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.

Influence Predictions of Contact Effects on Mesh Stiffness of Face Gear Drives with Spur Gear

Mesh stiffness is one of important base parameters of face gear dynamic studies.However,a calculation solution of mesh stiffness of face gear drives is not to be constructed due to complex geometric flakes of face gear teeth.Thus,a calculation solution of mesh stiffness of face gear drives with a spur gear,which is based on the proposed equivalent face gear teeth and Ishikawa model,is constructed,and the influence of contact effects on mesh stiffness of face gear drives is investigated.The results indicate the mesh stiffness of face gear drives is sensitive to contact effects under heavy loaded operating conditions,specially.These contributions will benefit to improve dynamic studies of face gear drives.

Heat treatment process optimization for face gears based on deformation and residual stress control

In this paper, based on the principle of heat transfer and thermal elastic-plastic theory, the heat treatment process optimization scheme for face gears is proposed according to the structural characteristics of the face gear and material properties of 12Cr2Ni4 steel. To simulate the effect of carburizing and quenching process on tooth deformation and residual stress distribution, a heat treatment analysis model of face gears is established, and the microstructure, stress and deformation of face gear teeth changing with time are analyzed. The simulation results show that face gear tooth hardness increases, tooth surface residual compressive stress increases and tooth deformation decreases after heat treatment process optimization. It is beneficial to improving the fatigue strength and performance of face gears.

Grinding-Hardening of Face Gears Under Minimum Quantity Lubrication with Disc Wheels

To shorten the process of face gears,the grinding-hardening effect experiment of face gears under minimum quantity lubrication(MQL)was carried out.Firstly,the grinding method of face gears was analyzed based on the envelope principle,and the control equation of grinding movement was constructed.Secondly,the distribution ratio equation of heat flux density was established,and the theoretical calculation formula of triangle heat source was derived.Thirdly,since a MATLAB calculation program was compiled,the temperature change law under MQL grinding was analyzed.In the end,the influence of grinding parameters on the grinding-hardening layer depth was analyzed.The results demonstrate that MQL grinding achieves the grinding-hardening effect.

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.

Efficient Grinding Method for Face Gear with Long Radius Disk Wheel

In order to improve the machining efficiency of the dish wheel grinding face gear, two changes are proposed:a disk wheel grinding face gear with a long radius and a multi-axis movement optimization method for tooth surface correction. Based on the grinding principle of face gears, the equation of the long radius disk wheel is deduced. Based on the structure of the machining tool, the tooth surface equations of the face gear shaped by the long radius disk wheel are established. Furthermore, an optimization model of face gear tooth surface correction is established, and the machine tool motion optimization of face gear tooth surface correction is completed;Finally, a long radius disk wheel grinding face gear test is performed. After the face gear tooth surface correction, the maximum value of the tooth surface deviation is reduced from 180 μm to 16 μm which verified the correctness of the machining method.

Integrity of grinding face-gear with worm wheel

Aiming at the issue of the grinding integrity of face-gear with worm wheel, the envelope mathematical model of shaper, worm wheel and face-gear is established based on theories of differential geometry and gear mesh. The judgment of completely grinding the face-gear with the avoidance of singularities is established, and the mathematical expression to show the reason why singularities appear is derived, through the research on the surface contact area and singularity rules of the worm thread surface. The disadvantage of current face-gear grinding method that only part of the working surface of the face-gear can be covered is analyzed and the influence of coefficient of judgment is studied through changing the design parameters.

Loaded multi-tooth contact analysis and calculation for contact stress of face-gear drive with spur involute pinion

The analytical method based on "Hertz theory on normal contact of elastic solids" and the numerical method based on finite element method (FEM) calculating the contact stress of face-gear drive with spur involute pinion were introduced, and their relative errors are below 10%, except edge contact, which turns out that these two methods can compute contact stress of face-gear drive correctly and effectively. An agreement of the localized bearing contact stress is gotten for these two methods, making sure that the calculation results of FEM are reliable. The loaded meshing simulations of multi-tooth FEM model were developed, and the determination of the transmission error and the maximal load distribution factor of face-gear drive under torques were given. A formula for the maximal load distribution factor was proposed. By introducing the maximal load distribution factor in multi-tooth contact zone, a method for calculating the maximal contact stress in multi-tooth contact can be given. Compared to FEM, the results of these formulae are proved to be reliable, and the relative errors are below 10%.

Parametric Analysis of the End Face Engagement Worm Gear

A novel specific type of worm drive, so-called end face engagement worm gear(EFEWD), is originally presented to minimize or overcome the gear backlash. Different factors, including the three different types, contact curves, tooth profile, lubrication angle and the induced normal curvature are taken into account to investigate the meshing characteristics and create the profile of a novel specific type of worm drive through mathematical models and theoretical analysis. The tooth of the worm wheel is very specific with the sine-shaped tooth which is located at the alveolus of the worm and the tooth profile of a worm is generated by the meshing movement of the worm wheel with the sine-shaped tooth, but just the end face of the worm(with three different typical meshing types) is adapted to meshing, and therefore an extraordinary manufacturing methods is used to generate the profile of the end face engagement worm. The research results indicates that the bearing contacts of the generated conjugate hourglass worm gear set are in line contacts, with certain advantages of no-backlash, high precision and high operating efficiency over other gears and gear systems besides the end face engagement worm gear drive may improve bearing contact, reduce the level of transmission errors and lessen the sensitivity to errors of alignment. Also, the end face engagement worm can be easily made with superior meshing and lubrication performance compared with the conventional techniques. In particular, the meshing and lubrication performance of the end face engagement worm gear by using the end face to meshing can be increased over 10% and 7%, respectively. This investigate is expect to provide a new insight on the design of the future no-backlash worm drive for industry.

Optimal Design for an End Face Engagement Worm Gear with Multiple Worm-wheel Meshing

To solve the problem for lacking a special mechanical transmission that could provide multiple outputs with high transmission efficiency and good lubrication in the modern industrial, a novel worm gear, named end face engagement worm gear, with multiple worm-wheel meshing is proposed for the first time. The essential parameters for the worm gear are optimized to enhance lubrication and meshing properties. Moreover, analysis of variance(ANOVA) is applied to determine the optimum levels and to determine the influence of parameters. The ANOVA results show that the novel end face engagement worm gear with multiple worm wheels provides high lubrication(the lubrication angle is more than 89°) and meshing performance(the induce normal curvature is less than 0.0002 mm^(-1)). The interaction between center distance and roller slant distance most strongly influences the lubrication angle(contributed 51.6%), followed by the parameters of center distance(contributed 25.0%), roller slant distance(contributed 16.4%), tooth angle of gear, gear ratio, and roller radius. In addition, roller radius most strongly influences the induced normal curvature(contributed 39.4%), followed by roller slant distance(contributed 15.2%), tooth angle of the gear(contributed 9.0%), center distance, and gear ratio. The proposed worm gear helps to enrich the no-backlash high precision worm drive and the optimal design method can provide a useful reference on performance improvement of other worm gear.

Research on cutting vibration characteristics of face-milling involute gear

Traditional machining methods, such as gear hobbing, gear shaping and gear milling, etc, are commonly used for cutting machining of gear tooth profile, which cannot meet huge machining demand of gears to a certain extent. This article proposes to utilize a face-milling machining method in involute gear machining, which can be used to reduce production cost effectively. Cutting vibration generated during cutting machining has a direct effect on the machining accuracy and machined surface quality of workpiece. Therefore, it is desiderated to perform in-depth research regarding this issue. ADAMS software was used to establish a rigid-flexible coupling virtual prototyping model of face-milling gear milling system and a cutting vibration system model. Cutting vibration analysis was performed for face-milling gear by adopting quick sine frequency sweep method, so that the frequency response characteristics of workpiece in three directions X, Y and Z and space were acquired. The research results will provide reference and theoretical foundation for actual application of face-milling gear machining technology.

Mathematical Model and Machining Method for Spiral Flute Rake Faces of Hourglass Worm Gear Hob

To improve the cutting performance of an hourglass worm gear hob and the accuracy of the resulting worm gear,the rake angles of the teeth on the pitch circle should be reduced.A method of forming the spiral flutes by using a variable transmission ratio was developed.This method ensures that the rake angles on the indexing torus of each tooth are approximately 0°.Based on the gear meshing theory and the hourglass worm forming method,the discretization mathematical model of the rake face of a planar double enveloping worm gear hob was established by using cylindrical generating surface,and the feed parameters for machining the rake face for a variable transmission ratio were obtained.The spiral flute was simulated and the hob was machined on a four axis CNC milling machine.A contourgraph was used to measure the rake angle.The measurement results showed that the proposed method can reduce the absolute value of the rake angle on both sides of the cutting teeth,which can be used for machining the spiral flute rake face of an hourglass worm gear hob.

面齿轮展成磨削表面残余应力优化方法

面齿轮展成磨削表面残余应力优化是一个复杂的非线性问题,传统的优化算法无法实现高效率和高精度的求解。因此,文章提出了以齿面磨削实验数据为驱动的面齿轮表面残余应力智能优化方法。通过设计系列实验获取齿面残余应力数据集,建立以基础数据为驱动的响应曲面模型,实现了以齿面残余应力和磨削效率为优化目标的智能粒子群多目标优化,解决了面齿轮表面残余应力的优化问题。实验表明该方法的相对误差介于0.89%~1.61%,证明了面齿轮展成磨削表面残余应力优化方法的有效性。分析发现:齿面残余压应力与磨削深度和工件速度呈正相关,与砂轮速度和砂轮分度角呈负相关。从敏感性角度分析,齿面残余应力对磨削深度的敏感性最大,其次是砂轮分度角,而齿面残余应力对砂轮速度和工件速度的敏感性相对较小。

对置端曲面齿轮柱塞泵动态特性仿真研究

为了研究对置端曲面齿轮柱塞泵参数对泵动态特性的影响,根据端曲面齿轮柱塞泵工作原理,推导柱塞运动方程。利用Adams与AMESim软件建立对置端曲面齿轮柱塞泵联合仿真模型,通过联合仿真得到不同转速与偏心率下的柱塞泵出口流量与压力的相应曲线。结果表明:转速增大,泵出口流量与压力增大,脉动幅值与脉动频率增大;偏心率增加,泵出口流量与压力增大,脉动幅值增大,脉动频率不变。

格里森CONIFACE面齿轮磨齿加工原理与误差分析

研究并给出格里森最新的CONIFACE面齿轮磨齿加工原理。推导砂轮刀具的形状和齿面方程,基于齿轮啮合原理获得磨削后的面齿轮的齿面方程;研究分析该方法加工的面齿轮齿面与理论齿面的齿面误差及误差的影响规律;结果表明,采用该方法加工获得的面齿轮齿厚较NASA报告中提供的阿帕奇直升机面齿轮齿厚要薄,加工误差在齿宽中点处最小,并逐渐向两端增大,类似于圆柱齿轮鼓形修形后的效果,通过改变砂轮刀具的锥角和砂轮半径的值可调控鼓形量误差的大小。

面齿轮车齿加工研究与试验验证

为了实现面齿轮的高精度、高效率加工,研究面齿轮的车齿加工技术。分析面齿轮车齿加工原理,建立刀具数学模型,根据车齿展成原理推导面齿轮的齿面及齿根过渡曲面方程。以配对渐开线圆柱齿轮共轭的面齿轮齿面作为基准齿面,构建车齿齿面的偏差齿面,分析不同刀具螺旋角、齿数和前角对车齿齿面的影响规律。使用YK2260MC数控车齿机床进行车齿加工,使用格里森650GMS齿轮检测中心,进行齿面误差检测。结果表明:左侧齿面和右侧齿面的误差最大分别为14.7、14.1μm,验证了所提车齿加工数学模型的正确性,为提高面齿轮的加工精度和效率,进一步改进面齿轮车齿工艺提供了参考。

航空非正交偏置面齿轮分汇流系统非线性动力学

在面齿轮传动系统研究领域,研究对象多为单级面齿轮副,针对面齿轮分汇流传动系统动态特性的研究内容相对较少.聚焦航空非正交偏置面齿轮分汇流系统的非线性动力学特性,建立轴承滚动体变形、齿侧间隙以及综合传递误差的数学模型,推导出包含轴承在内的非正交偏置面齿轮传动多自由度耦合弯扭组合动力学模型.利用数值方法求解航空非正交偏置面齿轮分汇流系统的振动微分方程,结合时域图、频域图、相图、Poincaré映射、李雅普诺夫指数以及分岔图研究复杂系统非线性动态特性.研究了激励频率和啮合阻尼比变化对分流级与汇流级齿轮副之间啮合线位移的影响,结果表明:系统分流级与汇流级在特定参数下表现出不同的非线性特性,随激励频率增大,分流级出现单周期、多周期以及混沌现象,而汇流级无混沌现象产生;随啮合阻尼比增大,分流级状态变化近似于逆倍周期分岔过程,而汇流级在较小的阻尼比也可能保持周期运动状态;合理的激励频率和啮合阻尼比能使得系统跳出混沌并保持稳定.

Effects of Comprehensive Eccentricity of Involute Cam on Gear Profile Deviations

The manufacturing accuracy of ultra-precision master gears signifies the technological capability of the ultra-precision gear.Currently,there is little report about the manufacturing technologies of ultra-precision master gears at home and aboard.In order to meet the requirement of grinding ultra precision master gear,the gear grinder with flat-faced wheel Y7125 is chosen as the object machine tool and the geometric model of its precision generating part,the involute cam,is established.According to the structure of the involute cam,the effective working section and its adjustable range of the cam are determined,and the mathematical expressions of the effects of comprehensive eccentricity of the involute cam on gear profile deviations are derived.According to the primary harmonic trends of the deviation curve,it is shown that gear profile form and slope deviations in different work generating sections of the involute cam are different which the latter changes with the cam eccentricity obviously.Then,the issues of extreme values and methods of error compensation are studied and the conclusion that large adjustable range is benefit to search the optimal involute-cam section which is responding to the minimum gear profile deviations is obtained.A group of examples are calculated by choosing master gears with d=120 mm and m=2-6 mm and an involute cam with base diameter djcam =117 mm.And it is found that the maximum gear profile deviation counts for no more than 5% of the cam eccentricity after error compensation.A gear-grinding experiment on the master gear with m=2 mm is conducted by choosing different sections of the involute cam and the differences of gear profile deviations then the existence of the cam eccentricity are verified.The research discloses the rule of gear profile deviations caused by the comprehensive eccentricity of the involute cam and provides the theoretical guidance and the processing methods for grinding profile of the ultra precision master gear.

可展直纹面面齿轮传动的承载接触分析

为了研究可展直纹面面齿轮的承载接触特性,从而说明其与传统齿面的差异,建立了正交直齿面齿轮的可展直纹面表达式,因其相对传统齿面的偏差为微观量,为满足局部共轭条件,对该直纹面进行了双向修形,并令其与标准渐开线圆柱齿轮啮合;基于齿面接触分析和有限元承载接触分析,对比研究了两种传动比的修形直纹面和传统齿面的主曲率、几何(空载)接触特性、承载接触特性,结果表明:传动比较大时该直纹面与传统齿面具有几乎相同的几何特征与承载特性,传动比较小时边缘接触使得接触和弯曲应力大幅增加。因此,传动比较大时可展直纹面可替代传统齿面,提高其可加工性;将所提有限元法获得的传统齿面结果与文献实验结果进行了对比,结果表明:齿面接触应力、面齿轮齿根弯曲应力、圆柱齿轮齿根弯曲应力误差率分别为2.17%、12.33%、3.97%,满足计算精度要求,证明了所提计算方法的可靠性。

合成气压缩机机组轴向位移负增长原因分析与处理

从合成气压缩机机组运行趋势、鼓形齿式联轴器结构特点、检修过程质量控制、汽轮机机组热膨胀特性等方面,分析鼓形齿式联轴器安装问题造成汽轮机轴向位移负增长的原因,制定相应处理措施,并修订完善检修作业指导书。