120吨电机车行走齿轮齿根强化装置设计含6张CAD图
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附录 中文翻译行星齿轮传动与圆柱齿廓几何设计摘要：这项工作,提出了这样一个概念初等齿轮传动齿廓的圆拄。球场半径取而代之的是它们之间的距离齿轮中心和齿根为中心的半径齿轮。基于坐标变换,三重矢量积微分几何，与理论共轭曲面,方程啮合导出。程式开发,以解决共轭曲面方程,并显示出扎实的造型建议初等行星齿轮传动。 关键词:行星齿轮系；几何设；圆计柱齿廓1引言减速器被广泛应用于各种应用的速度和扭矩转换词组。机制被称为行星机制,如果它包含至少一个刚性会员即需轮换另一轴1。例如，行星齿轮传动，弗格森喜程减速器,摆线传动行星机制。行星齿轮传动很紧凑。重量轻装置能生产高速还原以及高机械专程观望一个阶段。 它们广泛用于减速或传动装置。 摆线传动更为紧凑, 重量轻装置能生产高减速比行星齿轮传动以及高机械优势,设计阶段2。以上，它具有精度高,定位,所以这是一个具吸引力的候选人,在许多应用。 带动和齿轮的使用往往在初等行星齿轮传动。这项工作提供了一个概念初等行星齿轮传动齿廓的圆拄1。数字2是一个环形齿轮,其齿形是由齿轮齿构成的3个构件,其中包括构件第3A (鸟羽)成员及图3b (圆柱齿) ,其中有一多余的自由度。四段是一个曲柄。构件5B号(盘针)浮动结合国际民航组织3A和5A号(光碟片)。由于构件5B条有一个多余的自由度,构件5A及5B被视为构件5。这里的目的是为当前的几何设计这个亲初等构成行星齿轮传动。 几何共轭曲面主要关心的是在设计齿轮和发电轭啮合要素。利特温3研究的啮合齿轮空间,并生成共轭曲面。陈4和利特温5成功调查了表面几何空间共轭齿轮副。芳和蔡6提出了一个数学模型,对齿面几何圆弧螺旋锥齿轮。利特温及健7研究单包络环面蜗杆传动。闫刘8提出的几何设计和加工可变螺距导致螺钉啮合圆柱组成。后来,闫陈9推导公式的表面几何弧面凸轮啮合圆柱组成。汉森和丘吉尔10应用理论的信封一参数曲线确定曲率。goetz 11得出的理论信封为期家庭参数曲面。蔡黄12应用理论信封一家面两个独立参数的地确定亲辅导camoids翻译与球的追随者。colbourne 13提出了几何方法腾云驾雾的信封trochoids ,开展行星运动。林仔14研究几何轨迹产生的一个点在地球的行星锥齿轮 列车。一些应用摆线机械设计研究了pollitt15。布兰奇和杨16考察了加工公差的摆线驱动器。石田等17研究了牙齿负荷瘦身辋摆线齿轮。 最近,利特温,冯18用邸给出了几何产生的共轭曲面摆线齿轮。 本文运用理论信封一家面带参数的形式,以获取表面几何对拟议的初级行星齿轮系中的齿轮是圆柱齿。在下面,我们目前的拓扑结构,这个基本计划膳食齿轮火车踏。然后,坐标系统和坐标转换矩阵德termined ,方程啮合导出基于基本传动运动学,坐标转换, 三重向量乘积邸给出了几何,理论共轭曲面。最后,设计的例子来说明此方法的可行性。2拓扑结构1显示二00二年行星齿轮传动与齿圈。这个行星的机制,运作上是独一无二的原则,采用曲柄(四段),歪斜的鸟羽( 3构件) ,约轨道中心的输入轴由于偏心轴。在同一时间,小齿轮转动自己的中心,在相反的方向上的输入轴, 由于该接触齿圈(二段)。由此议案的鸟羽,是一个复合运动。这种摆动议案转为纯旋转运动的输出轴的等速万向节(盘边构件5B号)。为初等行星齿轮传动装置传送恒定角速度比,它采用一盘盘(构件5A )款机制作为输出轴。圆盘密码(构件5B号)的浮动结合鸟羽和盘盘。盘板,旋转方向相同的鸟羽,是输出.从经营的角度来看,之间的相对运动圆柱齿的齿轮和牙齿的齿圈可以代表乙 y在旋转的音高曲线的鸟羽的音高曲线的齿圈。 直接投资文化程度高低圆周之间的环形齿轮和小齿轮的成果切议案特制 一个或多个圆形球场。2( a )的拓扑结构,初等行星齿轮传动系列图。 1 . 它由五个成员组成:帧( 1人) ,齿圈(二段) ,小齿轮(行星齿轮, 构件3 ) ,曲柄(承运人,构件四) ,盘盘(构件5 ) . 关节之间架和齿圈,帧和曲柄 画框和盘板,齿轮和曲柄的回转件。环形齿轮和小齿轮事件是一个齿轮; 齿轮和圆盘钢板事件凸轮一双。如果运动的行星齿轮所需的输出轴行星齿轮可举例来说,它可耦合到另一轴(输出轴)的万向节。在这里,盘板输出的构件。为了设计的共轭曲面的初级行星齿轮传动, 这五个环节和六个联合机制是仿制动成三个环节和三个联合机制如图。2款( b ) 只有链接1 , 2 , 三是考虑,因为其他环节,不影响几何分析这个基本行星齿轮传动。3坐标系统 之前产生的曲面方程的齿圈建议初等行星齿轮火车, 坐标系统相应的行星机制应予以界定。3显示坐标系之间的相对运动而面貌一新的行星机制。4显示的坐标系中的圆柱齿。动产联系演出旋转轴平行,以恒定角速度的比例。固定统筹制度exyztf硬性连接到帧。方便的坐标变换,坐标系统exyztg连接到帧太。移动统筹制度exyzt2 , exyzt3 , exyztpi分别是硬性连接的环形齿轮,齿轮和均值圆柱齿廓。环形齿轮转动有关的Z2轴以恒定角速度。齿轮转动关于Z3的轴上。为方便协调跨之间形成的圆柱齿的齿轮,移动坐标系exyztpi隶属均值齿圆柱成立和角度铋是由关系昆明术和斧头。起源1和O2吻合和位于中心的齿圈。丝绸起源和O3是巧合和位于中心的鸟羽。原产维基巧合的是,位于中心的带状齿圆柱表面基地。xf轴平行轴与星光。方向轴的ZF , ZG的,的Z2 , Z3的, zpi都是垂直的纸张。角度/ 2 / 3的角位移的齿圈和齿轮,分别。积极/ 2 / 3是以顺时针方向与轴的Z2和Z3的轴线,分别。距离轴线旋转的齿圈与齿轮为E。距离中心的齿圈与中心环齿是R2中。距离中心的鸟羽及中心的圆柱齿是0427-7104。厚度的圆柱齿是汤匙 ,圆柱齿是一个圆的半径问题。4设计实例 当两个齿轮啮合的每一个瞬间,在某一个区间,其齿面可能会触及对方要么在一个点或沿一条曲线。大体来说,两齿面跟着直线联络,说是共轭。为避免干涉齿轮传动,方程啮合必须考虑使外壳表面R2中的家人圆柱齿概况决心与有效性。( 10 )和( 16 )一并考虑。该信封被称为共轭曲面的插齿。计算机程序开发,以解决方程和啮合面方程。 5和6显示的实体建模的齿圈和齿轮。环形齿轮产生的插齿。而齿轮是圆齿。5显示实体建模速比等于10时,共轭曲面的齿圈可以生成的插齿如果改变速比,偏心距e ,齿轮,齿圈尺寸,齿数齿轮和齿圈。因此,我们可以设计所需的速度比初级内部行星齿轮系中的行星齿轮与圆柱齿根。齿轮传动都非常紧凑。5结论 这项工作产生的曲面方程拟初等新型行星齿轮传动圆柱齿廓。我们使用三重矢量积微分几何处理方程啮合。当断面的齿根是圆的,为方便几何分析,球场半径代替齿轮半径即距离齿轮中心和齿中心。数学表达式的信封方程设计中的应用初等内部行星齿轮传动在其中。鸟羽是圆柱齿廓。 我们还制定了解决方案信封方程,可以设计所需的速度比内部初等行星齿轮传动两个实体造型前粘结剂列演示程序表面生成建议初等行星齿轮传动。参考文献1 Z. Levai, Structure and analysis of planetary gear trains, J. Mech. 3 (1968) 131148.2 D.W. Botsiber, Leo Kingston, Design and performance of cycloid speed reducer, Mach. Des. (June 28) (1956) 6569.3 F.L. Litvin, The synthesis of approximate meshing for spatial gears, J. Mech. 4 (1968) 187191.4 C.H. Chen, Boundary curves, singular solution, complementary conjugate surfaces, in: Proceedings of the 5thWorld Congress on Theory of Machines and Mechanisms, Montreal, Canada, 1979, pp. 14781481.5 F.L. Litvin, Theory of Gearing, NASA, Washington, DC, 1989.6 Z.H. Fong, C.B. Tsay, A study on the geometry and mechanisms of spiral gears, ASME Trans., J. Mech. Des. 113(1991) 346351.7 F.L. Litvin, V. Kin, Computerized simulation of meshing and bearing contact for single-enveloping worm-geardrives, ASME Trans., J. Mech. Des. 114 (1992) 313316.8 H.S. Yan, J.Y. Liu, Geometric design and machining of variable pitch lead screws with cylindrical meshing elements, ASME Trans., J. Mech. Des. 115 (4) (1993) 490495.9 H.S. Yan, H.H. Chen, Geometry design and machining of roller gear cams with cylindrical rollers, Mech. Mach.Theory 29 (6) (1994) 803812.10 D.R.S. Hanson, F.T. Churchill, Theory of envelope provided new cam design equation, Prod. Eng. (August 20)(1962) 4555. 附录2：外文原文 Geometry design of an elementary planetary gear trainwith cylindrical tooth-profilesValerii Kushner.Michael Storchak1 IntroductionSpeed reducers are used widely in various applications for speed and torque conversion pur-poses. A mechanism is termed a planetary mechanism if it contains at least one rigid member that isrequired to rotate about another axis 1. For examples, planetary gear trains, Ferguson Hi-Rangespeed reducers, and cycloid drives are planetary mechanisms. Planetary gear trains are compact,light-weight devices capable of producing high speed reduction as well as high mechanical ad-vantage in a single stage. They are widely used in speed reduction or transmission devices. Thecycloid drive is more compact, light-weight devices capable of producing high speed reductionthan planetary gear trains as well as high mechanical advantage in a single stage 2. Above, it hashigh precision pointing, so that it is an attractive candidate for many applications today.Spur and bevel gears are often used in elementary planetary gear trains. This work provides aconcept of elementary planetary gear trains such that the tooth-profiles of the pinion are cylin-drical, Fig. 1. Member 2 is a ring gear and its tooth-profile is generated by the pinion tooth.Members 3, including member 3a (pinion) and member 3b (cylindrical tooth) has one redundantdegree-of-freedom. Member 4 is a crank. Member 5b (disc pin) is floating connection with mem-bers 3a and 5a (disc plate). Since member 5b has one redundant degree-of-freedom, members 5aand 5b are treated as member 5. The purpose here is to present the geometric design of this pro-posed elementary planetary gear train.The geometry of conjugate surfaces is of major concern in designing the gears and generatingthe conjugate meshing elements. Litvin 3 studied the meshing of spatial gears and the generationof conjugate surfaces. Chen 4 and Litvin 5 successfully investigated the surface geometry ofspatial conjugate gear pairs. Fong and Tsay 6 proposed a mathematical model for the toothgeometry of circular-arc spiral bevel gears. Litvin and Kin 7 studied the single-enveloping wormgear drives. Yan and Liu 8 proposed the geometric design and machining of variable pitch leadscrews with cylindrical meshing elements. Later, Yan and Chen 9 derived equations for thesurface geometry of roller gear cams with cylindrical meshing elements. Hanson and Churchill 10applied the theory of envelope for one-parameter of curves to determine the curvatures of planarcams. Goetz 11 derived the theory of envelope for a two-parameter family of surfaces. Tsay andHwang 12 applied the theory of envelope for a family of surfaces with two independent pa-rameters to determine the profiles of camoids with translating spherical followers. Colbourne 13proposed a geometry method to find the envelopes of trochoids that performs a planetary motion.Lin and Tsai 14 studied the geometry of trajectories generated by a point on the planet of bevelplanetary gear trains. Some applications of the cycloid in machine design are studied by Pollitt15. Blanche and Yang 16 investigated the machining tolerances of the cycloid drives. Ishidaet al. 17 studied the tooth load of thin rim cycloidal gear. Recently, Litvin and Feng 18 used differential geometry to generate the conjugate surfaces of cycloidal gearing.This paper applies the theory of envelope for a family of surfaces with parameter form to derivethe surface geometry of the proposed elementary planetary gear trains in which the pinion is withcylindrical tooth. In what follows, we present the topological structure of this elementary plan-etary gear train first. Then, coordinate systems and coordinate transformation matrices are de-termined. And, equation of meshing is derived based on the fundamental gearing kinematics,coordinate transformation, triple vector product of differential geometry, and theory of conjugatesurfaces. Finally, design examples are presented to demonstrate the feasibility of this approach.2 Topological structureFig. 1 shows an elementary planetary gear train with a ring gear. This planetary mechanism,operating on a unique principle, employs a crank (member 4) to deffect the pinion (member 3) thatorbits about the center of the input shaft due to the eccentricity of the shaft. At the same time, thepinion rotates about its own center, in the opposite direction of the input shaft, due to theengagement with the ring gear (member 2). The resulting motion of the pinion is a compoundmotion. This wobble motion is converted to pure rotary motion of the output shaft by a constantvelocity joint (disc pin, member 5b). In order for the elementary planetary gear train to transmit aconstant angular velocity ratio, it adopts a disc plate (member 5a) mechanism as the output shaft.The disc pins (member 5b) are floating connection with the pinion and the disc plate. The discplate, rotating in the same direction as the pinion, is the output. From the operating viewpoint,the relative motion between the cylindrical teeth of the pinion and the teeth of the ring gear can berepresented by the rotation of the pitch curve of the pinion on the pitch curve of the ring gear. The difference in pitch circumference between the ring gear and the pinion results in a tangentialmotion with a magnitude of one or more circular pitches.Fig. 2(a) is the topological structure of the elementary planetary gear train shown in Fig. 1. Itconsists of five members: the frame (member 1), the ring gear (member 2), the pinion (planet gear,member 3), the crank (carrier, member 4), and the disc plate (member 5). The joints between theframe and the ring gear, the frame and the crank, the frame and the disc plate, and the pinion andthe crank are revolute pairs. The ring gear and the pinion are incident to a gear pair; the pinionand the disc plate are incident to a cam pair. In case the motion of the planet gear is the requiredoutput, the shaft of the planet gear can, for example, be coupled to another shaft (output shaft) byuniversal joints. Here, the disc plate is the output member.In order to design the conjugate surfaces of the elementary planetary gear train, this five-linkand six-joint mechanism is modeled kinematically into a three-link and three-joint mechanism asshown in Fig. 2(b). Only links 1, 2, and 3 are considered because the other links do not affect thegeometry analysis of this elementary planetary gear train.3 Coordinate systemsBefore deriving the surface equation of the ring gear of the proposed elementary planetary geartrain, coordinate systems corresponding to the planetary mechanism should be defined. Fig. 3 shows the coordinate systems based on the relative motion and the arrangement of theplanetary mechanism. Fig. 4 shows the coordinate system of the cylindrical tooth. The movablelinks perform rotation about parallel axes with a constant angular velocity ratio. The fixed co-ordinate system exyzTf is rigidly connected to the frame. For convenience of the coordinatetransformation, the fixed coordinate system exyzTg is connected to the frame, too. Moving co-ordinate systems exyzT2, exyzT3, and exyzTpi are rigidly connected to the ring gear, the pinion, andthe ith cylindrical tooth, respectively. The ring gear rotates about the z2-axis with a constantangular velocity. The pinion rotates about the z3-axis. For convenience the coordinate trans-formation between the cylindrical teeth of the pinion, a moving coordinate system exyzTpi attachedto the ith cylindrical tooth is set up and angle bi is comprised between yp and ypi axes. Origins of1and o2 are coincident and located at the center of the ring gear. Origins og and o3 are coincidentand located at the center of the pinion. Origin opi is coincident and located at the center of the ithcylindrical tooth base surface. Axis xf is parallel with axis xg. The directions of axes zf, zg, z2, z3,and zpi are all perpendicular to the paper. Angles /2 and /3 are the angular displacements of thering gear and the pinion, respectively. Positive /2 and /3 are measured clockwise with respect toaxis z2 and axis z3, respectively. The distance between the axes of rotation of the ring gear and thepinion is e. The distance between the center of the ring gear and the center of the ring-gear-tooth isr2. The distance between the center of the pinion and the center of the cylindrical tooth is r3. Thethickness of the cylindrical tooth is t. And, the cylindrical tooth is a circle of radius q.4 Design examplesWhen two gears are in mesh at every instant in a certain interval, their tooth surfaces may toucheach other either at a point or along a curve. Roughly speaking, two tooth surfaces moving withlinear contact are said to be conjugate. For avoiding interference in gear driving, the equation ofmeshing must be considered so that the envelope of surface R2 to the family of cylindrical tooth-profile is determined with Eqs. (10) and (16) considered simultaneously. The envelops are calledthe conjugate surfaces of the pinion tooth. A computer program is developed to solve theequation of meshing and the surface equations.Figs. 5 and 6 show the solid modeling of the ring gear and the pinion. The ring gear is generated by the pinion-teeth. And, the pinion is with cylindrical teeth. Fig. 5 shows the solid modeling forspeed ratio equal to 10. The conjugate surfaces of the ringgear can be generated by the pinion-teeth if we change the speed ratio, eccentric distance e, thepinion and ring gear dimensions, and the tooth numbers of pinion and ring gear. Therefore, wecan design required speed ratios of internal elementary planetary gear trains in which the planetgear is with cylindrical tooth. And, the gear trains are very compact.5 ConclusionsThis work derives the surface equation of a proposed novel elementary planetary gear trainswith cylindrical tooth-profiles. We use the triple vector product of differential geometry to dealwith the equation of meshing. When the cross-section of the tooth is round, for convenience ofgeometric analysis, the pitch radius is replaced by gear radius that is the distance between the gearcenter and the tooth center. The mathematical expressions of the envelope equations are appliedto design the internal elementary planetary gear trains in which the pinion
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