dynamics of chain timing drive ing pavel novotný ph d brno university of technology prof ing václav píštěk drsc brno university of technology 1 introduction development of combustion engines can be characterized by continuous increase in the number of computational simulations being applied in all areas there is a clear trend to use chain or belt drives for the design of timing drives computational simulation of these drives has not been developing too long due to high demands on the computational technology the paper focuses on simulation of dynamics of the timing chain drive with the use of a multi-body system a mass-produced four cylinder in-line engine with two camshafts and two valves per cylinder has been used as a computational model 2 general approach to modelling in general the chain drive is influenced in particular by the crank mechanism as well as by the timing gear if the model did not reflect these effects the results would show a significant error the most accurate seems to be creating of a whole engine model consisting of the crank mechanism timing gear and the chain drive such solution is theoretically possible in practice however it is found inappropriate due to huge demands laid on the computational technology thus it is better to arrange the crank mechanism and the timing gear individually and to apply the results to the belt model as reaction torques it has been proved that the crank mechanism in particular is only little influenced by other accessories of the engine and therefore the following reaction torques have been applied to the belt drive model driving angular velocity in the point of installation of the sprocket on a crankshaft reaction torques in place of the sprocket of suction and exhaust camshaft reaction torque from the oil pump in place of the pump sprocket behaviour of the chain drive values is not a periodical one through one revolution of the crankshaft or a camshaft and that is why a so called sweep has been selected for the solution sweep represents a gradual increase in the angular engine velocity in the given time figure 1 mbs model of chain timing drive with driving inputs 2 1 mbs model a complete computational model is composed of individual submodels figure 2 stiffness calculation of chain drive components the components such as the chain guide or the sprocket are modelled as solid bodies and that is why the following aspects are sufficient weight centre of gravity and the inertia tensor elements then the curve defining the surface of the component is added the contact force between two parts is defined by a modified impact function for a penetration larger than zero the force is zero when there is no penetration 0 max cvkpf ec −= 1 where k is stiffness e is exponent p is penetration v is velocity and c denotes effective damping coefficient with a value of damping cmax for a penetration larger than penetration depth d the actual stiffness values can be detected by contact fem analysis among different parts of the mechanism as an example can serve the contact between the pin of the chain link and the sprocket see fig 2 dependency of the force on the shift is determined in several points then the coefficients for equation 1 are set applying the least-squares method and with the use of matlab software the chain model comprises individual parts that are being modelled as solid bodies with six degrees of freedom in general the individual chain elements are connected by means of general force element according to the relation ⎥⎥
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00000 2 coefficients k or b represent the stiffness or damping in the given direction important is in particular ktran that represent the chain element stiffness in the longitudinal direction then btran which is damping in the longitudinal direction as well as brot that includes damping moment in the chain rotation around the axis of the element pin figure 3 mbs model of chain element each chain element includes also the contact force between the chain pin and the sprocket or the chain guide all contacts are of a curve-cylinder type left chain guide is being stretched by a hydraulic tensioner the hydraulic tensioner consists of a system of oil chambers with springs for more detailed information about tensioner computational model see references 6 3 solution a complex model of chain timing drive is assembled in multi-body system adams c hht integrator is used for the solution of differential algebraic equations dae the hht integrator is based on the α-method proposed by h m hilber t j r hughes and r l taylor 1 the α-method is widely used in the structural dynamics community for the numerical integration of second order ordinary differential equations that are obtained at the end of finite element discretization the chain model is very sensitive on integration scheme the solution error has to be carefully handled otherwise high oscillations that are of no interest or parasitic oscillations that are a byproduct of the finite element discretization process can occur see references 2 for details about a numerical solution of differential equations in general chain drives consist of many components which results in models with a high number of dof a complete model of the dohc timing chain drive is composed of approximately 156 chain links 5 sprockets and 3 chain guides which means several hundreds of contacts and thus lays high demands on the computer technology 4 result discussion the polygon effect is one of the main causes of the relatively high noise and vibration level of roller chains and bushing chains besides the excitation of longitudinal and transversal vibrations of the chain spans meshing impacts between the chain links and the sprocket mesh occur figure 3 presents chain element contact force during one chain cycle for engine speed 1000 rpm and shows a chain element contact in sequence left guide intake camshaft sprocket exhaust camshaft sprocket right guide crankshaft sprocket the noise excitation induced by the polygon effect usually occurs predominantly at the meshing frequency of the chain drive = polygon frequency if this frequency coincides with a natural frequency of the structure of the engine resonance occurs which leads to an additional increase in the level of structure borne noise the resulting disturbing noise is known as whine noise figure 4 chain element contact force during one chain cycle end sprocket-chain element contact force figure 5 chain tension force and chain radial force during one chain cycle figure 5 also presents chain tension force and radial force during one cycle for one chain cycle and engine speed 1000 rpm the given chain span is located directly behind the crankshaft sprocket the main harmonic order of chain forces bores from crankshaft sprocket vibrations 5 conclusion virtual prototypes of the timing chain drive are being created as higher-level computational models based on a multi-body system dynamics these enable a detailed solution of the timing chain drive dynamics and can find weaknesses of the design before first prototypes are made they will speed up the development of the timing chain drive with better technical and economic parameters 6 acknowledgement published results were acquired using the subsidization of the ministry of education of czech republic project 1m6840770002 josef božek research centre for engine and vehicle technologies ii 7 references 1 belmer s fink t timing drives for internal combustion engines mtz 5 2006 2006 2 hilbert h m hudges t j r taylor r l improved numerical dissipation for time integration algorithms in structural dynamics earthquake eng and struct dynamics 5 283292 1977 3 belmer s fink t timing belts development milestones and innovations mtz 12 2005 2005 4 korse t sopouch m a new timing chain with no chordal action mtz 5 2004 2004 5 adams solver c reference guide adams version 2005 r2 6 adams engine reference guide adams version 2005 r2 8 reviewer prof ing jiří stodola drsc