Analysis and elimination of the cause of vibrations in paper rolling machines
Two-drum winders are used for cutting and winding a wide variety of papers. Figure 1 shows the schematic structure of a two-drum winder. A web tension (web tension) is created between unwinding and support rollers in the paper web to guide the paper web through the cutting section without defects and creases, where the paper web is cut lengthwise. In order to counteract the formation of wrinkles before the cutting section, the paper web is stretched crosswise to the paper running direction and then rolled up continuously on individual cores.
When operating at high processing speeds, especially when processing solid papers with high coefficients of friction, strong paper roll vibrations occur again and again, which in extreme cases can lead to the levering out of individual rolls. Although paper roll vibrations are currently controlled to such an extent that roll ejection can be prevented, the cause of vibration and the mechanism of origin were still largely unknown. Numerous influences must be taken into account when investigating the dynamic behaviour of the machine. These include
- Operating parameters such as web tension or web speed
- Product properties such as friction behaviour, geometric errors or penetration stiffness, and
- Constructive parameters such as machine geometry or the type of web guidance
Model elements and linking structure of the multi-body model
Since the complex interplay of all influencing variables cannot be fully determined by tests and measurements, the Institute of Mechanism Theory, Machine Dynamics and Robotics has developed a multi-body model of the two-drum winder. The model includes numerous model elements and parameters to simulate a wide variety of physical effects. These effects include e. g.
- Paper roll geometry error
- the mutual penetration of support rollers and paper rolls as well as the associated development of frictional forces and slippage in the contact zones; and
- the translational and rotational suspension and damping properties of the roll bodies and bearings
The model represents the physical model of the parts of the technical system that can be decisive for system behavior. When modelling, it was important to note that the model parameters introduced for the model description could be determined on the real system with sufficient accuracy. Spring and damper constants were calculated, for example, from the material properties and the geometric data of the actual roll body.
Initially, the model parameters were optimized within the framework of a validation of the model in such a way that the simulation results corresponded sufficiently well with the measured values. In a subsequent sensitivity analysis with the parameterized multi-body model, a fully automated variation and evaluation of operating parameters, product properties and design parameters with regard to their influence on vibration was carried out. Sensitivity analysis also provided information on which parameters are relevant for the vibrations and where to look for the excitation mechanism.
Some model parameters showed only a minor influence on the vibration behaviour, which could exclude some effects such as torsional natural vibrations of the support rollers as the cause of vibration. Other model parameters such as the friction coefficients of the paper or the penetration stiffness of the support roll coating, on the other hand, had a large influence on the movement behaviour.
Strongly simplified flat replacement model of the two-drum winder
The evaluation of the results of the sensitivity analysis provided indications that the vibrations are caused by a self-excitation mechanism. The calculation results of the sensitivity analysis provided the basis for the creation of the simplified model for investigating the self-excitation effect, Figure 3.
However, it was also shown that the self-excitation effect is only the primary cause of vibration. The resulting vibrations produce two secondary effects, which can only be calculated with the complex multi-body model.
With the simplified model it was possible, for example, to analyse the dependency of the stability behaviour on various parameters by calculating the eigenvalues for different parameter combinations. The calculation of the eigenvalues for the output configuration showed that this was an unstable system, with the oscillations growing very slowly.
The starting points for an improvement of the vibration behavior are on the one hand a targeted increase of the dissipation, so that it becomes greater than the energy supply through the self-excitation effect (e. g. installation of dampers) and on the other hand a reduction of the energy supply through the self-excitation effect (e. g. reduction of the penetration stiffness or friction coefficients). The effectiveness of these measures can be calculated with the multi-body model, whereby a decision can be made on the basis of the multi-body simulation which measures are implemented in practice.
[Har 2002] Harmeling, F.; Veuskens, B.: Analysis and reduction of vibrations in two-drum winders with the aid of multi-body simulation, In: Conference proceedings on friction and vibrations in vehicles, machines and plants; VDI-Verichte 1736; Düsseldorf, VDI Verlag, 2002