Stochastic analysis of the critical velocity of an axially moving cracked elastic plate

• Critical speeds of moving cracked plates are studied under fracture and instability.
• Solutions for models with different sources of uncertainty are derived.
• Solutions by different models are compared in paper industry context.
• Random crack length and tension have the most significant effect on the solution.

In this study, a probabilistic analysis of the critical velocity for an axially moving cracked elastic and isotropic plate is presented. Axially moving materials are commonly used in modelling of manufacturing processes, like paper making and plastic forming. In such systems, the most serious threats to runnability are instability and material fracture, and finding the critical value of velocity is essential for efficiency. In this paper, a formula for the critical velocity is derived under constraints for the probabilities of instability and fracture. The significance of randomness in different model parameters is investigated for parameter ranges typical of paper material and paper machines. The results suggest that the most significant factors are variations in the crack length and tension magnitude.