Effect of diffusion-induced bending on diffusion-induced stress near the end faces of an elastic hollow cylinder

Diffusion-induced stress plays an important role in determining structural integrity of mechanical structures used in lithium-ion batteries and microelectromechanical devices. Incorporating the diffusion-induced bending in the analysis of the diffusion-induced stress in an elastic hollow cylinder, analytical forms of the diffusion-induced resultant axial stress and hoop stress have been formulated for the traction-free condition and the built-in condition at the end faces of the cylinder. Using these results, the evolution of the diffusion-induced stress at the end faces of a hollow, elastic electrode due to the insertion of lithium is discussed under the potentiostatic operation. The end faces of the electrode experience compressive hoop stress through the thickness in contrast to the stress state in the hollow cylinder far away from the end faces. The magnitude of the resultant hoop stress decreases with increasing the diffusion time for the traction-free end faces; it increases with increasing the diffusion time near the inner surface for the built-in end faces.     

Effect of parameters on the rubbing condition of an unbalanced rotor system with initial permanent deflection

A rotor-stator rubbing Jeffcott model of a rotor system with mass unbalance including the mass eccentricity and the initial permanent deflection was set up and the corresponding governing motion equation was derived by d’Alembert principle. Through the analytical method, the rubbing condition was analyzed. Whether the rub would happen and when the rub would happen were well solved. The amplitude of the rotor center was calculated, and the rubbing factor was introduced to determine whether the rub would happen or not for all rotating speeds. Rubbing speeds when rub began to happen were obtained. Parameters such as the mass eccentricity, the initial permanent deflection, damping coefficients, and the phase angle between the mass eccentricity and the permanent deflection were used to analyze their effect on the rubbing condition. Results were obtained and could be used to prevent the rubbing fault or decrease the damage of the rub and diagnose or balance the initial permanent deflection fault.