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 modem 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 ＇）. 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.

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%.

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.

Efficient and accurate worm grinding of spur face gears according to an advanced geometrical analysis and a closed-loop manufacturing process

Worm grinding has been applied to manufacture gears to pursue high accuracy and fine surface finish.When the worm used to grind face gears is manufactured with multi-axis computer numerical control(CNC)machining,the machining accuracy is usually improved by increasing the number of tool paths with more time cost.Differently,this work proposes a generated method to improve the efficiency by dressing the worm surface with only one path,and a closed-loop manufacturing process is applied to ensure the machining accuracy.According to an advanced geometric analysis,the worm surface is practically approximated as a swept surface generated by a planar curve.Meanwhile,this curve is applied as the profile of a dressing wheel,which is used to dress the worm surface.The practical machining is carried out in a CNC machine tool,which was originally used to grind helical gears.Finally,a closed-loop manufacturing process including machining,measurement,and modification is proposed to compensate the machining errors.The proposed method is validated with simulations and practical experiments.

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.

Complex geometric modeling and tooth contact analysis of a helical face gear pair with arc-tooth

A complex geometric modeling method of a helical face gear pair with arc-tooth generated by an arc-profile cutting(APC)disc is proposed,and its tooth contact characteristics are analyzed.Firstly,the spatial coordinate system of an APC face gear pair is established based on meshing theory.Combining the coordinate transformation matrix and the tooth profile of the cutter,the equations of the curve envelope of the APC face gear pair are obtained.Then the surface equations are solved to extract the point clouds data by programming in MATLAB,which contains the work surface and the fillet surface of the APC face gear pair.And the complex geometric model of the APC face gear pair is built by fitting its point clouds.At last,through the analysis of the tooth surface contact,the sensitivity of the APC face gear to the different types of mounting errors is obtained.The results show that the APC face gear pair is the most sensitive to mounting errors in the tooth thickness direction,and it should be strictly controlled in the actual application.

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.

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.

A precision generating hobbing method for face gear with assembly spherical hob

In order to improve the processing precision and shorten the hob manufacturing cycle of the face gear,a precision generating hobbing method for face gear with the assembly spherical hob is proposed.Firstly,the evolution of the cylindrical gear to spherical hob basic worm is analyzed,then the spherical hob basic worm is designed,thus the basic worm and spiral angle equation of spherical hob are obtained.Secondly,based on the design method of the existing hob,the development method of the assembly spherical hob is analyzed,the cutter tooth and the cutter substrate of the assembly hob are designed,and the whole assembly is finished.Thirdly,based on the need of face gear hobbing,a numerical control machine for gear hobbing is developed,and the equation of the face gear is obtained.Fourth,for reducing the face gear processing errors induced by equivalent installation errors,the error analysis model is established and the impacts of each error on the gear tooth surface are analyzed.Finally,the assembly spherical hob is manufactured and the gear hobbing test is completed.According to the measurement results,the processing parameters of face gear hobbing are modified,and the deviation of tooth surface is significantly reduced.

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.

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.

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.

Simulation Analysis on Quasistatic Characteristics of Multistage Face Gears with Double Crown Surfac

The multistage face gears are the core component of the planetary gear train,which is symmetrically meshed by multiple single-stage face gear and multiple cylindrical gears.However,it is difficult to synchronize the contact between face gears and cylindrical gear due to the tooth number differences.Thus,the interference problems between two stages and big stress concentration are obvious.The crown surface configuration technology and structure design were introduced to optimize the meshing condition.To improve the double crown design feasibility and meshing stability,it is necessary to establish a reasonable multistage face gears pair simulation model to evaluate various influence factors on the contact condition and quasi-static characteristics of multistage face gears structure.The relevant scatter plots are fitted by comparing the contact results with different crown quantities and friction coefficients to intuitively obtain the variation regularity of maximum deformation,maximum strain,maximum stress and maximum strain energy.The natural frequency and mode coefficient are also determined by modal analysis under these two conditions.All the above mentioned studies verified the contact conjugate properties of double crown surface configuration were suitable.The results can provide a foundation for structure optimization and transmission reliability of multistage face gears.

Effects of Temperature and Centrifugal Force on Fretting Wear of Contact Interface of Face Gear

Taking the typical face gear connection structure of the combined rotor as the research object,this paper studies the distribution rules of the contact state,contact stress and slip distance of the contact tooth surface of face gear under different centrifugal force and temperature conditions by using the finite element method,in order to improve the reliability of face gear connection structure.And the influence of centrifugal force and temperature on the maximum wear depth of the tooth surface is studied based on the fretting wear model proposed by McColl.Results show that:(1)The external diameter has an opening phenomenon on the contact surface of the face gear under the centrifugal effect,which reduces the load-bearing area;(2)The contact stress at the inner root of the face gear is the largest and the wear is the most serious;(3)The temperature field causes the contact surface to be thermally expanded,resulting in the large uneven deformation,and the tooth surface appears drum-shape;(4)The maximum contact stress and the maximum wear depth occur in the middle of the tooth root;(5)As the temperature increases,the maximum wear depth of the tooth surface increases significantly.Consequently,reducing temperature of the combined rotor plays an important role in effectively reducing the wear of the face gear and improving the connection life of face gear connection structure.

Study on the Technique of Double-faced Embroidery on Chinese Palace Fans

Double - faced iso - object embroidery is carried out byusing the uneven intercalated stitch crafts of the parallel- lines stitch as a main body, being accompanied by oth-er stitch crafts and miscellaneous stitches, done on thesame textile material. This paper deals with the flower -bird double - faced embroidery fan of the Qing Dynasty,from pattern design, stitching formation and techniqueof color arrangement, describes the possible way of mak-ing double - faced embroidery with iso - object effectboth in the front and in the back.

Dislocation stability in three-phase nanocomposites with imperfect interface

Interface imperfection can significantly affect the mechanical properties and failure mechanisms as well as the strength and toughness of nanocomposites. The elastic behavior of a screw dislocation in nanoscale coating with imperfect interface is studied in the three-phase composite cylinder model. The interface between inner nanoin- homogeneity and intermediate coating is assumed as perfectly bonded. The bonding between intermediate coating and outer matrix is considered to be imperfect with the assumption that interface imperfection is uniform, and a linear spring model is adopted to describe the weakness of imperfect interface. The explicit expression for image force acting on dislocation is obtained by means of a complex variable method. The analytic results indicate that inner interface effect and outer interface imperfection, simultaneously taken into account, would influence greatly image force, equilibrium position and stability of dislocation, and various critical parameters that would change dislocation stability. The weaker interface is a very strong trap for glide dislocation and, thus, a more effective barrier for slip transmission.

采用NSGA-Ⅱ算法的面齿轮副小轮拓扑修形多目标优化

为合理确定面齿轮副小轮的修形参数,设计了均由2段抛物线与1段直线组成的直齿小轮齿廓和齿向修形曲线,将由三次B样条拟合得到的修形曲面与理论齿面相叠加来构造拓扑修形齿面。采用带精英策略的快速非支配排序遗传算法(NSGA-Ⅱ),结合面齿轮副的几何接触分析(TCA)和承载接触分析(LTCA)技术,提出了以修形曲线参数为优化变量,使抛物线几何传动误差曲线两端对称、接触印痕限制在齿宽中部、承载传动误差波动幅值最小的小轮拓扑修形多目标优化设计方法,并编制了相应的Matlab程序。算例表明:优化修形参数后得到了对称的抛物线几何传动误差和位于大轮齿宽中部的接触印痕,并大幅度减小了承载传动误差波动,从而可有效降低安装误差敏感性和齿轮副的振动、噪声。

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。