Abstract

The present work studies the effect of temperature on the dynamic response for
a camshaft as rotor –bearing system contains branches. The effect of temperature
distribution along camshaft length on the critical speeds and on the distribution of
lateral amounts of vibration (eigen mode) along camshaft length with three
dimension are accounted for. Also this work considers the multi effect of
temperature distribution and bearings number and its positions. The response has
been calculated at different interval of time with different temperatures.
The study has been applied on petrol engine camshaft of Volkswagen 1994 car
with 4 cylinders; the camshaft has 8 cams, 5 bearings, total length of 39.5cm and
total weight of 2.32Kg working with rang (20-80Cº) and SAE 40 oil type. The
dynamic investigation of the camshaft has been achieved depending on the
combined Finite Element – Transfer Matrices technique (FETM). It is accounted
for the shear effect and gyroscopic effect of camshaft gear and the effect of
unbalance forces resulting from the existence of the out of balance of the shaft and
cams masses, Also it considered the dynamic loads that are applied on the cams
surfaces and the temperature effect on the material elasticity and rigidity. Eight
coefficients of damping and stiffness have been computed for each bearing at each
angle of rotation with the considering of the temperature effect on the bearing's oil
viscosity. A FORTRAN language computer programs have been developed to
embrace the theoretical work, the programs are able to calculate the camshaft
dynamic response and its critical speeds, Also calculating forces on cams surfaces
as a function of camshaft rotation angle.
It has been found that there are a certain critical speeds and eigen modes for
each temperature distribution, In general case, the results show that the critical
speeds values decrease as temperature increases and the gradient in the speeds
depends on the rank of critical speed. Also it has been found that the reduction of
bearings number leads to reduce the values of critical speeds and the reduction
ratio depends on temperature and the rank of critical speed. Also it has been found
that the distribution of lateral amounts of vibration are affected by the eight
coefficients of the bearing wich are changed according to the temperature, speed
and camshaft rotation angle.