrow-faced gear,wide-faced gear and gear with tooth profile errors.Finally,the responses of an example helical gear system are also studied to demonstrate the influence of the lead crown reliefs and misalignments.The results show that both of the lead crown relief and misalignment soften the gear mesh stiffness and the responses of the gear system increase with the increasing lead crown reliefs and misalignments.

Tooth surface error correction of hypoid gears machined by duplex helical method

In this work,synchronous cutting of concave and convex surfaces was achieved using the duplex helical method for the hypoid gear,and the problem of tooth surface error correction was studied.First,the mathematical model of the hypoid gears machined by the duplex helical method was established.Second,the coordinates of discrete points on the tooth surface were obtained by measurement center,and the normal errors of the discrete points were calculated.Third,a tooth surface error correction model is established,and the tooth surface error was corrected using the Levenberg-Marquard algorithm with trust region strategy and least square method.Finally,grinding experiments were carried out on the machining parameters obtained by Levenberg-Marquard algorithm with trust region strategy,which had a better effect on tooth surface error correction than the least square method.After the tooth surface error is corrected,the maximum absolute error is reduced from 30.9μm before correction to 6.8μm,the root mean square of the concave error is reduced from 15.1 to 2.1μm,the root mean square of the convex error is reduced from 10.8 to 1.8μm,and the sum of squared errors of the concave and convex surfaces was reduced from 15471 to 358μm^(2).It is verified that the Levenberg-Marquard algorithm with trust region strategy has a good accuracy for the tooth surface error correction of hypoid gear machined by duplex helical method.

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.

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

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.

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.

Pinion Tooth Surface Generation Strategy of Spiral Bevel Gears

Aviation spiral bevel gears are often generated by spiral generated modified（SGM） roll method.In this style,pinion tooth surface modified generation strategy has an important influence on the meshing and contact performances.For the optimal contact pattern and transmission error function,local synthesis is applied to obtain the machine-tool settings of pinion.For digitized machine,four tooth surface generation styles of pinion are proposed.For every style,tooth contact analysis（TCA） is applied to obtain contact pattern and transmission error function.For the difference between TCA transmission error function and design objective curve,the degree of symmetry and agreement are defined and the corresponding sub-objective functions are established.Linear weighted combination method is applied to get an equivalent objective function to evaluate the shape of transmission error function.The computer programs for the process above are developed to analyze the meshing performances of the four pinion tooth surface generation styles for a pair of aviation spiral bevel gears with 38/43 teeth numbers.The four analytical results are compared with each other and show that the incomplete modified roll is optimal for this gear pair.This study is an expansion to generation strategy of spiral bevel gears,and offers new alternatives to computer numerical control（CNC） manufacture of spiral bevel gears.

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.

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%。

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%。

齿轮传动误差峰峰值最小化的拓扑修形优化研究

为了满足齿轮传动系统低噪声、小振动和高传动精度等要求,提出了一种基于传动误差峰峰值最小化的齿轮拓扑修形优化方法。基于直线与抛物线的复合修形叠加曲线,在标准渐开线齿轮的齿廓和齿向方向对齿轮进行修形设计,提出一种拓扑修形齿面形成方法;以齿轮传动误差峰峰值最小为优化目标,基于遗传算法对提出的拓扑修形齿轮齿面进行参数优化,得出拓扑修形齿轮齿面的最佳修形参数;将拓扑修形齿轮和标准齿轮进行对比,分析修形前后齿轮的齿面受载情况和齿根应力分布情况,验证了提出的拓扑修形优化方法的有效性。

高接触比螺旋锥齿面修形方法及动态特性研究

为抑制高接触比螺旋锥齿轮传动的振动,提出一种新的高阶齿面修形方法。根据高接触比螺旋锥齿轮的啮合特点,提出一种新的修形曲线,采用辅助齿面修形方法生成高阶修形螺旋锥齿轮。在考虑齿变形的情况下,计算了高阶修正弧齿锥齿轮传动的载荷传递误差和啮合冲击,在此基础上建立了降低高接触比螺旋锥齿轮传动的载荷传递误差和啮合冲击的优化模型。仿真结果表明:与二阶修形弧齿锥齿轮相比,高阶齿面修形方法不仅可以有效降低高接触比螺旋锥齿的载荷传递误差、啮合冲击和动态负载系数,而且可以提高其在全速范围内的动态性能。

基于二维混合式位置编码的高精度测角

针对具有精密旋转轴系类的高端制造装备或精密测量仪器,其旋转角度采用传统圆光栅难以消除偏心误差对测量角度精度的影响,提出了一种基于二维混合式位置编码的旋转角度高精度测量方法。该测角系统由一个二维混合式位置编码盘、两个CCD相机和远心镜头组成,二维混合式位置编码盘被固定在精密旋转轴系上以获得其旋转角度。然后,建立了测角模型并从数学上证明了测角精度与安装偏心无关。利用多齿分度台对已提出测角系统精度进行检测,测量角度误差在±1″。最后,利用已提出测量方法对直驱转台的角度定位精度进行测量,角度定位误差在±5″内。与传统圆光栅测角相比,该方法不需要考虑安装偏心误差对测角精度的影响,具有稳定性好、使用简单等特点,可用于角度定位误差的检测。

参数化设计减小矩形花键滚刀代用圆弧的误差

针对矩形花键滚刀代用圆弧相对于理论法向齿形的误差进行了参数化的程序设计,根据最大误差最小法算法以及回代算法,减小了矩形花键滚刀齿形代用圆弧的误差、获得了合理的代用圆弧的圆心坐标及半径值以及缩短了设计周期。其基本方法:首先计算出矩形花键滚刀法向齿形的坐标点公式,然后用双圆弧来代替理论齿形,推导出双圆弧拟合公式。之后基于最大误差最小法算法和回代算法,最后以ObjectARX为开发工具,基于C#.NETAPI的技术,利用优化后的代用圆弧的圆心坐标和半径值以及数据库中的其他相关参数完成矩形花键滚刀法向齿形图的绘制,并且自主研发设计出一套集矩形花键滚刀参数设计、滚齿自动加工参数仿真、干涉参数验算和滚齿数据处理控制于一体的通用矩形花键滚刀参数人性化自动设计绘制平台,实现渐变和矩形状的花键法向滚刀的滚齿参数自动化绘制设计。

铣刀多重刀齿分布及其动态切削行为特性

受刀齿误差影响,铣刀沿轴向存在多种刀齿分布,振动作用下具有多重刀齿分布的铣刀,其切削行为呈现多时变特性,导致切削过程中切削层厚度变化和铣削表面形貌分布具有复杂性和不确定性。依据铣刀结构和刀齿误差,获取沿铣刀轴向的多重刀齿分布序列,构建振动作用下多重刀齿分布的瞬时切削层厚度和铣削表面形貌分布解算模型,揭示沿铣刀轴向的单齿、多齿不等齿距和多齿等齿距分布的动态切削行为特征,阐明刀齿误差和铣削振动对铣刀瞬时切削层厚度及铣削表面形貌分布多样性的影响机制,并进行试验验证。结果表明,采用上述模型与方法,可揭示出振动作用下多重刀齿分布铣刀的动态切削行为及铣削表面的形成过程。

齿盘误差对扭振测量的影响及消除方法

传统扭振测试受齿盘加工和安装精度影响会产生测量误差,严重时会对测试结果产生影响。为此,提出了一种消除齿盘误差对扭振测量影响的方法。根据扭振测量原理优化了扭振提取算法,建立了误差机理模型,并推导了齿盘分度不均以及安装偏心导致的扭振测量误差;此外,分别提出了基于多周期时域同步平均的齿盘分度不均误差校正方法和基于高通滤波器的齿盘偏心误差校正方法;最后,通过仿真和实验验证了理论推导和误差校正方法的有效性,并将上述扭振提取算法和误差校正方法封装形成了LabVIEW软件包,实现了对旋转轴系扭振的准确实时测量。

正交直齿面齿轮车齿刀具精确设计方法

为提高正交直齿面齿轮的加工精度,提出了一种针对正交直齿面齿轮的车齿刀具精确设计方法。基于齿轮交错轴啮合原理,对面齿轮的车齿加工过程进行解析;通过与面齿轮啮合的圆柱齿轮渐开线齿廓,包络出车齿刀齿面方程;基于法向平面,设计了刀具结构并推导了刀具切削刃表达式;求解切削刃与面齿轮的啮合条件式,推导数控加工规律并对面齿轮齿面进行了理论计算与仿真加工;将结果与面齿轮理论齿面进行了数值对比。结果表明,当刀具不存在误差时,可以得到面齿轮理论齿面;通过Vericut仿真,齿面误差保持在10 μm以内。

螺纹参数误差对钻杆接头密封性的影响分析

为探究钻杆接头螺纹参数极限误差对其密封性的影响,基于API NC38钻杆接头,分析了锥度、牙侧角和螺距3种螺纹参数极限误差的存在情况,建立了12种内、外螺纹极限误差组合的钻杆接头有限元模型,分析了不同误差组合的钻杆接头在上扣扭矩单独作用、上扣扭矩和轴向载荷组合作用下的密封性和应力分布。分析结果表明:螺距极限误差对钻杆接头密封性影响最为明显,且极易出现接触面屈服失效的情况;锥度极限误差使钻杆接头在受拉伸载荷时密封性显著降低;内外螺纹牙侧角极限误差变化情况相反时,钻杆接头局部出现塑性变形,影响密封效果。因此钻杆接头螺纹加工时有必要进一步控制螺纹参数的误差范围,避免出现标准规定的极限误差,降低钻杆接头密封失效的风险。研究结果可为快速、安全钻井提供技术支撑。

Optimizing circumferential assembly angle of rotor parts connected by curvic couplings based on acquired tooth surface error data

Due to the excellent self-centering and load-carrying capability,curvic couplings have been widely used in advanced aero-engine rotors.However,curvic tooth surface errors lead to poor assembly precision.Traditional physical-master-gauge-based indirect tooth surface error measurement and circumferential assembly angle optimization methods have the disadvantages of high cost and weak generality.The unknown tooth surface fitting mechanism is a big barrier to assembly precision prediction and improvement.Therefore,this work puts forward a data-driven assembly simulation and optimization approach for aero-engine rotors connected by curvic couplings.The origin of curvic tooth surface error is deeply investigated.Using 5-axis sweep scan method,a large amount of high-precision curvic tooth surface data are acquired efficiently.Based on geometric models of parts,the fitting mechanism of curvic couplings is uncovered for assembly precision simulation and prediction.A circumferential assembly angle optimization model is developed to decrease axial and radial assembly runouts.Experimental results show that the assembly precision can be predicted accurately and improved dramatically.By uncovering the essential principle of the assembly precision formation and proposing circumferential assembly angle optimization model,this work is meaningful for assembly quality,efficiency and economy improvement of multistage aero-engine rotors connected by curvic couplings.