KinematicAnalysisandT_省略_erBeating_UpMec.pdf

Received date:2010- 01- 19 Foundation items:National Natural Science Foundation of China ( No 50875243) ;Zhejiang Technique Innovation Group of Modern Textile Machinery，China ( No 2009R50018) ;Foundation of Education Department of Zhejiang Province，China ( No Y201019088) ;Foundation of New Textile R D Emphasised Laboratory of Zhejiang Province，China ( No 2009FZD004) *Correspondence should be addressed to CHEN Jian- neng，E- mail:jiannengchen zstu edu cn Kinematic Analysis and Test Study of Elliptic-Gear and Crank-Rocker Beating-Up Mechanism ZHAO Xiong( 赵雄) ，REN Gen- yong( 任根勇) ，CHEN Jian- neng( 陈建能) * College of Mechanical Engineering and Automation，Zhejiang Sci- Tech University，Hangzhou 310018，China Abstract:In order to analyze the kinematic performances of elliptic- 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 This software can display the kinematic characteristics and simulation motion of the mechanism according to different parameters It also supplies a platform for human- computer interaction A group of satisfactory parameters were selected by the software A test bed of EGCR beating- up mechanism was developed according to these parameters The kinematic performances of the mechanism were verified by high- speed video tape recorder Keywords: beating- upmechanism; elliptic- gear; crank- rocker; kinematics CLC number:TS103 135Document code:A Article ID:1672 -5220( 2011) 02-0222 -04 Introduction Beating- up mechanism is one of the key mechanisms of a loom It beats the weft which is inserted by weft- insertion mechanism to form the fabric Its function is to transform the constant speed rotation of the looms spindle to the non- constant speed reciprocating swing of the sleyIn order to allow the weft- insertion mechanism to finish inserting the wefts，the sley of the beating- up mechanism should have adequate dwell time or relative dwell time in the front position The performances of beating- up mechanism determine the fabricsquality， andalsodecidethequalityand competitiveness of a loom1 Nowadays，there are three general kinds of beating- up mechanisms:four- bar linkage beating- up mechanism，six- bar linkage beating- up mechanism，and conjugated cam beating- up mechanismGenerally，four- barlinkagebeating- up mechanism is the simplest mechanism with 65- 75 relative dwell time Six- bar linkage beating- up mechanism has about 120 relative dwell time It has more hinges which produce larger cumulative errors The dwell time of conjugated cam mechanism is 220- 240，but the conjugated cam mechanism needs veryhigh precision machiningIf there are some processing errors it will cause certain vibration 2- 4 In this paper，a new type of beating- up mechanism based on elliptic- gear and crank- rocker( EGCR)was produced5 ， and its kinematic mathematic models were established A test bed was developed and the kinematic performances of the mechanism were verified by high- speed video tape recorder， which demonstrated that this new mechanism could meet the requirements of weft beating- up 1EGCR Beating- Up Mechanism Figure 1 shows the EGCR beating- up mechanism in its initial position O is one of the focuses of the active elliptic- gear 1 and the rotation centre of the looms spindle A is one of the focuses and the rotation centre of the driven elliptic- gear 2 Crank 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 reciprocally together with CD By optimizing the eccentricity k ( the ratio of the elliptic- gears minor radius( b)to major radius( a) ， the angle ( the included angle between AD ( l4)and crank AB when crank AB and linkage BC are collinear，that is the sley DE will be in the front position) ， ( the included angle between the major axis of the active elliptic- gear and AO) ， ( the included angle between AD and x- axis) ，and the lengths oflinkagesincrank- rockermechanism， thekinematic performances of this novel beating- up mechanism become excellent，which are similar to those of the conjugated cam beating- up mechanism 1 Active elliptic- gear;2 Driven elliptic- gear;DESley Fig 1EGCR beating- up mechanism with its initial position 2Kinematic Mathematic Models of EGCR Beating- Up Mechanism 2 1Mathematical models of the driven elliptic- gear In Fig 1，when the active gear 1 rotates anticlockwise at a constant speed，gear 2 will rotate clockwise at a non- constant speed Given the angular displacements of the active gear 1 1 and driven gear 2 2，the distance from mesh point P to axis O is r1and PA is r2 With calculation，then r1= b2/( a + ccos 1) ，( 1) r2= b2/( a + ccos 2) ，( 2) where，c is the distance between the elliptic- gear center and the focus;1ranges from 0 to 2，and 2from 0 to 2 6 According to the transmission principles of elliptic- gears r1= 2a r2，( 3) 222Journal of Donghua University ( Eng Ed )Vol 28，No 2 ( 2011) that is， cos 2= ( a + ccos 1) b 2 ( 2a2+ 2accos 1 b2) c a c ( 4) From Eq ( 4) ，the relationship between 2and 1can be obtained According to the principles of gear transmission 2 = 1r1 r2 ( 5) Given that the velocity of active gear is constant， 2 = 1 r 1r2 r1r 2 r2 2 = 2a r 2 r2 2 1 ( 6) TakingthederivativeofEqs (1 ) and(3 ) ， r 1 = b2csin 1 ( a + ccos 1) 2 1and r 2 = r 1， so in Eq ( 6) r 2 = b2csin 1 ( a + ccos 1) 2 1 ( 7) 2 2Kinematical models of rocker CD Since the crank is fixed on the driven elliptic- gear，its angular velocity and angular acceleration are the same as those of the driven elliptic- gear That is to say，j 1 = 2，j 1 = 2， and j1= + + 2 From Fig 2，the following equations can be deduced7 Fig 2Crank- rocker mechanism j2= arctan yC yB xC xB ( 8) j4= arctan( yB yD xB xD) ( 9) j3= arccos( l3 2 + ( xD xB) 2 + ( yD yB) 2 l2 2 2l3( xD xB) 2 + ( yD yB) 槡 2 )+ j4 ( 10) j 2 = Vx Bcos j3 + Vy Bsin j3 l2sin( j2 j3) ( 11) j 3 = Vx Bcos j2 + Vy Bsin j2 l3sin( j2 j3) ( 12) j 2 = c1cos j3+ c2sin j3 l2sin( j2 j3) ( 13) j 3 = c1cos j2+ c2sin j2 l3sin( j2 j3) ( 14) In Eqs ( 13)and ( 14) ， c1= ax B + l3j 2 3cos j3 l2j 2 2cos j2， ( 15) c2= ay B + l3j 2 3sin j3 l2j 2 2sin j2 ( 16) 2 3Kinematic models of E in x- axis direction on the sley DE Displacement equation: sx E = xD+ lDEcos( j3 ) ( 17) Velocity equation: Vx E = lDEj 3cos( j3 /2) ( 18) Acceleration equation: ax E = lDEj 3 2cos j 3 + lDEj 3jcos( j3 /2) ( 19) 3AidedAnalysisandSimulation SoftwareofMechanismand Parameter Optimization 3 1Aided analytical software The visualization of the mechanism is analyzing and optimizing process that can display more information of the process to users Users can observe the whole process and find out the essential parameters ofthe mechanismHuman- computer interaction analysis and optimization combine the virtues of both human and computersHumans possess the capabilities of illegible illation， judgment and innovation， which can help to dispose random events as well Meanwhile， computers are good at accurate calculation and repeative work Human andcomputercanfullydisplaytheirrespective advantages in human- computer interaction optimization Thus satisfactory parameters can be easily achieved 8- 10 Based on the above kinematic models of EGCR beating- up mechanism，an aided analysis and simulation software are compiled which is shown in Fig 3 It can be used to analyze the influences of different mechanism parameters and verify whether there exist interferences among the components of the mechanism Fig 3Aided analysis and simulation software of mechanism With this software，users can input mechanism parameters such as a，k， ，l1，l2，l3，l4， and rotary speed of the looms spindle The mechanism motion simulation will be shown on the left of the interface;the displacement，velocity，and acceleration curves of point E will be shown respectively on the right of the interface;the optimal value of will be shown on the left- bottom of the interface The displacement curve shows that 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 maximal acceleration also decreases as k increasesFor kinematic performances of the mechanism，k needs to be optimized according to the requirements of the beating- up weft;l1，l2， l3， and l4also need to be modified by the user in company with k，so as to achieve ideal kinematic performances 3 2Optimization results analysis One of the most important performances of beating- up mechanism is the dwell time of sley Increasing mechanism parameter k can prolong dwell time，meantime the maximal acceleration increases remarkably，and the oversize fluctuation of acceleration will degrade mechanism dynamic performance Designer must therefore make a balance between prolonging dwell time and controlling acceleration fluctuation With the above aided analysis and simulation software，a group of parameters was obtained: = 4，k = 0 85， = 135，a = 71 233 mm，l1= 40 mm，l2= 100 mm，l3= 180 mm，l4= 199 mm，and lDE= 189 5 mm Based on these parameters，when the loom has a speed of 300 r/min，the kinematical curve of the beating point E is shown in Fig 4 When the beating- up mechanism is on the rear position，the displacement curve is almost flat The dwell time of sley is close to 200 ( ranging from 92 to 285) ，which will not lead to interference of the beating- up mechanism and weft- insertion mechanism In addition，during this period，the curves of the velocity and acceleration of the sley are almost close to 0 Therefore it will not cause vibration，which will benefit the wefts entery and exit from shed At the end of the beating- up， the maximaldisplacementis 85mmandthemaximal acceleration is 615 843 4 m /s2，which both can meet the requirements of the beating- up weft Fig 4The kinematic curves of EGCR beating- up mechanism 4Test Study Based on the above parameters，a test bed of EGCR beating- up mechanism is developed ( Fig 5) Using the high- speed video tape recorder and video analysis software Blasters MAS，the displacement and velocity are obtained with loom spindlesrotaryspeedat100r/minTheoreticaland experimental displacements of beating point E are shown in Fig 6，and theoretical and experimental velocities of beating point E are shown in Fig 7 The actual measured displacement curve is consistent with the theoretical one，but the actual measured velocity curve shows some fluctuationThere are two reasons for this finding:the gap among the components of the mechanism causes vibration;the video analysis contains errors 422Journal of Donghua University ( Eng Ed )Vol 28，No 2 ( 2011) 5Conclusions ( 1)In this paper，the EGCR beating- up mechanism had been producedIts kinematic mathematic models had been established and an aided analysis and simulation software had been compiled byvisual basicAgroup ofsatisfactory parameters had been got by this software ( 2)A test bed of the EGCR beating- up mechanism was developedWiththevideotaperecorder， itskinematic performances were verified This demonstrated the validity of the models and the feasibility of the mechanism References 1Zhu 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 Optimization Design ofthe Four- Link Weft Beat- Up Mechanism J Machine Design and Research，2005，21 ( 2 ) :72- 75( in Chinese) 3Ma S POptimal Design and Si