Although a significant amount of research on robot joint reducer was conducted, there are few systematic investigations on a novel joint reducer adopting inner worm-gear plane enveloping drum worm drive. To satisfy the development of modular robot joint, the primary objective of this paper was to systematically investigate the drum worm drive adopted in the novel joint reducer with integrated structure of drive, transmission, and support in the following aspects: meshing theory, design, analysis, and manufacture. According to the gear meshing theory, mechanical design method, classical mechanics, finite element method, and machining principle of virtual center distance, the systematic investigations around the drum worm pair applied in the novel joint reducer were conducted including the macro and micro meshing theory, structure design, mechanical and contact properties analyses, and manufacturing method. The novel joint reducer’s integrated structure was designed, and the drum worm pair’s mechanical and contact properties analyses were conducted, which showed: (1) the worm’s bending stress and deflection, worm-gear teeth’s shear stress and bending stress as well as the maximum contact stresses were all below their corresponding allowable values; (2) the maximum contact stresses appeared at the engage-in position of the worm pair opposing to the engaging-out position where the largest contact areas appeared. Then the manufacturing of drum worm’s spiral tooth was conducted via the modified 4-axis linkage CNC grinder according to the conjugate motion. Finally the novel joint reducer’s industrial prototype was assembled. The novel joint reducer with integrated structure of drive, transmission and support was designed and manufactured for the first time. The flowchart of design and manufacture of the reducer’s drum worm pair in this process was formulated, which provides a new insight on the research of joint reducers as well as other fields.

This paper proposes a single-roller enveloping hourglass worm gear design and verifies its advantages compared to the existing double-roller worm gear system and the conventional worm gear set. Our hypothesis is that the single-roller worm gear with appropriate configurations and parametric values can eliminate the backlash in mating gear transmission while maintaining advantages of the double-roller worm gears. Also, the self rotation of the rollers when they are in the worm tooth space (TS) will help the gear system to avoid jamming and gear tooth scuffing/seizing problems caused by zero backlash and thermal expansion. In order to test that hypothesis, a mathematical model for the single-roller enveloping hourglass worm gear is developed, which includes a gear engagement equation and a tooth profile equation. Using that model, a parametric study is conducted to inspect the influences of center distance, roller radius, transmission ratio, and the radius of base circle on the worm gear meshing characteristics. It is found that the most effective way in eliminating the backlash is to adjust the roller radius and the radius of base circle. Finally, a single-roller enveloping hourglass worm gear set is manufactured and scanned to generate a 3D computer model. That model is compared with a theoretical model calculated from the developed mathematical model. Comparison results show that both models match very well, which verifies the accuracy of the developed mathematical model and our initial hypothesis that it is possible to achieve transmissions with zero backlash by adjusting the design parameters.

为了分析关键参数对滚子包络内啮合蜗杆传动接触与润滑性能的影响,构建了该新型蜗杆传动的数学模型,通过啮合方程构建了该传动的润滑角与诱导法曲率方程,利用数值计算方法分析了中心距、传动比、蜗轮偏转角、滚子半径等关键参数对蜗杆传动润滑与接触性能的影响。分析研究得知,在这些关键参数中,蜗轮偏转角对滚子包络内啮合蜗杆传动的接触性能与润滑性能有较大的影响,建议蜗轮偏转角取值在0°～40°为最佳。选取了相应参数进行三维建模,验证了分析参数的有效性。该研究为滚子包络内啮合蜗杆传动的进一步研究提供了参考。

变齿厚内齿轮鼓形蜗杆传动是一种新型蜗杆传动,它由变齿厚内齿轮和利用包络形成的鼓形蜗杆两部分组成.它具有体积小、重量轻、结构紧凑以及大传动比等特点,在机器人智能关节领域有着广阔的应用前景.蜗杆传动在工作时会产生大量的热,同时电机置于蜗杆内部也会产生大量的热,使蜗轮蜗杆发生变形,产生热应力.为了掌握内齿轮包络鼓形蜗杆传动副的热应力分布及其热变形情况,探讨温度对最大应力的影响,做了以下研究.首先,利用微分几何与啮合理论通过Creo建立齿面数学模型;其次,将模型导入AnsysWorkbench中对其进行热分析和热力学分析;最后,利用参数化设计的方法,分析出在特定结构载荷的作用下,温度对蜗轮蜗杆的最大等效应力的影响,并得出最大应力与温度变化的关系曲线.

The drum-worm transmission device was designed as a robot reducer applied to the robot joint, which benefits the domestic localization of robot reducer. Surfaces of the beveloid internal gear tooth were used as the tool surfaces. By analyzing the internal meshing motion of the drum-worm pair, 6 frames were established. Relationships between the worm-wheel’s rotation angle, the worm’s rotation angle and working angle were determined by the auxiliary frame and the working frame on the internal gear. According to meshing principles, equations of the drum-worm pair’s meshing, second limit curve and first limit curve were established and then drawn by MATLAB R2013b. According to parameters of the U10PLUS KV170 motor, design parameters of the drum-worm transmission device were determined. Spirals of the worm-tooth’s surfaces were drawn by MATLAB to output ibl files, and then 3D-models of the drum-worm transmission device were drawn by Creo 2.0. The assemble of the internal gear and the worm in the Creo simulation environment without interference-fit was realized by adjusting the relative axial position of the beveloid internal gear with symmetrical wedge teeth. Comparing with the 220 mm-center-distance toroidal worm pair with same design parameters, the center distance of the drum-worm pair was reduced to 100 mm, which indicated that the drum-worm pair was more compact. According to distributions of the drum-worm pair’s contact lines on both surfaces of a tooth, the internal gear’s width was reduced from the 110 mm design-width to the 75 mm working width. Analyzing relative positions between the worm pair’s first limit curve and tooth-root lines, the non-undercutting was determined by the first curve distributed inside the worm’s tooth-root. Combined with traditional design methods, the beveloid internal gear plane enveloping external-rotor drum-worm transmission device with an integrated structure of drive, transmission and support was designed. In terms of driving, the motor was installed inside the worm to realize the integration of the worm and the motor. In terms of transmission, the relative axial position of the internal gear was adjusted to realize the worm pair’s backlash adjustment and wear compensation. In terms of support, the support shaft was used for positioning and installation to simplify the device structure without cabinet installation. Symmetrical wedge teeth of the internal gear benefited installation and adjustment of the worm pair to realize the backlash adjustment and the wear compensation as well as the improvement of utilization ratio of the worm pair. Designing internal gear according to working width benefited the reduction of manufacture cost of the internal gear. Rationalities of the meshing transmission were verified by analyzing spacial positions of the worm pair’s contact lines, second limit curve and first limit curve as well as the worm’s tooth-root lines. The design scheme of an integrated structure of drive, transmission and support applied to the robot joint was proposed, and the design of the beveloid internal gear plane enveloping external-rotor drum-worm transmission device was realized.

变齿厚内齿轮包络鼓形蜗杆传动是一种新型蜗杆传动,由变齿厚内齿轮及其包络形成的鼓形蜗杆所组成.运用零间隙法分析计算在误差情况下该传动副接触点的偏移量和误差影响矩阵,得到了误差对该传动副接触点的影响规律.结果表明:单因子误差下,母平面倾角与轴间角误差、喉径系数与基圆半径误差、中心距与蜗杆轴向位移误差、蜗轮轴向位移误差的影响对接触线的影响依次减小.

为了研究关键设计参数对平面包络内啮合蜗杆传动接触性能及承载能力的影响。基于齿轮啮合原理,构建平面包络内啮合蜗杆传动的空间齿面接触线方程,利用数值计算方法求得空间齿面接触线,并将其映射到蜗轮齿面,通过分析中心距、传动比、母平面倾角、蜗轮回转轴倾角、蜗轮转角、蜗杆分度圆系数、主基圆系数等不同参数对蜗杆齿面接触区域的分布情况,找出合理的设计参数范围,此外,根据初步分析结果,选取一组较为合理参数生成了平面包络内啮合蜗杆传动的三维模型。研究表明,传动比、母平面倾角、蜗轮转角对平面包络内啮合蜗杆传动的接触区域有较大影响,母平面倾角在18°～36°、蜗轮回转中心轴倾角在30°～54°、蜗轮转角在90°～138°之间取值时,平面包络内啮合蜗杆传动的具有较好的接触区域。研究结果为平面包络内啮合蜗杆传动的后续研究奠定了理论基础。

提出一种新型蜗杆传动——滚子包络端面啮合蜗杆传动.首先分析滚子包络端面啮合蜗杆传动的工作原理和蜗杆齿面成形原理,建立了滚子包络端面啮合蜗杆传动的数学模型;然后利用建立的数学模型推导啮合方程、接触线、齿面方程、诱导法曲率、润滑角、相对卷吸速度和自转角公式;最后讨论滚子包络端面啮合蜗杆传动的啮合特性.分析表明,滚子包络端面啮合蜗杆传动具有滚动接触特性,摩擦磨损小,发热小,寿命长的优点.

In order to improve the machining efficiency of non-standard trapezoidal internal thread of high-temperature alloy Monel K50 material, designed a kind of trapezoidal internal threading insert with strong targeting, used UG software establish 3D model of the insert, Vericut simulation checked the correctness of the threading size and shape, AdvantEdge simulation checked the cutting performance of different cutting tool materials, and finally obtained a non-standard trapezoidal internal threading insert with various excellent performance.

In order to obtain the end face engagement worm gear (hereinafter called as EWG),which has the features of small volume,rational structure and large bearing capacity,by using the finite element and elasticity theory,the three-dimensional finite element model of EWG is set up.Based on the theory of dynamics and modal analysis,the modal parameters for natural frequency and main vibration mode of EWG are obtained.At last,based on the response surface method of WORKBENCH,taking the first natural frequency and volume as optimization objective,the rational compact structure and large bear capacity of EWG is obtained by multidimensional optimization design.The analysis results show that the volume of the worm reduced by 15.5％,which guarantee the dynamic property.The results provide basis for modal test,transient analysis and process and manufacturing.

Abstract:In order to obtain the dynamic characteristics of the end face engagement worm gear,the relationship of carrying capacity and deformation between different structure types of worm was analyzed,and the scientific analysis and demonstration were made.The Dynamic analysis model of worm was set up by using the finite element method,and transient dynamic analysis of meshing moment was analyzed.At first,by transient dynamics analysis which based on the dynamic model,the contact stress,equivalent effective stress and Total deformation of the end face engagement worm gear were obtained,respectively.Secondly,the dynamic characteristics of the end face engagement worm gear were analyzed theoretically and compared.The transient dynamic performance and deformation were analyzed and compared,respectively between the end face engagement worm gear and anti-backlash double-roller enveloping hourglass worm gearing,and between the end face engagement worm gear and double roller end face meshing worm pair.The results showed that the worm gear are at least simultaneously engaged with eight pairs of teeth,and the yellow part can clearly see the maximum stress at the tooth top.Under the same condition,the contact stress of the end face of the engaging worm gear is reduced more than 33%,compared with the backlash double roller enveloping hourglass worm.The maximum equivalent stress of the end face engagement worm gear is only 22% of backlash double roller worm,equivalent stress of the end face of the worm have a clear relationship with selecting the location of spiral position.Compared with the double roller end face meshing worm pair,the end face meshing worm pair has strong anti-deformation ability. Transient analysis result of double roller end worm showed that when t=0.056 5 s the deformation of the worm is significant over time.This method provides a theoretical basis and engineering applications for the new worm reducer,and other applications in the field.

Aiming at the development trend of the robot's modular structure and the problem of industrial robot joint deceleration device,a beveloid internal gear enveloping external-rotor crown worm drive for industrial robot intelligent joint is put forward.A mathematic model for the worm drive is established according to the space meshing theory,in which the meshing equation,the contact helix line equation and the tooth surface equation of the worm drive is derived.Then the induced normal curvature,the lubrication angle and the relatively entrainment velocity of the worm drive is derived.On the basis of a numerous calculation,analysing the impact of the worm throat diameter coefficient,the inclination angle of generating plane and the radious of main basic circle on the meshing performance.

By using the differential geometry and meshing theory,the mathematical model of the tooth surface of drum-type worm gear enveloped by internal variable-tooth-thickness gear is established.Through finite element method,the load distribution under different conditions is analyzed,and the effect of the inclination angle δ along tooth width direction on the worm gear pair is discussed.The stress distribution along tooth surface and the load distribution among teeth are analyzed,and the finite element method is compared with the empirical strength formula method.The results show that the tooth surface stress is mainly distributed in the middle plane of the internal gear,and the maximum stress appears at the top of the internal gear teeth.The loads of the first two meshing teeth are higher than the rest two meshing teeth.In the rated load condition,the tooth load distribution is relatively uniform.

To research the lubrication performance of the conjugating tooth-pairs in anti-backlash endface meshing of planar enveloped toroidal worm in an operating cycle,a 3D mathematical model of the reconstructed contact line is obtained by utilizing meshing theory and altering the tool generatrix angle parameter.A corresponding elastohydrodynamic lubrication (EHL) model is also built according to the feature of the two-stage meshing worm gear to analyse the lubrication characteristics and the minimum film thickness distribution of the conjugating tooth meshing point in a working cycle.The research results show that the engaging-in section's minimum film thickness along the contact line is thicker than that of the engaging-out section,and that by referring to the distribution situation of the minimum film thickness and the film thickness ratio,this transmission is dominated by the partial EHL in a working cycle.Finally,through studying the relationship between the transmission parameters and the lubrication performance,it is found that the lubrication behavior can be effectively improved by properly increasing the worm's pitch circle diameter and planar inclination angle.

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.

The purpose of the study is to make the planar enveloping crown worm gearing transmission have better carrying capacity and good transmission performance.Through using the differential geometry and meshing theory,the envelop theory of the planar double-enveloping crown worm drive is established,and the entity model crown worm tooth profile is created in accordance with the crown worm helix,then the secondary development of the crown worm is adopted to have Boolean operation with this internal gear characteristics.Thus,the high precision double enveloping internal worm gear is solved.Compared with this planar enveloping crown worm,the resulted crown worm has number of advantages.It has a two-way contact with a large contact surface between the tooth surface,and is easy to form hydrodynamic oil film bearing capacity.It′s built in worm structure lays a good theoretical foundation for further research on robot intelligent joint.

According to Hertz contact theory, this paper derived the checking formula for contact strength of the circular-arc-tooth-trace cylindrical gear (C-gear) train. The contact strength calculation formula is particularly considering the effect of radius of tooth trace and position angle. The contrast analysis of contact strength between the C-gear, spur gear and helical gear was investigated by computer simulation. The results reveal that the C-gear may be better than spur gear and helical gear in the contact strength. Moreover, decreasing the ratio between radius of tooth trace and tooth width and increasing contact ratio can contribute to improving the contact strength of the C-gear. In this paper, the checking formula of contact strength and the research methods can provide basis for the design of this kind of gear transmission.

为了掌握平面齿内齿轮一次包络鼓形蜗杆传动副的齿面真实啮合状况,对其进行误差分析.建立含误差的传动副啮合几何学理论,构建传动副的三维精确实体模型,研究理想状态下传动副的齿面啮合情况,并重点分析中心距及倾角等各项误差值对传动副真实啮合状态的影响规律.研究结果表明:传动副在理想状态下有5对齿同时啮合,瞬时接触线为直线且沿齿高方向平行分布;中心距误差和蜗杆轴向位移误差为负值时比其为正值时对传动副有利;轴间角误差、倾角误差及基圆半径误差对平面齿内齿轮一次包络鼓形蜗杆传动副啮合状况的影响较大.

In order to realize smooth gait planning and stability control of a quadruped robot, a new controller algorithm based on CPG-ZMP (central pattern generator-zero moment point) is put forward in this paper. To generate smooth gait and shorten the adjusting time of the model oscillation system, a new CPG model controller and its gait switching strategy based on Wilson-Cowan model are presented in the paper. The control signals of knee-hip joints are obtained by the improved multi-DOF reduced order control theory. To realize stability control, the adaptive speed adjustment and gait switch are completed by the real-time computing of ZMP. Experiment results show that the quadruped robot's gaits are efficiently generated and the gait switch is smooth in the CPG control algorithm. Meanwhile, the stability of robot's movement is improved greatly with the CPG-ZMP algorithm. The algorithm in this paper has good practicability, which lays a foundation for the production of the robot prototype.

为高效加工出B114.66X1.5875-7h 15°/30°钛合金材料的外螺纹,通过研究,本文介绍一种特殊锯齿形螺纹刀片的设计方法和过程.通过分析,该方法能达到锯齿形螺纹零件加工工艺要求.具体做法是:采用UG建立刀片模型,用VERCUT验证加工螺纹形状合理性,再用DEFORM仿真加工验证刀具切削性能.