Study the Temperature Effect on the Dynamic Response for a Camshaft by Using the Combined Finite Element - Transfer Matrices Method


The present work studies the effect of temperature on the dynamic response fora camshaft as rotor –bearing system contains branches. The effect of temperaturedistribution along camshaft length on the critical speeds and on the distribution oflateral amounts of vibration (eigen mode) along camshaft length with threedimension are accounted for. Also this work considers the multi effect oftemperature distribution and bearings number and its positions. The response hasbeen calculated at different interval of time with different temperatures.The study has been applied on petrol engine camshaft of Volkswagen 1994 carwith 4 cylinders; the camshaft has 8 cams, 5 bearings, total length of 39.5cm andtotal weight of 2.32Kg working with rang (20-80Cº) and SAE 40 oil type. Thedynamic investigation of the camshaft has been achieved depending on thecombined Finite Element – Transfer Matrices technique (FETM). It is accountedfor the shear effect and gyroscopic effect of camshaft gear and the effect ofunbalance forces resulting from the existence of the out of balance of the shaft andcams masses, Also it considered the dynamic loads that are applied on the camssurfaces and the temperature effect on the material elasticity and rigidity. Eightcoefficients of damping and stiffness have been computed for each bearing at eachangle of rotation with the considering of the temperature effect on the bearing's oilviscosity. A FORTRAN language computer programs have been developed toembrace the theoretical work, the programs are able to calculate the camshaftdynamic response and its critical speeds, Also calculating forces on cams surfacesas a function of camshaft rotation angle.It has been found that there are a certain critical speeds and eigen modes foreach temperature distribution, In general case, the results show that the criticalspeeds values decrease as temperature increases and the gradient in the speedsdepends on the rank of critical speed. Also it has been found that the reduction ofbearings number leads to reduce the values of critical speeds and the reductionratio depends on temperature and the rank of critical speed. Also it has been foundthat the distribution of lateral amounts of vibration are affected by the eightcoefficients of the bearing wich are changed according to the temperature, speedand camshaft rotation angle.