Final machining operations, such as surface grinding, play a crucial role in manufacturing of paper machine rolls. Due to developing new web-tension-measuring systems and due to demand on reduction of roll masses, a grinding operation of thin-walled rolls is required. In this paper first, delay differential equations describing the dynamics of the grinding system are introduced. The dynamic model consists of a rotating thin-walled roll and its drive and a rotating grinding stone with its drive attached to an axially moving sledge. The derivation of the cutting forces is based on wear theory. The roll is modelled in two ways for later comparison: (1) as a flexible simply supported rotor using Euler-Bernoulli beam theory and (2) as a simply supported flexible shell using Love’s equations. In both cases, a method of eigenfunctions expansion is employed for obtaining the responses. The effect of the time delay, shape error, overlapping and the PD-controller are included. The set of the delay differential equations is solved numerically. Finally, the dynamic response of the roll to the cutting forces is presented. An influence of different wall-thicknesses on the dynamic behaviour of the roll during the grinding process is studied as well. Lastly, a comparison of results obtained by using the beam theory and the shell theory are discussed.

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