Center Distance Change of Silent Chain Drive Effect on Sprocket Tooth Profile Modification Wei Sun 1,a, Xiaolun Liu 1,b, Jiajun Liu 1 and Wei Zhang 1

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1 Key Engineering Materials Online: ISSN: , Vol. 522, pp doi: / Trans Tech Publications, Switzerland Center Distance Change of Silent Chain Drive Effect on Sprocket Tooth Profile Modification Wei Sun 1,a, Xiaolun Liu 1,b, Jiajun Liu 1 and Wei Zhang 1 1 College of Mechanical Science and Engineering, Jilin University, Changchun, , China a wsun10@mails.jlu.edu.cn, b borntotry10@163.com Keywords: Silent chain, Chain link, Center distance, Modified sprocket. Abstract. The principle of modified gear was applied to silent chain transmission, and tooth profile equation of the involute sprocket was derived, then method of processing gear using imaginary rack cutter solved modification coefficient of involute sprocket. When Center distance of silent chain drive changed smaller, processing method of sprocket modification coefficient and range of modification coefficient values were analysed. The method by changing the modification coefficient of involute sprocket solves the problem that the chain links are increased or decreased in the actual application to be unable to meet the requirements of specific center distance, thus improve transmission performance of silent chain. Introduction Chain transmission is widely applied in the mechanical engineering. Nowadays, with the continuous development of high speed chain transmission technology, the ordinary roller chain can not meet the requirements, and the silent chain is used more widely[1-3]. The traditional silent chain sprocket uses the straight edge tooth profile, and when the sprocket and chain plate mesh, there is big strike, transverse vibration and noise. In recent years, domestic and foreign researchers found the involute tooth profile sprocket could improve the transmission property of silent chain because it could be considered as a larger negative modified involute cylindrical gear[4,5]. Through the mesh of sprocket tooth profile curve and chain plate, polygon effect and mesh strike could be reduced, then the conjugate transmission could be realized, therefore the chain could work smoothly and the transmission property of silent chain was improved[3,6]. In the transmission mechanism of silent chain, centre distance had a great influence on the performance of transmission. When the centre distance of silent chain transmission mechanism changed, we usually increased or decreased the number of chain links. But in practical applications, no matter how to increase or decrease the chain links, the specific requirement of the center distance could not be satisfied. In this case, we would consider the principle of modified gear transmission and change the modification coefficient of involute tooth profile to solve this problem. Therefore, studying the influence of center distance change on sprocket tooth profile has great significance to improve the transmission property both in theoretical and practical guidance. Sprocket Tooth Profile Involute tooth profile equation of the sprocket. Through sprocket wheel centre line parallel to the chain centre line to the right for the x axis, sprocket wheel centre straight up established for the y axis at right angles to the direction of the coordinate system, Cartesian coordinate system was set up that sprocket center was the origin O, the right straight of paralleling to the chain centerline through the sprocket cente was X-axis, vertically upward direction through the sprocket center was the Y-axis[4]. So involute equation could be deduced from Figure 1: x= rb sin( θk + αk) ru b cos( θk + αk) (1) y = rb cos( θk + αk) + ru b sin( θk + αk) Among them, u= ( θ + α ), u was called the roll angle of the involute at the point K. k k All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-05/03/16,21:35:40)

2 Key Engineering Materials Vol Method for Sprocket modification coefficient. Silent chain sprocket formulated by the German standard DIN8190 was actually the involute profile of the negative variation coefficient[7], its pressure angle was 30 degrees. Method of processing gear using imaginary rack cutter could solve modification coefficient of involute sprocket.when the rack and gear without addendum modification meshed, the middle line of rack n-n was the tangent to gear pitch circle. When the rack cutter of the pitch P hypothetically was used to process involute sprocket, we need to make the middle line of rack cutter move towards the sprocket center at a certain distance χ m, and make the position of the rack cutter and the plate seated on the sprocket the same, as shown in Figure 2. Modification coefficient could be calculated from the geometric relation[3] : 3 π π z 2π f χ = π + cot (2) 4 2 z 2 p Of which: p was pitch, f the distance from a pin center to outside flank, pressure angle α = 60, z the tooth number of sprocket, and m the module. Fig.1 Involute Fig.2 Rack cutter processing method for modification coefficient Center Distance Changing the Distance of the Integer Number Links When the transmission ratio was i= 1:1, if the center distance changed the integer multiple of half pitch, np, just correspondingly increasing chain link numberncould meet the requirements. 2 When the transmission ratio was i 1:1, As shown in Figure 3, the original Center distance was a, the angle of center line and chain tight span was ϕ r, 2 r1 ϕ = arcsin( ). a When the chain increased chain link number n, center distance increased a, then the angle of r2 r1 center line and chain tight span became ϕ = arcsin( ) a+ a. The following relations could be approximately got: ( r r) ( acos np/2) ( a a) ϕ+ = + (3) r2 r1 Where: r1 = p/sin π, r2 = p/sin π, ϕ = arcsin( ). z1 z2 a So, when the center distance change was a= a+ 4 a + 4 anp cos ϕ+ n p 8( r2 r1 ), 2 increasing or decreasing link number n could meet their needs.

3 576 Progress in Advanced Manufacturing Technologies Sprocket Tooth Profile Modification If the center distance variation was small, increasing and reducing chain links was not feasible. In this case, the modified gear transmission principle was used to appropriately increase or decrease the modification coefficient of the sprocket. Then the chain can be installed on the sprockets so that the problem was resolved. The center distance increase. When the center distance increased, the links were not increased, and which could result in insufficient chain length. While increasing chain may make chain sag larger. Appropriately reducing modification coefficient of the sprocket made sprocket tooth thickness thin and mesh circle decreased, then the chain could be installed on the sprocket. As the sprocket was the negative modification, if the sprocket tooth number was less, and then reducing the modification coefficient may result in sprocket tooth thickness being too thin. So modification processing was better done on the driven sprocket with more tooth number, not the driving sprocket. If transmission ratio was 1:1, modification processing could be simultaneously taken on both sprocket to ensure the sprocket tooth thickness. The center distance decrease.when the center distance decreased, the chain sag increased and chain vibration hop may occur, and some effects such as movement being not smooth affected the transmission. In this case, if the center distance variation was smaller, the method by reducing the chain link did be not applied, processing method of modified sprocket could be used to solve the issue. Therefore, modification coefficient should be increased to make the sprocket tooth thickness increased, and chain and sprocket meshing circle increased, in order to achieve the purpose of the chain stretched. Fig.3 Scheme of center distance increase Fig.4 Position relationship of plate and sprocket tooth Modification Coefficient Range The minimum modification coefficient value.sprocket modification coefficient was of the minimum range, but could not be infinitely reduced. When chain plate and involute sprocket meshed and located, the outside straight flank of the chain plate and the sprocket was tangent, and the tangent point moved up along the straight flank of the chain plate as sprocket modification coefficients decreased. If the sprocket modification coefficient was too small and the tooth thickness was too thin, which may result in the chain plate and sprocket tooth profile being the no cut point on the straight flank of the chain plate. In which case, the chain plate and sprocket tooth would not be able to locate, and the tip of the chain plate directly contacted with the sprocket tooth root circle, unable to drive. If the chain and sprockets meshed and located, then the tangent point of the chain and sprocket teeth could not be above the point B. If the tangent point of the chain and sprocket teeth was B, now, modification coefficient of sprockets was the permissible minimum valueχ min. And then we could get: When the center distance increased, sprocket tooth profile modification was ways to tackle, then the permissible maximum value of center distance was a.

4 Key Engineering Materials Vol The maximum modification coefficient value.sprocket modification coefficient was also of maximum value range. Point of tangency of outer straight flank of the plate and sprocket meshing and positioning moved down along the straight flank of the plate as sprocket modification coefficient increased.if the sprocket modification coefficient was too large and tooth thickness was too thick, which could lead to the tip of chain plate directly contacted with sprocket tooth tip. In this case, chain and sprocket will not be able to drive. The distance CE of the lowest point of the work tooth surface to the pitch line was h. As shown in figure 4, the coordinates point B on the outer l straight flank of the plate could also be taken. If the chain and sprocket meshed and located, then the tangent point of the chain and sprocket tooth could not be under the point E, otherwise will not be able to drive. Now, modification coefficient of sprockets was the permissible maximum valueχ max. And then we can get: When the center distance was reduced, sprocket tooth profile modification was ways to tackle, then the permissible minimum ' value of center distance was a Discussion and Conclusion. When the center distance of the silent chain drive was non-standard center distance, although the method by sprocket modification could be used to solve the issue, but the method had some limitations. When the sprocket modification coefficient was the larger, chain and sprocket would not be able to very good mesh, so the method was not applicable. If the modification coefficient was too small or too large, the meshing of the chain and sprockets would be affected, which could lead to large mesh noise, chain elongation to speed up and compressional deformation of the mating surface. In serious cases, It could cause a serious extrusion deformation of mesh surface or interference with the sprocket and chain plates, and make silent chain drive unable to work. In short, selection of the modification coefficient is very important, need to be selected according to the actual working conditions, and addendum circle and root circle of the sprocket can be adjusted appropriately according to the actual situation. References [1] ANSI B29.2M: Inverted Tooth (Silent) Chains and Sprockets (the American Society of Mechanical Engineers, New York 2007). [2] J. A. Calvo, V. Diaz, J.L. San Roman and M Ramirez: Int. J. Vehicle Noise and Vibration, Vol. 2 (2006) No.1, pp [3] J.M. Wang: Machine Design, Vol.13 (1996) No.7, pp [4] F.Z. Meng: The Meshing Principle of Silent Chain (China Machine Press, China 2008). (In Chinese) [5] M. Wada, S. Ide, S. Miki, and A. Ehira: International Congress and Exposition (Detroit, Michigan, March 1-4, 1999) Vol. 1, pp.1-7 [6] Z.F. Zheng, Y.X. Wang: Chain Drive (Machinery Industry Press, China 1984).(In Chinese) [7] DIN 8191: Tooth Form for Chain Wheels for Inverted Tooth Chains Complying with DIN 8190 Dimensions of Profile (German Industrial Standards, Berlin 1998).

5 Progress in Advanced Manufacturing Technologies / Center Distance Change of Silent Chain Drive Effect on Sprocket Tooth Profile Modification / DOI References [2] J. A. Calvo, V. Diaz, J.L. San Roman and M Ramirez: Int. J. Vehicle Noise and Vibration, Vol. 2 (2006) No. 1, pp /IJVNV