Self-Excitation Mechanisms in Paper Calenders Formulated as a Stability Problem

In one of the last stages of paper production the surface of the paper is refined in calenders. The paper is compressed in the nip by rollers which sometimes tend to exhibit self-excited vibrations. These vibrations may lead to wear and dramatically reduce the durability of the expensive rollers. The reason for the self-excited vibrations is to be found in the interaction of the rollers with the paper. The interaction process in the nip is very complex and has not been completely understood from a mechanical point of view. The purpose of this paper is to develop simple mechanical models of the nip which can lead to an explanation of the phenomenon

Non-linear investigation of an asymmetric disk brake model

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Among design engineers, it is known that breaking symmetries of a brake rotor can help to prevent squeal. From a modelling point of view, in the literature brake squeal is almost exclusively treated using models with a symmetric brake rotor, which are capable of explaining the excitation mechanism but yield no insight into the relation between rotor asymmetry and stability. In previous work, it has been demonstrated with linear models that the breaking of symmetries of the brake rotor has a stabilizing effect. The equations of motion for this case have periodic coefficients with respect to time and are therefore more difficult to analyse than in the symmetric case. The goal of this article is to investigate whether due to the breaking of symmetries also, the non-linear behaviour of the brake changes qualitatively compared to the symmetric case

Low Order Model for the Dynamics of Bi-Stable Composite Plates

This article presents the derivation and validation of a low order model for the non-linear dynamics of cross-ply bi-stable composite plates focusing on the response of one stable state. The Rayleigh–Ritz method is used to solve the associated linear problem to obtain valuable theoretical insight into how to formulate an approximate non-linear dynamic model. This allows us to follow a Galerkin approach projecting the solution of the non-linear problem onto the mode shapes of the linear problem. The order of the non-linear model is reduced using theoretical results from the linear solution yielding a low order model. The dynamic response of a bi-stable plate specimen is studied to simplify the model further by only keeping the non-linear terms leading to observed oscillations. Simulations for the dynamic response using the derived model are presented showing excellent agreement with the experimentally observed behaviour. Additionally, deflection shapes are measured and compared with the calculated mode shapes, showing good agreement

An efficient approach for the assembly of mass and stiffness matrices of structures with modifications

The finite element method is one of the most common tools for the comprehensive analysis of structures with applications reaching from static, often nonlinear stress–strain, to transient dynamic analyses. For single calculations the expense to generate an appropriate mesh is often insignificant compared to the analysis time even for complex geometries and therefore negligible. However, this is not the case for certain other applications, most notably structural optimization procedures, where the (re-)meshing effort is very important with respect to the total runtime of the procedure. Thus it is desirable to find methods to efficiently generate mass and stiffness matrices allowing to reduce this effort, especially for structures with modifications of minor complexity, e.g. panels with cutouts. Therefore, a modeling approach referred to as Energy Modification Method is proposed in this paper. The underlying idea is to model and discretize the basis structure, e.g. a plate, and the modifications, e.g. holes, separately. The discretized energy expressions of the modifications are then subtracted from (or added to) the energy expressions of the basis structure and the coordinates are related to each other by kinematical constraints leading to the mass and stiffness matrices of the complete structure. This approach will be demonstrated by two simple examples, a rod with varying material properties and a rectangular plate with a rectangular or circular hole, using a finite element discretization as basis. Convergence studies of the method based on the latter example follow demonstrating the rapid convergence and efficiency of the method. Finally, the Energy Modification Method is successfully used in the structural optimization of a circular plate with holes, with the objective to split all its double eigenfrequencies

Dynamics of a milkshaker - Passage through resonance and frequency transformation

Rotor dynamics is a fascinating subject both from an experimental and a theoretical point of view. Most often experiments on various phenomena require more or less sophisticated test rigs, either because the experiments are dangerous or because the effects are difficult to reproduce. In teaching it is, however, beneficial to have experiments that are simple and can be performed by the students themselves. One of these examples is a standard milkshaker, which at a closer look, exhibits rich dynamical phenomena. The first phenomenon that can be observed and studied is the passage through resonance. Depending on the eccentricity of the rotor, the driving torque of the motor is strong enough or not to reach supercritical speeds. If for a given torque the eccentricity is too large, the system gets stuck in the resonance with a rather large amplitude. A second phenomenon that can be observed is the following: When the milkshaker is placed on an even surface it starts to move on the surface. The movement is caused by a wobbling motion of the system due to the eccentricity. Although the angular velocity of the rotor is high, the motion on the surface is quite slow in comparison. This is an interesting phenomenon that can be related to mechanical frequency transformation which occurs in the contact between the milkshaker and the ground. Depending on whether the rotor is running in a supercritical range or stuck below the resonance frequency, different motions can be observed. The system can be analyzed with a relatively simple nonlinear rigid body model. In this paper we study both phenomena mentioned above from a theoretical point of view. The equations of motion are derived in analytical form and their nonlinear behavior is investigated. Due to its relatively simple nature, the system has been used in lectures as a demonstrator and for student tutorial projects