Dynamic response of a cylinder cover under a moving load

• 1D Analytical model for a damped elastic cylinder cover is developed.
• The 1D model is validated by a comparison with a 2D FE model.
• Critical speed for a moving point load is given by a resonance condition.
• The critical speed is also the minimum wave phase velocity in an undamped cover.
• Damping decreases the wave speeds, lowering and blurring the critical load speed.

Cylinders with thin covers are used in high-speed rolling contact industrial applications such as a two-cylinder soft calender of a paper machine. In this paper, the dynamic behavior of an elastic cylinder cover is studied using a 1D Pasternak-type foundation model with Kelvin–Voigt damping. The cover is subjected to a moving point load, which is taken to represent a load resultant due to rolling contact. Analytical expressions for the natural frequencies, vibration response, wave dispersion relation, total strain energy and dissipation power of the cover are obtained. To validate the 1D approach, the calculated natural frequencies and modes are compared to those given by a 2D plane strain finite element model, and a good agreement is found. The critical load speed at which traveling waves first appear in the cover is derived for the undamped analytical model on the basis of a resonance condition. The critical speed is shown to be also the minimum phase velocity of the waves in the cover. When damping is included, the wave speeds decrease, lowering also slightly the critical speed, which, in addition, becomes blurred due to the damping. Once a traveling wave has emerged, it remains in the cover also at supercritical speeds due to a spectrum of resonant speeds induced by wave dispersion. At supercritical speeds, reinforced resonances are observed when the head and tail of a traveling wave interact. High shear damping leads to a substantial increase in dissipation power related to heat generation and rolling resistance of the cover already at subcritical speeds.

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