Steady-state vibration of a viscoelastic cylinder cover subjected to moving loads

Abstract

Abstract The dynamic steady-state response of a viscoelastic cylinder cover subjected to circumferentially moving constant point and distributed loads is studied using a 1D Pasternak-type foundation model. The cover material is modeled according to the generalized Maxwell model as an incompressible frequency-dependent viscoelastic material spanning a wide relaxation spectrum. The vibration response of the cover for a moving twin point load is obtained using a modal expansion approach. On the basis of the solution, additional moving load cases are derived. In the case of a single moving point load, representing a load resultant due to rolling contact, numerical calculations show that regardless of the viscoelastic damping in the model, the critical load speed for the system can be well estimated by a resonance condition. In the vicinity of the critical speed, an incipient traveling wave arises behind the moving load. The viscoelastic cover stiffens for increasing excitation frequencies, thus, the cover response divides into two separate mode branches, of which the low-mode branch is dominant. A method to suppress the traveling wave vibrations in the cover at supercritical speeds using a moving twin point load, adjusted according to a dominant resonating mode, is presented. Using a distributed moving load, it is shown that depending on the wavelength, a traveling wave generated at the leading edge of the load may be reinforced at the trailing edge, the lift-off point, of the load. The developed model offers a fast and reliable way for practitioners to estimate the critical speeds of rolling contact machines with viscoelastic covers.