DP31-250機(jī)械壓力機(jī)主機(jī)及傳動(dòng)系統(tǒng)設(shè)計(jì)
DP31-250機(jī)械壓力機(jī)主機(jī)及傳動(dòng)系統(tǒng)設(shè)計(jì),DP31-250機(jī)械壓力機(jī)主機(jī)及傳動(dòng)系統(tǒng)設(shè)計(jì),dp31,機(jī)械,壓力機(jī),主機(jī),傳動(dòng)系統(tǒng),設(shè)計(jì)
附錄１ 中文翻譯
行星齒輪傳動(dòng)與圓柱齒廓幾何設(shè)計(jì)
摘要：這項(xiàng)工作,提出了這樣一個(gè)概念初等齒輪傳動(dòng)齒廓的圓拄。球場(chǎng)半徑取而代之的是它們之間的距離齒輪中心和齒根為中心的半徑齒輪。基于坐標(biāo)變換,三重矢量積微分幾何，與理論共軛曲面,方程嚙合導(dǎo)出。程式開發(fā),以解決共軛曲面方程,并顯示出扎實(shí)的造型建議初等行星齒輪傳動(dòng)。
關(guān)鍵詞:行星齒輪系；幾何設(shè)；圓計(jì)柱齒廓
1引言
減速器被廣泛應(yīng)用于各種應(yīng)用的速度和扭矩轉(zhuǎn)換詞組。機(jī)制被稱為行星機(jī)制,如果它包含至少一個(gè)剛性會(huì)員即需輪換另一軸[1]。例如，行星齒輪傳動(dòng)，弗格森喜程減速器,擺線傳動(dòng)行星機(jī)制。行星齒輪傳動(dòng)很緊湊。重量輕裝置能生產(chǎn)高速還原以及高機(jī)械專程觀望一個(gè)階段。 它們廣泛用于減速或傳動(dòng)裝置。 擺線傳動(dòng)更為緊湊, 重量輕裝置能生產(chǎn)高減速比行星齒輪傳動(dòng)以及高機(jī)械優(yōu)勢(shì),設(shè)計(jì)階段[2]。以上，它具有精度高,定位,所以這是一個(gè)具吸引力的候選人,在許多應(yīng)用。
帶動(dòng)和齒輪的使用往往在初等行星齒輪傳動(dòng)。這項(xiàng)工作提供了一個(gè)概念初等行星齒輪傳動(dòng)齒廓的圓拄1。數(shù)字2是一個(gè)環(huán)形齒輪,其齒形是由齒輪齒構(gòu)成的3個(gè)構(gòu)件,其中包括構(gòu)件第3A (鳥羽)成員及圖3b (圓柱齒) ,其中有一多余的自由度。四段是一個(gè)曲柄。構(gòu)件5B號(hào)(盤針)浮動(dòng)結(jié)合國際民航組織3A和5A號(hào)(光碟片)。由于構(gòu)件5B條有一個(gè)多余的自由度,構(gòu)件5A及5B被視為構(gòu)件5。這里的目的是為當(dāng)前的幾何設(shè)計(jì)這個(gè)親初等構(gòu)成行星齒輪傳動(dòng)。
幾何共軛曲面主要關(guān)心的是在設(shè)計(jì)齒輪和發(fā)電軛嚙合要素。利特溫[3]研究的嚙合齒輪空間,并生成共軛曲面。陳[4]和利特溫[5]成功調(diào)查了表面幾何空間共軛齒輪副。芳和蔡[6]提出了一個(gè)數(shù)學(xué)模型,對(duì)齒面幾何圓弧螺旋錐齒輪。利特溫及健[7]研究單包絡(luò)環(huán)面蝸桿傳動(dòng)。閆劉[8]提出的幾何設(shè)計(jì)和加工可變螺距導(dǎo)致螺釘嚙合圓柱組成。后來,閆陳[9]推導(dǎo)公式的表面幾何弧面凸輪嚙合圓柱組成。漢森和丘吉爾〔10〕應(yīng)用理論的信封一參數(shù)曲線確定曲率。goetz [11]得出的理論信封為期家庭參數(shù)曲面。蔡黃[12]應(yīng)用理論信封一家面兩個(gè)獨(dú)立參數(shù)的地確定親輔導(dǎo)camoids翻譯與球的追隨者。colbourne [13]提出了幾何方法騰云駕霧的信封trochoids ,開展行星運(yùn)動(dòng)。林仔[14]研究幾何軌跡產(chǎn)生的一個(gè)點(diǎn)在地球的行星錐齒輪 列車。一些應(yīng)用擺線機(jī)械設(shè)計(jì)研究了pollitt〔15〕。布蘭奇和楊[16]考察了加工公差的擺線驅(qū)動(dòng)器。石田等[17]研究了牙齒負(fù)荷瘦身輞擺線齒輪。 最近,利特溫,馮[18]用邸給出了幾何產(chǎn)生的共軛曲面擺線齒輪。
本文運(yùn)用理論信封一家面帶參數(shù)的形式,以獲取表面幾何對(duì)擬議的初級(jí)行星齒輪系中的齒輪是圓柱齒。在下面,我們目前的拓?fù)浣Y(jié)構(gòu),這個(gè)基本計(jì)劃膳食齒輪火車踏。然后,坐標(biāo)系統(tǒng)和坐標(biāo)轉(zhuǎn)換矩陣德termined ,方程嚙合導(dǎo)出基于基本傳動(dòng)運(yùn)動(dòng)學(xué),坐標(biāo)轉(zhuǎn)換, 三重向量乘積邸給出了幾何,理論共軛曲面。最后,設(shè)計(jì)的例子來說明此方法的可行性。
2拓?fù)浣Y(jié)構(gòu)
1顯示二00二年行星齒輪傳動(dòng)與齒圈。這個(gè)行星的機(jī)制,運(yùn)作上是獨(dú)一無二的原則,采用曲柄(四段),歪斜的鳥羽( 3構(gòu)件) ,約軌道中心的輸入軸由于偏心軸。在同一時(shí)間,小齒輪轉(zhuǎn)動(dòng)自己的中心,在相反的方向上的輸入軸, 由于該接觸齒圈(二段)。由此議案的鳥羽,是一個(gè)復(fù)合運(yùn)動(dòng)。這種擺動(dòng)議案轉(zhuǎn)為純旋轉(zhuǎn)運(yùn)動(dòng)的輸出軸的等速萬向節(jié)(盤邊構(gòu)件5B號(hào))。為初等行星齒輪傳動(dòng)裝置傳送恒定角速度比,它采用一盤盤(構(gòu)件5A )款機(jī)制作為輸出軸。圓盤密碼(構(gòu)件5B號(hào))的浮動(dòng)結(jié)合鳥羽和盤盤。盤板,旋轉(zhuǎn)方向相同的鳥羽,是輸出.從經(jīng)營的角度來看,之間的相對(duì)運(yùn)動(dòng)圓柱齒的齒輪和牙齒的齒圈可以代表乙 y在旋轉(zhuǎn)的音高曲線的鳥羽的音高曲線的齒圈。 直接投資文化程度高低圓周之間的環(huán)形齒輪和小齒輪的成果切議案特制 一個(gè)或多個(gè)圓形球場(chǎng)。2( a )的拓?fù)浣Y(jié)構(gòu),初等行星齒輪傳動(dòng)系列圖。 1 . 它由五個(gè)成員組成:幀( 1人) ,齒圈(二段) ,小齒輪(行星齒輪, 構(gòu)件3 ) ,曲柄(承運(yùn)人,構(gòu)件四) ,盤盤(構(gòu)件5 ) . 關(guān)節(jié)之間架和齒圈,幀和曲柄 畫框和盤板,齒輪和曲柄的回轉(zhuǎn)件。環(huán)形齒輪和小齒輪事件是一個(gè)齒輪; 齒輪和圓盤鋼板事件凸輪一雙。如果運(yùn)動(dòng)的行星齒輪所需的輸出軸行星齒輪可舉例來說,它可耦合到另一軸(輸出軸)的萬向節(jié)。在這里,盤板輸出的構(gòu)件。
為了設(shè)計(jì)的共軛曲面的初級(jí)行星齒輪傳動(dòng), 這五個(gè)環(huán)節(jié)和六個(gè)聯(lián)合機(jī)制是仿制動(dòng)成三個(gè)環(huán)節(jié)和三個(gè)聯(lián)合機(jī)制如圖。2款( b ) 只有鏈接1 , 2 , 三是考慮,因?yàn)槠渌h(huán)節(jié),不影響幾何分析這個(gè)基本行星齒輪傳動(dòng)。
3坐標(biāo)系統(tǒng)
之前產(chǎn)生的曲面方程的齒圈建議初等行星齒輪火車, 坐標(biāo)系統(tǒng)相應(yīng)的行星機(jī)制應(yīng)予以界定。3顯示坐標(biāo)系之間的相對(duì)運(yùn)動(dòng)而面貌一新的行星機(jī)制。4顯示的坐標(biāo)系中的圓柱齒。動(dòng)產(chǎn)聯(lián)系演出旋轉(zhuǎn)軸平行,以恒定角速度的比例。固定統(tǒng)籌制度exyztf硬性連接到幀。方便的坐標(biāo)變換,坐標(biāo)系統(tǒng)exyztg連接到幀太。移動(dòng)統(tǒng)籌制度exyzt2 , exyzt3 , exyztpi分別是硬性連接的環(huán)形齒輪,齒輪和均值圓柱齒廓。環(huán)形齒輪轉(zhuǎn)動(dòng)有關(guān)的Z2軸以恒定角速度。齒輪轉(zhuǎn)動(dòng)關(guān)于Z3的軸上。為方便協(xié)調(diào)跨之間形成的圓柱齒的齒輪,移動(dòng)坐標(biāo)系exyztpi隸屬均值齒圓柱成立和角度鉍是由關(guān)系昆明術(shù)和斧頭。起源1和O2吻合和位于中心的齒圈。絲綢起源和O3是巧合和位于中心的鳥羽。原產(chǎn)維基巧合的是,位于中心的帶狀齒圓柱表面基地。xf軸平行軸與星光。方向軸的ZF , ZG的,的Z2 , Z3的, zpi都是垂直的紙張。角度/ 2 / 3的角位移的齒圈和齒輪,分別。積極/ 2 / 3是以順時(shí)針方向與軸的Z2和Z3的軸線,分別。距離軸線旋轉(zhuǎn)的齒圈與齒輪為E。距離中心的齒圈與中心環(huán)齒是R2中。距離中心的鳥羽及中心的圓柱齒是0427-7104。厚度的圓柱齒是湯匙 ,圓柱齒是一個(gè)圓的半徑問題。
4設(shè)計(jì)實(shí)例
當(dāng)兩個(gè)齒輪嚙合的每一個(gè)瞬間,在某一個(gè)區(qū)間,其齒面可能會(huì)觸及對(duì)方要么在一個(gè)點(diǎn)或沿一條曲線。大體來說,兩齒面跟著直線聯(lián)絡(luò),說是共軛。為避免干涉齒輪傳動(dòng),方程嚙合必須考慮使外殼表面R2中的家人圓柱齒概況決心與有效性。( 10 )和( 16 )一并考慮。該信封被稱為共軛曲面的插齒。計(jì)算機(jī)程序開發(fā),以解決方程和嚙合面方程。 5和6顯示的實(shí)體建模的齒圈和齒輪。環(huán)形齒輪產(chǎn)生的插齒。而齒輪是圓齒。5顯示實(shí)體建模速比等于10時(shí),共軛曲面的齒圈可以生成的插齒如果改變速比,偏心距e ,齒輪,齒圈尺寸,齒數(shù)齒輪和齒圈。因此,我們可以設(shè)計(jì)所需的速度比初級(jí)內(nèi)部行星齒輪系中的行星齒輪與圓柱齒根。齒輪傳動(dòng)都非常緊湊。
5結(jié)論
這項(xiàng)工作產(chǎn)生的曲面方程擬初等新型行星齒輪傳動(dòng)圓柱齒廓。我們使用三重矢量積微分幾何處理方程嚙合。當(dāng)斷面的齒根是圓的,為方便幾何分析,球場(chǎng)半徑代替齒輪半徑即距離齒輪中心和齒中心。數(shù)學(xué)表達(dá)式的信封方程設(shè)計(jì)中的應(yīng)用初等內(nèi)部行星齒輪傳動(dòng)在其中。鳥羽是圓柱齒廓。 我們還制定了解決方案信封方程,可以設(shè)計(jì)所需的速度比內(nèi)部初等行星齒輪傳動(dòng)兩個(gè)實(shí)體造型前粘結(jié)劑列演示程序表面生成建議初等行星齒輪傳動(dòng)。
參考資料
[1] Z. Levai, Structure and analysis of planetary gear trains, J. Mech. 3 (1968) 131–148.
[2] D.W. Botsiber, Leo Kingston, Design and performance of cycloid speed reducer, Mach. Des. (June 28) (1956) 65–
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[3] F.L. Litvin, The synthesis of approximate meshing for spatial gears, J. Mech. 4 (1968) 187–191.
[4] C.H. Chen, Boundary curves, singular solution, complementary conjugate surfaces, in: Proceedings of the 5th
World Congress on Theory of Machines and Mechanisms, Montreal, Canada, 1979, pp. 1478–1481.
[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) 346–351.
[7] F.L. Litvin, V. Kin, Computerized simulation of meshing and bearing contact for single-enveloping worm-gear
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elements, ASME Trans., J. Mech. Des. 115 (4) (1993) 490–495.
[9] H.S. Yan, H.H. Chen, Geometry design and machining of roller gear cams with cylindrical rollers, Mech. Mach.
Theory 29 (6) (1994) 803–812.
[10] D.R.S. Hanson, F.T. Churchill, Theory of envelope provided new cam design equation, Prod. Eng. (August 20)
(1962) 45–55.
附錄2：外文原文
Geometry design of an elementary planetary gear trainwith cylindrical tooth-profiles
1 Introduction
Speed 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 [10]applied 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 [13]
proposed 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 Pollitt[15]. 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 structure
Fig. 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 systems
Before 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 examples
When 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 Conclusions
This 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 is with cylindricaltooth-profiles. We further develop a program to solve the envelope equations that can designrequired speed ratios of the internal elementary planetary gear trains. Two solid modeling examples are presented for demonstrating the procedures of surface generating of the proposede lementary planetary gear trains.
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