機械設計外文翻譯-橢圓齒輪曲柄搖桿打緯機構的運動學分析及試驗研究【中文2867字】【PDF+中文W,中文2867字,機械設計,外文,翻譯,橢圓,齒輪,曲柄,搖桿,打緯,機構,運動學,分析,試驗,研究,中文,2867,PDF 【中文2867字】 橢圓齒輪曲柄搖桿打緯機構的運動學分析及試驗研究 趙雄 任根勇 陳建能 機械工程及自動化學院，浙江理工大學，杭州310018，中國 摘要：為了分析橢圓齒輪曲柄搖桿打緯機構的運動學性能，建立了一個運動學的數(shù)學模型，編制了一個輔助分析與仿真軟件。根據(jù)不同的參數(shù)，這軟件能顯示運動特性及仿真運動的機制。它還為人機交互提供了一個平臺。通過軟件可以選定一組令人滿意的參數(shù)。通過這些參數(shù)對曲柄搖桿打緯機構的測試床進行優(yōu)化。通過高速視頻磁帶記錄器驗證運動性能的機理。 關鍵詞：打緯機構 橢圓齒輪 曲柄搖桿 動力學 引言 打緯機構是紡織機的一個重要部位。它是由引緯緯紗插入機制形成的織物。它的功能是把主軸的恒定速度旋轉(zhuǎn)改變?yōu)轶刈牟缓愣ㄍ鶑蛿[動。為使引緯機構完成插入緯紗，筘座的打緯機構應該有足夠的停留時間或相對停留時間在前方位置。打緯機構的性能測定織物的質(zhì)量，也決定織機的質(zhì)量競爭力[1]。 現(xiàn)在，有三種普遍的打緯機構：四連桿打緯機構，六連桿打緯機構和共軛凸輪打緯機構[2]。一般來說，四連桿打緯機構是最簡單的，它有65°-75°的相對停留時間。六連桿打緯機構有120°的相對停留時間[3]。它更多的取決于它的生產(chǎn)較大累計誤差。共軛凸輪的停留時間為220°-240°，但共軛凸輪機構需要很高的加工精度。如果有一些加工誤差會造成一定的振動[4]。 在本文中，一種新型的依據(jù)橢圓齒輪和曲柄搖桿的打緯機構產(chǎn)生了[5]，它的運動學數(shù)學模型也建立了。通過一個測試裝置的開發(fā)和對運動性能的機制進行了高速視頻磁帶記錄，這表明，這種新的機制可以滿足打緯要求。 1 橢圓齒輪曲柄搖桿打緯機構 圖1顯示了橢圓齒輪曲柄搖桿打緯機構初始位置。，0為主動橢圓齒輪的焦點，也是織機主軸轉(zhuǎn)動中心，a為從動橢圓齒輪轉(zhuǎn)動中心，為該橢圓齒輪的一個焦點，曲柄ab(長度z )與從動橢圓齒輪固接，通過連桿bc(長度z )帶動搖桿cd(長度z。)作往復擺動。cd與筘座de通過軸d固連，使筘座de前后往復擺動。通過優(yōu)化橢圓齒輪的短長軸之比k(偏心率)、當曲柄ab與連桿bc共線時(即筘座de在前心位置)與支座ad(長度z )夾角 、初始安裝角 (安裝時主動橢圓齒輪長軸與ao線的夾角)、四根桿件的長度和支座ad位置角y，可以獲得類似共軛凸輪打緯機構運動規(guī)律。 1—主動橢圓齒輪 2—從動橢圓齒輪 DE—筘座 圖1 橢圓齒輪一曲柄搖桿打緯機構示意圖 2 橢圓齒輪曲柄搖桿打緯機構的運動學數(shù)學建模 2.1 橢圓齒輪驅(qū)動的數(shù)學模型 當主動齒輪1一恒定的速度逆時針旋轉(zhuǎn)時，齒輪2會以一個變速順時針旋轉(zhuǎn)。設主動輪1轉(zhuǎn)角φ1，，從動輪2轉(zhuǎn)過角φ2，點P到軸O的距離是r1，PA的距離是r2。經(jīng)推導得： r1=b2/(a+c*cosφ1) (1) r2=b2/(a+c*cosφ2) (2) c的范圍是橢圓中心到焦點，φ1，φ2的變化范圍是0到2π[6]。 由橢圓齒輪的傳動特性得：r1=2a- r2 （3） 即 （4） 由式（4）可計算從動輪角位移φ2與主動輪角位移φ1的關系。 （5） 對（5）求導得： （6） 由（1）和（3），根據(jù)求導公式， ，， （7） 2.2 搖桿CD的運動學運動學模型 由于曲柄固定在從動橢圓齒輪，其角速度和角加速度與橢圓齒輪驅(qū)動一樣。即：，，根據(jù)圖2，下列方程可以被推導出[7]。 圖2 曲柄搖桿機構 （8） (9) （10） （11） （12） （13） （14） 根據(jù)（13）和（14）， （15） （16） 2.3 E在筘座DE的X方向上的運動學模型 位移方程： （17） 速度方程： （18） （19） 3 輔助分析與仿真軟件的機構參數(shù)優(yōu)化 3.1 計算機輔助分析軟件 可視化的機制分析優(yōu)化的過程，可以顯示更多的信息到用戶的過程。用戶可以觀察整個過程和發(fā)現(xiàn)的基本參數(shù)的機制。人機交互分析和優(yōu)化是人類和電腦的優(yōu)點結合在一起。人類擁有的能力，模糊推理，判斷和創(chuàng)新，這可以幫助處理以及隨機事件。同時，計算機擅長精確計算及相關工作。人類和計算機能充分發(fā)揮各自的人-計算機交互優(yōu)化的優(yōu)勢。因此，令人滿意的參數(shù)可以很容易的實現(xiàn)[8-10]。 基于以上橢圓齒輪曲柄搖桿打緯機構，一個輔助分析與仿真軟件被實現(xiàn)，在圖3中顯示出來。它可以用于分析對不同的機構參數(shù)和驗證是否存在干擾在組成部分之間的機制中。 圖3 分析和仿真機制的軟件 有了這個軟件，用戶可以輸入機構參數(shù)，像a，k，γ，l1，l2，l3，l4和織機主軸旋轉(zhuǎn)速度。機構運動仿真將顯示在界面左側；位移，速度和加速度曲線的點將會分別顯示在接口的右側；最優(yōu)值將會顯示在接口的左下方。位移曲線會隨著k的增加而減少顯示在后方位置；同時加速度曲線顯示，最大加速度會隨k的增加而減少。從運動學機制的性能看，k需要根據(jù)打緯機構的要求進行優(yōu)化。l1，l2，l3，l4也需要修改根據(jù)k，從而獲得理想的運動性能。 3.2 優(yōu)化結果分析 打緯機構最重要的性能之一是筘座的駐留時間。增加機制的參數(shù)可以延長停留時間，同時最大加速度明顯增加，而且特大型加速度波動會降低機構動態(tài)特性。設計師必須在延長停留時間和控制加速度波動之間做一個平衡。 根據(jù)上述輔助分析與仿真軟件，可以獲得一組參數(shù)：δ=4°,k=0.85,γ=135°,a=71.233mm,l1=40mm,l2=100mm,l3=180mm,l4=199mm,lDE=189.5mm?；谶@些參數(shù)，當織機速度300轉(zhuǎn)/分鐘，點E運動曲線顯示在圖4。當打緯機構是在后方的位置，位移曲線幾乎是平的。筘座的駐留時間接近200°（從92°到285°），這就不會導致打緯機構和打緯插入機構之間的干擾。此外，在這一時期，筘座曲線的速度和加速度幾乎接近0°因此，他不會產(chǎn)生振動，將有利于緯紗的入境和出境。在打緯結束時，最大位移為85mm，最大加速度為615.8434m/s2，滿足了打緯的要求。 圖4 橢圓齒輪曲柄搖桿打緯機構的運動曲線 4 試驗研究 根據(jù)上述參數(shù)，橢圓齒輪曲柄搖桿打緯機構的測試床被開發(fā)出來了。（圖5）利用高速視頻磁帶記錄器和視頻分析軟件MAS，得到了當織機的主軸轉(zhuǎn)速在100轉(zhuǎn)/分鐘的時候的位移和速度。點E的理論和實驗位移顯示在圖6，點E的理論和實驗速度顯示在圖7。實測位移曲線是和理論一致，但實際測量速度曲線顯示一些波動。對此有2個原因：該機制組件之間的差距引起的振動；視頻分析包含錯誤。 圖5 橢圓齒輪-曲柄搖桿打緯機構測試床 圖6 打緯機構位移曲線分析圖 圖7 打緯機構速度曲線分析圖 5 總結 （1）在本文中，橢圓齒輪曲柄搖桿打緯機構已經(jīng)生產(chǎn)出來了。其運動學數(shù)學模型已經(jīng)建立，一個輔助分析與仿真軟件通過基本視覺已經(jīng)完成。通過這個軟件一組令人滿意的參數(shù)已經(jīng)得到。 （2）關于橢圓齒輪曲柄搖桿打緯機構的測試床已經(jīng)比較成熟。通過視頻磁帶記錄器，運動學性能得到了驗證。這表明模型的有效性和機制的可行性。 文獻 [1] Zhu S K,Gao W D. 織機[M]. 第二版.北京：中國紡織&服裝出版社，2004：267-268. [2] Liang H S，Hu Q E，Wang G C，等等. 四連桿打緯機構模糊優(yōu)化設計[J]. 機械設計與研究，2005，21（2）：72-75. [3] Ma S P. 基于matlab的六連桿打緯機構優(yōu)化設計和仿真[J]. 紡織研究學報，2006，27（3）：40-43. [4] Zheng Z Y. 分析劍桿織機打緯機構[J]. 紡織研究學報，2004，25（4）：73-74. [5] 浙江理工大學 橢圓齒輪曲柄搖桿打緯機構的引緯打緯：中國，200810162178.O[P]. 2008-11-18. [6] Chen J N，Zhao X，Xu B，等等。建立關于橢圓齒輪曲柄搖桿引緯機構的運動學模型[J]. 中國工程機械，2007，18（19）：2294-2297. [7] Zhao Y. 機理數(shù)學分析與合成[M].北京：中國工業(yè)出版社，2005：177-181. [8] Yang C J，Chen Y，Lu Y X．研究人機系統(tǒng)及其應用[J]. 中國工程機械雜志，2000，36（6）：42-47. [9] Teng H F，Wang Y S，Shi Y J．人機合作的關鍵技術研究[J]. 中國工程機械雜志，2006，42（11）：1-9. [10] Liu J，Teng H F，Qu F Z．人機界面交互式基本算法[J].大連大學技術學報，2005，45（1）：58-63. Received date:2010-01-19Foundation items:National Natural Science Foundation of China(No 50875243);Zhejiang Technique Innovation Group of Modern TextileMachinery，China(No 2009R50018);Foundation of Education Department of Zhejiang Province，China(No Y201019088);Foundation ofNew Textile R D Emphasised Laboratory of Zhejiang Province，China(No 2009FZD004)*Correspondence should be addressed to CHEN Jian-neng，E-mail:jiannengchen zstu edu cnKinematic Analysis and Test Study of Elliptic-Gear and Crank-Rocker Beating-UpMechanismZHAO Xiong(趙雄)，REN Gen-yong(任根勇)，CHEN Jian-neng(陳建能)*College of Mechanical Engineering and Automation，Zhejiang Sci-Tech University，Hangzhou 310018，ChinaAbstract:In order to analyze the kinematic performances ofelliptic-gear and crank-rocker(EGCR)beating-up mechanism，kinematic mathematic models of the mechanism were established，and an aided analysis and simulation software were compiled Thissoftware can display the kinematic characteristics and simulationmotion of the mechanism according to different parameters It alsosupplies a platform for human-computer interaction A group ofsatisfactory parameters were selected by the software A test bed ofEGCR beating-up mechanism was developed according to theseparameters The kinematic performances of the mechanism wereverified by high-speed video tape recorderKeywords:beating-upmechanism;elliptic-gear;crank-rocker;kinematicsCLC number:TS103 135Document code:AArticle ID:1672-5220(2011)02-0222-04IntroductionBeating-up mechanism is one of the key mechanisms of aloom It beats the weft which is inserted by weft-insertionmechanism to form the fabric Its function is to transform theconstant speed rotation of the looms spindle to the non-constant speed reciprocating swing of the sleyIn order toallow the weft-insertion mechanism to finish inserting thewefts，the sley of the beating-up mechanism should haveadequate dwell time or relative dwell time in the front positionThe performances of beating-up mechanism determine thefabricsquality，andalsodecidethequalityandcompetitiveness of a loom1 Nowadays，there are three general kinds of beating-upmechanisms:four-bar linkage beating-up mechanism，six-barlinkage beating-up mechanism，and conjugated cam beating-upmechanismGenerally，four-barlinkagebeating-upmechanism is the simplest mechanism with 65-75 relativedwell time Six-bar linkage beating-up mechanism has about120 relative dwell time It has more hinges which producelarger cumulative errors The dwell time of conjugated cammechanism is 220-240，but the conjugated cam mechanismneeds veryhigh precision machiningIf there are someprocessing errors it will cause certain vibration2-4 In this paper，a new type of beating-up mechanism basedon elliptic-gear and crank-rocker(EGCR)was produced5，and its kinematic mathematic models were established A testbed was developed and the kinematic performances of themechanism were verified by high-speed video tape recorder，which demonstrated that this new mechanism could meet therequirements of weft beating-up1EGCR Beating-Up MechanismFigure 1 shows the EGCR beating-up mechanism in itsinitial position O is one of the focuses of the active elliptic-gear 1 and the rotation centre of the looms spindle A is one ofthe focuses and the rotation centre of the driven elliptic-gear 2Crank AB(l1)is fixed on the driven elliptic-gear Rocker CD(l3)is driven by BC(l2)and swings reciprocally Sley DE(l5)is fixed with CD by axis D and swings reciprocallytogether with CD By optimizing the eccentricity k(the ratioof the elliptic-gears minor radius(b)to major radius(a)，the angle (the included angle between AD(l4)and crank ABwhen crank AB and linkage BC are collinear，that is the sleyDE will be in the front position)，(the included anglebetween the major axis of the active elliptic-gear and AO)，(the included angle between AD and x-axis)，and the lengthsoflinkagesincrank-rockermechanism，thekinematicperformances of this novel beating-up mechanism becomeexcellent，which are similar to those of the conjugated cambeating-up mechanism1 Active elliptic-gear;2 Driven elliptic-gear;DESleyFig 1EGCR beating-up mechanism with its initial position2Kinematic Mathematic Models ofEGCR Beating-Up Mechanism2 1Mathematical models of the driven elliptic-gearIn Fig 1，when the active gear 1 rotates anticlockwise at aconstant speed，gear 2 will rotate clockwise at a non-constantspeed Given the angular displacements of the active gear 1 1and driven gear 2 2，the distance from mesh point P to axis Ois r1and PA is r2 With calculation，thenr1=b2/(a+ccos 1)，(1)r2=b2/(a+ccos 2)，(2)where，c is the distance between the elliptic-gear center and thefocus;1ranges from 0 to 2，and 2from 0 to 26 According to the transmission principles of elliptic-gearsr1=2a r2，(3)222Journal of Donghua University(Eng Ed)Vol 28，No 2(2011)that is，cos 2=(a+ccos 1)b2(2a2+2accos 1 b2)cac(4)From Eq(4)，the relationship between 2and 1can beobtained According to the principles of gear transmission2=1r1r2(5)Given that the velocity of active gear is constant，2=1r1r2 r1r2r22=2a r2r221(6)TakingthederivativeofEqs(1)and(3)，r1=b2csin 1(a+ccos 1)21and r2=r1，so in Eq(6)r2=b2csin 1(a+ccos 1)21(7)2 2Kinematical models of rocker CDSince the crank is fixed on the driven elliptic-gear，itsangular velocity and angular acceleration are the same as thoseof the driven elliptic-gear That is to say，j1=2，j1=2，and j1=+2 From Fig 2，the following equations canbe deduced7 Fig 2Crank-rocker mechanismj2=arctanyC yBxC xB(8)j4=arctan(yB yDxB xD)(9)j3=arccos(l32+(xD xB)2+(yD yB)2 l222l3(xD xB)2+(yD yB)槡2)+j4(10)j2=VxBcos j3+VyBsin j3l2sin(j2 j3)(11)j3=VxBcos j2+VyBsin j2l3sin(j2 j3)(12)j 2=c1cos j3+c2sin j3l2sin(j2 j3)(13)j 3=c1cos j2+c2sin j2l3sin(j2 j3)(14)In Eqs(13)and(14)，c1=axB+l3j23cos j3 l2j22cos j2，(15)c2=ayB+l3j23sin j3 l2j22sin j2(16)2 3Kinematic models of E in x-axis direction onthe sley DEDisplacement equation:sxE=xD+lDEcos(j3)(17)Velocity equation:VxE=lDEj3cos(j3/2)(18)Acceleration equation:axE=lDEj32cos j3+lDEj 3jcos(j3/2)(19)3AidedAnalysisandSimulationSoftwareofMechanismandParameter Optimization3 1Aided analytical softwareThe visualization of the mechanism is analyzing andoptimizing process that can display more information of theprocess to users Users can observe the whole process and findout the essential parameters ofthe mechanismHuman-computer interaction analysis and optimization combine thevirtues of both human and computersHumans possess thecapabilities of illegible illation，judgment and innovation，which can help to dispose random events as well Meanwhile，computers are good at accurate calculation and repeative workHuman andcomputercanfullydisplaytheirrespectiveadvantages in human-computer interaction optimization Thussatisfactory parameters can be easily achieved8-10 Based on the above kinematic models of EGCR beating-upmechanism，an aided analysis and simulation software arecompiled which is shown in Fig 3 It can be used to analyzethe influences of different mechanism parameters and verifywhether there exist interferences among the components of themechanismFig 3Aided analysis and simulation software of mechanismWith this software，users can input mechanism parameterssuch as a，k，l1，l2，l3，l4，and rotary speed of the loomsspindle The mechanism motion simulation will be shown onthe left of the interface;the displacement，velocity，andacceleration curves of point E will be shown respectively on theright of the interface;the optimal value of will be shown onthe left-bottom of the interface The displacement curve showsthat dwell time in the rear position decreases as k increases;322Journal of Donghua University(Eng Ed)Vol 28，No 2(2011)meanwhile the acceleration curve shows that the maximalacceleration also decreases as k increasesFor kinematicperformances of the mechanism，k needs to be optimizedaccording to the requirements of the beating-up weft;l1，l2，l3，and l4also need to be modified by the user in company withk，so as to achieve ideal kinematic performances3 2Optimization results analysisOne of the most important performances of beating-upmechanism is the dwell time of sley Increasing mechanismparameter k can prolong dwell time，meantime the maximalacceleration increases remarkably，and the oversize fluctuationof acceleration will degrade mechanism dynamic performanceDesigner must therefore make a balance between prolongingdwell time and controlling acceleration fluctuationWith the above aided analysis and simulation software，agroup of parameters was obtained:=4，k=0 85，=135，a=71 233 mm，l1=40 mm，l2=100 mm，l3=180mm，l4=199 mm，and lDE=189 5 mm Based on theseparameters，when the loom has a speed of 300 r/min，thekinematical curve of the beating point E is shown in Fig 4When the beating-up mechanism is on the rear position，thedisplacement curve is almost flat The dwell time of sley isclose to 200(ranging from 92 to 285)，which will not leadto interference of the beating-up mechanism and weft-insertionmechanism In addition，during this period，the curves of thevelocity and acceleration of the sley are almost close to 0Therefore it will not cause vibration，which will benefit thewefts entery and exit from shed At the end of the beating-up，the maximaldisplacementis 85mmandthemaximalacceleration is 615 843 4 m/s2，which both can meet therequirements of the beating-up weftFig 4The kinematic curves of EGCR beating-up mechanism4Test StudyBased on the above parameters，a test bed of EGCRbeating-up mechanism is developed(Fig 5)Using the high-speed video tape recorder and video analysis software BlastersMAS，the displacement and velocity are obtained with loomspindlesrotaryspeedat100r/minTheoreticalandexperimental displacements of beating point E are shown inFig 6，and theoretical and experimental velocities of beatingpoint E are shown in Fig 7 The actual measured displacementcurve is consistent with the theoretical one，but the actualmeasured velocity curve shows some fluctuationThere aretwo reasons for this finding:the gap among the components ofthe mechanism causes vibration;the video analysis containserrors422Journal of Donghua University(Eng Ed)Vol 28，No 2(2011)5Conclusions(1)In this paper，the EGCR beating-up mechanism hadbeen producedIts kinematic mathematic models had beenestablished and an aided analysis and simulation software hadbeen compiled byvisual basicAgroup ofsatisfactoryparameters had been got by this software(2)A test bed of the EGCR beating-up mechanism wasdevelopedWiththevideotaperecorder，itskinematicperformances were verified This demonstrated the validity ofthe models and the feasibility of the mechanismReferences1Zhu S K，Gao W D Weaving MachineM 2nd ed Beijing:China Textile Apparel Press，2004:267-268(in Chinese)2Liang H S，Hu Q E，Wang G C，et al The Fuzzy OptimizationDesign ofthe Four-Link Weft Beat-Up Mechanism JMachine Design and Research，2005，21(2):72-75(inChinese)3Ma S POptimal Design and Simulation on 6-Link BeatingConstruction Based on MATLAB JJournal of TextileResearch，2006，27(3):40-43(in Chinese)4Zheng Z 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