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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( 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， 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 Key words: beating-up mechanism; elliptic-gear; crank-rocker; kinematics CLC number: TS103 135 Document 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 sley In 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 fabrics quality， and also decide the quality and competitiveness of a loom 1 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 mechanism Generally， four-bar linkage beating-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 very high precision machining If 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 produced 5 ， 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 1 EGCR 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 ( l 1 ) is fixed on the driven elliptic-gear Rocker CD ( l 3 ) is driven by BC ( l 2 ) and swings reciprocally Sley DE ( l 5 ) 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 ( l 4 ) 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 of linkages in crank-rocker mechanism， the kinematic performances of this novel beating-up mechanism become excellent， which are similar to those of the conjugated cam beating-up mechanism 1Active elliptic-gear; 2Driven elliptic-gear; DESley Fig 1 EGCR beating-up mechanism with its initial position 2 Kinematic Mathematic Models of EGCR Beating-Up Mechanism 2 1 Mathematical 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 r 1 and PA is r 2 With calculation， then r 1 = b 2 /( a + ccos 1 ) ， ( 1) r 2 = b 2 /( a + ccos 2 ) ， ( 2) where， c is the distance between the elliptic-gear center and the focus; 1 ranges from 0 to 2， and 2 from 0 to 2 6 According to the transmission principles of elliptic-gears r 1 = 2a r 2 ， ( 3) 222 Journal of Donghua University ( Eng Ed ) Vol 28， No 2 ( 2011) that is， cos 2 = ( a + ccos 1 ) b 2 ( 2a 2 + 2accos 1 b 2 ) c a c ( 4) From Eq ( 4) ， the relationship between 2 and 1 can be obtained According to the principles of gear transmission 2 = 1 r 1 r 2 ( 5) Given that the velocity of active gear is constant， 2 = 1 r 1 r 2 r 1 r 2 r 2 2 = 2a r 2 r 2 2 1 ( 6) Taking the derivative of Eqs ( 1 ) and ( 3 ) ， r 1 = b 2 csin 1 ( a + ccos 1 ) 2 1 and r 2 = r 1 ， so in Eq ( 6) r 2 = b 2 csin 1 ( a + ccos 1 ) 2 1 ( 7) 2 2 Kinematical 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 j 1 = + + 2 From Fig 2， the following equations can be deduced 7 Fig 2 Crank-rocker mechanism j 2 = arctan y C y B x C x B ( 8) j 4 = arctan( y B y D x B x D ) ( 9) j 3 = arccos( l 3 2 + ( x D x B ) 2 + ( y D y B ) 2 l 2 2 2l 3 ( x D x B ) 2 + ( y D y B ) 槡 2 ) + j 4 ( 10) j 2 = V x B cos j 3 + V y B sin j 3 l 2 sin( j 2 j 3 ) ( 11) j 3 = V x B cos j 2 + V y B sin j 2 l 3 sin( j 2 j 3 ) ( 12) j 2 = c 1 cos j 3 + c 2 sin j 3 l 2 sin( j 2 j 3 ) ( 13) j 3 = c 1 cos j 2 + c 2 sin j 2 l 3 sin( j 2 j 3 ) ( 14) In Eqs ( 13) and ( 14) ， c 1 = a x B + l 3 j 2 3 cos j 3 l 2 j 2 2 cos j 2 ， ( 15) c 2 = a y B + l 3 j 2 3 sin j 3 l 2 j 2 2 sin j 2 ( 16) 2 3 Kinematic models of E in x-axis direction on the sley DE Displacement equation: s x E = x D + l DE cos( j 3 ) ( 17) Velocity equation: V x E = l DE j 3 cos( j 3 /2) ( 18) Acceleration equation: a x E = l DE j 3 2 cos j 3 + l DE j 3 jcos( j 3 /2) ( 19) 3 Aided Analysis and Simulation Software of Mechanism and Parameter Optimization 3 1 Aided 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 of the mechanism Human- computer interaction analysis and optimization combine the virtues of both human and computers Humans 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 and computer can fully display their respective 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 3 Aided analysis and simulation software of mechanism With this software， users can input mechanism parameters such as a， k， ， l 1 ， l 2 ， l 3 ， l 4 ， 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 increases For kinematic performances of the mechanism， k needs to be optimized according to the requirements of the beating-up weft; l 1 ， l 2 ， l 3 ， and l 4 also need to be modified by the user in company with k， so as to achieve ideal kinematic performances 3 2 Optimization 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， l 1 = 40 mm， l 2 = 100 mm， l 3 = 180 mm， l 4 = 199 mm， and l DE = 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 maximal displacement is 85 mm and the maximal acceleration is 615 843 4 m /s 2 ， which both can meet the requirements of the beating-up weft Fig 4 The kinematic curves of EGCR beating-up mechanism 4 Test 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 spindles rotary speed at 100 r/min Theoretical and 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 fluctuation There are two reasons for this finding: the gap among the components of the mechanism causes vibration; the video analysis contains errors 422 Journal of Donghua University ( Eng Ed ) Vol 28， No 2 ( 2011) 5 Conclusions ( 1) In this paper， the EGCR beating-up mechanism had been produced Its kinematic mathematic models had been established and an aided analysis and simulation software had been compiled by visual basic A group of satisfactory parameters had been got by this software ( 2) A test bed of the EGCR beating-up mechanism was developed With the video tape recorder， its kinematic performances were verified This demonstrated the validity of the models and the feasibility of the mechanism References 1 Zhu S K， Gao W D Weaving Machine M 2nd ed Beijing: China Textile Apparel Press， 2004: 267-268 ( in Chinese) 2 Liang H S， Hu Q E， Wang G C， et al The Fuzzy Optimization Design of the Four-Link Weft Beat-Up Mechanism J Machine Design and Research， 2005， 21 ( 2 ) : 72-75 ( in Chinese) 3 Ma S P Optimal Design and Simulation on 6-Link Beating Construction Based on MATLAB J Journal of Textile Research， 2006， 27( 3) : 40-43 ( in Chinese) 4 Zheng Z Y Analysis of Beating-Up Mechanism of TT96 Rapier Loom J Journal of Textile Research， 2004， 25( 4) : 73-74 ( in Chinese) 5 Zhejiang Sci-Tech University Weft Inserting and Beating-Up Mechanism with Elliptic-Gear Crank-Rocker: CN， 200810162178 0 P 2008-11-18 ( in Chinese) 6 Chen J N， Zhao X， Xu B， et al Establishment of Kinematics Models and Performance Analysis of Elliptic-Gear Crank- Rocker Weft Insertion Mechanism J China Mechanical Engineering， 2007， 18( 19) : 2294-2297 ( in Chinese) 7 Zhao Y Mechanism Mathematics Analyses and Synthesis M Beijing: China Machine Press， 2005: 177-181 ( in Chinese) 8 Yang C J， Chen Y， Lu Y X Study on the Human-Machine Intelligent System and Its Application J Chinese Journal of Mechanical Engineering， 2000， 36( 6) : 42-47 ( in Chinese) 9 Teng H F， Wang Y S， Shi Y J Key Supporting Techniques of Human-Computer Cooperation J Chinese Journal of Mechanical Engineering， 2006， 42( 11) : 1-9 ( in Chinese) 10 Liu J， Teng H F， Qu F Z Interface of Human-Computer Interactive Genetic Algorithm J Journal of Dalian University of Technology， 2005， 45( 1) : 58-63 ( in Chinese) 522Journal of Donghua University ( Eng Ed ) Vol 28， No 2 ( 2011)