Microsoft Word - 11 X.H.Yang，C.H. Li--Design and Simulation for Conjugate Cam Mechanism.doc 286-293 Advances in Systems Science and Applications (2011), Vol.11, No.3-4 ISSN 1078-6236 International Institute for General Systems Studies, Inc Design and Simulation for Conjugate Cam Mechanism X.H. Yang and C.H. Li School of Mechanical engineering, Shandong University of Technology, Zibo , 255049, China Abstract Fuzzy synthetically appraising theory is put forward and to be used in the optimal selection of the law-of-cam motion. And its model is also established. An example has been given to illustrate the validity of this method. By compiling program about the optimal design and the simulation system, the motion and process simulation of the conjugate cams mechanism are realized. So the system can improve the efficiency, reduce the cost and solve the precision problem of high speed and over-loading about cam segmentation. Keywords Conjugate cam mechanism Fuzzy evaluation Simulation Software 1.Introduction The conjugate cam mechanism has many excellences, including high speeding and over- loading, exact and effective control, steady capability and so on. It is a part of intermission and displacement mechanism, ATC equipment and walking equipment, which is widely used in wrapping machine, agricultural machine, printed machine and wiring assemble line and so on. Meanwhile, there exist a lot of faults. For example, there are complicated design processes, uneasy to ensure design quality, difficult to manufacture, to depend on import product for domestic need of high speeding and over-loading conjugate cam [1-4]. The cam’s dynamic capability can be effectively improved by fuzzy synthetically appraising theory and optimal selection the cam’s contour line. Some problems appeared during the process of design can be earlier solved by combining with advanced virtual design and manufacture technology which can shorten the cycle of design, improve the precision of design and effectively enhance the conjugate cam’s design and the manufacture level. 2.Fuzzy synthetically selection of the-law-cam mation It is important to select the-law-follower in the process of conjugate cam design. According to some fuzzy factors including the cam’s working condition, economy, precision, and kinematics and dynamics characteristics of the motion law, meanwhile, synthetically considering a few relevant factors influenced the law-of-follower, the motion capability of conjugate cam can be effectively improved by fuzzy synthetically appraising theory. During the process of confirming the motion law, both loading and speed must be satisfied. So, we regard the two factors as sub-factors of the basic requirements[5-8]. Other factors include working conditions, economics, and precision and so on. Its secondary appraising rational tree, such as Fig. 1: The process to choose the optimal motion law of the cam’s followers by fuzzy synthetically appraising as follows: A. The motion law-of-follower deduced by positive sequence is known as spare set. It can be denoted by the following set Fundatin of Shan Dong and SDUT ( No Y2008F02、2005KJM04) { }1 11 12 1, , , mV v v v= ⋅⋅⋅ Advances in Systems Science and Applications (2011), Vol.11, No.3-4 287 Fig.1. Secondary appraising tree of connection B. The necessarily considered factors such as the maximum speed mV , the maximum acceleration mA , extracted the root-mean-square of speed rmsA , and move-loading torque characteristic value ( )m AV and so on, are known as key factors, denoted by iu { }1 11 12 1, , , nU u u u= ⋅⋅⋅ C. As a result of different design requirement and the use spot, the importance of key factors is different. So, a fuzzy subset is established by analysing every key factor. { } ( )1 11 12 13 1 1, , , ,0 1, 1,2, ,n iW w w w w w i n= ⋅⋅⋅ ≤ ≤ = ⋅⋅⋅ In the set, iw1 is important degree coefficient of iu , which is known as weight coefficient. D. According to ( )1,2, ,iu i n= ⋅⋅⋅ , satisfactory subject degree of every element in the spare set is confirmed., forming the following matrix: 111 112 121 122 1 1 ~ 1 1 1 2 1 ... ... ,0 1 ... ... ... ij n n nm r r r r R r r r r ⎡ ⎤ ⎢ ⎥ ⎢ ⎥= ≤ ≤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ It denotes the subject degree from element jv to factor iju in the spare set. E. The choice of motion law ( ) ( )1m1211 1nm1n21n1 12m122121 11m112111 11211 11 b,...,b,b r...rr ............ r...rr r...rr ,...,, = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⋅= ⋅= nwww RWB Hereinto, ( )1 1 1 1 1, 2,..., , n k j jk j b w r k m = = ⋅ =∑ jv corresponding to 1max kb , jv is the best choice.The flow chart of synthetically choice is denoted as Fig. 2. Whole requirement Precision EconomyWorking condition Basic requirement SpeedLoad 288 Yang: Design and Simulation for Conjugate Cam Mechanism F. Example ①Requirement of use: middle speed, light-load, low noise. Condition choice Condition analysis, pick-up the spare set Pick-up the weight A>− Compute ija Aa/a ij >− Pick-up the parameters of characteristic curves Compute ijr ( ) Rd/f,f0.1 ijimax >− RAB1 ×= Whether to choose the other requirements 1BB = Pick-up the weight C>− Compute c Cc/cij >− RCB2 ×= Pick-up the secondary weight ( )21, wwW =>− 2211 B*wB*B +=×= wBW For i=0 to 5 Extract ( )ibmax , output the relevant motion law End Y N Fig.2 The flow chart of the cam’s followers’ motion law confirmed by fuzzy synthetically theory Advances in Systems Science and Applications (2011), Vol.11, No.3-4 289 ②Spare set: { }1 11 12 13 14 15, , , ,V v v v v v= = {sine, amending constant speed, amending trapezoid, amending sine, equal addition and minus} ③Characteristic values of every curve are regarded as key factors: ( ){ }1 , , , , ,m m rms m mm U V A AV A Jτ= Because of the higher speed, mA and mJ should be lower. So, its weight coefficient should be a little bigger; because of the light-load, weight coefficient of mV and ( )m AV can be a little lower; because of the lower noise, weight coefficient of mτ should be proper bigger. Synthetically considering various requirements, the right weight modulus can be taken as: { } { } 1 11 12 13 14 15 16, , , , , 0.2,1,0.1,0.5,0.6,0.8 W w w w w w w= = After computing every percentage of their weights: { }0.0625,0.3125,0.03125,0.15625,0.1875,0.25W = ④Characteristic values of various motion law, such as Tab.1: Tab.1 Characteristic values of various motion law Subject degree can be formed with ( )max0.1 /ij i ijr f f d= + − ( ) ( )max min / 1 0.1i id f f= − − . The matrix can be formed: ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = 082.011.057.0 083.088.01.01 85.0145.084.01.0 15.0113.092.01.0 166.08.01.05.0 1.04.01.011.0 R1 ⑤Adopting synthetic appraise model of weighted average, namely: 1 , 1, 2,..., m j j ij j b w r i m = = ⋅ =∑ That: ( )1 0.511,0.298,0.746,0.779,0.456B W R= ⋅ = Hereinto, the amending sine curve is the best choice which is corresponding to max 0.779,jb = the following curve is amending trapezoid curve (corresponding to 0.746jb = ), Sequenc e number Curve’s name mV mA ( )m AM rmsA mJ mΤ 1 2 3 4 5 amending equal speed equal addition and minus amending trapezoid sine the mending sine 1.275 2.0 2.0 2.0 1.76 8.013 4.0 4.888 6.238 5.528 5.671 8.0 8.048 8.126 5.435 4.001 4.0 4.232 4.443 3.908 201.4 ∞ 61.43 39.48 69.47 63.3 — 26.71 44.14 34.17 290 Yang: Design and Simulation for Conjugate Cam Mechanism sine, equal addition and minus, amending constant speed. Known by experience, amending sine curve among several curves has the strongest use, the better capability/performance. The method’s accuracy and feasibility are validated. The amending trapezoid is in the second place. 3.Motion simulation for conjugate cam Because contour curve of cam is formed by multiple curves, the correct contour curve of cam will not be gained if the input cam’s parameters and motion law aren’t proper (Fig. 3). In order to avoid manufacturing the unqualified cam, the cam’s rationality and accuracy must be detected by motion simulation after gaining the relevant datum of designing cam model. We pick up the above data of the design model and change them into date format which can be recognized by graph software AutoCAD and UG. The cam’s accurate contour graph and three- dimensional dynamic simulation model can be automatically built in the graph environment. In the whole process of design, No only the relevant datum can be disposed of; but the visualization of designing results can be achieved by motion simulation. The designer can amend design parameters at any moment. So, the optimal design scheme can be gained, the ratio of waster during the practical process can be reduced, meanwhile, the cost can be reduced too. Fig.3. The error cam’s contour curve The flow of simulation analysis and numerical controllable programming module is mainly divided into two parts: First, implement graph simulation in AutoCAD2006 by compiling data interface files (Camshape.scr) on the platform of VC++6.0, we can extremely intuitively judge whether contour is distortion or comes to a point. Meanwhile, we can compile the interface files that numerical controllable line incision machine tool needs by AutoLISP language. Fig.4. The flow chart of simulation and program model Second, implement three-dimensional graph simulation and numerical controllable programming in UG NX3.0 by compiling data interface files (Camshape.scr) on the platform of Advances in Systems Science and Applications (2011), Vol.11, No.3-4 291 VC++6.0, simulate the processing movement of the cutting tool and cutting situation of the workpieces by using the UG’s formidable processing module. Examine whether there occurs over-cutting or interference collision in order to validate the accuracy and the rationality of the procedure in front of the post-processing and make the prompt revision, thus guarantee accuracy of numerical controllable programming of cam’s contour. Its flow chart of simulation and program model is denoted as Fig. 4. The motion simulation is denoted as Fig. 5. Fig.5 The three-dimensional motion simulation of conjugate cam 4.Machining simulation for conjugate cam For the regular cam tested by motion simulation model, we pick up the data which program needs from the graphics software and send data files to the automatic program model, and meanwhile, we choose the type of program, then, the numerical control line incision 3B or machining G programming can be realized according to practical needs. And the accuracy can be detected by machining simulation. If there were some problems, the program would be compiled over again. By the procedure of drawing data in AutoCAD, the cam’s counter data can be gained and changed into 3 B line cutting codes such as Fig. 6. And the knife track codes such as Fig. 7; the machining simulation is denoted as Fig. 8. Fig.6. The 3 B line cutting codes 292 Yang: Design and Simulation for Conjugate Cam Mechanism Fig.7. The knife track codes At last, by the program’s transferring model, send the correct program to the cam machining tool and complete the cam’s machining. To do so, the design, simulation and manufacture are integrated; it can share the datum and enhance the work efficiency. Fig.8. The machining simulation of conjugate cam 5.Conclusions According to some fuzzy factors including the cam’s working condition, economy, precision, and kinematics and dynamics characteristics of the motion law, the fuzzy optimal design for the conjugate cam is realised by applying the fuzzy synthetically appraising theory. And its model is also established. Meanwhile, program the procedure of the fuzzy optimal design and simulation system. By combining existing advanced graphic simulation software, the design, simulation and manufacture are integrated. Therefore, integration work of design and manufacture is completed. 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