Journal of Advanced Mechanical Design, Systems, and Manufacturing

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1 Numerical Analysis on Paper Separation Usin the Overlap Separation echanism * Hui CHENG **, Hiroshi IKEDA ** and Kazushi YOSHIDA ** ** echanical Enineerin Research Laboratory, Hitachi Ltd. 8- Horiuchi-machi, Hitachinaka-shi, Ibaraki, -00 Japan hui.chen.qk@hitachi.com Abstract The overlap separation mechanism is widely used to separate paper sheets rom each other in automatic teller machines. In this study, we irst derived a ormula used or expressin the normal separation condition o paper sheets. Then we analyzed the deormation orce actin on the paper sheet suraces by treatin the paper sheet as an elastic beam and usin Clapeyron s theorem o three moments. Furthermore, by usin the inite element analysis sotware LS-DYNA, we developed a three-dimensional simulation method that can accurately reproduce normal separation, miseedin, and double eedin behaviors. Finally, the eects o the main parameters on deormation orce will be discussed. The results show that the deormation orce is proportional to the overlap; the bier the width o ate-roller or the distance o roller edes, the bier the deormation orce. oreover, the width o the eed-roller has hardly any eect on deormation orce. It is shown that separation deects obtained by the elastic beam model aree well with those obtained by the FE model. Key words: Separation, Overlap, Paper, Friction, Finite Element ethod, Elastic Beam, Clapeyron s Theorem o Three oments. Introduction *Received 5 July, 009 (No [DOI: 0.99/jamdsm..9] Copyriht 00 by JSE Paper sheet separation is one o the most important handlin procedures in many inormation devices, such as automatic teller machines (ATs, copiers and printers. In ATs, the overlap separation mechanism is widely used to separate paper sheets one by one precisely and quickly. hen paper sheets enter the overlap nip, the deormation orces and the riction orces act on contact suraces to separate them. Because the rictional condition may chane and sheets can be in dierent states (olded, partly-cut, wrinkled, etc., called situation sheets in this paper, miseedin and double eedin can easily occur in the separation mechanism. To achieve the low-cost and hiher reliability in desinin the separation device, the numerical simulation method that can correctly reproduce or predict the sheet separation behavior and clariy the jam mechanism is becomin more and more important. Some researchers []-[] have treated a paper sheet as an elastic beam and have optimised the roller shape by analysin the deormation shape and the riction orce o paper sheets. Others []-[5] have reported that the simulated results o sheet separation approached to actual behaviour when usin their inite element (FE simulation methods. However, only usin a sinle method cannot completely describe the whole separation phenomena. For example, in the irst method, it is diicult to use an elastic beam model to describe the complicated sheets that have non-continuous shapes. In the latter FE method, no researched results have been reported on the three-dimensional separation behaviour with plural sheets, especially 9

2 or situation sheets. Thereore, it cannot be said that the relationship between the deormation orce and structural parameters was totally clariied, and the simulated results cannot be directly applied to the actual separation mechanism desin. In this study, we irst introduced the separation structure with the overlap nip. Then, a ormula used or expressin the normal separation condition was derived. Furthermore, by considerin the sheet is an elastic beam and usin Clapeyron s theorem o three moments [6], the deormation orce o paper sheets in the overlap nip was analyzed. Ater that, by usin the FE analysis sotware LS-DYNA [*], we developed a three-dimensional simulation method that reproduces normal eedin behavior as well as the separation deects: miseedin and double eedin. Finally, the eects o main structural parameters on the deormation orce were observed by the above-mentioned methods.. Structure o Overlap Frictional Separation The structure o the overlap separation mechanism is shown in Fi.. It mainly consists o three rollers (pick-up roller (PR, eedin roller (, and ate roller ( and a push plate (Fi. (a. Positions o the s and the s are arraned with a shit in the shat direction and an overlap in the radial direction (Fi. (b. The pressure is irst enerated by a sprin ixed on the PR when the push plate moves up. Ater that, accumulated paper sheets are drawn out by the rotation o the PR and when the hih riction part A comes into contact with the irst paper sheet (Fi. (a. Once the paper sheets enter the overlap nip, the waved deormation occurs (shown in Fi. (b, and the deormation orces that acts on the sheet suraces in the nip area are enerated. Finally, the transportation orce rom the rotatin /PR and the resistance orce rom the ixed / act simultaneously to separate paper sheets rom each other. Feed roller ( Pick-up roller (PR B B Sprin C Nip A A s Gate roller (, ixed Push plate C direction (a ain structure (b Overlap and waved deormation Fi. Separation mechanism. Normal Separation Condition Once the paper sheet enters the overlap nip, the rictional orce is applied and can be obtained by Coulomb s riction theorem (multiplyin the deormation orce or the pressure p and rictional coeicients (reer to Fi.. hen only one paper sheet has entered the overlap nip (in Fi. (a, the normal separation condition is one in which the transportation orce (alon the let direction was larer than the resistance orce; and can be described by equation (. hen two paper sheets have entered the overlap nip simultaneously, (shown in Fi. (b, considerin the transportation orce was larer than the resistance orce on the irst paper sheet and the reverse was true or the second, the normal separation condition can be expressed by equations ( and (. 50

3 µ µ µ µ 0 ( s + p ps p ss µ µ µ µ 0 ( s + p ps ss p ss µ µ + µ µ 0 ( ss p ss p ss Here, the subscripts, and p respectively mean the,, and PR, and s denotes the paper sheet. µ is the rictional coeicient, and ~ represent the irst, second and third paper sheet. Generally, because o the ollowin relationships: µ > µ s > µ, and ss µ = µ = µ, we only need consider equation ( and nelect equation (, so inally, the normal separation condition are iven as ollows. µ s s µ s s µ ps µ ss ( µ µ µ µ ss p s Nip position µ s µ µ ps µ ss PR position p (a Only sheet (b Both sheets and Fi. Analysis o separation orces e can discuss the miss and double eedin deects rom equation (. hen the rictional coeicients become bier or smaller, the requirements o the latter or ormer hal o equation ( may not be satisied, so the irst paper sheet may be mised, or the irst and the second paper sheets are transported at the same time and so may be double ed. This will be discussed in detail ater we have examined the deormation orce in the next chapter. µ s µ ps µ ss µ ss µ ss µ ss µ µ ss p p p. Deormation Force in the Overlap Nip Althouh we derived the normal separation conditions, we must obtain the value o deormation orce. Here we used a simpliied elastic beam model to estimate the values caused by the overlap nip. Accordin to the symmetry structure shown in Fi. (b, and considerin that the ap between the central s is loner than those on either side, we concentrate on only the let hal structure o the symmetry line, I-I. oreover, to more easily obtain the deormation orce, we reverse the hal model. The paper sheet is treated as a continuous elastic beam and is simply supported at points ~ by three edes, and at the upper side, two s edes are pressed down at points 5~8 with overlap (Fi. (b. The paper sheet receives the reaction orces R ~ R rom the s and pressures ~ rom the s. Thus the total deormation orce in the out-o-plane direction can be iven as ollows: 5

4 i = = i = R (5 i = i Here, Δ Ⅱ Ⅱ Ⅱ l l 56 l 7 8 R R R R 0 x Ⅱ l (a The hal model (b The hal model with reverse Fi. Deormation orce in the overlap nip l and l are the width o and. l is the distance between and edes. ~ represents the moment at points ~ respectively. Considerin the symmetry o line II-II shown in Fi. (b, we have ollowin equations. = = (6, R = = (7 R, R R = = (8, Clapeyron s theorem o three moments ives the relationship amon the applied orce, moment, slope anle, and the lenth o span between two continuous spans [6]. For the two spans between points ~ and ~, we can obtain the ollowin relationship. Here θ, θ ( θ l + (l + l = 6 EI ( θ + (9 is the slope anle at point when only the centralized orce applies on the let or on the riht span respectively. EI is the bendin stiness o the paper sheet ( E is Youn s modules, and I is the eometrical moment o inertia. θ e can acquire the moments ~ at points ~ and the slope anles θ and at point. For the riht span, no orce is applied, so we have the ollowin equation. θ 0 (0 = Because no constraint exists at points and, the ollowin equation is obtained. = 0 ( = Finally, the equation (9 can be simply expressed as l l = 6 ( + EI θ ( The slope anle θ can be obtained by considerin only the centralized orce 5

5 and applied on the let span between points and, and is iven as the ollowin equation. l( l θ = θ w + θ w = [ (l + (l ] ( 6EI (l So the is obtained rom equations ( and (, l ( l = [ (l + (l ] ( (l ( l Furthermore, the delections at points 5 and 6 o the let span (between points and, which are respectively caused by orces, and moment, can be easily obtained by usin known ormulas [6]. Here, we do not introduce the detailed value and only show the procedures. Finally, we let the summations o these delections at point 5 and 6 equal the overlap which are iven by the ollowin equations. δ δ + δ + = (5 x = l ( po int 5 = ( w w δ x = l δ δ ' + δ ' + ' = (6 x = l = ( po int 6 ( w w δ x = l Here, δ, w δ and w δ are delections respectively acted by the, and at point 5. δ, δ ' and δ ' are the deections at point 6. x is a distance rom the ' w w point to the load actin position (point 5 or 6 in the axis direction. For simplicity, we cite the ollowin sinatures. (l a + = [ + ]( l l (7 (l ( l d e ( l ( ( l l = [( l l + ] (8 (l ( l ( l ( l = [( l l + ] (9 (l ( l 6EI (l Ebh (l = = (0 l l Here, h is the thickness and b is the eective deormation lenth (the eometrical moment o inertia I = bh /. Finally, we can obtain the deormation orces and as shown in the ollowin. ( e a = ( de a ( d a = ( de a The eects o main sizes o the separation structure will be discussed in next chapter. 5

6 5. Reproducin Separation Behaviors by FE 5. FE simulation model An FE simulation method or the separation mechanism was established by treatin the riid shell or rollers and the elastic shell elements or the paper sheets. The three-dimensional initial FE model or separatin our sheets o paper is shown in Fi.. Four paper sheets are put one on top o the other with a certain ap. To reduce undesirable vibration o paper sheets in calculation, contact dampin and the stiness are added to each contact pair. The FE model has been validated to ensure the pressure p and the deormation orce are nearly equal to those o an actual experiment. The normal separation parameters used in the simulation are iven in Table. Low rictional parts PR Push plate Riid shell (Fixed Hih rictional parts Elastic shell Fi. Initial FE model o paper sheets separation Table Simulation parameters Rollers Items PR Dimensions (width radius [mm] l b h = [K/m ] ρr = 7800 ρs = 500 aterials [GPa] E = 06 E = 5. (0.5 or olded part ν = 0. ν = 0. Frictional coeicients µps =.5 µs = 0.68 µ = 0.8 µss = 0. Handlin velocity [m/s] V =.0 5. Simulation results Fiure 5 shows some simulation results o the separation behavior or normal lat sheets and our-olded sheets by usin the established FE model (the PRs are not shown here. ~ Nip centerline Nip centerline aved deormation Nip centerline (a Normal lat sheet (b Four-olded sheet Fi. 5 Simulated results with normal lat and our-olded sheets 5

7 From Fi. 5, it is known that the heads o the second sheets in both cases cannot be ed and stopped at the nip centerline. This means the irst sheet is normally separated rom sheets ~ by usin the parameters iven in Table. It is also said that our separation mechanism can also be used or eedin and separatin the situation sheets. 6. Discussion on Eects o ain Parameters 6. ain structure parameters Now we can calculate the deormation orce by the equations ( ( and (5. For our standard structure and parameters o the overlap nip shown in Table, let the eective deormation lenth b in equation (0 equal the nip lenth 6.0mm. Fiure 6 shows the eect o the deormation orce on parameters o l, l, l and. From this iure, it is known that the deormation orce is proportional to the amount o the overlap. The smaller l or l, the bier the deormation orce. The value l has too little insensitivity to chane the deormation orce. Thereore, the deormation orce can be desined by chanin the structure sizes o the separation mechanism. Deormation orce (N 0 l l 8 l Δ Dimensions (mm Fi. 6 Eects on the deormation orce by main structure parameters 6. Frictional coeicients Once the structure o the overlap nip is decided, the deormation orce can also be worked out. However, sometimes the rictional coeicients between roller/sheet or sheet/sheet are unstable and easily chaned, and urthermore they may destroy the satisaction o equation (. Here, we discuss the separation deects rom equation ( and the FE simulation. hen µ s decreased rom 0.68 to 0.5, and µ ps chaned rom.5 to 0.8, the latter hal o equation ( was not satisied. The irst paper sheet could not be sent and so may be mised. The simulation result is shown in Fi. 7(a. Even when the hih riction parts o the and PR had inished turnin, the tip o the irst sheet stayed in the nip. oreover, when this happened, a bi deormation occurred between the and PR, and the paper sheet was buckled. Fiure 7(b shows the simulation result o when µ ss decreased rom 0. to 0.0. This condition did not satisy the ormer hal o equation (. The irst and the second paper sheets are seen to enter the overlap nip simultaneously. These separation problems (miseedin and double eedin also exist in actual machines. Thereore, the FE simulation accurately reproduced actual separation conditions. Additionally, the separation deects obtained by the elastic beam model aree well with those obtained by the FE simulation. 55

8 s & Nip centerline Buckled Push plate Nip centerline Push plate (a iseedin (b Double eedin Fi. 7 Reproduction o separation deects 7. Conclusions By usin the elastic beam model, we analyzed the deormation orce applied on sheet suraces in the nip area, and discussed the separation behavior caused by the established FE model. e now summarize the main points o this study. ( The eect o deormation orce in the overlap nip was clariied by treatin the paper sheet as a continuous elastic beam and usin Clapeyron s theorem o three moments. ( A normal separation conditional expression was derived. The relationships between the rictional coeicients and miseedin/double eedin were clariied. ( An FE simulation method that can reproduce the separation behavior accurately was developed. The results o separation behaviors by FE simulation aree well with those by the elastic beam model and the derived separation conditions. These can be used or desinin the separation mechanism. Reerences ( Yasuo SHIA, Syunsuke HATTORI, Yuko KOBAYASI, and okoto UKAI, Optimum o ate-roller shape in paper isolatin methods, Proceedin o 996 Conerence on Inormation, Intellience, and Precision Equipment (IIP996, JSE, No. 96-6, pp (In Japanese ( You-Hoon Yoon, Yoon-Kil Kaek, and Joon-Hyun Yoon, Analysis o double eedin on the notes separation mechanism, ASE 5th Annual Inormation Storae and Processin Systems Conerence 005 (ISPS, extended abstract, CA, USA. ( asao OKAYAA, Shienori SATOU, Yutaka NAGASAA and Yutaka KAKO, echanism o double sheet eedin on the roller overlappin riction eeder, Transactions o the Japan Society o echanical Enineers, Series C, 996, Vol. 6, No. 600, pp (In Japanese ( Yukihiro TAKANO, Tetsuji KAASAKI, Hiroyuki KOJIA, Dynamic analysis o D deormation o paper in overlap-roller method o accumulation mechanism, Proceedin o th Conerence on Computation echanism o JSE, 00, No. 0-0, pp. -. (In Japanese (5 Joint committee o industry-university cooperation o JSPE, Research Report o Handlin Technoloy and echanism or the Flexible edia, Vol. : Research activities and Vol. : Results o mechanism research (00. (In Japanese (6 Oobashi G., Strenth o materials, SBN C05 (00, Tsuchikauukan Print Company, pp (In Japanese * LS-DYNA Sotware, Reistration Commodity o Finite Element ethod Sotware, Copyriht o Livemore Sotware Technoloy o the USA. 56