Modelling of rotors with three-dimensional solid finite elements

A shaft is modelled using three-dimensional solid finite elements. The shea r-deformation and rotary inertia effects are automatically included through the three-dimensional elasticity formulation. The formulation allows warpi ng of plane cross-sections and takes care of gyroscopic effect. Unlike a be am element model, the present model allows the actual rotor geometry to be modelled. Shafts with complicated geometry can be modelled provided that th e shaft cross-section has two axes of symmetry with equal or unequal second moment of areas. The acceleration of a point on the shaft is determined in inertial and rotating frames. It is found that the finite element formulat ion becomes much simpler in a rotating frame of reference that rotates abou t the centre-line of the bearings with an angular velocity equal to the sha ft spin speed. The finite element formulation in the above frame is ideally suited to non-circular shafts with solid or hollow, prismatic or tapered s ections and continuous or abrupt change in cross-sections. The shaft and th e disc can be modelled using the same types of element and this makes it po ssible to take into account the flexibility of the disc. The formulation al so allows edge cracks to be modelled. A two-dimensional model of shaft disc systems executing synchronous whirl on isotropic bearings is presented. Th e application of the two-dimensional formulation is limited but it reduces the number of degrees of freedom. The three-dimensional solid and two-dimen sional plane stress finite element models are extensively validated using s tandard available results.