Resonance phenomena of polymer-covered cylinders under rolling contact

Anssi Karttunen

    Research output: ThesisDoctoral ThesisCollection of Articles


    In paper machines the paper is fed through the contact areas, the nips, between rolling cylinders which are often covered with polymers. A soft polymer nip gives the paper a glossy surface and a smooth thickness profile with uniform density. Although the use polymer covers is beneficial in terms of end-product quality, the covers also induce and suffer from harmful dynamic phenomena. In this dissertation two such phenomena, a self-excited vibration mechanism and a traveling wave phenomenon, were studied in detail to understand their essential features. At all instances, the studied system consisted of two steel-core cylinders with a polymeric cover on the other cylinder. The self-excited vibration mechanism was first investigated using a one-dimensional (1D) analytical model. It was found that the mechanism is active when the frequency of the cover deformation induced excitation is close to that eigenfrequency of the system, which corresponds to the eigenmode in which the cylinders are vibrating in opposite phases. The vibrations are strongest when the phase of the residual deformation of the cover leads the phase of the nip gap between the cylinders by 90 degrees. Next, simulations were performed using a two-dimensional (2D) plane strain finite element (FE) model and cover deformation patterns were obtained. The results from the 1D and 2D models were found to be in good agreement. Finally, the computational and obtained experimental results were compared to validate the model-based physical interpretations. The physical explanation given by the 1D analytical model for the self-excited vibration mechanism was found to be valid. The traveling wave phenomenon was first studied using a 2D plane strain FE model. A critical speed below which the traveling waves did not appear was calculated on the basis of a resonance condition using modal information from eigenmode analysis. After dynamic rolling contact simulations it was found that the traveling wave phenomenon is best described as a Rayleigh wave resonance in which contact-induced modified Rayleigh waves arise in the nip at critical and supercritical rolling speeds and the waves superpose to form a strong traveling wave. Next, a 1D analytical cover model was developed for an elastic cylinder cover with damping. It was found that the 1D model captures the essential features of the traveling wave phenomenon. The 1D model was developed further so that the cover material was described as a frequency-dependent viscoelastic polymer. The viscoelastic model offers a simple tool for calculating estimates for the critical speeds of polymer covers in industrial use.
    Translated title of the contributionPolymeeripinnoitettujen pyörivien kontaktitelojen resonanssi-ilmiöt
    Original languageEnglish
    QualificationDoctor's degree
    Awarding Institution
    • Aalto University
    • Tuhkuri, Jukka, Supervising Professor
    • von Hertzen, Raimo, Thesis Advisor
    Print ISBNs978-952-60-6501-4
    Electronic ISBNs978-952-60-6502-1
    Publication statusPublished - 2015
    MoE publication typeG5 Doctoral dissertation (article)


    • vibration
    • wave propagation
    • resonance
    • polymer
    • viscoelasticity
    • contact


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