NUMERICAL SIMULATION OF TIMING BELT CAMSHAFT LAYOUT

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1 NUMERICAL SIMULATION OF TIMING BELT CAMSHAFT LAYOUT Eric AYAX, Stéphane HUOT, Daniel PLAY, Nicolas FRITCH FEDERAL MOGUL Sintered Products Voie des Collines Le Pont-de-Claix, France Abstract: Mechanical behaviour of power transmission systems have to be defined during preliminary design. Numerical simulations such as Finite Elements Analysis is the method used to design transmission components. This method aims to replace classical tests after experimental validation of computer software results. Sintered camshaft pulleys are designed using the same way. Design of this component can be optimised by simulating the quasi-static response of timing belt camshaft layout on a pulley under loading. The quasi-static belt response is related to the local behaviour of the transmission system while dynamic response of the whole camshaft layout is related to global behaviour. Because of the complex phenomena involved in such system and due to practical requirements of design office in terms of computer time, local and global analyses are performed separately, however, results from local analysis is used as input data for the second one. The purpose of this paper is to analyse the quasi-static behaviour of a timing belt setting on a pulley subjected to a torque. In order to take the environmental effects into account, the interaction between the belt and pulley is analysed with and without clearance. The analysis is performed using Abaqus Standard. The Finite Elements results show a significant influence of clearance on stresses distribution throughout the belt. When the belt is set up on pulley with clearance, reverse bending stresses are observed between the groove and teeth pulley, creating a polygonal effect. This effect generates a transmission error which may cause vibrations and then alter the behaviour of the belt during engine working. Without clearance between the two components, polygonal effect and transmission error are insignificant, and therefore dynamic excitations are smaller. Clearance is probably one of the major parameters governing the fatigue life of timing belt. Polygonal effect and quasi-static transmission error then constitute one of the input data for global dynamic simulations using a specific in-house. Keywords: Timing belt, Pulley, Polygonal effect, Transmission error 2003 ABAQUS Users Conference 1

2 1. INTRODUCTION Timing belt are widely used for power engine valve controlled distribution. The rule of this component is to ensure the transmission of the torque between each element of the engine distribution. Distribution elements such as pulleys mounted on shafts, timing belt, idlers and automatic tensional elements constitute a sub-system of the engine. Even with a small number of pulleys, camshaft drive layout architecture are still considered complex. Many phenomena take place during engine working and several interactions occur between constitutive elements of this sub-system. Pulleys and timing belts have then to be design in detail. In the last twenty years, studies focused on the simulation of belt behaviour. At the beginning, tooth load distribution was modelled and the influences of geometrical parameters were investigated [1 to 4]. Later, timing belt life attended to be predicted regarding to loading [5 to 7]. This lead to the identification of mechanisms responsible of noise vibration and failure of belt [8 to 11]. More recently, the dynamic behaviour of timing has been simulated and effects of belt and tensional elements stiffness have been analysed [12 to 16]. Although interesting results have been observed from these different studies, it is still difficult to understand the interaction between distribution elements. Furthermore, improvement of the in-service life of belt remains a key issue for the development of camshaft layout system. The purpose of this paper is then to simulate the quasistatic response of the timing belt setting on a camshaft pulley subjected to a torque. The final goal being to improve pulley profiles. In this study, the interaction between camshaft pulley and timing belt is analysed with and without clearance. Abaqus Standard is the non-linear software used for this analysis. The first part of this paper describes the numerical approach used for the Finite Elements simulation. Results are presented in the second part. The mechanisms due to transmission is identified and the influence of clearance on the belt behaviour discussed. 2. DESCRIPTION OF THE FINITE ELEMENTS MODEL 2.1. Geometry and meshing Complete profile of the belt and pulley are considered in order to simulate the interaction between these two elements in detail. In order to simplify the model and reduce computing time, the belt and pulley are modelled in 2D. Detail of the geometry is given in figure 1The belt is meshed using quad elements with four nodes (figure 2). Fine mesh is defined in the whole belt because of the high deformations of this component under loading. In this present study, the pulley is assumed rigid Material Typically, the belt structure is composed of three different material which are the cord, the woven and the bulk part. The cords are made of helical glass fibres and its rule is to resist to the tensile forces due to the applied load. The woven cover is generally made in polyamide facing fabric. The rule of this component is to improve the contact between pulleys and belt. The bulk part is in ABAQUS Users Conference

3 rubber and its rule consists in adapting the belt to the teeth profile of pulleys. Material localisation is detailed in figure 3. The cords and woven are assumed linear elastic. The mechanical properties of these two material are reported in table 1. The behaviour of the rubber is non-linear and modelled using a 2 order Money Rivling relation ship: U = j i j C ij( I1 3).( I 2 3) i Figure 5 gives the coefficients C ij of the material model calculated by simulating tensile, compressive and planar shear tests with Abaqus Loading procedure and boundary conditions The history of loading described in the literature is simulated to reproduce the interaction between the pulley and the belt. First, a setting tension F 0 is applied on the belt and secondly, the tight and slack load side increase simultaneously and progressively up to the values F 1 and F 2 creating a torque. In this particular case, F 0 is equal to 25 Nm -1 and F 1, F 2 respectively equal to 35 and 15 Nm -1. For a belt width of 20 mm, corresponding torque is 11.5 Nmm. The pulley is assumed fixed and consequently resists to the created torque (figure 5). Clearance is defined between the belt and pulley corresponding to the actual configuration of the distribution system (figure 6). The case without clearance is treated later in this paper. 3. ANALYSIS RESULTS 3.1. Simulation of transmission with clearance Figure 7 show the deformation of the belt under setting loading. As a result, the belt teeth bend meanwhile the cord stretches. The stresses distribution throughout these two elements is visualised in figure 8 and 9. For the teeth, the stress peaks are situated near the tight load side where the tooth load distribution is maximum. The maximum stresses decrease along the rest of the contact arc in the slack load side. For the cord, the stresses distribution varies with the tooth profile and the clearance between pulley and belt. A reverse bending is observed on the tooth root and top, and pure traction between these two areas. In order to describe the physical phenomenon further we have plotted the variation of the radius of the circular pitch line versus the angle position in the contact area 2003 ABAQUS Users Conference 3

4 including four sectors T1, T2, T3, T4. In order to have significant effect, high loading has been applied. The physical representation of the radius is illustrated in figure 10. According to the figure 11, the average value of the radius decreases. As a result, the belt is more stretched in this area than anywhere else. Figure 12 represents the belt before and after setting loading. Furthermore, largest variations of the radius are observed in the central position of both sectors. What happens is the belt teeth penetrate into the groove of the pulley during the elongation. The rubber crushes in the groove, where the clearance is maximum, meanwhile the pulley s teeth push the belt away. The mechanism responsible of that variation is called polygonal effect. Figure 13 represents the variations of stresses throughout the cord. The cross section of this element is divided into five parts and only three angular position are considered. Position 3 corresponds to the middle zone of a tooth, pitch radius variation is lower than the variation in position 5. Position 4 corresponds to a transition zone between pulley groove and tooth. In accordance with the observations described above, reverse bending occurs between position 3 and 5 while practically pure traction appears in position 4. Once initial load is set, a F 1 and F 2 are applied on the belt to create rotating motion. Same phenomenon is observed than before. Five angular positions are considered for describing the motion of one pitch. After each new angular fixed position, the setting tension is applied before F 1 and F 2. The elongation of the belt is measured on the tight span out of the contact arc, enabling to calculate the variation of linear motion due to transmission. The transmission error can then be calculated for each step by dividing the variation of linear motion by the angle between two consecutive teeth (figure 14). Variation of the transmission error is plotted in figure 15. Again, high loading case has been chosen in order to amplify the variation of this parameter. If the prescribed load was applied, the error transmission would be lower than the meshing error. 3.2 Simulation of transmission without clearance The same loading conditions are applied. The mean radius remains constant and radius variations are much smaller than those observed in the previous case (figure 16). In the same way, variations of the stresses are lower than those presented in figure 12 (figure 17). It is then clear that no clearance induces lower values of bending stresses. Difference in pure traction values between the two study cases is due to the influence of clearance on tooth load distribution. This means that there is no significant polygonal effect without clearance. The same effect is observed for the transmission error. The values of this parameter with clearance are twice those obtained without clearance, the ratio is almost the same that the ratio calculated for pitch radius variations (figure 18). Displacement of curves corresponds to the rotation due to closing gap belt tooth and pulley groove surfaces. Variations of pitch radius and transmission error are reported on table 2, bending stresses variation on table ABAQUS Users Conference

5 4. CONCLUSION The present study has demonstrated the ability of Abaqus Standard to simulate the transmission of torque in quasi-static regime, between pulleys and belt. The Finite Elements results have shown a significant influence of clearance on stresses distribution throughout the belt. When the belt is set up on pulley with clearance, reverse bending stresses are observed between the groove and teeth pulley, creating a polygonal effect. This effect generates a transmission error which may cause vibrations and then alter the in-service behaviour of the belt. Without clearance between the two components, polygonal effect and transmission error are insignificant and fatigue life of the belt may be better. It is then clear that optimisation of pulley profiles is necessary to enhance the inservice life of belt, for a design given of this element ABAQUS Users Conference 5

6 5. REFERENCES [1] : Gerbert, G. & al, 1978, Load Distribution in Timing Belt, Trans. ASME J of Mechanical Design, Vol. 100, pp [2] : Koyama, T. & al, 1979, A study of Strength of Tooth Belt, 2 nd to 6 th report, JSME, Vol.22, N 169, pp [3] : Naji, M. & al, 1983, Toothed Belt-Load Distribution, Trans. ASME J of Mechanisms, Transmissions and Automation in Design, Vol. 105, pp [4] : Dancé, J-M. & al, 1991, Geometrical Design parameters Influence on Timing Belt Load Distribution, MPT 91 JSME Inter. Conf. on Motion and Power trans. Hiroshima, pp [5] : Childs, T. & al, 1990, Tooth Loading and Life of Automotive Timing Belts, Proc. 17 th Leeds Lyon Symposium on tribology, Leeds, pp [6] : Dalgarno, K. & al, 1994, Synchronous Belt Materials and Belt Life Correlation, J. of Automotive Engineering Proc. IME, Vol.208, Part D, pp [7] : Childs, T. & al, 1991, Life prediction of Automotive Timing Belts, MPT 91 JSME Inter. Conf. on Motion and Power Trans. Hiroshima, pp [8] : Kagotani, M. & al, 1983, A study on Transmission Characteristics of Tooth Belt Drives, JSME, Vol. 26 N 211, pp [9] : Kagotani, M. & al, 1991, A study on Transmission Error in Synchronous Belt Drives, MPT 91 JSME Inter. Conf. on Motion and Power Trans. Hiroshima [10] : Fawcett, J. & al, 1980, An Experimental Investigation of the Vibration of Toothed Belt, Pro. ASME Century 2 Inter. Power Transmission & Gearing Conference of San Fransisco 80- C2/DET -94, 6p [11] : Play, D., 1994, Load Distribution, Transmission Error and Dynamic Behaviour of Timing Belts and Roller Chains, Proc. ImechE, European Seminar on Belt Drives, London, 10p [12] : Monternot,C. & al, 1996, Dynamic Transmission Error and Load Distribution for Timing Belt, ASME Congress Power Transmission of San Diego, pp [13] : Play, D., 1999, Dynamic Behaviour Simulation and Load Distribution for Timing Belts Drives, Proc. Of 4 th World Congress on Gearing and Power Trans. Paris, Vol 2, pp [14] : Manin, L. & al, 2000, L. & al, Experimental Validation of a Dynamic Numerical Model for Timing Belt Drives Behaviour Simulation ASME Pro. DETC 2000, PTG 14408, 7p 1315 [15] : Manin, L. & al, 2001, Analysis and Prediction of a Pulley Tensioner Effect on the Behaviour of an Automotive Timing Belt Drive, MPT2001 JSM E Inter. Conf. on Motion and Power Trans. Fukuoa, pp [16]: Johanesson, T & al, 2002, Dynamic Loading of Synchronous Belts, ASME J. of Mechanical Design, Vol 24, pp ABAQUS Users Conference

7 6. TABLES Material Young modulus Coeff Poisson Cord 1575 MPa 0.3 Woven 204 MPa 0.3 Table 1 Material properties Under setting loading F 0 Under torque Clearance Radius variation (mm) Transmission error (radian) No clearance Radius variation (mm) Transmission error (radian) Table 2 Variations of pitch radius and transmission error Bending stresses (MPa) Clearance No clearance Under Setting Tension F to to 3.3 Under torque -9.6 to to 3.5 Table 3 Variations of bending stresses 2003 ABAQUS Users Conference 7

8 7. FIGURES Figure 1 Belt and pulley design ABAQUS Users Conference

9 Figure 2 Detail of the belt and pulley meshing Cords Rubber 4.5 Woven 0.2 Figure 3 Description of material 2003 ABAQUS Users Conference 9

10 Nominal stresses (MPa) C 01 = 3.5 MPa C 10 = 11.6 MPa C 11 = MPa C 20 = 0.22 MPa C 02 = MPa Nominal strain (%) Figure 4 Elastomeric material characterisation under compression F 0 F 1 Tight side Slack side F 0 F 2 Figure 5 Representation of the setting and in-service loading ABAQUS Users Conference

11 0.12 mm Clearance 0.08 mm 0.11 mm Figure 6 Clearance definition between belt and pulley Figure 7 Visualisation of stresses distribution 2003 ABAQUS Users Conference 11

12 Figure 8 Stresses distribution throughout the cord Figure 9 Stresses distribution in the rubber part T4 R T3 T2 R T1 Figure 10 Definition of the pitch circular line radius ABAQUS Users Conference

13 28, 9 Radi us (mm) 28,8 5 28, 8 28,7 5 with clearance Belt free 28, 7 28,6 5 28, 6 T1 T2 T3 T4 Figure 11 Radius variations of the circular pitch line (high loading) with clearance Angular position ( ) circular pitch line - belt Tight load side R R circular pitch line - belt under loading Pulley Slack load side Figure 12 Schematic explaining the belt behaviour in the contact area 2003 ABAQUS Users Conference 13

14 5 a 4 b 3 c 2 d 1 e Positio Tensile stresses (MPa) 5 a 4 b 3 c 2 d 1 e Geometric position of cord 21. Positio Tensile stresses (MPa) Figure 13 Graphs showing the stresses distribution throughout the cord with clearance a 4 b 3 c 2 d 1 e Positio Tensile stresses L L a Position point A before loading Position point A after loading Figure 14 Definition of the transmission error ABAQUS Users Conference

15 2 1.9 Transmission error (10-2 radian) Step Figure 15 Variation of the transmission error 28, 28,8 Radius (mm) 28, 28,7 With clearance No clearance Belt free 28, 28,6 T1 T2 T3 T4 28, Angular position ( ) Figure 16 Radius variations of the circular pitch line (high loading) comparison 2003 ABAQUS Users Conference 15

16 Geometric position of cord 5 5 Positio Positio Positio Tensile stresses Tensile stresses Tensile stresses Figure 17 Graphs showing the stresses distribution throughout the cord without clearance Transmission error (10-2 radian) Clearance effect No clearance With clearance Step Figure 18 Transmission error calculated with and without clearance ABAQUS Users Conference