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.

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.

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.

Mathematical Model and Geometrical Model of Double Pitch ZN-type Worm Gear Set Based on Generation Mechanism

The current researches on the tooth surface mathematical equations and the theory of gearing mainly pay attention to the ordinary type worm gear set（e.g., ZN, ZA, or ZK）. The research of forming mechanism and three-dimensional modeling method for the double pitch worm gear set is not enough. So there are some difficulties in mathematical model deducing and geometry modeling of double pitch ZN-type worm gear set based on generation mechanism. In order to establish the mathematical model and the precise geometric model of double pitch ZN-type worm gear set, the structural characteristics and generation mechanism of the double pitch ZN-type worm gear set are investigated. Mathematical model of the ZN-type worm gear set is derived based on its generation mechanism and the theory of gearing. According to the mathematical model of the worm gear set which has been developed, a geometry modeling method of the double pitch ZN-type worm and worm gear is presented. Furthermore, a geometrical precision calculate method is proposed to evaluate the geometrical quality of the double pitch worm gear set. As a result, the maximum error is less than 6′10–4 mm in magnitude, thus the model of the double pitch ZN-type worm gear set is available to meet the requirements of finite element analysis and engineering application. The derived mathematical model and the proposed geometrical modeling method are helpful to guiding the design, manufacture and contact analysis of the worm gear set.

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.

Temperature Field Simulation and Experimental Study of Anti‑backlash Single‑Roller Enveloping Hourglass Worm Gear

In gear transmission,temperature rise has a non-negligible impact on the accuracy,noise and transmission efficiency.However,there is no relevant research on the temperature rise of the anti-backlash single-roller enveloping hourglass worm(ASEHW)gear.To solve this problem,based on tribology principle and Hertz contact theory,the thermal power calculation method of the ASEHW gear was proposed for the first time and thermal analysis was carried out by Ansys software.The bulk temperature of the ASEHW gear under four different rotating speed(300 r/min,600 r/min,900 r/min,1200 r/min)is calculated.The main factors causing temperature rise of the ASEHW gear are analyzed theoretically.Meanwhile,an experimental study is performed to verify the simulation results and validate the theory methods.The theory presented in this paper provides a solution for the thermal power calculation of ASEHW gear.This research provides a theoretical basis for further optimization of ASEHW gear.

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.

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.

Parametric 3D Modeling of Worm and Worm Gear Based on AutoCAD

Worm and worm gear are modeled under development environment in AutoCAD based on the principle of ordinary cylindrical worm drive. The drawing commands available in AutoCAD are used to develop worm blank and cutter models. The solid models of worm and worm gear are obtained through the use of the commands, move, rotate and subtract, to simulate the generating cutting movement on the gear cutting machine. Autolisp language is utilized in programming for parametric modeling of worm and worm gear. The developed program can automatically draw worm and worm gear when users load the wlwg program, input the modulus and the number of threads, handedness, and other parameters. The operation is simple and accurate, providing potentials to speed up product design process and improve efficiency.

DIRECT DIGITAL DESIGN AND SIMULATION OF MESHING IN WORM-GEAR DRIVE

A direct digital design method （DDDM） of worm-gear drive is proposed. It is directly based on the simulation of manufacturing process and completely different from the conventional modeling method. The loaded tooth contact analysis （LTCA） method is analyzed, in which the advanced surface to surface searching technique is included. The influence of misalignment errors and contact deformations on contact zone and transmission error （TE） is discussed. Combined modification approach on worm tooth surface is presented. By means of DDDM and LTCA, it is very conven- ient to verify the effect of worm-gear drive＇s modification approach. The analysis results show that, the modification in profile direction reduces the sensitivity of worm-gear drive to misalignment errors and the modification in longitudinal direction decreases the TE. Thus the optimization design of worm-gear drive can be achieved prior to the actual manufacturing process.

Contact analysis and load distribution of double-envelop hourglass worm gearing affected by errors and load

An approach for the contact analysis and load distribution of double-envelop hourglass worm gearing is presented, which is based on a 3-D elastic contact finite element method (FEM) model that accommodates the influence of errors and load. As compared with existing tooth contact analysis model that assumes rigidity for the contacting surfaces, the proposed model provides a more realistic analysis on the contact patterns, the distribution of contact load and transmission errors. It is also capable of exploring the influence of different errors on meshing performances, the contact deformation, the shift of the contact zone and load share among the meshing tooth-pairs under different load.

A New Manufacturing Method for Hourglass Worm Gear Hob Based on a Semi⁃automatic CAD

The top relief surfaces of an hourglass worm gear hob are ground manually in the traditional manufacturing process,which cannot ensure the width of the land surfaces of the hob.Moreover,each geometric feature of the hob has been produced through different manufacturing techniques and machine tools,which results in low efficiency.To solve this problem,we propose a semi-automatic computer aided design(CAD)method for hobs.The point clouds of each feature surface of a hob are calculated by combing mathematical equations of the top relief surfaces built by the proposed method with other existing equations of hob surfaces.According to the point clouds,the method can achieve the automatic modeling for the hob in three-dimensional(3D)software by classifying and extracting the parameter information of the feature-hierarchical knowledge of the hob.Based on the generated 3D model,the entire surfaces of the hob can be manufactured on a four-axis computer numerical control(CNC)milling machine through only twice clamping.Verification of the width of the land surface of the hob manufactured by semi-automatic CAD method on a measuring projector proved the precision of the designed width can be ensured.The edge of the contact area on the worm wheel in a meshing experiment is clear and distinct,which means the worm gear drive is meshed well and the hob manufactured by the proposed method has improved machinability.The method simplifies the processing technique,and improves the design efficiency and production accuracy.

YK7232——GEAR GRINDING MACHINE WITH WORM GRINDING WHEEL

The machine is used for precisiongrinding of hardened cylindricalgears with medium module inbatches for the industries ofaircraft,automobile,machine tool,gear box and various transmissiondevices.

STUDY ON CONTROLLABLE MISMAT－CHED ENGAGEMENT OF CONE－GEN－ERATED CYLINDRIC WORM GEARING

Controllable modification of cone-generated cylindric worm gearing has been carriedout. The tooth contact state of modified gearing can be controlled by selecting the positions of con-tact points of worm surfaee and the correction amount of curvature. The modification machiningcan be conveniently implemented by changing the geometrical sizes and setting parameters of grind-ing wheel. Therefore the research has better scientific basis and practical value.

LOAD SHARING AND CONTACT OF HOURGLASS WORM GEARING

Based on solid modeling, the geometry and the FE model of the hourglass worm gearing are established. By the hybrid method of FEM and penalty function, the load sharing among tooth paris and the stress of contact teeth are calculated, the contact zones and the distribution of the contact pressure are investigated. The variation of the contact states with the load is investigated by comparision of its contact patterns under different loads.

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。

蜗杆-斜齿轮传动齿面啮合干涉分析

蜗杆-斜齿轮传动具有传动比大、传动平稳等优点,广泛应用于各种小型交错轴传动。与蜗杆完全共轭的理论斜齿轮与常规的标准斜齿轮存在齿形差异,因此蜗杆和标准斜齿轮传动存在齿面间的啮合干涉,会影响传动性能。基于螺旋面圆柱蜗杆与斜齿轮的双参数包络成形原理,建立了阿基米德蜗杆和齿槽法向直廓蜗杆与斜齿轮的啮合方程,推导了理论共轭斜齿轮齿面,并与实际标准斜齿轮齿面比较,分析了传动过程中齿面接触干涉区域和干涉量。分析结果表明,蜗杆头数和节圆半径对蜗杆齿轮传动的啮合干涉有影响,增加蜗杆头数、减小蜗杆节圆半径都会使干涉量增加;在相同的蜗杆设计参数条件下,齿槽法向直廓蜗杆的干涉量要大于阿基米德蜗杆,以上结论为蜗杆斜齿轮传动的设计提供了参考依据。

高阶变性Pascal蜗线齿轮生成机制分析

为满足多样性变速传动的设计要求,文章在研究Pascal蜗线非圆节曲线的基础上,通过引入高阶和变性原理,建立了高阶变性Pascal蜗线型非圆齿轮节曲线数学模型及其凹凸性判别公式。为分析高阶变性Pascal蜗线型非圆齿轮传动特性,利用MATLAB编写可视化设计分析平台,对影响高阶变性Pascal蜗线型非圆齿轮形状和传动特性的因素进行分析,为后续高阶变性Pascal蜗线型非圆齿轮的设计及应用提供了便捷的设计参考;将Pascal蜗线非圆齿轮驱动的曲柄滑块式压力机与对心曲柄滑块式压力机进行对比分析,验证了Pascal蜗线型非圆齿轮的优势和在实际应用中的可行性。

巴斯噶蜗线齿轮-曲柄滑块式引纬机构设计

为了优化引纬机构性能,在现有引纬机构的基础上进行了创新研究,提出了一种巴斯噶蜗线齿轮-曲柄滑块组合传动的新型引纬机构。为便于分析新型引纬机构的运动特性,基于数值分析和几何图形建立了该机构的运动学数学模型,并利用MatLab建立了该引纬机构的可视化设计分析平台。为分析各设计参数对该引纬机构的运动特性的影响,以剑带加速度为优化目标,利用正交试验优化方法对该机构进行优化分析,得出展长与发生圆直径比值、连杆长度与曲柄长度比值和传剑轮半径这3个参数对引纬运动规律有较大影响;变性系数和丝杠螺距则影响不大。研究结果可为全面研究引纬机构运动特性提供参考意见。

ZC1蜗杆齿廓测量测头对准误差修正

测头对准误差对齿轮测量中心ZC蜗杆齿廓偏差测量结果的影响较大,需要建立测头对准误差修正方法。基于ZC1蜗杆齿面方程,建立了蜗杆轴向齿廓测量误差模型,修正得到轴截面上齿廓测量点的轴向坐标,再依据精度标准评定得到蜗杆齿廓偏差,并分析了蜗杆的不同头数、模数和分度圆直径对蜗杆轴向齿廓测量误差的影响规律。在齿轮测量中心上开展了蜗杆轴截面齿廓测量实验,测头对准误差对齿廓形状偏差的影响较小;测头对准误差修正前后齿廓测量总偏差的最大差异由1.2μm降为0.2μm;齿廓形状测量偏差的最大差异由0.5μm降为0.3μm;齿廓倾斜测量偏差的最大差异由2.5μm降为0.4μm。该方法可有效减小齿轮测量中心测头对准误差对蜗杆轴截面齿廓偏差测量的影响。