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Inverse Methods for Continuous Balancing of Flexible Rolls

Research output: Book/ReportDoctoral thesisCollection of Articles


Original languageEnglish
Place of PublicationTampere
PublisherTampere University of Technology
Number of pages107
ISBN (Print)978-952-15-2501-8
Publication statusPublished - 2010
Publication typeG5 Doctoral dissertation (article)

Publication series

NameTampereen teknillinen yliopisto. Julkaisu
PublisherTampere University of Technology
ISSN (Print)1459-2045


This thesis presents inverse methods to define imbalance distribution of rolls on the basis of whirling and bearing force measurements. Three different methods have been evaluated, of which the first is based on modal balancing of flexible rotors and is herein called “mode-based determination of distributed imbalance”. The other two methods are based on influence coefficient balancing. Accordingly, the second method uses well-chosen trial functions to define the imbalance distribution when forming an influence matrix; the third method expresses the imbalance distribution as the superposition of eigenmodes, and the orthogonality properties of these mode shapes are used to simplify the subsequent calculations. The goal of the present research is to improve the quality and efficiency of balancing paper machine rolls by the continuous balancing method wherein the balancing mass is distributed over the whole length of a roll tube. The proposed method is new and not known to be used in practice in roll balancing applications; rather, rolls are currently balanced with point masses on the basis of two or three-plane balancing principles. Rigid body balancing is accomplished by adding balancing masses to the roll ends, and whirling may be balanced by adding a third mass in the centre of the roll. The roll model used in calculations has significant effects on the accuracy of balancing results and the residual whirling of a balanced roll. Accordingly, a lot of effort has been dedicated towards the development of this model. The roll is modelled as a continuous system and mode shapes of a flexibly supported beam are used. It is shown that other boundary conditions, such as hinged or free supports, may also be used to achieve similar results. The advantage of using flexible mode shapes is that they enable the model to properly account for the shaft flexibility as well as the boundary conditions. The cross section of the roll is not constant. This circumstance affects not only the stiffness of the roll, but also the transverse inertia forces caused by rotation of the imbalanced roll. This work suggests taking this latter phenomenon into account by incorporating it into the mass matrix. So inertia forces of the roll endings are thereby added to the roll model, but it is assumed that these inertias do not modify the mode shapes of the roll. It is shown that all three proposed inverse methods lead to the same solution of the imbalance distribution if the roll whirling is known exactly. Since, in practice, there are always some measurement errors present, there is also a discernable limitation on the conformance of the imbalance distribution. This phenomenon is also studied, and a compromise solution with a limited number of trial functions is presented; this gives reasonable results without overreacting to observation errors.

Publication forum classification

Field of science, Statistics Finland

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